Morse Monte

ORNL=4972/R I

The Morse Monte Carso Radiation Transport

ode System

M. B. Emmett

MASTER

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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Printed in the United States of America. Available from National Technical Information Service

U . S . Department of Commerce 5285 Port Royal Road, Springfield, Virginia 22161

NTlS price codes-Printed Copy: A05; Microfiche A01

This report was prepared as an account of work sponsored by an agency of the United StatesGovernment. Neither theunited StatesGovernment nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information. apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United StatesGovernment or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of theunited StatesGovernment or any agency thereof.

Contract No. W-7405-eng-26

Engineering Physics Division

ORNL-497 2/ R1

Revisions and Additions for ORNL-4972

THE MORSE MONTE CARLO RADIATION TRANSPORT CODE SYSTEM

M. B. Emmett*

- - - .=r- c

*Computer Sciences Division, UCC Nuclear Division

Date Published: FEBRUARY 1983

OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37830

operated by UNION CARBIDE CORPORATION

for the DEPARTMENT OF ENERGY

. ...

iii

Pre face

T h i s r e p o r t is an addendum t o t h e MORSE r e p o r t , ORNL-4972, o r i g i -

n a l l y publ i shed i n '1975. T h i s addendum c o n t a i n s d e s c r i p t i o n s of

s e v e r a l m o d i f i c a t i o n s t o t he MORSE Monte Car lo Code, replacement pages

c o n t a i n i n g c o r r e c t i o n s , Part I1 of t h e r e p o r t which was p rev ious ly

unpubl ished, and a new Table of Contents . A l l pages have been three-

h o l e punched so t h a t u s e r s having loose - l ea f c o p i e s of t h e o r i g i n a l

r e p o r t can i n s e r t o r r e p l a c e pages i n t h e i r b inde r s ; o t h e r s can t reat

t h i s as a second volume of ORNL-4972.

The m o d i f i c a t i o n s inc lude a Klein Nish ina e s t i m a t o r f o r gamma r a y s

which i s desc r ibed on pages 4.6-41 t o 4.6-44. Use of such a n e s t i m a t o r

r e q u i r e d changing t h e c r o s s s e c t i o n r o u t i n e s t o p rocess p a i r p roduct ion

and Compton s c a t t e r i n g c r o s s s e c t i o n s d i r e c t l y from ENDF t a p e s and

w r i t i n g a new v e r s i o n of s u b r o u t i n e RELCOL.

Another m o d i f i c a t i o n i s t h e use of f r e e form i n p u t f o r t h e SAMBO

a n a l y s i s d a t a desc r ibed on page 4.6-24.1. This r e q u i r e d changing sub-

r o u t i n e s SCORIN and adding new s u b r o u t i n e RFRE.

References on page 4.12-2 were updated.

E r r o r s have

n a l r e p o r t :

T i t l e page

4.3-7

4.3-11

4.3-12

4.3-13

4.4-38

4.4-3 9

4.4-48

been c o r r e c t e d i n t h e fo l lowing pages from t h e o r i g i -

4.4-49

4.5-14

4.6-23

4.7-5

4 7-14

4.7-18

4.7-30

4.8-5 4.10-11

4.8-8 4.10-17

4.10-5 4.10-18

4.10-6 4.10-20

4.10-8 4.10-23

4.10-9 4.10-25

4.10-10 4.10-26

4.10-27

Part I1 of t h e MORSE r e p o r t i s a guide on us ing MORSE. It

a t t e m p t s t o h e l p t h e u s e r s o l v e some of t h e more cornmon problems

i n c u r r e d i n running t h e code. It i s by no means a complete l i s t of

t r o u b l e s , r a t h e r , i t i s an a t t empt t o h e l p t h e u s e r do h i s own

t roub le shoo t ing .

iv

.

MORSE-CG i s now a v a i l a b l e f o r t h e CRAY computer. I t has been

t e s t e d on t h e Lawrence Livermore L a b o r a t o r i e s MFE CRAY and i s now

a v a i l a b l e f r o m ' t h e Rad ia t ion S h i e l d i n g In fo rma t ion Center (RSIC) a t

ORNL.

This report -was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

ORNL-4972/R1

C o n t r a c t No. W-7405-eng-26

.

.

Engineer ing Phys ics D i v i s i o n

THE MORSE MONTE CARLO RADIATION TRANSPORT CODE SYSTEM

M. B. E m m e t t *

I NOTE : I This Work Supported by DEFENSE NUCLEAR AGENCY

*Computer S c i e n c e s , UCC Nuclear D i v i s i o n

O r i g i n a l l y P u b l i s h e d February 1975

REVISED FEBRUARY 1983

OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37830

o p e r a t e d by UNION CARBIDE CORPORATION

f o r t h e DEPARTMENT OF ENERGY

1.0-3

TABLE OF CONTENTS Page

PART I - General Introduction to the MORSE Code 1.1-1

1.2-1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . 1 . 2 References . . . . . . . . . . . . . . . . . . . . .

PART I1 . A Guide on How to Use the Various Codes. . . . . . . 2.0-l

2.1 Introduction 2.1-1 2.2 Is Core Storage Space a Problem? . . . . . . . . . . 2.2-1

. . . . . . . . . . . . . . . . . . . .

2.3 Is Amount of Computer Time Too Large?. . . . . . . . 2.3-1

2.4 Are There Too Many Abnormal Terminations . . . . . . 2.4-1

2.5 Is There Too Much Output?. . . . . . . . . . . . . . 2.5-1

2.6 Special Cases. . . . . . . . . . . . . . . . . . . . 2.6-1

2.7 Are the Standard Deviations Too Large? . . . . . . . 2.7-1

2.8 References . . . . . . . . . . . . . . . . . . . . . 2.8-1

PART I11 - A Sample Problem Notebook 3 . 1 Introduction . . . . . . . . . . . . . . . . . . . . 3.1-1

3 .2 MORSE Sample Problem 1 . . . . . . . . . . . . . . . 3.2-1

3 . 3 PICTURE Sample Problem . . . . . . . . . . . . . . . 3 . 3 - 1

PART IV - 4 . 1

4 . 2

4.3

4 . 4

4 . 5

4 . 6

4.7

4 . 8

4 . 9

4.10

4.11 4.12

MORS E Abstract . . . . . . . . . . . . . . . . . . . . . . 4.1-1

Introduction . . . . . . . . . . . . . . . . . . . . 4 . 2 - 1

Input Instructions . . . . . . . . . . . . . . . . . 4.3-1 Random Walk Module . . . . . . . . . . . . . . . . . 4.4-1

MORSEC Module . . . . . . . . . . . . . . . . . . . 4.5-1

SAMBO - the Analysis Module . . . . . . . . . . . . 4.6-1 CG - The Combinatorial Geometry Module . . . . . . . 4.7-1

The Diagnostic Module . . . . . . . . . . . . . . . 4 . 8 - 1

Hardware and Software Requirements . . . . . . . . . 4.9-1

The Many Integral Forms of the Boltzmann Transport Equation and i’ts Adjoint . . . . . . . . . 4.10-1

Generalized Guassian Quadrature . . . . . . . . . . 4.11-1

References . . . . . . . . . . . . . . . . . . . . . 4.12-1

1.0-4

TABLE OF CONTENTS ( c o n t ' d )

Page

PART V - P r o g r a m PICTURE 5 . 1 Abs t r ac t . . . . . . . . . . . . . . . . . . . . . . 5.1-1

5.2 I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . 5.2-1

5 . 3 Rout ines . . . . . . . . . . . . . . . . . . . . . . 5.3-1

5.5 Options . . . . . . . . . . . . . . . . . . . . . . 5.5-1

5.4 I n p u t D a t a . . . . . . . . . . . . . . . . . . . . . 5.4-1

2.0-1

P a r t I1

A Guide on How t o Use the Various Codes

2 -0-3

TABLE OF CONTENTS

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Is Core Storage Space a Problem? . . . . . . . . . . . . . . 2 . 3 I s Amount of Computer Time Too Large? . . . . . . . . . . . 2 .4 Are There Too Many Abnormal Terminations? . . . . . . . . . 2 . 5 Is There Too Much Output? . . . . . . . . . . . . . . . . . 2.6 Special Cases . . . . . . . . . . . . . . . . . . . . . . . 2 . 7 Are the Standard Deviations Too Large? . . . . . . . . . . . 2.8 References . . . . . . . . . . . . . . . . . . . . . . . . .

Pap e

2.1-1

2.2-1

2.3-1

2.4-1

2.5-1

2.6-1

2.7-1

2.8-1

~

2.1-1

2.1 I n t r o d u c t i o n

With a code system as l a r g e as MORSE, it r e q u i r e s a g r e a t dea l of One

types expe r i ence i n us ing i t be fo re i t s p o t e n t i a l i s r e a l l y apprec i a t ed . might say t h a t t h e u s e r must a c q u i r e a " f ee l " f o r running v a r i o u s of problems.

It i s t h e i n t e n t of t h i s p a r t of t h e r e p o r t t o h e l p t h e u s e r a c q u i r e t h i s " f ee l ing" by p o i n t i n g ou t c e r t a i n s i t u a t i o n s which may a r i s e i n h i s a p p l i c a t i o n of t h e system t o h i s p a r t i c u l a r problem. Know- i n g how t o handle t h e s e s i t u a t i o n s w i l l save him a l o t of t ime and/or te lephone c a l l s t o t h e au tho r .

This r e p o r t makes no p r e t e n s e of so lv ing a l l p o t e n t i a l problem a r e a s bu t a t t e m p t s t o a l l e v i a t e some of t h e more common ones.

2.2-1

ds 2.2 Is Core S to rage Space a Problem?

Depending on t h e complexity of a problem t h e amount of s t o r a g e r e q u i r e d can be p r o h i b i t i v e . Cross s e c t i o n s r e q u i r e t h e l a r g e s t amount of s t o r a g e except when us ing DOMINO wi th a l a r g e q u a d r a t u r e s e t .

The very f i r s t s o l u t i o n t h a t p r e s e n t s i t s e l f should be the use of program XCHEKR t o pre-mix t h e c r o s s s e c t i o n s . Tnput i n s t r u c t i o n s f o r running XCHEKR appear i n S e c t i o n 4.3. It r e q u i r e s only one inpu t c a r d i n a d d i t i o n t o t h e s t anda rd MORSEC i n p u t and us ing i t w i l l c u t your c r o s s s e c t i o n s t o r a g e requi rements by approximately h a l f i n t h e t y p i c a l case . d i s k o r t a p e , t h e u s e r w i l l know e x a c t l y how much permanent c r o s s s e c t i o n s t o r a g e w i l l be r e q u i r e d when running MORSE. S t o r i n g d a t a only f o r t h e groups you w i l l use n o t n e c e s s a r i l y f o r a l l t h e groups a l s o saves s t o r a g e . Unless t h e u s e r i s us ing a next f l i g h t e s t i m a t o r , he should not s ave Legendre c o e f f i c i e n t s ; i..e., he should s e t ISTAT = 0. Another way of sav ing some s t o r a g e i s t o use dummy s u b r o u t i n e s f o r t h e mixing r o u t i n e s ANGLES, GTSCT, READSG, JNPUT, BADt4OM, GETMUS, FFREAD, F I N D , RESTOR, STORE and GTNDSK when us ing premixed c r o s s s e c t i o n s .

Once XCHEKR has mixed t h e d a t a and put i t e i t h e r on

I n running a DOT-DOMINO-MORSE problem, t h e u s e r may f i n d the amount of DOMINO d a t a q u i t e l a r g e . The MORSE r o u t i n e s t h a t hand le t h e DOMINO d a t a i n t h e IBM v e r s i o n have t h e o p t i o n of u s ing d i r e c t access dev ices t o s t o r e t h i s da t a . D i rec t access s t o r a g e i s chosen whenever t h e u s e r ' s dimension i n blank common i s i n s u f f i c i e n t t o hold a l l t h e da t a . It does r e q u i r e some u s e r f o r e s i g h t though, because t h e u s e r must s p e c i f y t h e amount of space needed on t h e d i s k both on a DD card and i n a DEFINE FILE s t a t emen t . (See t h e DOMINO r e p o r t s ORNL-4853 and ORNL/TM-7771).

I f t h e u s e r s e l e c t s a se t of a n a l y s i s parameters which r e q u i r e a l a r g e amount of s t o r a g e , he could run t h e a n a l y s i s a s a s e p a r a t e program by us ing t h e o p t i o n of w r i t i n g a c o l l i s i o n tape .

Another way of sav ing s t o r a g e i s t o a l low fewer p a r t i c l e s p e r batch ( a s m a l l e r NSTRT and NMOST) s i n c e a p a r t i c l e bank con ta in ing 12* NMOST l o c a t i o n s i s r e q u i r e d on t h e IBM machines and 14" NMOST on CDC and UNIVAC common. Cut i t down t o t h e s i z e you need a f t e r you make t h e f i r s t run (which w i l l t e l l you how much was r e q u i r e d ) .

2.3-1

2 .3 Is Amount of Computer Time Too Large?

There a r e any number of r easons why t h e computer t i m e r e q u i r e d may be q u i t e l a r g e . The m a t e r i a l s used may be such t h a t t h e number of s c a t - t e r i n g s i s tremendous. "he complexity of t h e geometry i s a l s o a f a c t o r because of t h e number of boundary c r o s s i n g s involved. The use of a n e x t - f l i g h t e s t i m a t o r r e q u i r i n g t r a c k i n g through t h e geometry from t h e c o l l i s i o n p o i n t t o t h e d e t e c t o r p o i n t can a l s o be q u i t e time-consuming e s p e c i a l l y i f t h e r e a r e many d e t e c t o r s . Following a r e some sugges t ions on c u t t i n g down running time.

I f t h e geometry of t h e problem i s such t h a t l a r g e p o r t i o n s of i t can be t r e a t e d i n two-dimensions, t h e u s e r can u s e a DOT-DOMINO-MORSE se t -up i n which DOT hand les t h e two-dimensional geometry and MORSE is coupled t o i t f o r t h e p o r t i o n of t h e geometry r e q u i r i n g three-dimensions. This can s a v e a s i g n i f i c a n t amount of time.

Another f e a t u r e which i s of p a r t i c u l a r i n t e r e s t i n r e a c t o r c a l c u l a - t i o n s i s t h e " f i c t i t i o u s ~ c a t t e r i n g ~ ' ~ method of choosing pa th l eng ths . Using t h i s method, p seudo-co l l i s ion s i t e s a r e chosen u s i n g t h e maximum t o t a l c r o s s s e c t i o n i n t h e sys tem. A r e j e c t i o n technique based on t h e r a t i o of t h e a c t u a l c r o s s s e c t i o n a t t h e pseudo-co l l i s ion t o t h e maximum c r o s s s e c t i o n i s u t i l i z e d t o de te rmine i f t h i s i s a r e a l c o l l i s i o n . I f t h e t e s t f a i l s , a new pseudo-co l l i s ion s i t e i s chosen. This method avo ids much of t h e geometry t r a c k i n g and thereby saves t i m e i n t h e e s t i - mation process . Rout ines t o hand le t h i s a r e a v a i l a b l e .

Sometimes t r a c k i n g thermal neu t rons i n v o l v e s a l a r g e number of c o l l i s i o n s and t h e r e f o r e a s i g n i f i c a n t amount of computer time. I n many problems, t h e thermal neu t rons do n o t make a s i g n i f i c a n t c o n t r i b u t i o n t o t h e answer s o t h e u s e r should cut-off t h e p a r t i c l e s b e f o r e they r each thermal ( u s e s n energy cu t -of f by s e t t i n g NGPQTN t o exc lude t h e thermal group) .

Another technique t h a t i s u s e f u l i n a c a s e where t h e geometry is symmetrical i s t o u s e t h i s symmetry t o advantage by t r a c k i n g through only p a r t of t h e sys t em and t h e n p r o p e r l y normal iz ing t h e r e s u l t s .

Two o t h e r minor improvements can be made as fol lows. The u s e r can i n c r e a s e t h e v a l u e of NAZ i n t h e geometry inpu t . This i n c r e a s e s t h e s i z e of t h e geometry a r r a y t h a t s aves t h e t r a c k i n g in fo rma t ion and thus a l lows more table-lookup and l e s s a c t u a l c a l c u l a t i o n . A l s o s i n c e t h e advent of COMBGEOM o r CG, t h e r e i s no compelling r eason f o r con t inu ing t o use GTMED t o e s t a b l i s h a correspondence between geometry and c r o s s s e c t i o n media numbers. ca rd involved t o make t h e correspondence one-to-one. The u s e r could thus e l i m i n a t e a l l c a l l s t o GTMED p l u s t h e GTMED r o u t i n e and s e t up h i s geometry acco rd ing ly . A t some f u t u r e d a t a , t h i s may be i n c o r p o r a t e d i n t h e s t a n d a r d MORSE.

I t i s q u i t e s imple t o change t h e one i n p u t

This w i l l s ave a number of s u b r o u t i n e c a l l s .

Grs

G3

2.4-1

2.4 Are There Too Many Abnormal Termina t ions?

There a re s e v e r a l a s p e c t s of any MORSE problem t h a t can be checked f o r e r r o r s b e f o r e a c t u a l l y running i t on t h e computer. This can save t i m e i n t h e long run .

Whenever s t a r t i n g on a geometry f o r t h e f i r s t t i m e , o r a f t e r modif- i c a t i o n of i t , t h e u s e r should make s e v e r a l p i c t u r e s of h i s mock-up us ing program PICTURE ( s e e p a r t f i v e ) . H e should t a k e "cuts" through a l l major p o r t i o n s i n each p lane . This w i l l r e v e a l most e r r o r s i n t h e geometry.

Pre-mixing c r o s s s e c t i o n s by us ing XCHEKRl can a l s o e l i m i n a t e many p o s s i b l e t r o u b l e s p o t s such a s i n c o r r e c t I D numbers. It a l s o a l lows t h e u s e r t o look a t t h e mixed c r o s s s e c t i o n s t o s e e i f they appear t o be c o r r e c t p r i o r t o making a MORSE run.

Double checking t h e i n p u t c a r d s i s always a good p r a c t i c e . Are t h e c a r d s i n t h e proper o r d e r ? Are any ca rds mis s ing? Is t h e number of media t h e same i n your i n p u t a s i t i s on t h e pre-nixed d a t a s e t ? What abou t your t a p e o r d i s k s p e c i f i c a t i o n s ? Have you de f ined your l o g i c a l u n i t s and s c r a t c h d i s k s ? D i d you a l l o c a t e enough d i s k space?

I f t h e u s e r r e q u i r e s a d i r e c t a c c e s s dev ice f o r h i s DOMINO d a t a , i s h i s DEFINE FILE s t a t emen t i n agreement wi th t h e DD c a r d h e s p e c i f i e d f o r i t ? Even i f i t i s i n agreement , i s i t c o r r e c t ?

Another major p i t f a l l i s f a i l u r e t o a l l o c a t e enough space i n b lank common. Do n o t guess : Ca lcu la t e ! I f XCHEKR was run , t h e amount of c r o s s s e c t i o n s t o r a g e i s known. The p a r t i c l e bank i s 12"NMOST on t h e IBM-360. Space f o r random walk i n p u t can be c a l c u l a t e d based on Fig . 4.2. A s a r e s u l t of having r u n PICTURE, t h e u s e r has enough informa- t i o n t o make a n i n t e l l i g e n t e s t i m a t e of t h e s t o r a g e r e q u i r e d f o r geometry da t a . Take t h e "Length of FPD a r r a y " *2+ "Length of i n t e g e r a r r ay" + 10" number of code zones as t h e estimate. This w i l l always equa l o r exceed what i s needed. The space r e q u i r e d f o r a n a l y s i s d a t a can be c a l c u l a t e d based on Fig . 4 . 6 . Needless t o say , a f t e r one MORSE run you w i l l know t h e exac t amount of b lank common r e q u i r e d from your ou tpu t .

2.5-1

2.5 Is There Too Much Output?

I f t h e u s e r f e e l s t h a t t h e volume of ou tpu t d a t a i s excess ive , he h a s s e v e r a l a l t e r n a t i v e s ,

One such a l t e r n a t i v e invo lves pre-mixing c r o s s s e c t i o n s when t h e same ones w i l l be used i n s e v e r a l p roduct ion runs. This w i l l e l i m i n a t e a l l bu t one page of output from t h e c r o s s s e c t i o n s (he w i l l a l r e a d y have a complete s e t of ou tpu t from t h e XCHEKR run ) . Even i f he does n o t pre-mix, he can t u r n o f f a l l t h e swi t ches i n t h e c r o s s s e c t i o n module t h a t p r i n t d a t a as r e a d , moments, a n g l e s , e t c .

Another p recau t ion i s t o be s u r e t h a t IDBG = 0 i n t h e geometry i n p u t excep t when debugging. The amount of ou tpu t produced when IDBG f 0 i s voluminous.

I n p roduc t ion runs where s e v e r a l hundred ba tches a re being run , ba tch ou tpu t can be suppressed by us ing a s p e c i a l s u b r o u t i n e OUTPT which i s a v a i l a b l e from t h e au thor .

2.6-1

2.6 S p e c i a l Cases

There a re a number of s p e c i a l cases which can a r i s e i n running MORSE, DOMINO, e tc . An a t t e m p t w i l l be made t o d e s c r i b e some of them and t h e a c t i o n r equ i r ed .

P l e a s e n o t e t h a t when running a DOT a d j o i n t t o use i n de te rmining t h e impor tan t r a d i a l areas f o r a MORSE source o r t o de te rmine importance f o r sou rce energy b i a s i n g , t h e DOT source should be i s o t r o p i c . Other- wise , improper a n g u l a r d i s t r i b u t i o n s f o r a n a d j o i n t sou rce w i l l r e s u l t .

I f t h e i n d i v i d u a l who makes t h e l i b r a r y t a p e f o r t h e c r o s s s e c t i o n s u s e s I D numbers w i t h more than f i v e d i g i t s , t h e u s e r must a l t e r t h e f o r - m a t i n s u b r o u t i n e XSEC from 1415 t o something e lse .

Another even t which h a s occur red i s t h a t a u s e r may have t h e d e s i r e t o use premixed c r o s s s e c t i o n s on ca rds . This i s accomplished by run- n ing XCHEKR, and l a t e r MORSE, u s i n g a s p e c i a l s u b r o u t i n e XSTAPE des igned t o r ead o r punch ca rds . This r o u t i n e i s a v a i l a b l e from t h e au tho r .

Anyone d e s i r i n g t o do a k - c a l c u l a t i o n only should u s e a dummy s u b r o u t i n e BANKR which w i l l p r ec lude doing any a n a l y s i s .

Many times t h e r e i s a need f o r some s p e c i a l no rma l i za t ion . This can be handled i n s e v e r a l ways. One "bu i l t - i n" method f o r d e t e c t o r dependent no rma l i za t ion i s by use of t h e "FACT" a r r a y ( s e e Table 4.21). This a r r a y can be se t -up e i t h e r i n I N S C O R o r STRUN. The a u t h o r p r e f e r s t h e STRUN way because INSCOR i s f r e q u e n t l y used f o r o t h e r t h ings . Another way of changing t h e no rma l i za t ion i s t o a l t e r WTSTRT i n t h e i n p u t d a t a ; i n o t h e r words, s t a r t t h e p a r t i c l e s w i t h a d i f f e r e n t weight .

Another very s p e c i a l case which r e q u i r e s some comment i s t h e type i n which t h e u s e r i s "sandwiching" MORSE between two DOT runs . That i s t o s a y , he runs a forward DOT t o some boundary which i s t h e n t h e sou rce f o r a forward MORSE run to some o the r boundary which w i l l be the sco r ing s u r f a c e based on a DOT a d j o i n t run. 'It shou ld be obvious t h a t t h i s type of run has l o t s of room f o r e r r o r and a l s o t h a t i t can n o t a l l be handled w i t h a MORSE r u n w i t h in-core a n a l y s i s . I n t h i s ca se , t h e u s e r runs MORSE wi th t h e DOMINO t a p e from t h e forward DOT as h i s sou rce and wr i tes a c o l l i s i o n t a p e of p a r t i c l e s c r o s s i n g t h e boundary where t h e DOT a d j o i n t w i l l be coupled t o i t . Then h e runs a SAMBO a n a l y s i s which r e a d s t h e c o l l i s i o n t a p e and u s e s t h e DOMINO t a p e from t h e a d j o i n t DOT run a s a s c o r i n g func t ion . I t would o r d i n a r i l y be imposs ib l e t o hand le two DOMINO t a p e s i n one r u n because of t h e number of 1/0 u n i t s ( d i s k s and t a p e s ) and t h e amount of s t o r a g e r equ i r ed . This n e c e s s i t a t e s a two-job set-up.

2 . 7 - 1

2.7 Are t h e S tandard Dev ia t ions Too LarPe?

One of t h e most d i f f i c u l t t h i n g s t o de te rmine i s how long a compu- t e r run i s needed t o g e t a c c e p t a b l e s t a t i s t i c s . A f t e r completion of a p roduc t ion run , t h e user may dec ide t h a t h e must have b e t t e r ( o r lower) s t a n d a r d d e v i a t i o n s . H i s cou r se of a c t i o n should be as fo l lows .

The o u t p u t from t h e run w i l l c o n t a i n t h e n e x t random number i n t h e sequence. This number should be used as t h e s t a r t i n g random number i n a new run. Upon completion of t h i s second r u n , h e can o b t a i n t h e average of t h e runs and a l s o t h e s t a n d a r d d e v i a t i o n s . This i s done a s fo l lows :

Assume a1 and a2 a r e t h e answers from runs one and two r e s p e c t i v e l y ; f , and f a r e t h e cor responding f . s . d ' s ( o r f r a c t i o n a l s t a n d a r d d e v i a t i o n s ? as o u t p u t ; ai = a . f . and c1 and c2 a re t h e number of ba t ches p e r run. The average answer i s t h e n x' = a.*cl + a2*c2 and t h e approxi- 1 1'

1 I--

c1 + c2

mate cor responding f.s.d. =

-

Any number of runs may be averaged t o g e t h e r by us ing an expanded form of t h e above e q u a t i o n s : i . e . ,

N N

i=l i= 1

- x = 1 a . c / 1 ci and i i

where N i s the number of runs .

2.8-1

2.8 References

1.

2.

3.

4.

M. B. Emmett, C. E. Burgart and T. J. Hoffman, DOMINO, A General Purpose Code for Compiling Discrete Ordinates and Monte Carlo Radiation Transport Calculations, OWL-4853 (1973).

M. B. Emmett, DOMINO-11. A General Purose Code for Coupling DOT-IV Discrete Ordinates and Monte Carlo Radiation Transport Calculations, ORNL/TM-7771 (1981).

C. E. Burgart, Capabilities of the MORSE Multigroup Monte Carlo Code in Solving Reactor Eigenvalue Problems, ORNL/TM-3662 (1971).

S. N. Cramer, Application of the Fictitious Scatterin? Radiation Transport Model for Deep-Penetration Monte Carlo Calculations, Nucl. Sci. & Eng., 65, 237-253 (1978).

4.0-3

TABLE OF CONTENTS

Page 4 . 1 . A b s t r a c t . . . . . . . . . . . . . . . . . . . . . . . . 4.1-1

4 . 2 . I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . 4.2-1

4 . 3 . I n p u t I n s t r u c t i o n s . . . . . . . . . . . . . . . . . . . 4.3-1

4 . 3 . 1 . Random Walk Inpu t I n s t r u c t i o n s . . . . . . . . . 4.3-1 -f-

4 . 3 . 2 . Combinator ia l Geometry I n p u t I n s t r u c t i o n s . . . . 4.3-7

4 . 3 . 3 . MgRSEC - Cross S e c t i o n Module I n p u t I n s t r u c t i o n s . . . . . . . . . . . . . . . . . . 4.3-11-f

4 . 3 . 4 . SAMBg Ana lys i s I n p u t I n s t r u c t i o n s . . . . . . . 4.3-14

4 . 4 . Random Walk Module . . . . . . . . . . . . . . . . . . . 4.4-1

4 . 4 . 1 . I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . 4.4-1

4 . 4 . 2 . Main Program . . . . . . . . . . . . . . . . . . 4.4-19

4 . 4 . 3 . Subrou t ines . . . . . . . . . . . . . . . . . . 4.4-21

Subrou t ine MORSE . . . . . . . . . . . . . . . . 4.4-21

Subrou t ine DATE . . . . . . . . . . . . . . . . 4.4-23

Funct ion D I R E C . . . . . . . . . . . . . . . . . 4.4-25

Subrout ine EUCLID . . . . . . . . . . . . . . . 4.4-26

Subrout ine FBANK . . . . . . . . . . . . . . . . 4.4-28

Random Number Package . . . . . . . . . . . . . 4.4-31

Subrou t ine FPROB . . . . . . . . . . . . . . . . 4.4-33

Subrou t ine FSOUR . . . . . . . . . . . . . . . . 4.4-34

Subrou t ine GETETA . . . . . . . . . . . . . . . 4.4-35

Subrou t ine GETNT . . . . . . . . . . . . . . . . 4 . 4 - 3 8 t

Subrou t ine @MST . . . . . . . . . . . . . . . . 4.4-39"

Subrou t ine GPRgB . . . . . . . . . . . . . . . . 4.4-40

Subrou t ine GSTdRE . . . . . . . . . . . . . . . 4.4-41

Subrou t ine INPUT . . . . . . . . . . . . . . . . 4.4-42

Subrou t ine INPUT1 . . . . . . . . . . . . . . . 4.4-43

Subrou t ine INPUT2 . . . . . . . . . . . . . . . 4.4-46

Subrou t ine IWEEK . . . . . . . . . . . . . . . . 4.4-47

Subrou t ine MSgUR . . . . . . . . . . . . . . . . 4.4-48

Subrou t ine NXTCgL . . . . . . . . . . . . . . . 4.4-50

Subrou t ine OUTPT . . . . . . . . . . . . . . . . 4.4-52

Subrou t ine OUTPT2 . . . . . . . . . . . . . . . 4.4-53

4 . 0.4 n

Subrou t ine SORIN . . . . . Subrou t ine SOURCE . . . . Subrou t ine TESTW . . . . . Subrou t ine TIMER . . . . .

4 . 4 . 4 . Energy Indexing i n MORSE . 4 . 5 . MORSEC - The Cross-Sect ion Module

4 . 5 . 1 . I n t r o d u c t i o n . . . . . . . 4 . 5 . 2 . Blank Common Cross S e c t i o n

4 . 5 . 3 . Subrou t ines . . . . . . . Subrout ine ALBDO . . . . . Subrou t ine ANGLES . . . . Subrou t ine BADMOM . . . . Subrou t ine CQLISN . . . . Subrou t ine FFREAD . . . . Subrou t ine F I N D . . . . . Subrou t ine FISGEN . . . . Subrou t ine GAMGEN . . . . Subrou t ine GETMUS . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . . Sto rage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Subrou t ine GTIgUT . . . . . . . . . . . . . . . Subrou t ine GTMED . . . . . . . . . . . . . . . . Subrou t ine GTNDSK . . . . . . . . . . . . . . . Subrou t ine GTSCT . . . . . . . . . . . . . . . . Subrou t ine JNPUT . . . . . . . . . . . . . . . . Subrou t ine LEGEND . . . . . . . . . . . . . . . Subrou t ine MAMENT . . . . . . . . . . . . . . . Subrou t ine NSIGTA . . . . . . . . . . . . . . . Subrou t ine PTHETA . . . . . . . . . . . . . . . . Subrou t ine Q . . . . . . . . . . . . . . . . . . Subrou t ine READSG . . . . . . . . . . . . . . . Subrou t ine RESTOR . . . . . . . . . . . . . . . Subrou t ine STORE . . . . . . . . . . . . . . . . Subrou t ine XSEC . . . . . . . . . . . . . . . . Subrou t ine XSTAPE . . . . . . . . . . . . . . .

4 . 6 . SAMBO - The Ana lys i s Module . . . . . . . . . . . . . . 4 . 6 . 1 . I n t r o d u c t i o n . . . . . . . . . . . . . . . . . .

+Revised .

Page

4.4-54

4.4-56

4.4-57

4.4-58

4.4-60

4 .5 -1

4 .5 -1

4.5-5

4.5-14

4 .5 -14 ?

4.5-15

4.5-17

4.5-18

4.5-20

4 .5 -21

4.5-23

4.5-24

4.5-25

4.5-27

4 .5 -28 4.5-29

4.5-30

4.5-32

4.5-33

4.5-35

4.5-37

4.5-38

4.5-40

4 .5 -41

4.5-43

4.5-44

4.5-45

4.5-47

4.6-1

4 . 6 - 1

4.0-5

SPH

RCC . . . . . . . . . . . REC

I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

Page

4.6-3

4.6-13

4.6-14

4.6-15

4.6-17

4.6-18

4.6-20

4.6-22 ?

4.6-25

4.6-26

4.6-27

4.6-29

4.6-31

4.6-31

4.6-33

4.6-33

4.6-36

4.6-37

4.6-38

4.6-38

4.6-39

4.6-40

4.7-1

4.7-1

4.7-1

4.7-5 ?

4.7-5

4.7-6

4.7-6

4.7-7

4.7-7

4.7-8

4.7-8

4.7-9

4.7-9

TRC . . . . . . . . . . .

? R e v i s e d .

1 1 ) , / . . . . . . . . . . .

4 . 0.6 n

Page

4.7.4. Subrou t ines . . . . . . . . . . . . . . . . . . 4.7-11

Subrout ine G 1 . . . . . . . . . . . . . . . . . 4.7-11 1- Subrout ine ALBERT . . . . . . . . . . . . . . . 4.7-13

Subrout ine G E N I . . . . . . . . . . . . . . . . 4.7-14

Subrout ine GG . . . . . . . . . . . . . . . . . 4.7-15

Subrout ine GTVLIN . . . . . . . . . . . . . . . 4.7-16

Subrout ine J @ M I N . . . . . . . . . . . . . . . . 4.7-17

Subrout ine L@@KZ . . . . . . . . . . . . . . . . 4.7-18 t Subrout ine N@RML . . . . . . . . . . . . . . . . 4.7-19

Subrout ine PR . . . . . . . . . . . . . . . . . 4.7-20

4.8. The Diagnos t i c Module . . . . . . . . . . . . . . . . . 4.8-1

4.8.1. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . 4.8-1

4.8.2. Subroutines . . . . . . . . . . . . . . . . . . 4.8-10

Subrou t ine BNKHLP . . . . . . . . . . . . . . . 4.8-10

Subrou t ine HELP . . . . . . . . . . . . . . . . 4.8-11

Subrou t ine HELPER . . . . . . . . . . . . . . . 4.8-13

Subrou t ine SUBRT . . . . . . . . . . . . . . . . 4.8-14

Subrou t ine XSCHLP . . . . . . . . . . . . . . . 4.8-15

4.9. Hardware and Sof tware Requirements . . . . . . . . . . . 4.9-1

4.9.2. L i b r a r y Rout ines and Funct ions . . . . . . . . . 4.9-2

General Comments . . . . . . . . . . . . . . . . 4.9-2

Funct ion ICL@CK . . . . . . . . . . . . . . . . 4.9-4

4.9.1. Hardware Requirements . . . . . . . . . . . . . 4.9-1

Funct ion ICQMPA . . . . . . . . . . . . . . . . 4.9-5

Subrou t ine IDAY . . . . . . . . . . . . . . . . 4.9-7

Funct ion L@C . . . . . . . . . . . . . . . . . . 4.9-8

Funct ion M@DEL . . . . . . . . . . . . . . . . . 4.9-8

Masking Funct ions . . . . . . . . . . . . . . . 4.9-9

Charac t e r Manipula t ion Rout ines . . . . . . . . 4.9-12

Subrout ine ERTRAN . . . . . . . . . . . . . . . 4.9-15

Funct ion TICKER . . . . . . . . . . . . . . . . 4.9-15

Subrou t ine SECQND . . . . . . . . . . . . . . . 4.9-15

4.9.3. Overlay S t r u c t u r e . . . . . . . . . . . . . . . 4.9-16

4.10. The Many I n t e g r a l Forms of t h e Boltzmann Transpor t Equat ion and i t s Adjo in t . . . . . . . . . . 4.10-1 f'

4.11. Genera l ized Gaussian Quadra ture . . . . . . . . . . . . 4.11-1

4.12. References . . . . . . . . . . . . . . . . . . . . . . . 4.12-1 ?

n

Table 4.1.

Table 4 . 2 .

Table 4 .3 .

Table 4 .4 .

Table 4 .5 .

Table 4.6.

Table 4 . 7 .

Table 4 .8 .

Table 4.9.

Table 4.10.

Table 4 .11 .

Table 4 . 1 2 .

Table 4.13.

Table 4.14.

Table 4.15.

Table 4.16.

Table 4 . 1 7 .

LIST OF TABLES

Page

Sample Group Inpu t Numbers f o r Some Represen ta t ive Problems . . . . . . . . . . . . . 4.3-2

Var i ab le s That May b e Wr i t t en on C o l l i s i o n Tape. . 4.3-5

Inpu t Required on CGB Cards f o r Each Body Type . . 4.3-9

D e f i n i t i o n of Var i ab le s i n Common AP@LL@ . . . . . 4.4-4

D e f i n i t i o n of Var i ab le s i n Common NUTR@N . . . . . 4.4-10

L i s t of Rout ines A l t e r i n g Var i ab le s i n NUTR@N Common . . . . . . . . . . . . . . . . . . 4.4-11

Subrout ines i n Which Var i ab le s i n NUTRQ)N Common are Changed . . . . . . . . . . . . . . . . 4.4-12

D e f i n i t i o n of Var i ab le s i n Random Walk Blank Common . . . . . . . . . . . . . . . . . . . 4.4-13

Indexing of Random Walk Blank Common A r r a y s . . . 4.4-16

Layout of Par t ic le Bank i n Blank Common . . . . . 4.4-18

Layout of F i s s i o n Bank i n Blank Common . . . . . . 4.4-29

D e f i n i t i o n s of Var i ab le s i n Common FISBNK . . . . 4.4-30

Numerical Examples f o r Various Options w i t h Corresponding Energ ies f o r Each Case . . . . . . . 4.4-61

Values of NGPQT1, NGPQT2, NGPQT3 f o r S e v e r a l Cases . . . . . . . . . . . . . . . . 4.4-62

D e f i n i t i o n s of Var i ab le s i n Common LgCSIG . . . . 4.5-7

Loca t ion of Permanent Cross S e c t i o n s i n Blank Common . . . . . . . . . . . . . . . . . 4.5-11

D e f i n i t i o n s of Var i ab le s i n Common GTSCl . . . . . 4.5-13

Table 4.18. D e f i n i t i o n s of Variables i n CommonUSER . . . . . 4.6-7

Table 4.19. D e f i n i t i o n s of Problem-Dependent Energy Group L i m i t s . . . . . . . . . . . . . . . 4.6-8

Table 4.20. D e f i n i t i o n s o E 4 a r i a b l e s i n Common PDET . . . . . 4.6-9

Table 4 .21 . Indexing of Analys is Arrays i n Blank Common . . . 4.6-11

Table 4 . 2 2 . BANKR Arguments . . . . . . . . . . . . . . . . . 4.6-30

Table 4.23. D e f i n i t i o n s of Var i ab le s i n Common @ML@C . . . . 4.7-26

Table 4.24. D e f i n i t i o n s of V a r i a b l e s i n Common PAREM as Found i n Combinator ia l Geometry . . . . . . . . 4.7-28

Table 4.25. D e f i n i t i o n s of Var i ab le s i n Common @RGI . . . . . 4.7-30 -/-

Table 4.26. Diagnos t ic Messages from INPUT Module i n M@RSE . . 4.8-2 -/-

Table 4 . 2 7 . D iagnos t i c Messages from Other Modules of M@RSE. . 4.8-6 -/-

?Revised.

4.3-7

CARDS M (7E10.4) (Omit i f MFISTP on Card L - < 0 )

(FWL@(I), I = 1, MXREG) v a l u e s of t h e weight t o b e a s s igned t o

f i s s i o n neu t rons .

CARDS N (7E10.4) (Omit i f MFISTP on Card L - < 0 )

(FSE(IG,IMED), I G = 1, NMGP), IMED = 1, MEDIA) t h e f r a c t i o n of

f i s s ion - induced source p a r t i c l e s i n group I G and medium I M E D .

NOTE: Inpu t f o r each medium must s t a r t on a new ca rd .

CARDS 0 (7E10.5) (Omit i f NGPQTN = 0 o r NGPQTG = 0 , i . e . , i n c l u d e i f

coup l e d neut ron- gamma-r ay p rob lem)

((GWLd(IG,NREG) I G = 1, NMGP o r NMTG - NMGP), N R E G = 1, MXREG) -

v a l u e s of t h e p r o b a b i l i t y of g e n e r a t i n g a gamma ray . NMGP groups

are read f o r each r eg ion i n a forward problem and NMTG-NMGP f o r

an a d j o i n t . Inpu t f o r each r e g i o n must s ta r t on a new ca rd .

4 .3 .2 . Combina tor ia l Geometry Inpu t I n s t r u c t i o n s

The combina to r i a l geometry i n p u t d a t a i s r ead by t h e JdMIN sub-

r o u t i n e , excep t f o r t h e r eg ion volumes VN@R(I), which a r e read by t h e

GTVLIN s u b r o u t i n e whenever IV0PT = 3. For c l a r i t y of terminology, t h e

terms "regions ' ' and "media" have e s s e n t i a l l y t h e same meaning as i n t h e

0 5 R Geometry Package, b u t a r e c o n s t r u c t e d i n a d i f f e r e n t manner. The

t e r m ''zone'' i s t h e same a s t h e "region" a s d e f i n e d i n t h e o r i g i n a l com-

b i n a t o r i a l geometry package. The t e r m "body" has t h e same meaning as i n

t h e o r i g i n a l combina to r i a l geometry package.

CARD CGA ( 2 1 5 , 1 0 X , l O A 6 )

I V ~ P T - opt.ion which d e f i n e s t h e method by which r eg ion volumes

are determined; i f

I V ~ P T = 0,- volumes . s e t equa l t o 1,

IV@PT. = 1, c o n c e n t r i c sphe re volumes are c a l c u l a t e d ,

IVdPT = 2 , s l a b volumes (1-dim.) are c a l c u l a t e d , *

IV0P.T = 3, volumes, are i n p u t by ca rd .

- i f I D B G > 0 , s u b r o u t i n e PR i s c a l l e d t o p r i n t r e s u l t s

of combina to r i a l geometry c a l c u l a t i o n s du r ing execu t ion .

U s e on ly f o r debugging. '

JTY - alphanumeric t i t l e f o r geometry i n p u t (columns 21-80).

I D B G

*Not o p e r a t i o n a l .

4.3-8

CARDS CGB (2X,A3,1X,I4,6D10.3)

One s e t of CGB c a r d s i s r e q u i r e d f o r each body and f o r t h e END c a r d

( s e e Table 4 .3) . Leave columns 1-6 b l a n k on a l l c o n t i n u a t i o n ca rds .

ITYPE - s p e c i f i e s body type o r END t o t e rmina te r ead ing of body

d a t a ( f o r example BdX, W P , ARB, e t c . ) . Leave b l ank

f o r c o n t i n u a t i o n c a r d s .

IALP - body number a s s igned by u s e r ( a l l i npu t body numbers

must form a sequence se t beg inn ing a t 1 ) .

numbers are a s s igned s e q u e n t i a l l y . E i t h e r a s s i g n a l l o r

none o f t h e numbers. Leave b l a n k f o r c o n t i n u a t i o n c a r d s .

I f l e f t b l a n k ,

FPD(1) - real d a t a r e q u i r e d f o r t h e g iven body as shown i n

Table 4 .3 . T h i s d a t a must be i n cm.

CARDS CGC (2X,A3,15,9(A2,15))

I n p u t zone s p e c i f i c a t i o n c a r d s . One se t of c a r d s r e q u i r e d for each

i n p u t zone, w i t h i n p u t zone numbers b e i n g a s s igned s e q u e n t i a l l y .

IALP - IALP must b e a nonblank f o r t h e f i r s t c a r d of each set

of c a r d s d e f i n i n g an i n p u t zone. I f IALP is b l a n k , t h i s

c a r d i s t r e a t e d as a c o n t i n u a t i o n of t h e p rev ious zone

ca rd .

IALP - END deno tes t h e end of zone d e s c r i p t i o n .

NAZ - t o t a l number of zones t h a t can b e e n t e r e d upon l e a v i n g

any of t h e b o d i e s d e f i n e d f o r t h i s i n p u t r eg ion (some

zones may b e counted more than once) . Leave b l ank f o r

c o n t i n u a t i o n c a r d s f o r a g iven zone.

t h e f i r s t ca rd of t h e zone c a r d s e t , t hen i t is set t o

5 ) . Th i s i s used t o a l l o c a t e b l ank common.

A l t e r n a t e IIBIAS(1) and JTY(1) f o r a l l bod ie s d e f i n i n g

t h i s i n p u t zone.

( I f NAZ - < 0 on

IIBIAS(1) - s p e c i f y t h e "@R" o p e r a t o r i f r e q u i r e d f o r t h e JTY(1)

body . JTY(1) - body number wi th t h e (+) o r (-) s i g n as r e q u i r e d f o r

t h e zone d e s c r i p t i o n .

4.3-11

CARDS CGD (1415)

MRIZ(1) - MRIZ(1) i s t h e r eg ion number i n which t h e " I th" i n p u t

zone i s con ta ined ( I = 1, t o t h e number of i n p u t zones) .

Region numbers must b e s e q u e n t i a l l y d e f i n e d from 1.

CARDS CGE (1415)

MMIZ(1) - MMIZ(1) i s t h e medium number i n which t h e " I th" i n p u t

zone i s con ta ined ( I = 1, t o t h e number of i n p u t zones ) .

Medium numbers must be s e q u e n t i a l l y d e f i n e d from 1.

CARDS CGF (7D10.5) (Omit i f IVOPT # 3 )

VN@R(I) - volume of t h e " I th" r eg ion (I = 1 t o MXREG, t h e

number o f r e g i o n s ) .

4.3.3. MgRSEC - Cross-Section Module I n p u t I n s t r u c t i o n s

CARD XA (20A4)

T i t l e c a r d f o r c r o s s s e c t i o n s . Th i s t i t l e i s a l s o w r i t t e n on t a p e

i f a p rocessed t ape i s w r i t t e n ; t h e r e f o r e , i t i s suggested t h a t

t h e t i t l e be d e f i n i t i v e .

CARD XB (1415)

NGP* - t h e number of pr imary groups f o r which t h e r e are c r o s s

s e c t i o n s t o be s t o r e d . Should be same as NMGP i n p u t i n

M ~ R S E .

NDS - number of pr imary downsca t t e r s f o r NGP ( u s u a l l y NGP).

NGG* - number of secondary groups f o r which t h e r e are c r o s s

s e c t i o n s t o be s t o r e d .

NDSG - number o f secondary downsca t t e r s f o r NGG ( u s u a l l y NGG).

INGP* - t o t a l number of groups f o r which c r o s s s e c t i o n s are t o

be i n p u t .

I T B L - t a b l e l e n g t h , i . e . , t h e number of c r o s s s e c t i o n s f o r

each group ( u s u a l l y e q u a l t o number of downsca t t e r s + number of u p s c a t t e r s + IHT).

ISGG - l o c a t i o n of within-group s c a t t e r i n g c r o s s s e c t i o n s

( u s u a l l y e q u a l 'to number of u p s c a t t e r s plus IHT+l).

NMED - number o f media f o r which c r o s s s e c t i o n s are t o be

s t o r e d - should be same as MEDIA i n p u t i n MgRSE.

*See Table 4 . 1 f o r sample i n p u t .

4.3-12

NELEM - number o f e lements f o r which c r o s s s e c t i o n s a r e t o be

r e a d .

N M I X - number of mixing o p e r a t i o n s (e lements t i m e s d e n s i t y

o p e r a t i o n s ) t o be performed (must b e - > 1 ) .

NCQ~EF - number of c o e f f i c i e n t s f o r each e lement , i n c l u d i n g P

NSCT

I S TAT - f l a g t o s t o r e Legendre c o e f f i c i e n t s i f g r e a t e r than

0' - number of d i s c r e t e ang le s ( u s u a l l y NC@EF/2integral > .

ze ro .

IHT - l o c a t i o n of t o t a l c r o s s s e c t i o n i n t h e t a b l e .

CARD XC (1115)

I R D S G t - swi t ch t o p r i n t t h e c r o s s s e c t i o n s as they are r ead

i f > 0.

I S T R ~ - swi t ch t o p r i n t c r o s s s e c t i o n s as they are s t o r e d i f

> 0 .

I FMUf - swi t ch t o p r i n t i n t e r m e d i a t e r e s u l t s of p ' s c a l c u l a t i o n

i f > 0.

I M o M t - swi t ch t o p r i n t moments of a n g u l a r d i s t r i b u t i o n i f > 0.

I P R I N ? - swi t ch t o p r i n t a n g l e s and p r o b a b i l i t i e s i f > 0.

IPLJNt - swi t ch t o p r i n t r e s u l t s of bad Legendre c o e f f i c i e n t s

i f > 0 .

IDTFt ' - swi t ch t o s i g n a l t h a t i n p u t format i s DTF-IV format

i f > 0 ; o t h e r w i s e , ANISN format i s assumed.

IXTAPE - l o g i c a l t a p e u n i t i f b i n a r y c r o s s s e c t i o n t a p e , se t

e q u a l t o 0 i f c r o s s s e c t i o n s are from c a r d s . I f

n e g a t i v e , t hen t h e processed c r o s s s e c t i o n s and o t h e r

necessa ry d a t a from a p rev ious run w i l l be r e a d ; i n

t h i s case (IXTAPE < 0) no c r o s s s e c t i o n s from c a r d s

and no mixing c a r d s may b e i n p u t . The a b s o l u t e v a l u e

of IXTAPE i s t h e l o g i c a l t a p e u n i t .

JXTAPE - l o g i c a l t a p e u n i t of a processed c r o s s - s e c t i o n t a p e t o

b e w r i t t e n . T h i s processed t a p e w i l l con ta in t h e t i t l e

c a r d , t h e v a r i a b l e s from common LQjCSIG and t h e p e r t i n e n t

c r o s s s e c t i o n s from b lank common

?Switches are ignored i f IXTAPE < 0.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3-13

106 RT - l o g i c a l t a p e u n i t o f a p o i n t c ros s - sec t ion t a p e i n

06R format .

IGQPT - l a s t group (M0RSE mul t igroup s t r u c t u r e ) f o r which t h e

06R p o i n t c r o s s s e c t i o n s a r e t o b e used ( - < NMGP).

CARD XD (1415) ( O m i t i f IXTAPE - < 0 )

Element i d e n t i f i e r s f o r c ros s - sec t ion t a p e . I f e lement i d e n t i f i e r s

are i n same o r d e r as e lements on t a p e , t h e e f f i c i e n c y of t h e code i s

i n c r e a s e d due t o fewer t ape rewinds.

CARDS XE (Omit i f IXTAPE # 0 )

I f c r o s s s e c t i o n s are i n f ree-form, a ca rd w i t h ** i n columns 2 and

3 must precede t h e a c t u a l d a t a .

ANISN format i f IDTF 0 ; o the rwise , DTF-IV format . Cross s e c t i o n s

f o r INGP groups wi th a t a b l e l e n g t h ITBL f o r NELEM e lements each

wi th NCgEF c o e f f i c i e n t s .

CARDS XF (215,E10.5) (Omit i f IXTAPE < 0 )

N M I X ( s e e Card XB) c a r d s are r e q u i r e d .

KM - medium number.

KE - element number o c c u r r i n g i n medium KM ( n e g a t i v e v a l u e

i n d i c a t e s l a s t mixing o p e r a t i o n f o r t h a t medium).

F a i l u r e t o have a n e g a t i v e v a l u e causes code n o t t o

g e n e r a t e angu la r p r o b a b i l i t i e s f o r t h a t media (LEGEND

and ANGLE n o t c a l l e d ) .

RH# - d e n s i t y of e lement KE i n medium KM i n u n i t s of

atoms / (ba rn cm) . CARDS XG (15) (Omit ' i f I a 6 R T - < 0) i

NXPM - number of p o i n t c r o s s - s e c t i o n sets p e r medium found on 7 3 8 a n 06R tape .

= 1, t o t a l c r o s s s e c t i o n o n l y ,

= 2 , t o t a l + s c a t t e r i n g c r o s s s e c t i o n ,

= 3 , t o t a l , s c a t t q r i n g , and v * f i s s i o n c r o s s s e c t i o n . ......................................................................... NOTE: Cross s e c t i o n s and c r o s s - s e c t i o n i n p u t d a t a may b e checked inde-

penden t ly of MgRSE u t i l i z i n g XCHEKR.'

t h e c ros s - sec t ion c a r d s XA through XG preceded by a ca rd a s fo l lows :

Format (415)

The i n p u t t o XCHEKR c o n s i s t s of

IADJM - se t g r e a t e r than zero f o r an a d j o i n t problem.

4.3-14

MEDIA - number of c ros s - sec t ion media; should e q u a l NMED on

Card XB.

NMGP - number of pr imary p a r t i c l e energy groups f o r which

c r o s s s e c t i o n s are t o b e s t o r e d ; should equa l NGP on

Card XB.

NMTG - t o t a l number o f energy groups f o r which c r o s s s e c t i o n s

are t o b e s t o r e d . Should be e q u a l t o INGP on Card XB.

4 .3 .4 . SAME@ Analys i s I n p u t I n s t r u c t i o n s

The fo l lowing d a t a are read from c a r d s by SCgRIN:

CARD AA (20A4)

T i t l e i n fo rma t ion - w i l l be immediately o u t p u t .

CARD BB (815)

ND

NNE - number of pr imary p a r t i c l e (neu t ron ) energy b i n s t o be

- number o f d e t e c t o r s ( s e t = 1 i f - < 0 ) .

used (must be N E ) .

NE - t o t a l number of energy b i n s ( s e t = 0 i f 1 ) .

N T - number of t i m e b i n s f o r each d e t e c t o r (may be n e g a t i v e ,

i n which case INTI v a l u e s are t o be r ead and used f o r

every d e t e c t o r ) ( s e t = 0 i f INTI - < 1 ) .

NA

NKESP - number o f energy-dependent response f u n c t i o n s t o b e

- number of a n g l e b i n s ( s e t = 0 i f 5 1 ) .

used ( s e t = 1 i f - < 0 ) .

NEX - number of extra a r r a y s of s i z e NMTG t o be set a s i d e

( u s e f u l , f o r example, as a p l a c e t o s t o r e an a r r a y of

group-to-group t r a n s f e r p r o b a b i l i t i e s f o r e s t i m a t o r

r o u t i n e s ) .

NEXND - number of extra a r r a y s o f s i z e N D t o b e s e t a s i d e

( u s e f u l , f o r example, as a p l a c e t o s t o r e d e t e c t o r -

dependent coun te r s ) . CARDS CC (3E10.4) (ND c a r d s w i l l be read)

X , Y , Z - d e t e c t o r l o c a t i o n . ( I f o t h e r than p o i n t d e t e c t o r s are

d e s i r e d , t h e p o i n t l o c a t i o n s must s t i l l b e i n p u t and

can be combined w i t h a d d i t i o n a l d a t a b u i l t i n t o u s e r

r o u t i n e s t o f u l l y d e f i n e each d e t e c t o r . ) n

. . . . . . . . . . .

4.4-33

Subrou t ine FPRgB

FPRgB c a l c u l a t e s t h e expec ted weight of f i s s i o n n e u t r o n s a t a c o l l i -

s i o n p o i n t and then s p l i t s o r p l a y s Russian r o u l e t t e so as t o produce t h e

c o r r e c t average number of f i s s i o n s , a l l of weight FWLg ( s p e c i f i e d i n

problem i n p u t f o r each r e g i o n ) . FBANK is c a l l e d f o r each neu t ron produced,

t o b e s t o r e d f o r p r o c e s s i n g i n t h e n e x t gene ra t ion .

f o r forward f i s s i o n problems.

from t h e FISH a r r a y i n b l ank common.

Ca l l ed from: MgRSE.

Subrou t ines c a l l e d : FISGEN, GTMED, BANKR(3), FBANK, FLTRNF, HELP, ERROR,

FPRgB ca l l s FISGEN

For a d j o i n t problems, vCf/Ct i s s e l e c t e d -

S I G N ( l i b r a r y ) .

Comons r e q u i r e d : Blank, NUTRgN, APgLLg, FISBNK.

Var i ab le s r e q u i r e d :

NMED, WATE , N R E G , I G (from NUTRgN common, see page 4.4-10)

IADJM - =1 i f a d j o i n t problem;

=O i f forward problem.

LQCFSN - l o c a t i o n i n b l ank common o f c e l l ze ro of a r r a y of

f i s s i o n c r o s s s e c t i o n s .

LOCNSC - l o c a t i o n i n b lank common of c e l l ze ro of s c a t t e r i n g

coun te r a r r a y s .

IMED - c r o s s - s e c t i o n medium of c o l l i s i o n p o i n t .

MXRE G

NMTG - t o t a l number of energy groups.

FTQTL - t o t a l of f i s s i o n we igh t s from a l l c o l l i s i o n s .

LOCFWL - l o c a t i o n i n b l ank common of c e l l ze ro of a r r a y FWLQ)W.

NPSCL(3) - f i s s i o n coun te r .

- maximum r e g i o n number.

- -

Var iab le s changed: " \

WATEF - f i s s i o n weight t r a n s f e r r e d t o FBANK.

NFIZ - a c t u a l number of f i s s i o n s p e r group and r eg ion .

WFIZ - weight e q u i v a l e n t t o NFIZ.

FT@TL

NPSCL(3)

S i g n i f i c a n t i n t e r n a l v a r i a b l e s :

FWL

ISCT - l o c a t i o n i n b l ank common of (IG,NREG) c e l l of s c a t t e r i n g

- c u r r e n t v a l u e from a r r a y FWLg.

coun te r a r r a y NFIZ (and l a t e r WFIZ).

4.4-34

Subrou t ine FSOUR

Th i s r o u t i n e i s c a l l e d by t h e sou rce e x e c u t i v e r o u t i n e , MSgUR, when

t h e sou rce f o r t h e p r e s e n t b a t c h i s t o be taken from t h e previous b a t c h

f i s s i o n s . Its f u n c t i o n i s t o t r a n s f e r t h e neu t ron parameters from t h e

f i s s i o n bank t o t h e neu t ron bank. I f t h e r e were no f i s s i o n s i n t h e

p rev ious b a t c h , i t sets a f l a g , p r i n t s a message, and r e t u r n s .

Ca l l ed from: MS@UR

Subrou t ines c a l l e d :

ST@RNT(N) - l o a d s parameters i n common NUTR@N i n t o t h e N t h l o c a t i o n

i n t h e neu t ron bank.

Commons r e q u i r e d : Blank, NUTRgN, FISBNK, APgLLg.


NFI SH - number of f i s s i o n s produced i n t h e p rev ious b a t c h .

NMEM - s e t e q u a l t o NFISH.

N I T S - number of b a t c h e s r eques t ed f o r t h e run.

ITERS - b a t c h c o u n t e r .

NFISBN - l o c a t i o n i n b l ank common of c e l l z e r o of t h e f i s s i o n bank.

V a r i a b l e s changed:

NITS - se t t o number of b a t c h e s completed i f NFISH = 0.

I TE RS - set t o zero i f NFISH = 0.

NAME NMED NRE G S e t t o zero ( i n NUTR@N common, see page 4.4-10).

BLZNT u , v , w

WATE S e t t o v a l u e s found i n f i s s i o n bank ( i n NUTR@N common,

see page 4. $-lo). AGE I G i NAMEX 1 NOTE: I G i s group index of neu t ron c a u s i n g f i s s i o n .

4 . 4 - 3 7

Funct ion used: DIREC. EXPRNF, AM@D(library), EXP(1ibrary)

Commons r e q u i r e d : Blank, NUTRflN, APdLLd.


I G , X , Y , Z , U , V , W , WATE, NREG (from NUTRON common, see page 4.4-10) . MAXGP - number of energy groups f o r weight s t a n d a r d s and lo r

pa th- length s t r e t c h i n g parameters PATH.

NdLEAK - an index f o r nonleakage b i a s i n g .

RAD - t h e l a r g e s t o v e r a l l dimension i n t h e system.

PATH - path- length s t r e t c h i n g parameters ( i n b l ank common).

Var i ab le s changed :

ETA - t h e number of mean-free p a t h s t o t h e n e x t c o l l i s i o n .

WATE - t he p a r t i c l e ’ s weight c o r r e c t e d f o r t h e b i a s i n g

employed d u r i n g t h e p r e s e n t f l i g h t s e l e c t i o n .


ARG - t h e d i s t a n c e i n mean-free p a t h s from t h e las t c o l l i s i o n

s i t e t o an e x t e r n a l boundary a long t h e p r e s e n t f l i g h t

d i r e c t i o n .

4.4-38

Subrou t ine GETNT(N)

Three e n t r y p o i n t s are used i n t h i s r o u t i n e . ? En t ry SETNT s a v e s

t h e addres s ( i n words) of t h e f i r s t c e l l a v a i l a b l e f o r t h e neu t ron bank

i n b l ank common and r e t u r n s t h e a d d r e s s of t h e l a s t c e l l i t w i l l u se .

En t ry ST@RNT(N) s t o r e s v a l u e s from common NUTR@N i n t o t h e Nth se t of

l o c a t i o n s i n t h e neu t ron bank and e n t r y GETNT(N) does t h e r e v e r s e ; i t

p i c k s up v a r i a b l e s from t h e bank and p u t s them i n common NUTRON.

Ca l l ed from: INPUT2 (SETNT), MdRSE (GETNT), MS@UR (STgRNT), FS@UR(ST@RNT),

~ U T P T (GETNT)’. TESTW(STORNT).

Commons r e q u i r e d : Blank, NUTR@N. The area of b l ank common used f o r t h e

neu t ron bank is shown i n Table 4.10. Not ice t h a t I G ,

NAME, NAMEX, NMED, and N R E G are s t o r e d i n 2-byte words

(and are t h e r e f o r e l i m i t e d t o - < 65535) on t h e IBM-360,

b u t are f u l l words on t h e UNIVAC-1108 and CDC-6600.

V a r i a b l e s r e q u i r e d :

SETNT: NLAST

NM@ST

GETNT: N

STORNT: N , NAME, NAMEX, NMED, NREG, I G , U, V , W , X , Y , Z , WATE,

BLZNT, AGE (from NUTR@N common, see page 4.4-10).


SETNT: NLAST

GETNT: v a r i a b l e s i n common NUTR@N r e q u i r e d by SETNT above.

ST@RNT: 1 2 l o c a t i o n s i n b l ank common.


NN@ - l o c a t i o n i n b l ank common of s t a r t of neu t ron bank.

?On t h e CDC-6600 3 s e p a r a t e s u b r o u t i n e s e x i s t .

drs

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .

4.4-39

Subrou t ine G@MST (TSIG, MARK)

Any boundary c r o s s i n g s between t h e p r e s e n t and n e x t c o l l i s i o n s i tes

are de termined by c a l l i n g t h e combina to r i a l geometry r o u t i n e G 1 . Before

t h e G 1 c a l l , combina to r i a l geometry v a r i a b l e s i n common PAREM are i n i t i a l -

i zed ; and a f t e r t h e c a l l , NUTRdN v a r i a b l e s are updated. I f an a lbedo

medium is encountered , t h e f l a g NALB i s set t o t h e a lbedo medium number,

and then N@RML i s c a l l e d t o de te rmine t h e normal t o t h e s u r f a c e encoun-

t e r e d . MARK i s set t o -1 f o r an e x t e r n a l v o i d .

Ca l l ed from: NXTCdL.

Subrou t ines c a l l e d : G 1 , NORML, PR.

Commons r e q u i r e d : AP@LL@, NUTR@N , G@ML@C, @RGI , PAREM.


X , Y , Z , NMED, U, V , W,.NREG) from NUTR@N common, see page 4.4-10.

IBLZN - v a l u e of I R from l a s t t r a c k o r from LOOKZ.

ETATH - d i s t a n c e t o b e t r a v e l e d ( i n cm) i f t h e f l i g h t remains

i n t h e s t a r t i n g medium.

MARK - i n i t i a l v a l u e of f l a g i n d i c a t i n g type of t r a j e c t o r y .

T S I G - t o t a l c r o s s s e c t i o n of s t a r t i n g p o i n t medium.

DIST - p r e s e n t d i s t a n c e from XB(3).


X, Y , Z - end p o i n t of f l i g h t .

NALB - albedo f l a g (= MEDALB o r 0 ) .

MARK - f l a g i n d i c a t i n g t y p e of t e r m i n a t i o n of f l i g h t ,

0 - normal boundary c r o s s i n g ,

1 - f l i g h t - w i t h i n one medium, , < .

-1 - p a r t i c l e esc

-2 - p a r t i c l e e n t e r e d i n t e r n a l v o i d . - 3

NMED

N R E G - r eg ion of end p o i n t .

ETAUSD - a c t u a l f l i g h t d i s t a n c e ( i n m.f .p . ) .

BLZNT - combina to r i a l geometry r e g i o n o f end p o i n t .

ETATH - a c t u a l f l i g h t d i s t a n c e ( i n cm).

DISTO - d i s t a n c e from XB(3) t o next c o l l i s i o n s i t e .

- - . ’.

I R

XB

WB

- se t t o v a l u e s from NUTRON Common.

4.4-40

Subrou t ine GPR#B

T h i s s u b r o u t i n e i s t h e e x e c u t i v e r o u t i n e f o r t h e g e n e r a t i o n and

s t o r a g e of secondary gamma r a y s ( o r n e u t r o n s f o r an a d j o i n t , coupled

problem).

GWL as t h e p r o b a b i l i t y of g e n e r a t i n g a gamma r a y . Thus, a random number

i s compared w i t h GWL, and i f g r e a t e r , no gamma ray i s gene ra t ed ; i f

less t h a n o r equa1;then a gamma r a y w i t h weight = WATE*PGEN/GWL i s

s t o r e d . This procedure produces gamma r a y s of v a r y i n g weights , b u t t h e

number o f gamma r a y s may b e c o n t r o l l e d e a s i l y . T h i s v e r s i o n i s t h e one

d i s t r i b u t e d t o u s e r s .

The v e r s i o n o f GPROB which i s found t o b e most u s e f u l u s e s

Another v e r s i o n of GPR#B which h a s been implemented i n some cases

u s e s GWL as a d e s i r e d gamma weight . The p r o b a b i l i t y of g e n e r a t i n g a

gamma r a y i s determined and t h e r e s u l t i n g gamma-ray we igh t , WATEG, i s

compared w i t h i n p u t v a l u e s of t h e d e s i r e d gamma-ray we igh t , GWL. Russian

r o u l e t t e and s p l i t t i n g are used t o produce gamma r a y s of weight GWL. That

i s , i f t h e gamma-ray weight i s less than t h e i n p u t v a l u e s , then t h e gamma

r a y i s k i l l e d w i t h p r o b a b i l i t y (GWL-IWATEGI)/GWL and s t o r e d w i t h prob-

a b i l i t y (IWATEGI)/GWL.

v a l u e , then t h e r e are J = WATEG/GWL gamma r a y s s t o r e d w i t h weight GWL w i t h

Russian r o u l e t t e played wi th t h e remaining gamma r a y of weight WATEG - J*GWL.

C a l l e d from: M#RSE.

Subrou t ines c a l l e d : GAMGEN, GST#RE, FLTRNF.

Commons r e q u i r e d : Blank, NUTRON, APgLLQ).


I f t h e gamma-ray weight i s g r e a t e r than t h e i n p u t

I G - primary p a r t i c l e energy group.

NMED - geometry medium.

WATE - primary p a r t i c l e we igh t .

GWL - i n p u t we igh t v a l u e s f o r gamma r a y s .

N R E G - geometry r e g i o n .

NMTG - t o t a l number of p a r t i c l e groups.

MXREG - number of r e g i o n s f o r which t h e r e are weight s t a n d a r d s .


WATEG - gamma-ray weight .

PGEN - gamma-ray g e n e r a t i o n p r o b a b i l i t y .

4.4-47

Funct ion IWEEK (MONTH, IDAT, IYEAR) - IBM-360 Version*

This r o u t i n e w i l l look up t h e d a t e f o r you i f you d o n ' t know i t and

f i l l i n i n t e g e r v a l u e s f o r MflNTH, I D A T , and IYEAR ( r e q u e s t e d w i t h MgNTH

- < 0 ) . I t a l s o r e t u r n s , as t h e f u n c t i o n v a l u e , an i n t e g e r from 1 t o 7

r e p r e s e n t i n g t h e day of t h e week. I f i t i s g iven a p o s i t i v e v a l u e of

MONTH, i t assumes you have g iven i t a month, day of month, and y e a r and

w i l l n o t d i s t u r b t h e s e b u t w i l l s imply de te rmine t h e day of t h e week.

I f you stump i t (by s p e c i f y i n g a y e a r b e f o r e 1901 o r a f t e r 2099) IWEEK

i s r e t u r n e d as zero .

Ca l l ed by: DATE

Rout ines c a l l e d :

I DAY - l i b r a r y r o u t i n e a t ORNL; t h e o u t p u t is two 4-byte words

c o n t a i n i n g 8 EBCDIC c h a r a c t e r s r e p r e s e n t i n g t h e number

of t h e month, a hyphen, t h e day of t h e month, a hyphen,

and t h e last two d i g i t s of t h e y e a r . That i s , on May

30, 1970, t h e argument f o r IDAY w i l l r e t u r n c o n t a i n i n g

t h e EBCDIC r e p r e s e n t a t i o n of 05-30-70.


MflNTH - < 0 - f l a g t o c a l c u l a t e MONTH, IDAT, and IYEAR.

> 0 - f l a g t o l e a v e arguments a l o n e .

V a r i a b l e s modif ied:

MflNTH - i n t e g e r r e p r e s e n t i n g month.

I DAT - i n t e g e r r e p r e s e n t i n g day o f month.

IYEAR - i n t e g e r r e p r e s e n t i n g y e a r .

IWEEK - in teger : . r ep resen t ing 'dayi of week.

i

J ,

*This r o u t i n e i s a dummy r o u t i n e i n t h e CDC-6600 and UNIVAC-1108 v e r s i o n s .

4.4-48

Subrou t ine MSOUR

MSQUR i s t h e e x e c u t i v e r o u t i n e f o r t h e . g e n e r a t i o n and s t o r a g e of t h e

sou rce parameters a t t h e s t a r t i n g of each b a t c h . The source parameters

may b e r ead i n t o INPUT on c a r d s , gene ra t ed by s u b r o u t i n e SQURCE o r ob-

t a i n e d from t h e f i s s i o n bank f o r a m u l t i p l y i n g system. For e i t h e r type

of problem t h e c a l c u l a t i o n s by s u b r o u t i n e SQURCE o v e r r i d e t h e f i s s i o n

bank i n p u t o r t h e v a l u e s r ead from ca rds . I f t h e d i r e c t i o n c o s i n e s are

a l l i n p u t as ze ro , an i s o t r o p i c sou rce d i r e c t i o n i s genera ted . The

group number ob ta ined from t h e f i s s i o n bank i s t h e group caus ing f i s s i o n

and may b e used i n t h e s e l e c t i o n of t h e sou rce group f o r t h e f i s s i o n

neu t rons . FSE i n b l ank common c o n t a i n s t h e group d i s t r i b u t i o n f o r each

medium.

Ca l l ed from: MORSE

Subrou t ines c a l l e d : FSOUR, GETNT, SQURCE, GTISO, STQRNT, BANKR(l), LQQKZ

Commons r e q u i r e d : NUTRQ)N, FISBNK, APQLLQ, GQMLQC, O R G I


ITSTR - an index which de termines i f t h e sou rce should b e ob ta ined

from t h e p r e v i o u s b a t c h f i s s i o n s (ITSTR # 0 ) o r gene ra t ed

by SOURCE o r from i n p u t d a t a (ITSTR = 0 ) .

ISOUR - an index which de termines t h e o p t i o n s f o r t h e energy

d i s t r i b u t i o n of t h e s o u r c e . I f ISOUR > 0 t h e sou rce

e n e r g i e s are a l l gene ra t ed i n energy group ISOUR.

ISOUR < 0 , o r i f ISOUR = 0 and NGPFS # 0 , s u b r o u t i n e

INPUT1 c a l l s SORIN and t h e energy i s s e l e c t e d by SOURCE.

I f

NMEM - t h e number of p a r t i c l e s t o be gene ra t ed f o r t h e b a t c h ,

= NSTRT f o r non- f i s s ion ing systems and NFISH f o r mul-

t i p l y i n g sys tems.

XSTRT9 YSTRT9 ZSTRT s t a r t i n g parameters i n p u t from c a r d s ,

from common A P ~ L L Q , see page 4.4-4 . WTSTRT, AGSTRT

UINP, VINP, ZINP

Var i ab le s changed:

UOLD, VOLD, WQLD, ETATH, XQLD, YQLD, ZQLD, IBLZO, ETA, I G Q ,

MEDOLD, Q)LDAGE - prev ious c o l l i s i o n parameters are zeroed f o r

t h e sou rce .

Q)LDWT - prev ious c o l l i s i o n weight se t e q u a l t o WTSTRT.

4.4-49

X, Y , Z , WATE, AGE, NAMEX, parameters set f o r each p a r t i c l e

I B L Z N , N R E G , NMED, NAME, gene ra t ed , pu t i n NUTRgN common,

U , V , W , I G see page 4.4-10,

NPSCL(1) - coun te r f o r number of sou rces .

NEWNM - se t t o name of l a s t p a r t i c l e gene ra t ed .

FWATE 1 zeroed f o r t h e n e x t b a t c h . NFISH

F T ~ T L

NMED } NREG de f ined based on NMEDG i n ORGI common.

4.4-50

A

Subrou t ine NXTCQL

Th i s s u b r o u t i n e i s c a l l e d by t h e main program t o determine t h e

s p a t i a l c o o r d i n a t e s , t h e b lock and zone number, p a r t i c l e ' s age, and non-

a b s o r p t i o n p r o b a b i l i t y a t t h e n e x t c o l l i s i o n s i t e and a t every boundary

c r o s s i n g encountered a long t h e way. The t o t a l number of boundary c ros s -

i n g s i s recorded as i s t h e number of e scapes . I f a p a r t i c l e e scapes ,

i t s weight i s se t equa l t o ze ro and t h e h i s t o r y w i l l be te rmina ted by t h e

main program.

Ca l l ed from: MQRSE

Subrou t ines c a l l e d : GETETA, N S I G T A , GQMST, BANKR(7), BANKR(8)

Commons r e q u i r e d : Blank, NUTRQN, APQLLO


AGE - c h r o n o l o g i c a l age of t h e p a r t i c l e a t t h e p rev ious

c o l l i s i o n s i t e .

IBLZN - a n i n t e g e r s p e c i f y i n g t h e zone number a t t h e p rev ious


NMED - t h e medium number a t t h e p rev ious c o l l i s i o n s i t e .

X ~ L D , YQLD, ZOLD - s p a t i a l c o o r d i n a t e s a t t h e p rev ious c o l l i s i o n

s i t e .

U ~ L D , VQLD, WOLD - t h e p a r t i c l e ' s p r e c o l l i s i o n d i r e c t i o n c o s i n e s .

T S I G - t o t a l c r o s s s e c t i o n .

Var i ab le s changed:

AGE - c h r o n o l o g i c a l age a t new c o l l i s i o n s i t e .

IBLZN - an i n t e g e r c o n t a i n i n g t h e zone number a t t h e new


NMED - end-o f - f l i gh t medium.

NPSCL(7) - t o t a l number of boundary c r o s s i n g s .

NPSCL(8) - number of e scapes .

X, Y , Z - end-o f - f l i gh t s p a t i a l c o o r d i n a t e s .

MATE - weight of p a r t i c l e undergoing f l i g h t t o t h e new c o l l i s i o n

s i t e .


MARK - an index which i d e n t i f i e s t h e type of even t a t (X,Y,Z);

MARK = 0 , normal boundary c r o s s i n g ; MARK = 1, f l i g h t

ended w i t h i n t h e medium; MARK = -1, p a r t i c l e escaped;

MARK = - 2 , p a r t i c l e e n t e r e d an i n t e r i o r vo id .

4.5-13

Table 4 . 1 7 . D e f i n i t i o n s of Var i ab le s i n Common GTSCl

-

V a r i a b l e D e f i n i t i o n

NPT (16) Number of p o i n t s p e r supergroup f o r each medium. 16 media are a l lowed. ) Redefined a t end of GTSCT as t h e t o t a l s t o r a g e r e q u i r e d f o r each c r o s s s e c t i o n f o r each medium.

(Only

NXSECT(17) S t a r t i n g l o c a t i o n of p o i n t c r o s s s e c t i o n s f o r each medium.

NDSGP T o t a l s t o r a g e r e q u i r e d p e r supergroup f o r a l l media.

11, I O Input and o u t p u t l o g i c a l u n i t numbers.

I06RT Log ica l t a p e number of 06R p o i n t c r o s s - s e c t i o n t ape .

IGQPT L a s t M@RSE mul t igroup f o r which p o i n t c r o s s s e c t i o n s w i l l be used ( - <,NMGP)

NEGP S Number of supergroup boundar ies .

ESPD (100) Energy boundar i e s ( i n eV) of t h e supergroups (on ly 100 supergroups are a l lowed) .

> ,

"IC S t a r t i n g l o c a t i o n of t h e p o i n t c r o s s s e c t i o n s .

NXPM Number of c r o s s s e c t i o n s p e r medium = 1, i f t o t a l o n l y = 2 , i f t o t a l + s c a t t e r i n g = 3 , i f t o t a l , s c a t t e r i n g , and v * f i s s i o n

N I N C Index f o r l o c a t i n g p o i n t c r o s s s e c t i o n s . Used as f l a g i n FISGEN t o de te rmine i f t r a n s p o r t p r o c e s s h a s begun.

4.5-14

4 . 5 . 3 Subrou t ines

SUBROUTINE ALBDO(IG,U,V,W,WATE,NMED,NREG) This r o u t i n e i s c a l l e d upon encoun te r ing an a lbedo s c a t t e r i n g su r -

f a c e and p rov ides t h e outgoing neu t ron parameters f o r t h e albedo c o l l i s i o n .

The sample r o u t i n e performs s p e c u l a r r e f l e c t i o n a t t h e a lbedo scatter-

i n g s u r f a c e . The requi rements of s p e c u l a r r e f l e c t i o n may be w r i t t e n as

1 . N = -R.N,

and

I x N = R x N ,

where I i s t h e incoming neu t ron d i r e c t i o n v e c t o r ,

R i s t h e r e f l e c t e d neu t ron d i r e c t i o n v e c t o r , and

N i s t h e outward normal t o t h e s u r f a c e (1.N < 0 ) .

Manipula t ion of t h e above two e q u a t i o n s r e s u l t s i n

R = I - Z(I.N)N.

Ca l l ed from: MORSE

Commons r e q u i r e d : NUTRON, NORMAL

V a r i a b l e s r e q u i r e d : U, V , W ( f rom common NUTRON, see page 4.4-10)

UNORM, VNgRM, WNgRM - components of u n i t v e c t o r normal t o boundary.

V a r i a b l e s changed: U, V , W

4.6-23

CARDS CC (3E10.4) (ND ca rds w i l l be read)

x ,y , z - d e t e c t o r l o c a t i o n . ( I f o t h e r than p o i n t d e t e c t o r s are

d e s i r e d , t h e p o i n t l o c a t i o n s must s t i l l be i n p u t and

can b e combined w i t h a d d i t i o n a l d a t a b u i l t i n t o u s e r

r o u t i n e s t o f u l l y d e f i n e each d e t e c t o r . )

Note t h a t t h e d i s t a n c e between t h e above p o i n t s and t h e XSTRT, YSTRT,

ZSTRT va lues and t h e i n i t i a l age, AGSTRT (see common USER w r i t e u p , page 4.6-

7 ) w i l l be used t o d e f i n e t h e lower l i m i t of t h e f i r s t t i m e b i n .

CARD DD (20A4)

U n i t s f o r SUD and SSD a r r a y p r i n t o u t s . W i l l b e used i n columns 54

through 133 of t h e t i t l e f o r t h e p r i n t of t h e s e a r r a y s .

CARD EE (20A4)

I d e n t i f i c a t i o n f o r each response f u n c t i o n . W i l l b e used as t i t l e

i n p r i n t o u t .

CARDS FF (7E10.4)

Response f u n c t i o n va lues . NMTG va lues w i l l be read i n each se t of

FF ca rds . Inpu t o r d e r i s from energy group 1 t o NMTG ( o r d e r of

d e c r e a s i n g energy) .

Note: Cards EE and FF are read i n t h e fo l lowing o rde r : EE,FFl, ... FFN,

EE,FFl, . . .FFN, e t c .

CARD GG (20A4) (omit i f NE - < 1)

Uni t s f o r t i t l e of SQE a r r a y p r i n t o u t .

CARDS HH (1415) (omit i f NE - < 1) Energy group numbers d e f i n i n g lower l i m i t of energy b i n s ( i n o r d e r

of i n c r e a s i n g group number). The NNE ( i f > 0) e n t r y must e q u a l

NGPQTN; t h e NE e n t r y must b e set t o NMGP + NGPQTG f o r a combined

problem, o r else NGPQTG o r NGPQTN.

CARD I1 (20A4) (omit i f NT 1 )

Un i t s f o r t i t l e of SQT a r r a y p r i n t o u t .

CARD JJ (20A4) (omit i f NT 1 o r NE 1)

Uni ts f o r t i t l e of SQTE a r r a y p r i n t o u t .

CARDS KK (7E10.4) (omit i f INTI 5 1 )

NT va lues of upper l i m i t s of t i m e b i n s f o r each d e t e c t o r ( i n o r d e r

of i n c r e a s i n g t i m e and d e t e c t o r number).

d e t e c t o r must s tart on a new ca rd .

NT i s n e g a t i v e . They are then used f o r every d e t e c t o r .

The v a l u e s f o r each

INT v a l u e s only are read i f

4.6-24

CARL) LL (20A4) (omit i f NA L 1) A

Uni t s f o r t i t l e of SQAE a r r a y p r i n t o u t .

CARL) MM (7E10.4) (omit i f NA 5 1) NA va lues of upper l i m i t s of ang le b i n s ( a c t u a l l y cos ine b i n s ; t h e

NAth v a l u e must e q u a l one ) .

4.6-24 1

drs Subrou t ine SCORIN w i t h Free-Form SAMBO Ana lys i s I n p u t

Subrou t ine SCORIN has been modi f ied t o a l low read ing t h e a n a l y s i s i n p u t d a t a , o t h e r t h a n t i t l e c a r d s , i n free-form us ing s u b r o u t i n e FFREAD which was a l r e a d y be ing used f o r c r o s s s e c t i o n i n p u t . S ince more o p t i o n s a r e allowed i n t h e a n a l y s i s free-form d a t a , a new r o u t i n e named RFRE was w r i t t e n which c a l l s FFREAD t o r e a d each a r r a y t o de te rmine whether i t i s i n t e g e r o r f l o a t i n g p o i n t and t o p r o p e r l y s t o r e t h e d a t a . RFRE i s d e s c r i b e d below.

This new f e a t u r e can be very u s e f u l when a r e sponse f u n c t i o n i s a l l o n e ' s o r when us ing a l a r g e number of energy b ins .

Old SAMBO i n p u t decks a r e compat ib le on ly i f

1. t h e r e a r e no spaces w i t h i n each number,

2. blanks a r e n o t used f o r ze roes and

(b l anks a r e ignored by FFREAD),

3 . u s e r p l a c e s a ca rd c o n t a i n i n g e i t h e r a $$ o r an ** i n Column Two and Three i n f r o n t of t h e a r r a y t o s p e c i f y i n t e g e r o r f l o a t i n g p o i n t .

Subrou t ine RFRE(N5,N6,ARRAY,IARR,NV)

This r o u t i n e r eads i n t h e a r r a y s p r e v i o u s l y con ta ined i n Cards BB, CC, FF, HH, KK and MM. The d a t a i s s t i l l r e a d i n t h e same o r d e r as d e s c r i b e d on pages 4.3-14 t o 4.3-16 of t h e MORSE r e p o r t , ORNL-4972. I t de termines whether each a r r a y i s i n t e g e r o r f l o a t i n g p o i n t by checking f o r $$ o r ** i n f r o n t of each array. RFRE a c c e p t s t h e o p t i o n s I , Z , and R desc r ibed i n Ref. 13 of t h e MORSE r e p o r t and p rocesses them accord ing ly .

Ca l l ed from: SCORIN

Subrou t ines c a l l e d : FFREAD, FLOAT

V a r i a b l e s r e q u i r e d : ! I

N5, N6 - Logica l u n i t numbers of 1/0 jtapes.

NV - The number of v a l u e s t o be read. / ;

I

1


ARRAY - An a r r a y of f l o a t i n g p o i n t d a t a which i s used on ly i f t h e t h e i n p u t numbers a r e f l o a t i n g p o i n t .

IARR - An a r r a y of i n t e g e r d a t a used on ly i f t h e i n p u t numbers a r e i n t e g e r s .

srs 4.6-41

4 . 6 . 6 . K l e i n Ni sh ina Option i n MORSE

The MORSE c r o s s s e c t i o n package (MORSEC) h a s been modi f ied t o a l low f o r r ead ing , s t o r i n g and p rocess ing gamma ray p a i r p roduc t ion and Compton s c a t t e r i n g c r o s s s e c t i o n s . This i s necessa ry i n o r d e r t o use t h e Kle in Nish ina formula f o r making estimates i n RELCOL.

P r e v i o u s l y , u se of t h i s e s t i m a t o r i n MORSE was accomplished by means of t h e OGRE c r o s s s e c t i o n package be ing c a l l e d t o g e t t h e p a i r p roduc t ion and Compton s c a t t e r i n g d a t a . It was dec ided t h a t a more au tomat i c p rocess based on t h e same ENDF l i b r a r i e s used i n MORSE neu t ron c a l c u l a t i o n s would be a b e t t e r s o l u t i o n , making such c a l c u l a t i o n s less user-dependent.

The MORSEC r o u t i n e s t h a t r e q u i r e d m o d i f i c a t i o n were XSEC, JNPUT, STORE, and NSIGTA. Both temporary and permanent c r o s s s e c t i o n s t o r a g e had t o be a l l o c a t e d f o r t h e two new c r o s s s e c t i o n s - p a i r p roduc t ion and Compton s c a t t e r i n g . MORSEC had two a r e a s of s t o r a g e i n b l ank common t h a t were n o t a l l o c a t e d f o r any d a t a . The p o i n t e r s t o t h e s e a r e a s w e r e t h e v a r i a b l e s I N G N and INGNP. I n o r d e r t o avoid adding new commons o r new v a r i a b l e s t o o l d commons, t h e s e p o i n t e r s were used - INGNP f o r t e m - po ra ry s t o r a g e l o c a t i o n and I N G N f o r permanent. This a l l o c a t i o n i s made i n XSEC on ly i f t h e u s e r i n d i c a t e s t h e presence of t h i s d a t a on h i s c r o s s s e c t i o n t a p e by s e t t i n g NCOEF = -N where N i s t h e number of c o e f f i c i e n t s . The va lue of IHT, t h e p o s i t i o n i n t h e t a b l e of t h e t o t a l c r o s s s e c t i o n i s now an i n p u t number i n XSEC, hav ing a d e f a u l t v a l u e of t h r e e which was t h e o r i g i n a l p o s i t i o n . THT should appear i n columns 66-70 ( r i g h t - a d j u s t e d ) of Card B of t h e c r o s s s e c t i o n inpu t . This change h a s been i n use f o r sometime a t Oak Ridge bu t h a s n o t p r e v i o u s l y been announced t o t h e pub l i c . This a l s o n e c e s s i t a t e d changing some of t h e indexing on ou tpu t t a b l e s t o make them correspond t o a v a r i a b l e IHT

data should be i n r a t h e r t han a f i x e d IHT=3. The p a i r p roduct ion , p o s i t i o n I H T - 4 ; and t h e Compton s c a t t e r i n g da t a , cc , i n IHT-3 of t h e c r o s s s e c t i o n t a b l e (IHT i s t h e p o s i t i o n of t h e t o t a l c r o s s s e c t i o n ) . Temporary s t o r a g e i s handled by s u b r o u t i n e STORE. In JNPUT t h e p a i r p roduc t ion and Compton s c a t t e r i n g d a t a must be mixed j u s t l i k e t h e o t h e r c r o s s s e c t i o n s and p laced i n permanent s t o r a g e . For a forward problem, JNPUT a l s o checks t o be s u r e t h a t

%P ,

2*CPP + ccs - - cs

where C i s t h e s c a t t e r i n g c r o s s s e c t i o n ; i f i t doesn ' t , an e r r o r message i s p r i n t e d b e f o r e cont inuing . Subrou t ine NSIGTA was modi f ied by t h e a d d i t i o n of a new e n t r y p o i n t , KLEINA, which looks up t h e proper C

S

and Ccs f o r each gamma group. The c a l l i n g sequence i s PP

CALL KLEINA( IG,NMED, PAIRR, COMR)

where PAIRR i s cPp and COMR i s Zcs. u s e r from h i s e s t l m a t o r r o u t i n e and on ly f o r gamma groups.

This r o u t i n e must be c a l l e d by t h e

4.6-42

A sample u s e r r o u t i n e , RELCOL, has a l s o been w r i t t e n ; bu t some of t h e burden of making s u r e i t w i l l work f o r t h e u s e r ' s problem on t h e u s e r . For example, u s e r s who r u n combined neutron-gamma problems as a l l primary p a r t i c l e s m u s t s p e c i f y i n t e r n a l t o RELCOL j u s t how many groups a re a c t u a l l y neu t rons . This i s necessa ry i n o r d e r t o i n s u r e t h a t KLEINA i s c a l l e d only f o r gamma r a y s and n o t f o r neu t rons . Es t ima tes f o r neu t rons do n o t i nvo lve t h e Kle in Nish ina formula but a r e done as t h e usua l p o i n t - d e t e c t o r n e x t - f l i g h t e s t i m a t o r . RELCOL i s somewhat l i k e two s e p a r a t e r o u t i n e s because i t uses two e n t i r e l y d i f f e r e n t methods of making estimates f o r n e u t r o n s and gammas. For gamma groups, a c h o i c e i s made between p a i r p roduc t ion and Compton e s t i m a t e s . A complete des- c r i p t i o n of t h i s RELCOL fol lows.

f a l l s

- . - . . . - . . . - . . . . . .

4 . 6 - 4 3

c_'

Subroutine RELCOL

The fluence estimate for neutron groups, from the normal collisions in RELCOL, is given by

WATE . emG. P( THETA, IG) R2

where WATE is the statistical weight of the particle leaving the collision, ARG is the negative of the number of mean free paths from collision to detector, R is the distance from collision to detector, P(THETA,IGO) is the probability, per steradian, for a particle with energy in the incoming group IGO scattering to a lower energy group through angle cos-' (THETA) and THETA is the.cosine of the angle between the incoming direction and the line from the collision site to the point detector. PTHETA generates the P array.

The fluence estimate for gamma groups, from the normal collisions in RELCOL, has several possible forms. For a forward problem, a choice is made between Compton and Pair Production estimates by selecting a random number, R1, and using a Compton scattering estimate if

otherwise Pair Production is used. The Compton scattering estimate is

WATE . em'. PMU R2

where WATE, ARG and R are as described above and PMU is scattering calculated by the usual Klein Nishina formulas.

probability of 17

ARG The Pair Production estimate is WATE . e and it is made to group

; 4 ~ R 2 ' (. IZ, the one containing .511 MeV.

Called by:

Routines called:

User at real collisions (in Subroutine BANKR when NBNKIP5).

NSIGTA - Looks,up total cross^ section and non-absorption probability. KLEINA - For gamma groups, looks up pair production and Compton

1

scattering cross sections. . I

SQRT,EXP - Library functions.

Grs PTHETA - Calculates probability P of scattering.

EUCLID - Determines ARG.

4.6-44

FLUXST - S t o r e s e s t i m a t e s i n a p p r o p r i a t e b ins .

FLTRNF - S e l e c t s random number R where OLRLl.

Commons r e q u i r e d : USER, PDET, NUTRON, APOLLO, Blank


X , Y , Z - C o l l i s i o n s i t e .

NMED - Medium number where X, Y, 2 i s loca ted .

I G O - Incoming energy index.

LOCXD - Locat ion i n b lank common of c e l l z e r o of d e t e c t o r p o s i t i o n .

LOCRSP - Locat ion i n b lank common of c e l l z e r o of r e sponse f u n c t i o n p o s i t i o n .

NMTG - Number of energy groups.

LOCRSP - Loca t ion i n b l ank common of c e l l z e r o of response f u n c t i o n p o s i t i o n .

NMTG - Number of energy groups.

NRESP - Number of r e sponse f u n c t i o n s .

ND - Number of d e t e c t o r s .

LADJM - Signa l f o r a d j o i n t problem ( = 1 i f a d j o i n t ; = 0 , o the rwise ) .

NGPQTN - Number of pr imary energy groups be ing fo l lowed.

MEDIA - Number of media i n problem.

NOPQTl ) NOPQT2 ) - See p. 4.4-6 of ORNL-4972. NOPQT3

WATE - S t a t i s t i c a l weight l e a v i n g X, Y, Z.

AGE - Chronologica l age a t X , Y , Z.

NEX = 1 f o r combined forward - used f o r p r o b a b i l i t i e s s t o r e d by PTHETA. = 0 f o r gamma only forward.

NEXND = 1 used f o r coun te r f o r number of times RELCOL g e t s c a l l e d p e r d e t e c t o r .

4.7-5

The geometry must b e s p e c i f i e d by e s t a b l i s h i n g two t a b l e s . The

f i r s t t a b l e d e s c r i b e s t h e type and l o c a t i o n o f t h e se t of b o d i e s used i n

t h e geomet r i ca l d e s c r i p t i o n .

zones i n t e r m s of t h e s e bod ies .

t o pu t t h e d a t a i n t h e form r e q u i r e d f o r ray t r a c i n g .

t r a c i n g r o u t i n e s cannot t r a c k a c r o s s t h e outermost body, a l l of t h e zones

must b e w i t h i n a sur rounding e x t e r n a l vo id so t h a t a l l e scap ing p a r t i c l e s

are absorbed. Also no p o i n t may b e i n more than one zone. This geometry

package i s i n double p r e c i s i o n on t h e IBM-360 system b u t remains i n s i n g l e

p r e c i s i o n on UNIVAC-1108 and CDC-6600 v e r s i o n s . Because of t h e change i n

p r e c i s i o n , v a r i a b l e s i n commons PAREM and ORGI had t o b e r eo rde red i n t h e

IBM-360 v e r s i o n . Media number 1000 i s an i n t e r n a l v o i d , and media number

0 i s a n e x t e r n a l vo id .

The second t a b l e i d e n t i f i e s t h e p h y s i c a l

The i n p u t r o u t i n e p rocesses t h e s e t a b l e s

Because t h e r a y

4 . 7 . 3 . D e s c r i p t i o n of Body Types

The in fo rma t ion r e q u i r e d t o s p e c i f y each type of body i s as

fo l lows :

a. Rectangular P a r a l l e l e p i p e d (WP)

Spec i fy t h e minimum and maximum v a l u e s of t h e x, y , and z

c o o r d i n a t e s which bound t h e p a r a l l e l e p i p e d .

Xmax

ORNL- DWG

i / Ymin

J X I ’

74 - 6762

Fig . 4 . 9 . Rec tangular P a r a l l e l e p i p e d (RPP).

4.7-6

b . Sphere (SPH)

Spec i fy t h e v e r t e x 1 a t t h e c e n t e r and t h e scalar, R ,

deno t ing t h e r a d i u s .

ORNL- DWG 74-6763

Fig . 4.10. Sphere (SPH).

c. Right C i r c u l a r Cy l inde r (RCC)

Spec i fy t h e v e r t e x 1 a t t h e c e n t e r of one b a s e , a h e i g h t

v e c t o r , g , expres sed i n t e r m s of i t s x, y , and z components,

and a scalar , R , deno t ing t h e r a d i u s .

ORNL-DWG 74-6764

Fig . 4 . 1 1 . Right C i r c u l a r Cyl inder (RCC).

- .

4.7-11

4 . 7 . 4 . Subrou t ines

Subrout ine G 1 ( S , MA, FPD, L@CFEG, NUMB@D, IRgR, I R 1 , IR2)

G 1 i s t h e c o n t r o l r o u t i n e f o r t h e combina tor ia l geometry. On one

c a l l , i t c a l c u l a t e s t h e d i s t a n c e t r a v e l e d i n t h e p r e s e n t zone, and t h e

number I R of t h e nex t zone t o be e n t e r e d . E s s e n t i a l l y , GG i s c a l l e d f o r

each body a d j a c e n t t o t h e p r e s e n t zone, c a l c u l a t i n g R I N and R@UT, t h e

d i s t a n c e s t o e n t r y and e x i t of t h e body a long t h e t r a j e c t o r y . The next

zone t o be e n t e r e d i s determined by aga in c a l l i n g GG t o c a l c u l a t e R I N

and R@UT f o r each body a d j a c e n t t o t h e nex t p o s s i b l e zone. These nex t

p o s s i b l e zones are determined by examining a l i s t of a l l t h e p rev ious

zones e n t e r e d on c r o s s i n g t h i s body.

t h e i n p u t zone d e s c r i p t i o n s t o determine t h e c o r r e c t zone. I f i t i s n o t

found i n t h e l i s t of p rev ious zones, a l l o t h e r zones are examined i n a

s imi l a r f a s h i o n , and when t h e c o r r e c t zone i s found, i t i s added t o t h e

l i s t of p rev ious zones f o r t h a t body, i f t h e s t o r a g e a l l o c a t e d is n o t

y e t exhaus ted .

t h e l i s t as i t w a s adding no more t o i t b u t examining a l l o t h e r zones

i f i t d o e s n ' t f i n d t h e c o r r e c t zone i n t h e e x i s t i n g l i s t . I f t h e new

zone i s d i f f e r e n t from t h e o l d , G 1 r e t u r n s ; o the rwise G 1 con t inues

t r a c k i n g u n t i l a d i f f e r e n t zone is encountered .

MgRSE v e r s i o n of G 1 i s t h a t if t h e d i s t a n c e t o t h e nex t boundary i s

g r e a t e r than t h e d i s t a n c e t o s c a t t e r i n g , G 1 r e t u r n s wi thout de te rmining

t h e nex t zone p a s t t h e boundary, s e t t i n g t h e f l a g MARKG i n common ORGI .

R I N and RgUT are checked a g a i n s t

I f no more s t o r a g e i s a v a i l a b l e , f u t u r e c a l l s w i l l s e a r c h

One change added t o the

Ca l l ed from: G@MST.,, EUCLID, MESH.

Subrou t ines c a l l e d : GG,, PR+, ,

Commons required: , -..PAREM, G@ML@C, DBG, @RGI., TAPE

Var iab le s required-:.. 'i 8

XB(3) - s t a r t i n g c o o r d i n a t e s of p r e s e n t t r a j e c t o r y .

wB(3) - d i r e c t i o n c o s i n e s of t r a j e c t o r y .

I R - . p r e sen t zone. , -

DIST

DISTO - d i s t a n c e from XB(3) t o n e x t s c a t t e r i n g p o i n t .

NAS C - less than zero i f t h i s is a new t r a j e c t o r y .

KL@@P - t r a j e c t o r y index .

P INF - machine i n f i n i t y .

I - p r e s e n t i n d i s t a n c e from XB(3).

4.7-12

MA, ETD, L@CREG, NUMB#D, IR@R, - l o c a t i o n s i n b l ank common used f o r v a r i a b l e I R 1 , I R 2 dimensioning.


KL@#P - t r a j e c t o r y index incremented i f t h i s i s a new

t r a j e c t o r y .

NAS C - nex t body i n t e r s e c t e d by t r a j e c t o r y .

LSURF - s u r f a c e of body NASC c rossed a t nex t i n t e r s e c t i o n

( n e g a t i v e i f l e a v i n g and p o s i t i v e i f e n t e r i n g NASC).

DIST - d i s t a n c e from XB(3) t o nex t i n t e r s e c t i o n o r c o l l i s i o n

s i t e .

MARK - se t t o 1 i f d i s t a n c e t o c o l l i s i o n (DISTO) i s less than

d i s t a n c e t o n e x t i n t e r s e c t i o n (o therwise 0 ) .

S - d i s t a n c e t r a v e l e d on t h i s c a l l t o G 1 .

IRPRIM - zone t o b e e n t e r e d on boundary c r o s s i n g .

MA(1NEXT) - new zone added t o t h e l i s t of next p o s s i b l e zones f o r

body NB#.

MA(1NEX) - l o c a t i o n i n MA of nex t i t e m i n t h e nex t p o s s i b l e zone

l i s t f o r body NB# ( t h e s e l i s t s l eap - f rog through t h e

end of t h e MA a r r a y ) .


NB@ - a b s o l u t e v a l u e i s body be ing cons idered w h i l e a n e g a t i v e

o r p o s i t i v e s i g n i n d i c a t e s t h a t zone I R o r IRF' i s o u t s i d e

o r i n s i d e t h e body r e s p e c t i v e l y .

R@UT

R I N

L R I - s u r f a c e of body NB@ e n t e r e d by t r a j e c t o r y .

LR# - s u r f a c e of body NB@ t r a j e c t o r y e x i t s .

IRP - zone be ing cons idered as nex t zone.

- d i s t a n c e t o e x i t of body NB# c a l c u l a t e d by GG.

- d i s t a n c e t o e n t r y of body NB@ c a l c u l a t e d by GG.

E r r o r s :

I f message i s " e x i t be ing c a l l e d . . . nex t r eg ion no t found'' -

NASC w i l l be nex t body t h e r ay w i l l i n t e r s e c t (NB@, N , NUM, ITYPE,

S M I N , IRP , LOCAT a l l apply t o maximum body number and have no

s i g n i f i c a n c e ) .

.

4.7-17

Subrout ine J @ M I N (NADD, 11, I O )

The i n p u t of t h e geometry d a t a is c o n t r o l l e d by t h e J g M I N s u b r o u t i n e ,

which performs t h e fo l lowing t a s k s :

*Reads a l l geometry i n p u t d a t a except t h e r eg ion volumes.

'Writes t h e body and zone d a t a on a mass s t o r a g e u n i t (I@UT=16).

*Determines t h e l e n g t h of a l l geometry a r r a y s .

* C a l c u l a t e s t h e beginning l o c a t i o n i n b l ank common of geometry

a r r a y s .

* I n i t i a l i z e s geometry a r r a y s .

*Cal ls t h e GTVLIN s u b r o u t i n e which r e t u r n s r eg ion volumes.

S ince combina to r i a l geometry i n p u t d a t a i s dynamical ly a l l o c a t e d t o con-

s e r v e s t o r a g e area, i t i s s t o r e d t empora r i ly on a mass s t o r a g e device .

This a l lows t h e co re s t o r a g e requi rements t o be determined. Hence, much

of t h e coding i n J @ M I N i s similar t o G E N I , which r eads t h e d a t a on t h e

m a s s s t o r a g e dev ice and p u t s i t i n t o b l ank common.

Ca l l ed from: INPUT1

Subrou t ines c a l l e d : G E N I , GTVLIN

Commons r equ i r ed : Blank, G@MLgC, PAREM, TAPE


A l l v a r i a b l e s i n GQ)ML@C, 11, I O .

V a r i a b l e s changed :

A l l v a r i a b l e s i n GQ)ML@C, IV@PT, IDBG, MRIZ(I), MMIZ(1).

Important i n t e r n a l v a r i a b l e s :

I@UT - mass s t o r a g e u n i t .

NAZT - t o t a l number of a d j a c e n t zones summed over a l l zones. ' . ~. I

4.7-18

Subrou t ine L@@KZ ( X , Y, Z , MA, FPD, LgCREG, NUMBOD, I R @ R , NS@R)

The purpose of t h i s r o u t i n e i s t o r e t u r n t h e combina to r i a l geometry

zone of p o i n t (X , Y , Z) s o t h a t t r a c k i n g can b e i n i t i a l i z e d . The coding

h a s been borrowed from t h e second h a l f of s u b r o u t i n e G 1 and adapted t o

de te rmine t h e zone of a sou rce p a r t i c l e . For e f f i c i e n c y Lg@KZ b u i l d s a

l i s t of p o s s i b l e sou rce zones t o s e a r c h on f u t u r e ca l l s . I f t h e r e g i o n

i s n o t found on t h i s l i s t , a l l o t h e r zones are examined and upon d e t e r -

mining t h e new source zone, i t too i s added t o t h e l i s t .

t h e s t a r t i n g d i r e c t i o n c o s i n e s ( .8 , .6, 0.0) are assumed i n L@@KZ, b u t

may b e changed e l sewhere .

Rout ines c a l l e d : GG

Commons r e q u i r e d : @ R G I , PAREM, G@MLQ)C, and DBG.


No t i ce t h a t

X, Y , Z - c o o r d i n a t e s f o r which a zone i s d e s i r e d .

MA, FPD, L@CREG, - l o c a t i o n s i n b l a n k common used f o r v a r i a b l e NUMBGD, I R @ R , NSQR dimensioning.


KL@@P - t r a j e c t o r y index i s incremented.

NMED - common @RGI v a r i a b l e set t o c o r r e c t zone number.

NSOR(1NEXT)- new zone added t o l i s t of p o s s i b l e sou rce zones.

XB - i n i t i a l i z e d t o x, y , z from NUTRON common.

IRPRIM - i n p u t zone number.

I R - code zone number.

DIST - i n i t i a l i z e d t o 0.

NBLZ - packed word c o n t a i n i n g IRPRIM and I R .

M D G - i n p u t zone number i n ORGI common.


wB(3) - set t o .8, .6 , 0.0 s o t h a t L@@KZ need n o t b e c a l l e d

w i t h a d i r e c t i o n .

d

4.7-29

Table 4 . 2 4 (Cont 'd.)

V a r i ab 1 e

LR0 E x i t s u r f a c e c a l c u l a t e d i n GG.

D e f i n i t i o n

KL00P T r a j e c t o r y index of p r e s e n t pa th incremented i n G1.

L00P Index of las t t r a j e c t o r y c a l c u l a t e d f o r body N B 0 . I f L00P ,is e q u a l t o KL@@P, GG r e t u r n s immediately wi th o l d v a l u e s i n R I N , RgUT, L R I , and LRd.

ITYPE Body type of body N B 0 ( i n d i c a t e s B@X, SPH, e t c . ) .

N 0 A Not used.

4.7-30

Table 4 . 2 5 . D e f i n i t i o n s of V a r i a b l e s i n Common Q)RGI*

V a r i a b l e D e f i n i t i o n

DISTO Di s t ance from p o i n t XB(3) t o nex t s c a t t e r i n g p o i n t . Used i n G 1 t o avoid c a l c u l a t i n g t h e nex t zone i f a s c a t t e r i n g event occur s b e f o r e t h e i n t e r s e c t i o n .

MARK S e t 1 i n G 1 i f t r a j e c t o r y end p o i n t i s reached b e f o r e nex t i n t e r s e c t i o n . Otherwise set t o 0.

NMEDG Zone number I R from a L@$KZ c a l l .

NBLZ Packed word c o n t a i n i n g b o t h i n p u t zone and code zone numbers. S to red i n BLZNT by MSOUR.

BLZOLD Packed word c o n t a i n i n g code and i n p u t zone numbers f o r p rev ious c o l l i s i o n .

A Note: V a r i a b l e names are n o t t h e Same i n a l l r o u t i n e s . Also, on

non-IBM-360 machines , t h e o r d e r of t h e v a r i a b l e s i s MARK, DISTO, NMEDG. IBM-360 v e r s i o n t o double p r e c i s i o n .

Reordering r e s u l t e d from t h e convers ion of t h e

4.8-5

Table 4.26 (Cont 'd . )

Sub r o u t i n e P r i n t i n g Message M e an i n g Mess age

JgMIN

G E N I

ALBERT

GTVLIN

'** ERROR I N NNE, NE OR

THE GROUP NUMBERS -- PRINT I S OF MODIFIED

VALUES '

DOES NOT 'ITYPE' = -- EQUAL ANY OF THE

FOLLOWING ' 'ITYPE = DOES NOT

EQUAL ANY OF THE 1 --- FOLLOWING

'ERROR IN SIDE DE- I

--- SCRIP T I ON

'ERROR I N FACE DE-

SCRIPTION -' '********* ERROR I N

VOLUME' CALCULATION

********9< -3'F I = - '?., , N I R = __ >

' S i

E i t h e r IB(NNE) does n o t e q u a l

NGPQTN o r IB(NE) does n o t e q u a l

t h e maximum number of groups. The

r o u t i n e mod i f i e s t h e u s e r ' s d a t a

t o c o r r e c t t h i s . User should change

h i s I B a r r a y i n h i s i n p u t .

The body type g iven does n o t e x i s t

i n t h e code.

The body type g iven does n o t e x i s t

i n t h e code.

There are less than 3 p o i n t s t h a t

d e s c r i b e t h i s s i d e - i . e . , t h e

u s e r h a s d e f i n e d a p o i n t o r a l i n e

r a t h e r t h a n a s u r f ace.

The p o i n t s d e s c r i b i n g t h i s f a c e

are n o t cop lana r .

The number o'f ' r e g i o n s f o r which

volumes w e r e c a l c u l a t e d does not

e q u a l t h e number of r e g i o n s i n

t h e geometry.

4.8-6

Table 4 . 2 7 . D i a g n o s t i c Messages From Other Modules of MORSE

Subrout ine P r i n t i n g M e s s age Meaning Message

FBANK 'WARNING***NO ROOM I N

BANK FOR SECONDARIES***'

GSTgRE 'WARNING***NO ROOM IN

BANK FOR SECONDARIES***'

FS@UR

MPRSE

CgLISN

PTHETA

' N O FISSIONS GENERATED

I N LAST BATCH, __ BATCHES COMPLETED'

- ' N R E G = __ MXREG =

MXREG ON CARD I MUST

BE GE TO THE NUMBER OF

REGIONS DESCRIBED I N

GEOMETRY INPUT ' ' I N GRP =

GRP =, J = -

PROB = RAND = -'

, OUT -

-

'ERROR i n PTHETA __

ISTAT = __ NCOEF = -'

Maximum number of p a r t i c l e s have

been g e n e r a t e d and t h e bank i s f u l l .

No more f i s s i o n p a r t i c l e s w i l l b e

g e n e r a t e d .

Maximum number of p a r t i c l e s have

been g e n e r a t e d and t h e bank is

f u l l . No more gamma r a y s w i l l be

g e n e r a t e d u n t i l bank decreases.

Problem c o n t i n u e s f o r a f i x e d s o u r c e

problem. For a c r i t i c a l i t y problem

t h e n e u t r o n p o p u l a t i o n h a s d i e d

away.

S e l f e x p l a n a t o r y - change your

i n p u t d a t a .

A l l t h e s c a t t e r i n g a n g l e p r o b a b i l i t i e s

are 0 o r n e g a t i v e f o r t h i s group.

An index is wrong o r t h e d a t a on

t h e a n g l e of s c a t t e r i n g h a s been

d e s t r o y e d .

The u s e r h a s c a l l e d PTHETA w i t h o u t

s a v i n g Legendre c o e f f i c i e n t s - ISTAT must b e non z e r o .

4.8-7

Table 4.27 (Cont 'd . )

Sub r o u t i n e P r i n t i n g M e s sa ge

Message Meaning

GqMST 'NAME = __ NMED = __

NREG = - x = - t h e geometry t r a c k i n g f o r t h i s

Y = - z = - p a r t i c l e . There should b e

An e r r o r has been encountered i n

I

messages b e f o r e and a f t e r t h i s

g i v i n g more in fo rma t ion . G 1 w i l l

p r i n t a message and PR w i l l be

c a l l e d h e r e . P a r t i c l e w i l l b e

t r e a t e d as an escape and c a l c u l a t i o n

w i l l con t inue .

An e r r o r h a s occurred i n c a l c u l a t i n g ' f

EUCLID 'IRPRIM = I N

EUCLID'

* E n t i r e I& a r r a y # ' * $ 4 5

p r i n t e d _, 3 1 I - \ IFPD ~ s y ~ "

E n t i r e ' FPD4 array

p r i n t e d

t h e number of mean f r e e p a t h s t o t h e

d e t e c t o r . There w i l l be a n e r r o r

message preceding t h i s which w i l l

come from G 1 . Program a l lows 5 such e r r o r s b e f o r e t e rmina t ion .

Par t ic le w i l l be t r e a t e d as an

escape and w i l l make no c o n t r i b u t i o n

t o estimate.

Zone h a s n o t been found. Check

your zone s p e c i f i c a t i o n s .

I**** EXIT BEING CALLED

FROM LOOKZ'

4.8-8

Table 4 . 2 7 (Cont 'd . )

Subrou t ine P r i n t i n g Message Mean i n g Message

N ~ R M L 'INVALID REGION OR BODY

I N NORMAL. I R =

NASC = -' -

GG ' I N GG ITYPE =

I R = NBO = I -

G 1 'NO V A L I D D I S T A N C E I N

G I , -'

'******k*****k*********

' I R = - X B = m = D I S T = -' -

'MA ARRAY'

E n t i r e MA a r r a y

p r i n t e d

' F P D ARRAY'

E n t i r e FPD a r r a y

p r i n t e d

NASC i s n ' t i n r eg ion I R Check ' to

see if I R o r NASC h a s been

o v e r w r i t t e n .

I T Y P E is n o t one of t h e body types

(1 - 9) a l lowed. User h a s u s u a l l y

o v e r s t o r e d on MA a r r a y .

Occurs i f body number o u t of range

i s used i n zone d e s c r i p t i o n (usu-

a l l y a mispunched i t e m ) .

G 1 could n o t de te rmine t h e nex t

body t h a t t h e r a y w i l l i n t e r s e c t .

There i s a p robab le e r r o r i n u s e r ' s

geometry s p e c i f i c a t i o n s , o r h e

may have w r i t t e n over h i s geometry

d a t a .

I n o r d e r t o save some computer t i m e ,

u s e r may want t o i n c r e a s e t h e v a l u e s

of NAZ on h i s zone s p e c i f i c a t i o n

c a r d s . Only harm done is i n c r e a s e

i n computer t i m e which i s o f t e n

i n s i g n i f i c a n t . G 1 could n o t f i n d t h e nex t r e g i o n

t h a t t h e p a r t i c l e would e n t e r . It

checked a l l r e g i o n s and is s a y i n g

t h a t t h e p a r t i c l e won' t e n t e r any

of them.

4.10-5

The t o t a l d e r i v a t i v e of t h e a n g u l a r f lux w i t h r e s p e c t t o R i s g iven by

a x a + a a @ az a + a t a + dR a R a x a R ay a R a z a R a t + - - - + - - d - +(?I , E , E , t ' ) = - - +

which, acco rd ing t o F i g . A . l and n o t i n g t h a t t h e p a r t i c l e ' s speed ( v ) i s

e q u a l t o ( - dR/dt) can be r e w r i t t e n as

A

Equa t ion (10) can b e expres sed i n group n o t a t i o n as

S u b s t i t u t i o n o f Eq. (11) i n t o Eq. (9) w i t h F F ' and t t ' y i e l d s

The i n t e g r a t i n g f a c t or R

i s i n t r o d u c e d i n t h e f o l l o w i n g manner:

n

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rl v

n

a3 ri V

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ffi I

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ffi I

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V

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4.10-7

Equat ion (18) w i l l b e r e f e r r e d t o as t h e " I n t e g r a l F lux Dens i ty Equa t ion . "

An e f f e c t of i n t e r e s t X i n group n o t a t i o n can b e expres sed as

where $ - - g

P ( r , n , t ) = t h e r e sponse f u n c t i o n of t h e e f f e c t of i n t e r e s t due t o a - unit angular group f lux (g roup g , r , a, t i m e t ) ,

h = t h a t p o r t i o n o f t h e e f f e c t o f i n t e r e s t a s s o c i a t e d w i t h t h e g t h g

energy group.

The h a r e so d e f i n e d t h a t t h e t o t a l e f f e c t of i n t e r e s t h i s g i v e n by t h e

summation g

G A = 1 A .

g-1 Q (20)

I n t e g r a l Event Dens i ty Equat ion

The "event density" Gg( r ,a ,t ) describes the density of part icles going

i n t o a c o l l i s i o n and i s r e l a t e d t o - t h e group angu la r f l u x i n t h e fo l lowing

I

where

r , E , t ) d E = t h e number of c o l l i s i o n l e v e n t s p e r u n i t volume and t ime

a t t h e space p o i n t F and t i m e i t expe r i enced by p a r t i c l e s having

e n e r g i e s w i t h i n t h e g t h energy group and d i r e c t i o n s i n d about f i .

* !if* e 1

The d e f i n i n g e q u a t i o n f o r t h e even t d e n s i t y i s o b t a i n e d ' b y m u l t i p l y i n g bo th

s i d e s of Eq. (18) by t h e group t o t a l c r o s s s e c t i o n Z E ( ? ) and i d e n t i f y i n g

t h e p roduc t Z g ( F ) $ g ( F y E y t ) as t h e even t d e n s i t y J, (?,Q,t): t g

4.10-8

Equat ion ( 2 2 ) w i l l be r e f e r r e d t o as t h e " I n t e g r a l Event Dens i ty Equa t ion . "

The e f f e c t o f i n t e r e s t A can be e x p r e s s e d ' i n terms of t h e even t den- g

s i t y ; c o n s i d e r Eq. (19) r e w r i t t e n as

where U J - - g

P ( r ,Q , t ) = t h e r e sponse f u n c t i o n o f t h e e f f e c t of i n t e r e s t due t o a

p a r t i c l e which e x p e r i e n c e s an event a t ( g r o u p g , F, E, t i m e t )

I n t e g r a l Emergent P a r t i c l e Dens i ty Equat ion

Def ine t h e emergent p a r t i c l e d e n s i t y x ( F , c , t ) as t h e d e n s i t y of g

p a r t i c l e s l e a v i n g a s o u r c e or emerging from a r e a l c o l l i s i o n w i t h phase

space c o o r d i n a t e s ( g r o u p g , r , fi, t ) -

Then E q . (18) can b e w r i t t e n as

. ...

. 4.10-9

The " I n t e g r a l Emergent P a r t i c l e Dens i ty Equation' ' i s o b t a i n e d by s u b s t i -

t u t i n g Eq. (2 '6 ) i n t o Eq . ( 2 5 ) :

The e f f e c t o f i n t e r e s t A can a l s o be expres sed i n terms of t h e emergent g

p a r t i c l e d e n s i t y

The r e sponse f 'unct ion P X ( F , f i , t ) i s o b t a i n e d by c o n s i d e r i n g a p a r t i c l e which

emerges from a c o l l i s i o n a t r w i t h phase space c o o r d i n a t e s (g roup g , n, t i m e t ) . a t t i m e t ' = t + R/v wi th t h e p r o b a b i l i t y

R

g -

T h i s p a r t i c l e will e x p e r i e n c e an even t i n dR about F ' = r + RE

- + R'5)d .R '

and t h e c o n t r i b u t i o n of t h i s even t i s t h e r e s p o n s e f u n c t i o n P 4 J - ( r ' ,fi,tf ) . g

The sum of all s u c h . c p n t r i b u t i o n s t o t h e e f f e c t o f i n t e r e s t i s g i v e n by

0

and should be t h e same as a re sponse f 'unct ion P X ( F , f i , t ) which i s based on

emergent p a r t i c l e d e n s i t y . T h i s l e a d s t o t h e f o l l o w i n g r e l a t i o n s h i p : g

m

4.10-10

where

$(? ,n , t , ) t h e r e sponse f u n c t i o n ( o f t h e e f f e c t of i n t e r e s t due t o a k3

p a r t i c l e which emerges from a c o l l i s i o n having t h e phase space

c o o r d i n a t e s (group g , 7 , f i , t i m e t )

R

B*(, ,R,fi) C E:(? + R'fi)dR' . ( 3 0 ) '. g I

0

It i s no ted t h a t B * ( F , R , f i ) d i f f e r s from t h e o p t i c a l t h i c k n e s s B ( ? , R , f i ) g g as d e f i n e d by Eq. (17) i n t h a t t h e i n t e g r a t i o n i s performed i n t h e p o s i t i v e

d i r e c t i o n and as such B * ( F , R , f i ) i s t h e a d j o i n t of B ( F , R , f i ) . can a l s o b e expres sed i n terms o f P ( r , n , t ) by s u b s t i t u t i n g Eq . ( 2 4 ) i n t o

Eq. (29), y i e l d i n g

$ ( ( r , z , t ) g Q 4 - -

g

g

Opera to r No ta t ion and Summary o f t h e Forward Equa t ions

Def ine t h e t r a n s p o r t i n t e g r a l o p e r a t o r

U

and t h e c o l l i s i o n i n t e g r a l o p e r a t o r

which can be r e w r i t t e n as

where

4.10-11

I n Eq. ( 3 4 ) , [ c ~ " g ( ~ , n t + n ) / Z g ' ( F ) l S i s a normal ized p r o b a b i l i t y d e n s i t y

f l m c t i o n from which t h e s e l e c t i o n of a new energy group and d i r e c t i o n can

be accomplished and [ Z g ' ( F ) / Z t ' ( ? ) 1 i s t h e nonabsorp t ion p r o b a b i l i t y . S

Using t h e t r a n s p o r t and c o l l i s i o n i n t e g r a l o p e r a t o r s , Eq. ( 2 2 ) can be

r e w r i t t e n as

The t e rm T (F',F,fi)Sg(: ' , n , t ' ) can be i d e n t i f i e d as t h e " f i r s t c o l l i s i o n

source" and denoted by g

S g ( ? , a , t ) T (? '+?,fl)S ( ? ' , n , t ' ) , ( 3 7 ) C g g

and t h e " I n t e g r a l Event Dens i ty Equation" becomes

Using t h e r e l a t i o n s h i p $ ( ? , n , t ) = Cg(?)$ (?,fi,t), Eq. (38) can be g t g

t r ans fo rmed i n t o t h e " I n t e g r a l F lux Dens i ty Equat ion:"

F i n a l l y , t h e i n t e g r a l o p e r a t o r s a r e i n t r o d u c e d i n t o Eq. (27) and t h e

f o l l o w i n g form f o r t h e " I n t e g r a l Emergent P a r t i c l e Dens i ty Equation" i s

o b t a i n e d :

An examination of Equa t ions (381, (391, and (40) would r e v e a l t h a t

e i t h e r t h e " I n t k g r d Event Density-EqAation" or t h e " I n t e g r a l Emergent

P a r t i c l e Dens i ty Equation" would p r o v i d e a r e a s o n a b l e b a s i s f o r a Monte

C a r l o random walk . Equat ion ( 4 0 ) w a s sel 'ected for' t h e MqRSE code s i n c e

t h e sou rce p a r t i c l e s would be: i n t r o d u c e d acco rd ing t o t h e n a t u r a l d i s t r i -

b u t i o n r a t h e r t h a n t h e d i s t r i b u t i o n of f irst c o l l i s i o n s . However, it i s

noted t h a t a f t e r t h e i n t n o d u c t i o n of t h e sou rce p a r t i c l e , t h e subsequent

4.10-12

random walk c a n . b e r ega rded i n terms o f e i t h e r E q . (38) or Eq. ( 4 0 )

w i t h t h e p a r t i c l e ' s weight a t a c o l l i s i o n s i t e b e i n g t h e weight b e f o r e

c o l l i s i o n (WTBC) o r t h e weight a f t e r c o l l i s i o n (WATE) , r e s p e c t i v e l y .

The random walk based on t h e " I n t e g r a l Emergent P: , i , t ic le Dens i ty

Equat ion" would introduce i ; p a r t i c l e i n t o t h e system accord ing t o t h e

s o u r c e f 'unct ion. The p a r t i c l e t r a v e l s t o t h e s i t e o f i t s f i r s t c o l l i s i o n

as de termined by t h e t r a n s p o r t k e r n e l . I t s weight i s modi f ied by t h e

non-absorp t ion p r o b a b i l i t y and a new energy group and f l i g h t d i r e c t i o n

are s e l e c t e d from t h e c o l l i s i o n k e r n e l . The t r a n s p o r t and c o l l i s i o n

k e r n e l s a r e a p p l i e d s u c c e s s i v e l y de t e rmin ing t h e p a r t i c l e ' s emergent

pi3?be sqace c o o r d i n a t e s co r re spond ing t o t h e second, t h i r d , e t c . , c o l l i s i o n

s i tes u n t i l t h e random walk i s t e r m i n a t e d due t o t h e r e d u c t i o n of t h e

p a r t i c l e ' s weight below some c u t - o f f v a l u e o r because t h e p a r t i c l e escapes

from t h a t p o r t i o n o f phase space a s s o c i a t e d w i t h a p a r t i c u l a r problem

( f o r example, escape f iom t h e sys t em, s lowing down below an energy cut-

o f f , o r exceeding some a r b i t r a r i l y s p e c i f i e d age c u t - o f f ) .

Random Walk Procedure

The aciiual imp1en;entation o f t h e random walk procedure i s accomplished

by approximat ing t h e i n t e g r a l s imp l i ed i n t h e c o l l i s i o n and t r a n s p o r t

i n t e g r a l o p e r a t o r s by t h e sum m

where - n - -

g x ( r , R , t ) d R = t h e emergent p a r t i c l e d e n s i t y of p a r t i c l e s emerging

from i t s n t h c o l l i s i o n and having phase space c o o r d i n a t e s (g roup

g , r , dn about h , t ime t ) , -

- - Thus, t h e sou rce c o o r d i n a t e s ( g r o u p go , ro, Ro, t i m e t ) a r e s e l e c t e d

- Bgo(',R,no) from S ( F , f i , t ) and a f l i g h t d i s t a n c e R i s p icked C t O ( F ) e

t o de t e rmine t h e s i t e f o r t h e f i r s t c o l l i s i o n ?land t h e p a r t i c l e ' s age

tl= to + R/vg . A l l

p a r t i c l e s a r e f o r c e d t o s c a t t e r and t h e i r weight i s modi f ied w i t h t h i s

0

g

The p r o b a b i l i t y of s c a t t e r i n g i s Z ~ o ( $ / C ~ o ( ? l ) . 0

p r o b a b i l i t y . A new group g i s s e l e c t e d acco rd ing t o t h e d i s t r i b u t i o n 1

i

4.10-17

The i:(F) , Cpg'(?,fi4' ) , and are a d j o i n t weighted group pa rame te r s S Q

and t h e i r u s e i n t h e s o l u t i o n of Eq. (51) p r o v i d e s group a d j o i n t f l u x e s

d e f i n e d by Eq. ( 5 2 ) where @ * ( F , E , n , t ) r e p r e s e n t s t h e s o l u t i o n of Eq. ( 5 0 ) .

Another approach f o r d e f i n i n g group a d j o i n t fluxes i s t o d i r e c t l y

d e v i s e t h e equa t ion 'wh ich i s a d j o i n t t o t h e group form of t h e Boltzmann

e q u a t i o n [Eq. (911. The group a d j o i n t e q u a t i o n so ob ta ined* i s g iven by

g = 1,2, ... G .

where v Zg( , ) a r e forward weighted group pa rame te r s i d e n t i c a l t o t h o s e

which occur i n Eq. ( 9 ) and t h e matrix Zg jg ' (F ,&f i l ) i s simply t h e t r a n s p o s t -

t i o n o f t h e forward weighted group-to-group d i f f e r e n t i a l s c a t t e r i n g c r o s s -

s e c t i o n m a t r i x .

g y t S

The group a d j o i n t fluxes @*( 7 ,fi ,t ) which r e p r e s e n t t h e s o l u t i o n o f g

Eq. ( 5 7 ) are a d j o i n t t o t h e group f l u x e s @ and do no t n e c e s s a r i l y assume

t h e same v a l u e s as t h e group a d j o i n t fluxes @*(r ,Q, t ) , i . e . , g * - -

g

Th i s f o l l o w s s i n c e ZE(F), -Es gtg' (? ,Gar ) , and v are , i n g e n e r a l , d i f f e r e n t

from t h e a d j o i n t weighted v a l u e s .

e t e r s , as i m p l i e d by Eq. ( 5 7 ) , are used i n MORSE. However, o t h e r we igh t ing

schemes, such as a d j o i n t or a d j o i n t and fo rward , deserve c o n s i d e r a t i o n

g Usua l ly forward weighted group param-

when c r o s s - s e c t i o n we igh t ing i s a problem. When a s u f f i c i e n t l y f i n e group

s t r u c t u r e i s employed, t h e group pa rame te r s become less s e n s i t i v e t o t h e

we igh t ing scheme and t h e co r re spond ing group a d j o i n t f l u x e s are a l s o

n e a r l y t h e same.

* The d e r i v a t i o n o f Eq. ( 5 7 ) i s n o t p r e s e n t e d h e r e because of i t s s i m i l a r i t y w i t h t h e p rev ious d e r i v a t i o n of Eq. ( 5 0 ) ; t h e i n t e g r a l s over energy are s imply r e p l a c e d by appr0pr i a t . e group summations.

4.10-18

I n t e g r a l Point-Value Equat ion

Equat ion ( 5 7 ) i s now t r ans fo rmed i n t o an i n t e g r a l form f o l l o w i n g essen-

t i a l l y t h e same p rocedures used w i t h t h e forward e q u a t i o n s . A s shown

b e l o w , l e t

t h e forward e q u a t i o n s .

R i s g iven by

- - = r + R 3 r a t h e r than. ; ' = r - RC as w a s t h e convent ion w i t h

The t o t a l d e r i v a t i v e of $ * ( F ' , a , t ) w i t h r e s p e c t t o g

Z

Y

c

4.10-19

R

- I:(, + R'E)dR'

p r o v i d e s t h e f o l l o w i n g 0 Use of t h e i n t e g r a t i n g f a c t o r e

r e l a t i o n s h i p :

Equat ion ( 5 9 ) , t o g e t h e r w i t h Eq. ( 5 8 ) , can be a r r anged t o g i v e

It i s no ted t h a t Eq. ( 6 0 ) i s i d e n t i c a l l y t h e l e f t - h a n d s i d e o f Eq. ( 57) which can now be r e w r i t t e n as

4.10-20

I n t e g r a t e Eq . ( 6 1 ) from R = 0 t o R = 00 and assume t h a t m

- E t ( ; + R ' 5 ) d R '

1 5 0 ; 0 { + * ( w ,E , t J e

g (62)

t h e n t h e fo l lowing i n t e g r a l e x p r e s s i o n f o r $ * ( F , a , t ) g is o b t a i n e d :

Equat ion (63 ) c o n t a i n s t h e a d j o i n t o p t i c a l t h i c k n e s s , 6 * ( ? , R , E ) g

d e f i n e d e a r l i e r by E q . ( 30) as

which w a s

R

B * ( ? , R , E ) 5 J E:(? + R ' E ) ~ R ' . g

0

Redef ine t h e sou rce t e r m as M

and E q . ( 6 3 ) can be r e w r i t t e n as

4.10-23

S u b s t i t u t i o n of Eq. (71 ) i n t o Eq. (64) y i e l d s

and acco rd ing t o Equa t ions ( 2 4 ) and ( 2 9 ) , Eq. ( 7 2 ) can b e r e w r i t t e n as

Equa t ions (73) and (741, r e s p e c t i v e l y :

and

s* ( G , s Z , t ) = P X ( F , f i , t ) . Tg g

(74)

S u b s t i t u t i o n o f Eq. (73 ) i n t o Eq. (67 ) and Eq. ( 7 4 ) i n t o Eq. (67) y i e l d s

t h e f o l l o w i n g forms f o r t h e " I n t e g r a l Point-Value Equat ion: 'I

and

I n t e p r a l Event-Value Equat ion

A t t h i s p o i n t l e t us i n t r o d u c e a v a l u e f u n c t i o n based on t h e even t

d e n s i t y and t o re la te t h i s q u a n t i t y t o t h e po in t -va lue f u n c t i o n by consid-

e r i n g a p a r t i c l e l e a v i n g a c o l l i s i o n a t F w i t h phase space c o o r d i n a t e s

( g r o u p g , f i , t i m e t ) .

i s t h e po in t -va lue f u n c t i o n x * ( F , f i , t ) . even t i n dR about

and t h e v a l u e o f t h i s even t ( t o t h e e f f e c t of i n t e r e s t ) w i l l be r e f e r r e d

t o as t h e "event-value:' andi be, denoted -by W '(-?I ,c ,t ) . That i s , t h e

"event-value" W ( F " , f i , t ' ) i s d e f i n e d as the v'alue ( t o t h e e f f e c t o f

i n t e r e s t ) o f having an even t a t F'+ . y i t h & _ _ . + a n - - . . in toming , p a r t i c l e which has

The v a l u e of t h i s p a r t i c l e t o t h e e f f e c t o f i n t e r e s t

T h i s p a r t i c l e w i l l e x p e r i e n c e an g .: 1- - !

= F + RQ w i t h t h e p r q b a b i l i t y [C,p(r')e- Bg(FyRy') dR1

g, ' a .

g

--.

4.10-24

phase space c o o r d i n a t e s (g roup g , f i , t i m e t ' ) . b u t i o n s t o t h e e f f e c t of i n t e r e s t i s g iven by

The sum o f a l l such c o n t r i -

0

and, i f t h e event -va lue f u n c t i o n i s p r o p e r l y d e f i n e d , should e q u a l t h e

po in t -va lue f u n c t i o n ; t h a t i s ,

A comparison o f Eq. (78) w i t h Eq. ( 7 5 ) would show t h a t W (?,fi,t) can be

i d e n t i f i e d as Q

and s u b s t i t u t i o n o f Eq. (78) i n t o Eq. (79 ) y i e l d s t h e d e f i n i n g e q u a t i o n

f o r t h e "Event-Value Funct ion"

Equat ion ( 8 0 ) w i l l be r e f e r r e d t o as t h e " I n t e g r a l Event-VEElue Equat ion ."

A comparison of Eq. (80) w i t h Eq. ( 3 8 ) would show .chat t h e event -va lue

f u n c t i o n W ( F , f i , t ) is' a d j o i n t t o t h e even t d e n s i t y 11, (?,fi,t). t h e e f f e c t of i n t e r e s t is given by

T h e r e f o r e g g

I n t e g r a l Emergent AdJuneton Dens i ty Equat ion

The s o l u t i o n of e i t h e r t h e po in t -va lue e q u a t i o n , Eq. (76 ) , o r t h e

event -va lue e q u a t i o n , E q . (80 ) , c o u l d be accomplished by Monte Car lo

p rocedures ; however, t h e random walk would not be t h e same as t h a t imp l i ed

by Eq. (40)*. Consider t h e f o l l o w i n g a l t e r e d form o f Eq. ( 7 6 ) ,

* The d e s i r e i n MGRSE i s t o use t h e same random walk l o g i c f o r b o t h forward and a d j o i n t c a l c u l a t i o n s .

4.10-25

The a d d i t i o n a l weight f a c t o r [E:( F 1 )/.I:( F ) 3 arises s i n c e Eq. (76 ) and i t s a l t e r e d form (Eq. ( 8 2 ) , are a c t u a l l y f l u x - l i k e e q u a t i o n s , even

though x*(F,b, t ) i s a d j o i n t t o t h e emergent p a r t i c l e d e n s i t y x ( ? , E , t ) . R E - v

I n a f a s h i o n ana logous t o t h e forward problem, t h e f o l l o w i n g new

q u a n t i t i e s a r e d e f i n e d :

and

S ince x * ( F , f i , t ) i s a f l u x - l i k e v a r i a b l e , t h e new v a r i a b l e H ( ? , E , t ) can

be r e g a r d e d as an even t d e n s i t y and G ( ? , E , t ) l i k e an emergent p a r t i c l e

d e n s i t y . g

p rope r b a s i s f o r an a d j o i n t random walk.

g g

g The d e f i n i n g i n t e g r a l e q u a t i o n f o r G ( F , b , t ) shou ld b e t h e

The d e f i n i n g e q u a t i o n f o r t h e a d j o i n t event d e n s i t y f u n c t i o n H (F,C,t) g

i s o b t a i n e d by c o n s i d e r i n g t h e f o l l o w i n g a l t e r e d form of Eq. ( 7 5 ) :

4.10-26

where

Not ing t h a t :

and

Eq. (86) becomes

A comparison of Eq. (88) w i t h Eq. (84) r e v e a l s t h a t

and t h e subsequent s u b s t i t u t i o n of Eq. ( 8 4 ) i n t o Eq. (89) y i e l d s t h e

f o l l o w i n g d e f i n i n g e q u a t i o n f o r t h e a d j o i n t emergent p a r t i c l e d e n s i t y :

Equat ion (90) i s a lmost i d e n t i c a l w i t h Eq. ( 4 0 ) which d e f i n e s t h e

forward emergent p a r t i c l e d e n s i t y x (?,fi,t) and a l s o s e r v e s as t h e formal g b a s i s f o r t h e forward random walk.

i n te rms o f t h e t r a n s p o r t of p s e u d o - p a r t i c l e s c a l l e d t t ad junc tons" i n t h e

(P'-+P) d i r e c t i o n o f phase space .

A t t h i s p o i n t , l e t us i n t e r p r e t Eq. (90)

T h i s p r e s e n t s two immediate problems :

The t r a n s p o r t of t h e ad junc tons from F ' = ? + Rfi t o F would be

i n a d i r e c t i o n o p p o s i t e t o t h e d i r e c t i o n v e c t o r 4 ,. -- t h e r e f o r e ,

t h e d i r e c t i o n v e c t o r f o r t h e ad junc ton should be R E .-fi, and

r ' = r - RS2 .

1)

- -

t

S i A , .

C (r,R'+R) = 1 dfi' g ' g

4.10-27

R . (92)

Grs 2 ) The c o l l i s i o n k e r n e l shou ld b e i n t e r p r e t e d as d e s c r i b i n g t h e

(E'+E) change i n phase space expe r i enced by t h e ad junc ton d u r i n g

i t s random walk; t h e r e f o r e , l e t

,. The s e l e c t i o n of new phase space c o o r d i n a t e s ( g r o u p g , R = -6) i s made

from t h e normal ized k e r n e l and t h e weight of t h e ad junc ton i s modi f ied by

t h e weight f a c t o r [ I * which i s no l o n g e r a s imple non-absorp t ion p r o b a b i l i t y

and may assume v a l u e s i n excess of u n i t y . T h e r e f o r e , t h e r e i s no "analogue"

s c a t t e r i n g f o r ad junc tons and t h e a d j u n c t o n ' s weight may i n c r e a s e a t some

c o l l i s i o n s .

Equa t ion (90) can be r e w r i t t e n as

which now cor responds t o t h e t r a n s p o r t o f ad junc tons and p r o v i d e s t h e d e s i r e d 1 , ' i:: .;

b a s i s for t h e a d j o i n t random walk i n t h e MORSE code. Note t h a t t h e sou rce 0 - - of ad junc tons i s provided by P ( r ,Q, t ) which i s r e l a t e d t o P ( r ,Q, t ) as

f o l l o w s :

* , , I - 0 - ,..- g 7 Q

- (94) P 0 * (F,n,t) = P@(F, - f i , t ) y I

g g ~ , . ' *

which must be t a k e n i n t o c o n s i d e r a t i o n i f t h e r e sponse f u n c t i o n P 0 ( r , R , t ) - - g

has angu la r dependence -- however, many p h y s i c a l s i t u a t i o n s permi t an

i s o t r o p i c assumption f o r t h e 5-dependence.

A Monte Car lo s o l u t i o n of Eq. (93) , t h e " i n t e g r a l emergent adjunctJon den

e q u a t i o n , " w i l l g e n e r a t e d a t a from which t h e ad junc ton f l u x x*(r,Q) and g

i t y

4

4.10-28

o t h e r q u a n t i t i e s of i n t e r e s t can be de termined .

x*(F,f i ) must t a k e i n t o account t h e r e v e r s a l of d i r e c t i o n between ad junc tons

and real p a r t i c l e s , i . e . , R = - R .

o f c a l c u l a t i n g t h e answer o f i n t e r e s t :

The g e n e r a l u se o f h

h g - For example, c o n s i d e r t h e v a r i o u s ways

F u r t h e r , i f outward boundary c r o s s i n g s would be s c o r e d i n t h e forward

problem, t h e co r re spond ing source ad junc tons would b e i n t r o d u c e d i n t h e

inward d i r e c t i o n . L ikewise , ad junc tons would be s c o r e d f o r e n t e r i n g a

volume from which t h e sou rce p a r t i c l e s i n t h e forward problem would b e

e m i t t e d . It should be noted t h a t many s o u r c e s and r e sponse f u n c t i o n s a r e

i s o t r o p i c and t h e problem of d i r e c t i o n r e v e r s a l need not be cons ide red .

n

Gs

4.12-1

4.12. REFERENCES

1. K. D. La throp , "DTF-IVY A FORTRAN-IV Program f o r So lv ing t h e

Mult igroup Transpor t Equat ion wi th A n i s o t r o p i c S c a t t e r i n g , "

LA-3373, Los Alamos S c i e n t i f i c Labora tory (1965) . 2 . W. W . Engle , J r . , "A User's Manual f o r ANISN," K-1693 (1967) .

3. W. A. Rhoades and F. R. Mynatt , "The DOT-111 Two-Dimensional

Discrete O r d i n a t e s T ranspor t Code," ORNL-TM-4280 (1973).

4. W. Guber, e t a l . , "A Geometric D e s c r i p t i o n Technique S u i t a b l e

f o r Computer Analys is of Both t h e Nuclear and Convent ional

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1967) .

5 . M. 0. Cohen, W. Guber, e t a l . , "SAM-CE - A Three Dimensional

Monte Car lo Code f o r t h e S o l u t i o n of t h e Forward Neutron and

Forward and Adjo in t Gamma Ray Transpor t Equat ions ," MR-7021

(DNA2830F) pp. 3.3-3.18 (November, 1971) .

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General Purpose Monte Car lo Neutron Transpor t Code," ORNL-3622

(1965) .

7 . C. L. Thompson and E . A . S t r a k e r , "@6R-ACTIFK, Monte Car lo

Neutron Transpor t Code," ORNL-CF-69-8-36 (1969).

8. D. C . I r v i n g , "Desc r ip t ion of t h e CDC-1604 Version of t h e @6R

Neutron Monte Car lo Transpor t Code," ORNL-CF-71-5-14 (1971) .

9 . C. E . Burgar t and E . A. S t r a k e r , "XCHEKR - A Mult igroup Cross

S e c t i o n E d i t i n g and Checking Code," ORNL-TM-3518 (1971) .

10. F. H . Clark and N . A. Be tz , "Importance Sampling Devices f o r

S e l e c t i n g Track Lengths and D i r e c t i o n s A f t e r Scat ter i n @5R,"

ORNL-TM-1484 (1966).

11. F. H . C lark , "The Exponent ia l Transform as an Importance-Sampling

Device - A Review," ORNL-RSIC-14 (1966) .

'0

4.12-2

12. V . R. Cain, E . A. S t r a k e r , and G. Thayer , "Monte Car lo Pa th

Length S e l e c t i o n Rout ines Based on Some S p e c i f i c Forms of t h e

Importance Funct ion ," ORNL-TM-1967 (1969) .

13. M. B . Emmet t , C. E . Burga r t and T . J. Hoffman, "DOMINO, A

General Purpose Code f o r Coupling Discrete Ord ina te s and Monte

Car lo Rad ia t ion Transpor t C a l c u l a t i o n s , " ORNL-4853 (1973) . 14. P r i v a t e Communication from W. W. Engle , J r . , ORNL,.

15. F. H. C la rk , Nucl. S c i . & Eng., 27, 235-239 (1967) .

16. T. J. T y r r e l l , "TDUMP - A T r a n s l a t i o n Rout ine f o r U s e i n Dumping

FORTRAN Arrays ," ORNL-CF-70-7-8 (1970) .

17. S. N. Cramer, "Adjoint Gamma-Ray Es t ima t ion t o t h e Sur face of a

Cy l inde r - Analyses o f a Remote Reprocess ing F a c i l i t y , " Nucl. S c i .

& Eng., 79, 417-425 (1981).

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C e n t r a l Research L ib ra ry ORNL - Y-12 Technica l L i b r a r y Document Refe rence .Sec t ion Labora tory Records Department Laboratory Records, ORNL RC RSIC L i b r a r y L. S. Abbott J. M. Barnes T. J. .Burns S. N. Cramer H. I,. Dodds M. R . Emmett W. W. Engle, Jr. T. A. G a b r i e l T. J. Hoffman

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