This IB a preprint of a paper intended tor publication in a journal or proceeding!. Since changes may be made before publication, this preprint is made avuiable with the understanding that it will r.ot be cited or reproduced MKhout the permission of the author. I O L - T6562 PREPRINT„ LAWRENCE UVERMORE LABORATORY University ol CaUccnia/Livermore. Caktomia COMPUTER APPLICATIONS IN CONTROLLED FUSION RESEARCH John Killeen February 1975 -NOTICE Tins report was prepared as an account of wort sponsored by the United Stales Govetnmc.-n. Neither the United States nor the 'United States Energy Research and Development Administration, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or ir.ipUed, 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 uwned rights. This paper has been prepared for the American Nuclear Society National Topical Meeting on Nuclear Engineering Education, the proceedings of which will appear in a special issue of Nuclear Technology. %;73 ? "'"BiBurioaoFTwsr.ocuMtKj UNLIMITED
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This IB a preprint of a paper intended tor publication in a journal or proceeding!. Since changes may be made before publication, this preprint is made avuiable with the understanding that it will r.ot be cited or reproduced MKhout the permission of the author.
I O L - T6562 PREPRINT„
LAWRENCE UVERMORE LABORATORY University ol CaUccnia/Livermore. Caktomia
COMPUTER APPLICATIONS
IN CONTROLLED FUSION RESEARCH
John Killeen
February 1975
-NOTICE Tins report was prepared as an account of wort sponsored by the United Stales Govetnmc.-n. Neither the United States nor the 'United States Energy Research and Development Administration, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or ir.ipUed, 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 uwned rights.
This paper has been prepared for the American Nuclear Society National Topical Meeting on Nuclear Engineering Education, the proceedings of which will appear in a special issue of Nuclear Technology.
%;73 ? "'"BiBurioaoFTwsr.ocuMtKj
UNLIMITED
COMPUTES APPLICATIONS 111 COIJTFIOI.LED Ft!. IN RESEARCH
John Killeen
Department of Applied Science University of California, Davis-Liveroore
and
National CTR Computer Center Lawrence Livermore Laboratory University of California
P.O. lox 8C3, Livermore, California '-hyy
February 197:
Communications should te addressed to
Professor John Killeen L-'.vrence Livenaore Laboratory P. 0. Box 8C8, Livermore 9*5:0
Telephone: {'•*!') 1)47-1100, ext. 5278
Number of pages: 22 Tables: none Figures; none
This paper has been prepared for the American Mucloar Society National Topical Meeting on Nuclear Engineering Education, the proceedings of which will appear in a special issue of Nuclear Teclinology.
•2-
AESTRACT
The role of Nuclear Engineering Education in the application of
computers to controlled fusion research can be a very important one.
In the ne£.r future the use of computers in the numerical modelling of
fusion systems should increase substantially. A recent study group
has identified five categories of computational models to study the
physics of magnetically confined plasmas. A comparable number of types
of models for engineering studies are called for. The development and
application of computer codes to implement these Todels is a vital step
in reaching the goal of fusion power. In order to meet the needs of
the .'usion program the National CTR Computer Center has been estab
lished at the Lawrence Livennore Laboratory. A large central computing
facility is linked to smaller computing centers at each of the roa.ior
CTR laboratories by a communications network. The crucial elemenx that
is needed for success is trained personnel. The number of peopje with
knowledgs of plasma science and engineering that are trained in numeri
cal methods and computer science is quite small, and must be increased
substantially in the next few years. Nuclear Engineering departments
should encourage students to enter this field and provide the necessary
courses and research programs in fusion computing.
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IUTRODUCTIOK
Large-scale digital computers will play an increasingly important
role in future controlled fusion research and in the development of
practical fusion reactors. The plasma state exhibits such a diverse
variety of phycical phenomena that only through extensive use of high
speed computers can the interplay of all factors that affect the per
formance of a fusion system be modelled.
The behavior of a plasma confined by a magnetic field is simu
lated by a variety of numerical models. Some models used on a short
time scale give detailed knowledge of the plasma on a microscopic scale,
while other models used on much longer time scales compute macroscopic
properties of the plasma dynamics. All of these models are under con
tinual development. but in the next few years there should be a sub
stantial increase in the development and use of numerical models in
order to meet the needs of the fusion power program.
A 1971* study gro-.'.p on the ''Applications of Computers to CTB"
rponsored by the AEC/DCTR identified five categories of computer codes
used to model the physics of fusion devices.
1. Time-dependent macroscopic (fluid) codes.
2- Tirce-independent macroscopic codes.
3- Vlasov and particle codes.
•i. Fokker-Planck codes.
p. Hybrid codes.
In later sections of this report we shall examine these problem areas
in more detail and consider their importance to the CTR program and
discuss future goals in each area.
- I t -
There are also a wide variety of engineering applications which
require extensive computing. These applications will become more and
and more important as we move into the reactor development phase. We
shall also discuss some of these problems in more detail later in the
report.
Computers are expected tc play an Important role in the acquisi
tion and analysis of experimental data as well as the control of
experiments.
In order to meet the need? of the controlled fusion program the
National CTR Computer Center has teen established at the Lawrence
Livermore Laboratory. This Center will be connected to all major CTR
laboratories, as well as selected universities, by means of a wide
band communications network. The increased computing power made avail
able by the Center will accelerate the development of the theoretical
models and associated computer codes needed to predict the behavior of
plasma confinement systems and the operating characteristics of fusion
power reactors. A more detailed description of the Center will be
given later in this report.
COMPUTER MODELS OF A MAGMETICALLY CONFINED PLASMA
1. Time-dependent macroscopic codes
The complex nature of the MHD fluid equations of motion is such
that our understanding of the macroscopic behavior of realistic
toroidal plasma devices has been most efficiently advanced by numerical
studies of simplified fluid models. When one considers the additional
complicating features Involved in realistic boundary conditions, the
presence of divertors, and extensions to non-axisymmetric systems,
-5-
it becomes clear that many new physical phenomena await investigation.
The range of time and space scales of the various physical phe
nomena leads to a fairly natural division from the physics point of
view—(a) fast time scale; and (b) diffusion time scale. Such a divi-
nion is also natural from the numerical point of view as the techniques
involved in the solution for each category are different. Not only do
the classification of the model equations change (i.e., from hyperbolic
to parabolic), but it is clear that even with Class IV and V computer
hardware, one wouli not, for example, attempt to reach confinement
time scales in a Tokamak simulation by time-stepping a code designed
to follow fast congressional Alfven waves,
a. Simulation on the Fast Time Scale
Detailed comparison of experimental data from Scyllacs and pinches
vith theory, taking iue account of experimental complications (plasma
heating, compression, progression of equilibria, stability, atomic
processes, etc.), vill depend on the development of 2-E and 3-D (two
and three dimensional) versions of codes analogous to the 1-D Hain-
Roberts code. Most of the physical phenomena important here lie in
the fast MKD timescale (nanoseconds to microseconds).
For Tokaraak configurations, the corresponding effects occur
primarily on rather longer time scales, milliseconds, and are discussed
in subsection (b). However, the questions of stability of Tokamak dis
charges toward MHD modes are very important for achieving efficiency
in a reactor system and for minimizing the cost of feasibility devices.
One example of great interest is the area of the early stages of a
Tokamak discharge and the formation and destruction of magnetic surfaces.
Here also the relevant tines are on the fast MHD time scale.
The potentially high inpflct of simulation techniques at th» com-
pressional Alfven tine scale lies In the possibility of determining
cor.figuratlons and determine their s tabi l i ty from 5W-type calculations
(especially important ir. high beta applications).
Experimental devices incorporating the idea of axial symmetry in
a torus appear to be capable of pla.-ria confinement for times which are
of great in teres t . One reason for this result i r the assurance of equi-
l i i r i a ir. s.;?h devices as predict? '. ly MHD ani p : i iing-center theories.
T-o-dimer.sior.al .TiO-lels :'or rlasma eq. i l it ria have "teen use i to compute 2 the equililri.;m f ie l :s for varices containment schemes ir.clu :i:.£ Astron,
Levitron, ToxaEah." and the _•'. iffe : cusp."'
Several containment scben/*s. is.ci u iir.g the stabilized mirror
devices, do not possess ar. icr.cratlc coordinate, allowing a reduction
of the equilibrium equations to two dimensions. Codec have leer, de
veloped to handle the general case for open containment—a three-
dimensional code that solves for plasma equil ibria in open-fioli 28 2r* geometries, which allows analysis of most i-inimura-E mirror systems. '
The c r i t i ca l problems in this area are the following:
(a) Develop "wo and three dimensional plasma equilibrium codes.
(b) Levelcp 5W codes to determine the s tab i l i ty of various plasma
cr .-.figurations.
(c) Apply these codes to Jeteraine what plasma equil i tr ie. exist
which look promising from thei r s tab i l i ty properties and from the
plasma that they can confine.
(d) Investigate the effects of divertors and other boundaries.
Some descriptions of equil ibr ia calculations are given in Hcfs.
2^-31 and time-independent s tab i l i ty codes are described in Refs. J52-31*.
18. P. M. Keeping, R. C. Grimm, and J. Killeen, in Proc. 5th European
Conf. or. Cont/olled Fusion and Plasma Physics. Grenoble, France,
1072, CEA Grenolle.
1?. F. 1. Hinton, J. C. Wiley. D. F. DUchs, II. P. Furth, and P. H.
Rutherford, Fhys. Rev. Letters £9., 6 GB (1972).
20. J. T. Hogan and R. A. Dory, in Proc. cth European Conf. on Con-
- 2 0 -
t r o l l e d Fusion and Plasma P h y s i c s , Grenoble, France , 1972, CEA
Grenoble.
2 1 . P- Dflchs and D. P f l r s c h , n e o c l a s s i c a l Di f fus ion and the In f luence
of A l p h a - P a r t i c l e s on t h e Energy Balance i n Large Tokamaks and
Fusion Reac tor Plasmas, paper IAEA-CN-5.5/A17-1 of IAEA F i f t h Con
ference on Plasma Phys ics and Cont ro l l ed Huclear Fusion Research,
Tokyo, November 11-15 , 177*.
22 . J . T. Hogan. Mul t i -F lu id Tokaiaak Transpor t Models, in Methods in
Computational Phys ics (Acadeaic p r e s s , Hew York, 1975) , Vol. 16,
Chapter TV.
2 } . M. L. Watkins, M- H. Hughes, P. M- Keeping, K. V. Rober t s , and
J . Ki l l ee r . , ICARUS--A One-Dinenslonal Plasma Diffus ion Code, i n
Methods In Computational Phys ics (Academic P r e s s , Ifev York, 1775) ,
Vol . l e , Chapter V.
a*. D. V. Anderson, J . Ki l l ee r . , a a i M. E. Renslnk, Phys. F l u i d s 1^,
5:1 (1.--72).
2- . E. F i s h e r a n ! J - Ki l l ee r . , Phi 's . F l u i d s lA, 12-v, (1771) .
2C. J . D. Caller, a n i S. A. Don', Phys. F lu ids l_, 1-2} (1772) .
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2 ? . D. V. Ar.der.-or. a n i J . Killee.-. , J . Conput. Phys. 10, 1}} (1772) .
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Methoir. in Ccnrp.;tatior,al phys i c s (Academic P r e s s , Hew York, l r ' 7 5 ) ,
Vol. It, Chapter VI.
•'•< . C. Mercior , E ^ u i l i l r l u s , Por t u r t a t Ion and Evolu t ion of a P la sna -
Vac:ura Jyrter. of the Tokauak Type, paper IAEA-CII-35/A11-1 o IAEA
F i f t h Conrorcr.ce on P l a r a Physics a n i Con t ro l l ed Nuclear Fusion
!
-21-
Research, Tokyo, November 11-15, 1971*.
Y. Suzuki, M, Masuzaki, and H. Toyaraa, Free Boundary MHD Equilibria,
paper IAEA-CH-33/A11-2 of above Conference.
J . P. Freidberg, W. Grossmann, and F. A. Haas, Stabi l i ty of Kink
Modes In High Beta Tokamaks, paper IAEA-CH-33/A13-4 o f above
Conference.
G. Berge, U. P. Freidterg, B. M. Marder, W. Grossmann, M. Hose,
G. 0. Spies, and G. Vahala, MHD Stabi l i ty of the Seyllac Confi
guration, and H. Weitzner, F.'.nite-Beta Stabi l i ty Theory, combined
paper 3AEA-CH-33/E1-1 of abovr Conference.
R. C. Grimm. J . M. Greene, ana J . L. Johnson, Computation of the
Magnetohydrodynaraic Spectrum in Axisymmetrie Confine, i t Systems,
in Method:- if. Coi:.putational Physics (Academic Press, Hew York,
ir'7?), Vol. lv, Chapter VJI.
M. Brett Schneider, J . Killeen, and A. A. Mirin, J . Comput. Phys.
i i , 3& (i:"'"-).
J. A- Eyers, J. P. Holdren, J. Killeen, A. E. Langdon, A. A. Mirin,
M. E. Rer.rink, a::d C. G. Thill, Phyy, Fluids 17, 2061 (197^)-
J . K. "Pav.-or. -xv.i H. Cfeuda, Corapvrter r-irc-jlation of Collective
Transports ir. Pla-ras, in Methods in Computational Physics
(Academic Pre^s, Hew York., I'-'l-), Vol. 16, Chapter VIII.
A. ?. Latgdo:., Electromagnetic and Relat ivis t lc Huoerical Models
of Plasmas, ir. Methods ir. Computations! Physi.'s (Academic Press,
New York. 1*>7"5, Vol. 16, Chapter T>:.
C. W. Hlelron, Part icle Co.ie Models for the Vlasov Equation, In
Methods In Computational Physics (Academic Press, New York, 1975),
-22-
Vol. 16, Chapter X.
1*0. J . K i l l e e n and K. D. Marx, The So lu t ion of the Fokker-Planck
Equat ion for a Mirror-Confined Plasma, in Methods i n Computational
Phys ics (Academic P r e s s , New York, 1970), Vol. 9 , pp. 421-489.
1*1. A. H. Futeh, J r . , J . P . Holdren, J . K i l l e e n , and A. A. Mir in ,
Plasma Phys. Ik, 211 (1972) .
1*2. J . D. Ca l l en , R. J . Colchin , R. R. Fowler, P . G. McAlees, and
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Plasma Phys ics and Cont ro l l ed Nuclear Fusion Research, Tokyo,
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1*3. J . K i l l e e n , A. A. Mi r in , and M. E. Rensink, The So lu t ion of t h e
K i n e t i c Equat ions fo r a Mul t i -Spec ie s Plasma, i n Methods i n
Computational Phys ics (Academic P r e s s , Nev York, 1975) , Vol . 16,
Chapter XI.
1*4. H. L. Eerk, e t a l . , Tuo-Energy-Component Toro ida l Fusion Devices ,
paper IAEA-CN-33/G2-3 of IAEA F i f t h Conference on Plasma Phys ics
and Cont ro l l ed Nuclear Fusion Research , Tokyo, November 11-15, 1971*.
" 5 . Thomas H. Johnson, Guiding-Center s i m u l a t i o n of Toro ida l Plasmas,
Ph. C T h e s i s , U n i v e r s i t y of C a l i f o r n i a , Davis , Lawrence Livermore
Laboratory Report UCRL-51725, 1?7*<.
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Phys ics and Cont ro l led Nuclear Fusion Research , Tokyo, November
11-15, n7"*.
N O T i r t
"Tot* report i n prepared »» JM account of work tpmnorcd hy Ihc Urulo] S l i m Government yctthrr the tinned Slate* nor Ik- Uuilcd State* Atonic tncrgy rontrhnuon. nor any ol thai employee*, not my of Iherr contractor*. *twcorHiacton. 01 thru employee*, make* any n m m y . ctpre** or winked, ot av-aimc* anyk»Wh»hi«ly«ic»pon»iliiliiyforlhe»t5™f«y.conifneIcitc« or inefutnci* of any infornution. apparatus product or pwc** dt*do*cd. or rcprctenl* that nv late would not wfrmfle pmalcly-owncd riffil*."