Spatially resolved determination of plasma parameters of a ...noble gas linear MHD generator Citation for published version (APA): Wetzer, J. M. (1984). Spatially resolved determination

Spatially resolved determination of plasma parameters of anoble gas linear MHD generatorCitation for published version (APA):Wetzer, J. M. (1984). Spatially resolved determination of plasma parameters of a noble gas linear MHDgenerator. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR141532

DOI:10.6100/IR141532

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Spatially resolved determination of plasma parameters of a noble gas linear MHD generator

los Wetzer

SPATIALLY RESOL VED DElERMINAll ON OF PLASMA PARAMEIERS OF A

NOBLE GAS LINEARMHD GENERATOR

PROEFSCHRIFT

ter verkrijging van de graad van doctor in de technische wetenschappen aan de Technische

Hogeschool Eindhoven, op gezag van de rector magnificus, Prof.dr. S.T.M.Ackermans, voor een commissie aangewezen door het college

van dekanen in het openbaar te verdedigen op vrijdag 7 september 1984 te 16.00 uur

door JOSEPH MARIA WETZER

geboren te 's-Hertogenbosch

Dit proefschrift is goedgekeurd

door de promotoren:

prof.dr. J.F. Uhlenbusch

prof.dr. L.H.Th. Rietjens

co-promotor:

dr. A. Veefkind

CIP-gegevens

Wetzer, Joseph Maria

Spatially resolved determination of plasma parameters of a noble gas linear MBD generator I Joseph Maria Wetzer. -[s.1. : s.n.] - Ill., fig., tab. Proefschrift Eindhoven. -Met lit. opg., reg. ISBN 90-9000705-9 SISO 662.1 UDC 621.313.52 UGI 650 Trefw.: magnetohydrodynamica I plasmafysica

The éMarf eeee fa1'theP tha:n the giant,

when he has the giant '8 e'houlder to mount on.

(Samuel TayZor CoZeridge 1772-1834}

This WOl'k has been pel'fonned as a pal't of the NSeal'Ch Pf'Ogl'a:m

of the Shock Tube MHD Pl'oject of the DiNct Ene:rogy Con.Ve'I'sion

G:rooup of the Eindhoven Unive:rosity of Techno'logy, the Nethe:ro'landa.

VOORWOORD

Het boekje dat voor U ligt vormt de neerslag van een stuk werk dat de

afgelopen jaren mij en mijn omgeving in niet geringe mate betnvloed

heeft. Naar ik hoop zal het kunnen fungeren als een zinvolle schakel in

de ontwikkeling van MHD conversie-systemen, en meer in bet algemeen van

verantwoorde technieken van energie-voorziening. Ik wil er vooraf ut

nadruk op wijzen dat dit werk niet uitgevoerd bad kunnen worden zonder

de medewerking en ondersteuning van een groot aantal collega's en vrien-

den. Op gevaar af onvolledig te zijn wil ik enkelen met name noemen.

Professor Rietjens bood me de gelegenbeid .om in zijn vakgroep het

werk uit te voeren en bleek telkens weer in staat waar nodig het werk te

voorzien van kritische kanttekeningen zonder het overzicht uit het oog

te verliezen. Professor Ublenbusch vormde tijdens onze wekelijkse dis-

cussies op de vrijdag een voortdurende bron van inspiratie en daadwerke-

lijke steun. Door toedoen van Bram Veefkind leerde ik het vakgebied van

de plasmafysica en de MBD eonversie kennen. Daarnaast was hij gedurende

afstudeer-, en promotie-periode een gedegen en kritische coaeb.

Een groot aantal collega's zowel binnen als buiten de vakgroep

Direkte Energie-omzetting wil ik bedanken voor hun bijdrage aan de uit-

voering van de experimenten en aan de totstandltOIIIing van dit proef-

schrift. Herman Koolmees bediende de schokbuis, bad een stevige band in

ontwerp en constructie van de generatorkanalen en verzorgde het teken-

werk voor het proefschrift. Loek Baede, en in een eerder stadium Beuk

Linders, hielpen de optische opstellingen te realiseren en construeerden

de ontladingskamer. Ad van Iersel fabriceerde de fijnmechanische compo-

nenten, en Kees Knijpers en Jos Nouwen waren verantwoordelijk voor com-

puter en electronica. Bram Bierens was betrokken bij de bediening van de

schokbuis en het opbouwen van de opstellingen. De generatorkanalen wer-

den in de afdelingswerkplaats gemaakt door Jan Bressera en Beuk Mare-

cbal. Henk Rooijakkers (EEA) maakte de ontladingsbuisjes. Het typewerk

was bij Mariet van B.ixtel-Kerlthoff in goede en vlotte banden waardoor

zij een rustgevende factor was in de laatste fase van mijn prqmotie.

De wetenschappelijke staf van de vakgroep ben ik dankbaar voor baar

bijdrage in de vorm van discussies en adviezen. Jos de Baas stelde de

framing foto's beschikbaar die ter illustratie zijn opgenomen in hoofd-

stuk 1. Cees Janaaen, Paul Feron en Gerd-Jan Dijkers leverden door mid-

del van bun stages een bijdrage aan bet promotiewerk.

Behalve voor bnn technische en wetenschappelijke ondersteuning wil

ik alle collega's van de groep, en in bet bijzonder die van bet sebok-

buisproject, bedanken voor de prettige samenwerking en voor de klets.

Buiten het hogeschoolgebeuren heb ik met name in het afgelopen jaar

veel steun en begrip ondervonden van vrienden en vriendinnen. Het is

juist deze hulp die mij in staat stelde het werk af te ronden. Heel in

het bijzonder geldt dat voor Ievon die in al die tijd mij serieuzer nam

dan mijn promotie.

Bedankt •••

Jos Wetzer

September 1984

CONTENTS

SUMMARY 9

1. INTRODUCTION 11

1.1. General introduetion 11

1.2. Diecharge strueture of noble gas linear MBD generator 14

1.3. Present work 16

Raferences 17

2. SHOCK TUBE MBD FACILITY 19

2.1. Introduetion 19

2.2. Deseription of tbe faei1ity 19

2.3. Haasurement of shock tube and generator parauters 23

2.4. Quas1-one-d1mensiona1 model 24

Raferences 27

3. PLASMA DIAGROSTICS 28

3.1. Introduetion 28

3.2. Spectroscopie techniques 28

3.2.1. Radlation mechanisms 28

3.2.2. Evaluation of plasma par81118ters 34

3.2.3. Evalustion of 11ne integrated measurements 37

3.3. Laser beam def1ect1on metbod 38

Raferences 38

3.4. Publ1cat1ons 39

(Pl) Electron dens1ty determ1nat1on in argon 40

cesium MBD plasmas

(P2) Asymmetr1cal Abel inversion of MBD

generator discharges

(P3) Messurement of argon denaity nonun1form1ties

in argon cesium MBD plasmas

50

54

4. STATIONARY ARC 68

4.1. Introduetion 68

4.2. (P4) : Pree burning stationary are fn an at.ospberic 69

cesiua seeded araon plaa.a

S. GEMERATOR BXPEIUMBNTS 88

5.1. Introduetion 88

5.2. (PS) : Microscopie and aacroacopic streaaar peraaetera 89

of a noble &a& linear MBD senerator 5.3. Discussion 109

5.3.1. Effect of the filaaent substructure of the atreaaera 109

5.3.2. Balance equations of the senerator are

llllferencea

6. COliCLIJSIONS

CURRICULUM VITAE

PUBLIC&TIONS IIICLUDBD

(P1) Physica 123 C (1984) P• 247

(P2) IEEE Trans. PS-11 (1983) P• 72 (P3) Subaitted for publication itu IEEE Trana. on Plaaaa Science

(P4) Accepted for pub1ication in: Phyaica C

(P5) 22nd Syap. on Eng. Aap. of MBD, Starkville,

Miaaiaaippi, USA (1984)

111

113

114

118

120

SUMMAR.Y

The discharge structure of noble gas linear MBD generators is strongly

nonunifora. It consiste of area, called streamers, tbat move with ap-

proximately the flow velocity of the working medium. A proper descrip-

tion of the interaction between the flow and the are structure is of

graat importsnee in the understanding and modelling of the MBD generator

performance. Deacription of the transport properties and of the mecha-

nisms of momentua and energy transfer requirea detailed knowledge of the

parameters of the discharge structure. It is tbe sim of this work to

provide detailed expertmental inforaation on these parameters.

A set of diagnostic techniques bas been developed for tbe spatially

reaolved determination of streamer parametera of a noble gas linear MBD

generator. The work.ing medium is an atmospberic cesium-seeded argon

plasma. The diagnostics involve spectroscopie tecbniques, and a quantt-

tative achlieren teehuiqua called the laser beam deflection method. The

methode are described and, as far as needed, have been verified in auz-

iliary experiment&. Specia~ attention. is paid to the requirements with

respect to spattal and temporal resolution. An advsneed reconstruction

technique bas been developed to derive the spattal distributton of plas-

ma parametera from stereoscopie radlation aeasurements.

The spectroscopie techniques have been applied to a free burning

stationary are in an atmospheric cesium-seeded argon plasma at currents

between 1 and 4 A. Using the expertmental data the balsnee equations of

electrous and hesvy particles have been solved. The investigation of the

stationary are provides inforaation on the accuracy of the diagnoetic

techniquea, and on tbe transport properties involved. Furtber it is used

to gain insigbt in some of the meebanisme governing the energy balsnees

of area at atmoapheric presaure.

The whole set of diagnoetic techniques bas been employed to e%8mine

the diacharge atructure of a shock tube MBD generator. The measurements

provide inforastion on the number of streamers as well as on their mi-

9

croscopie and macroscopie parameters. Tbe densities and teaperatures of

electrous and heavy partieles are regarded as microscopie par-ters.

Streamer size and sbape. streamer current and the streaaer propagation

velocity are defined as the macroscopie par-tere. Tbe dependenee of

streamer parameters on oparating eonditions bas been investigated. Tbe

expertmental results have been eompared with those obtained with the

blow down facility of the EUT.

Tbs eonsisteney of the measured set of parameters bas been investi-

gated taking into eonsideration the effect of the observed substructure.

Furtber tbe experiment& provide iuformation on tbs meebanisms governing

the balsnee equations of the MBD generator are.

10

CHAPTER 1

INTRODUCTION

1.1. General introduetion

The conversion of heat into electrica1 energy plays a prominent ro1e in

our modern- society. The optimization of the efficiency of this conver-

sion process is of graat economical, environments! and politica! inter-

est. Aecording to the secoud law of thermodynamica the maximum attain-

ab1e efficiency, as given by the Carnot efficiency, is determined by the

tempersture at which the heat is supplied to the conversion system (T 1)

and tbe tempersture at whicb the beat is carried off (T2). The conven-

tional way to couvert heat into e1ectrical energy on a large àcale is by

using a steam power plant. In the corresponding Carnot cycle T2 is the

tempersture of tbe cooling water (300 K) end T1 is 1imited to a value of

800 K due to the requirements imposed by the steam turbine. Hence the

Carnot efficiency is 62%. At present an efficiency of 38% can be obtain-

ed in an advsneed steam power plant, and no substantial impravement is

expected from further developments of the steam cycle. The total effi-

ciency can be increased by uslng an MBD topping cycle in combination

with the steam cycle. Because in an MBD generator beat is converted

directly into electrical energy, without the interpos i ti on of moving

machanical components, the permissib1e initial tempersture is higher.

When leeving tbe MBD generator tbe working medium can serve as tbe heat

souree for the steam cycle. Saveral studies have indicated that in this

way an overall efficiency approaching 50% can be. achieved (see e.g.

[ 1]).

MBD power generation is based on tbe expansion of a heated, elec-

trically conducting fluid tbrougb a 111agnetic fi_eld. The charge carriers

are subject to a Lorentz force. As a consequence an electric field is

established. When losding this field with a resistor, e1ectrica1 power

is supplied to the external circuit. The two most important types of MBD

power systeme are the open cycle and the closed cycle generator.

11

In an open cycle system the working mediWII consists of gassous

fossil fuel COllibustion products, seeded with sn alkali metal. In order

to attain sufficient electrical conductivity the fluid must be heated to

about 2700 K. In the last decade large progress has been achieved in the

field of open cycle MBD conversion [ 2). Tbe construction of the first

cOIIIIIISrcial MBD steam power plant bas been initiated in l!1àzan, near

Moscow, in the USSR. In the USA two ujor test facilities are avail-

able, the eo_,onent Development and lntegration Pacility in Montana, and

the Coal Pired Flow Pacili~y in Tennessee. Tbe aim is to provide the

necessary inforution for the design of a cOIIIIIISrcial prototype plant,

the Engineering Test Paeility. Tbis program however bas been seriously

delayed by the restrietion of the US government budget.

The working mediwa of a closed eyele MBD generator is sn alkali-

seeded noble gas. As was first suggested by Kerrebrock [3] this type of

generator ean work in a two tempersture regime: the electron tempersture

is elevated above the gas temperature. In this way the minimoa gas tem-

persture required in a closed eycle generator ean be approximately 700 K

lower than in an open cyele generator. After supplying energy to the MBD

generator and to the subsequent steam eycle, the working medium is fed

back to the heat aouree.

The MBD research program carried out at the Eindhoven Univarsity of

Tecbnology is eogaged on closed cycle MBD conversion. In 1975 large enthalpy extraction (over 20%) was reported in shock tube MBD generator

experiments [4]. These results were obtained at relatively high stagna-

tion temperatures up to 3000 K and during a test time of 5 as. The IIISg-

netie induetion, provided by sn air eo11 msgnet, was 3.5 T. The next

step was the design and building of an MBD blow down faeiU.ty, whieh

came into operation in 1980. In this faeility the hot flow, beving a

tempersture of 2000 K, is produeed by a fossil fuel fired heat exchans-

er. The attainable magnatie induction is 5 T, and is provided by a cryo-

genie magnet. Tbe test time is 10 s. An enthalpie efficiency of 7% bas been achieved [5]. At present the Southern California Edison Company is

considering to retrofit the Etiwanda Power Station in Californta, USA,

with a closed cycle MBD topping cycle.

Apart from the distinction made for the working medium, snother

distinction can be made with regard to the generator channel, wbich may be linear of disk-shaped, and with regard to the type of loading. This

can be illustrated by Ohm's law:

12

E* x B ..1 .. _a_ {E* - e =--=}

l + 1!2 - B (1)

with !* • ! +~x !· Here J. is the electrical current density, ! is the electdeal field strength, ~ is the flow velocity and ! is the magnette induction. Note that the velocity is perpendicular to the magnatie

field. The electrical conduetivity a and the Hall-parameter f! are given 2 - - -

by a • nee /meveb and f! • ~e/veh • eB/meveb' ne is the electron density, e and m are the electran's charge and mass respectively, and v h is the e e averaged momentum transfer collision frequency for collisions of elec-

trous with heavy particles.

R

Fig 1. Schematie ll'iew of Unear MHD ehanneZ

of the aegmented Faraàay type.

13

It ia aeen that the electdeal field consiste of a Faraday-,component,

perpendicular to the flow velocity ~ and the magnette inductio~ !• and a Hall-component in the flow direction. In a linear channel the Faraday

field as well as the Hall field can be loaded to extract electrical

power. In a disk channel the flow is radial, the Faraday current is

tangentlal and closed in itself, and the Hall field is used for power

extraction.

The work preaented bere concerns the plasma of a cloaed cycle lin-

ear MBD generator of the aegmented Faraday type, illuatrated in figure

1. The experiment& have been performed with a shock tube MBD generator,

with an atmospheric cesium-seeded argon plasma as the working fluid.

1.2. Discharge structure of noble sas linear MBD senerator

The current density in noble gas linear MBD generators is not uniformly

distributed. Earlier 1nvestigations have shown that the current is con-

centrated in area, called streamers, that move witb approximately tbe

flow velocity [6, 7, 8]. This discharge strueture can be visualized by

fast framing fotography perpendicular to the flow direction. Figure 2

shows the discharge structure for three different sets of operating

conditions corresponding to increasing levels of supplied power. The

pictures were taken through large windows in the insuiator walls using

an image convertor camera. It is clearly shown that the area are bent

out by the flow, and that the are structure varles strongly with oparat-

ing conditions. Further it is observed that the arcs exhibit a substruc-

ture, consisting of filaaents, wbich gets more pronounced at higher

power levels. The same picture ean be obtained from radlation messure-

meuts pedormed along an optical axis parallel to the magnetic field.

Figure 3 shows time resolved line emission measurements which,have been

performed simultaneously with the framing pictures of figure 2.

Inslde the area the electron tempersture ia elevated over the gas

tempersture and a substantial degree of tonization of the seed is estab-

liahed. Hence an increase of electrical conductivity is achieved yield-

ing current densities in the order of 105 A/m2, As a result the dia-

charge exerts a pronounced decalerating force upon the flow. Earlier

work bas indicated that a proper description of the interaction between

flow and are structure is of graat importsnee in the understanding and

modelling of the MBD generator performance [7, 9]. Deseription of the

transport properties and of the momentum and energy transfer meehaniams

14

B

T s

n

2.3 T

2400 K

8 . 2 %

B 3. 3 T

T 2680 K s

n 16.9 %

~·~~~

'(\,""' ~, \ ~ B 3.4 T

T 32SO K s

n 21.2 %

15

Figure 2.

Framing pictures of the

discharge st:ructu:re for

three sets of conditions

corresponding to increasing

power extraction levels

(the flow velocity is from

right to left, the magnetic

induction is pe:rpendicula:r

to the plane of the picture) .

B = magnetic induction T

8 = stagnation temperature

n = enthalpie efficiency

requires detailed information on the parameters of the discharge struc-

ture. In this work the detailed experimental determination of these

parameters, time and space resolved, is pursued.

line emission so ...

Fig 3. Line emission signaZ for three sets of conditions

corresponding to different power extraction ZeveZs

(B = magnetic induction, T8 = stagnation temperature,

n =enthalpie efficiency) .

1.3. Present work

The aim of the present work is to provide experimental information on

the discharge structure of noble gas Unear MHD generators. For this

purpose a set of diagnostic techniques has been developed. The diagnos-

tics involve spectroscopie methods aod a quantitative achlieren method.

16

Tbe undèrlying mechanisms and the evalustion are discuseed and, as far

as needed, have been verified in auxiliary experimenta. Special atten-

tion bas been payed to the requirements With respect to apatial and

temporal reaolution imposed by the characteriatic size and propagation

velocity of the area. Further stereoscopie radietion measurementa have

been performed and an advsneed analyzing technique bas been developed in

order to derive the spattal distributton of plasma parameters.

The spectroscopie tecbniques have been applied to a free burning

stationary are in an atsospheric ceaium-seeded argon plasma. Using the

expertmental data the balsnee equations of electrous and heavy particles

have been solved. The purpose of this auxiliary experiment is threefold.

First the modelling of the stationary are ia regarded as a first step in

the development of generator are modela. Further the balsnee equationa

provide a check on the expertmental data and on the diagnoetics used.

Finally this investigation is important in the study of the transport

coefficienta of partially ionized, MBD-like, plasmaa.

The generator experimenta have been performed With a shock tube MBD

generator. The meaaurements provide information on tbe nuaber of stream-

era as well as on their microscopie end macroscopie parameters. As mi-croscopie parameters are regarded the denaities and temperatures of

electrous end heavy particles. Streamer size and shape, streamer current

and streamer velocity are defined as the macroscopie parueters. The

dependenee of streamer parameters on operating conditiona bas been in-

vestigated.

The expertmental results have, as far as poaaible, been compared

with those obtained in the blow down experiment. The consisteney of the

measured set of are parameters bas been investigated. From the expert-

mental data conclusiona are drawn on the mechanisme governing tbe bal-

snee equations of tbe MBD generator are. Further tbe effect of the ob-

served substructure on tbe measured parameters is discusaed.

Tbe major part of tbis thesis is eontained in five publications.

They will be referred to as Pl u.i. P5 and are included in the sections

3.4 (Pl, P2, P3), 4.2 (P4) and 5.2 (P5).

Refereneea

[1] G.R. Seikel, et al., 15tb Symp. on Eng. Aspects of MBD, Pennsyl-

vania, USA (1976) III.4.

17

[2] L.B.Tb. lietjeus, Phys. Bl. 39 (1983) P• 207.

[3] J.L. lCeuebroelt, 2nd Symp. on Eng. Asp. of MBD, Pbiladelphia, Peun-

sylvania (1961) p. 327.

[ 4} J.H. Bloa, et al., 6th Int. Conf. on MBD Electdeal Power Genera-

tion, Washington DC (1975) III.73.

[5] P. Hassee, et al., 20th Symp. on Bng. Aspeeta of MBD, Irvine, Cali-

fornia (1982) P• 7.4.

[6] W.M. Bellebrekera, Instability analysis in a nonequilibriu. MBD

generator, Ph.D. thesis, Bindhoven Univeraity of Teehnology (1980).

[7] A.r.c. Sens, et al •• 20tb Syap. on Ins. Aspeeta of MBD, Irvine, California (1982) p. 10.6.

[8] A. Veefltind, et al., AIAA J.14 (1976) p. 1118.

[ 9] B.J. Fliusenberg, l'oa81l fnel fired elosed eyele MBD pover

generating experiaenta, Ph.D. theaia, Eindhoven Univèraity of Teehnology (198~)·

18

CBAPTBR 2

SHOCK TUBE MBD J'ACILITY

2.1. Introduetion

Tb• generator experimente described in thie worlr. have beea perfor.ecl

w1 th a shoclr. tube MBD generator [ 1]. !he shoclr. tube provides tbe hot gaa

required in the conversion procees. The ceaiua-aeeded argon test gas is

compressed by the ahoclr. wave to a preesure of 9 bar end ia tben expanded

through a supersoaie nozzle iato a eliverging geaerator ebanael. 'rlle

stagnation teapersture eau he varled froa 1750 up to 3500 lt. Tbe aa:a::l-

attainable tberaal input power nouuts 5 MW. Typtcal flow propertiea in

the MBD channel are: aass flow i • 3 lr.g/a, flow duration t • 5 •• exp velocity V .. 1000 a/a, preesure p - o.t t 1 bar, gas teapersture T -1000 K, aass density p • 0.3 kg/a3 and seedratio s • ne/nAr • 0.05%.

Tbe aagnetic field is provided by an air coil aagaet anergised by a

capacitor bank. The aa:a:i'lti.UIII attainable IIISgnetic induction is 3.5 T over

5 ms. In the subaequent sections the facility including the perforaance

diagnoetics will be described. Furtber a quaai-one-dimensional aodel of

the generator flow will be presented. It provides an approziaate, de-

aeription of the flow properties.

2.2. Description of the faeility

Tbe shoclr. tube fadlity is sch-tically sbown in tigure 1. The shoclr.

tube bas a dia.eter of 22.4 ca end consiste of a driver section, a dia-

phrap sect1on end a test section. The test section 18 f1lle4 with argon

which ia blown through a furnsce contaiain& saturate4 cesiua vapor. The

seed ratio is controlled by the furnace teapareture which daterainas the

vapour prassure. Tbe driver section is fitlei with heliua to a preesure

of 11 bar. Test section end driver section are saparateel by the dia-

phrap aection by Mans of tvo aluainua diaphragaa. Th1s aeetion is

fitled with heliUIII to a preesure of 5.5 bar and 18 separated froa a

"_ vesael by aeans of a Helinex diaphrap•

19

Fig 1. Shook tube MHD facnUty.

'!he upert.ent is initiated by the controlled rupture of the Melinex

diaphraaa. Due to the-faat preesure drop the alUidnua diaphragms buret.

As a reault a shock ia senerated wbich propasstea throush the teat aec-

tion and is reflected by the end plate of ths shock tube. The stagnation

region bebind the reflected shock acta as a reservoir of hot gas. The

shock tube ia opera~ed in tbe tailored interface .ade, hence the sound

veloeities in the driver sas and in the teat gas are equal [2]. A teat tille of S 1118 ia provided.

'•

A acbe.atic view of the l1near chennel ia preaented in figure 2. A

aaooth transition fros the teat aection through aupereonic nozsle to

ehennel inlet preventa the aceurenee of vorttees thet othervtae appear

at edsea [3]. The f1rat half of the chennel ia equiped with flat elec-

trades fluah to the walls. '!he effect of current eoncentration on elec-

trode edses is redueed by uaing a laqe nuaber of electrades per unit

length of cbannel. ror c

sure transdueers, voltage probes and small windove are mounted. The load

reaiatanee is S Q in the first half of the ehannel, and 1 Q in the sec-

oud half, tbus providing a constant loading per unit leugth. Further

details are given in figure 2.

I···

-0.15 • 11,4 ••• X(MI

Tbe gas par8118ters detendning the input conditions of the MBD

eonversion proeeaa are stagnation preesure p8

and stagnation t~erature

T8

• Tbe foraer is aeaaured, tbe latter is derived froa the iaentrop1e

shock relations ·and the Maanred shock velocity [2]. In the subaequent

part of this aeetion indices 1, 2 and 3 indieate the properties of the

sas in front of the incident shock, bebind the incident shock, and bebind the refleeted shock. This ia illuatrated with the ti• diatanee

diagraa of figure 3. The stagnation preesure and stagnation t~rature

are related to the aetual presaura Ps and t~rature T 3 aecording

..2/ 2.5 Pa - p3(l + ~ 3> .. p3 (1)

1 2 T8 • T3 + 2 u3/ep (2)

21

Fig 3. Time distanoe diagram of the shock

propagation in the test section.

Bence the aeasured preesure p3 equals the stagnation preesure p8• When

the shock tube end is closed the gas behind the reflected shock is at

rest (u3 • 0) and the stagnation teapersture is given by

(3)

where T1 is rooa teapersture and M8 is the shock Mach nuaber, whieh is

calculated from the aeasured shock velocity i8

according to

(4)

In the generator experiaent the gas bebind the reflected shock is not at

rest because of an outward flow to the generator channel. Introducing a

factor ~ • u3/u2 the stagnation teapersture is now given by

(5)

22

u2 and P2 are caleulated from the measured values for T 1' p2 end i 8 (or

K8). aeeording to

(6)

(7)

(8)

a end Xsa are derived from en itarative proeedure using

(9)

end

(10)

The stagnation te~~perature ean he varled by ebanging tbe shock Jfaeh

somber M8

• This is echieveel by varying the f1111ng pressure p1 of the

test gas. In order to aaintain tailored interface at various teat pres-

suras the sound velocity in the hel:f.UIIl driver gas is adjusted by aclcli-

tion of argon.

%.3. Meesurement of shock tube end generator paremeters

A uu.ber of diagnosties is used to obtain inforaation on the flow prop-

erties end tbe generator perforasnee of the shock tube MBD generator.

The inlet eonditions of the MBD ehannel are determined by the stagnation

preesure and stagnation teilpersture of the test ges. They are obtained

from presaura meaeurements in the test seetion using the issntropie

shock equations preeenteel in section 2.%. ln the test seetion three

pieao-eleetric pressure transducers are mounted. one neer the diaphras-

eeetion and two neer the end plate in the stagnation region. The inci-

dent shock velocity i8

is deterained froa tbe time delay between the stepvisa presaura increments at two different poaitions. Purther tbe

pressure bebind the rafleeteel shoCk (p3 • p8 ) sa well as the presaura

23

bebind the incident shock (p2 ) is involved. Thia requires tf.ee resolved

-~~r-nta.

In the senerator channel piezo-resistive preasure transclueers are

1100nted near the inlet and near the outlet. The voltage over a -ber of

load reelstors ia measured yielding the electrode eurrenta aud the Fara-

day voltage. The Hall field is deter.ined froa voltage differences ba-

tween electrades at·different positiona. Further at two locationa volt-

age probea are llOUDted flush in the diverging walla batween anode aud

catbode to eeasure the potentlal distribution. Froa this the indoeed

field and the voltage drop can be determined. The .. gnetic iudnetion ia

eeasured uaing a calibrated coil.

All signsls are aaplified and fed to a PDP ca.puter, saapled with a

rata of 10 kHz aud stored. The plas .. and atre-r properties are deter-

.tned froa optical diagnosties. These diagnoetics Will ba prasented and diacnssed in detail in cbapter 3 •

. 2.4. Qu!si-one-diunsional IIIOdel

Tbe flow properties of the linear MBD channel are calcnlated froa a

quasi-one-d.i-ional IlOdel preasnted aarlier bY Bloa [ 6 J. This IlOdel does not include the at-r-like current eoncentration aud thna pro-

vides only au. approd.•te descriptiou.. The geoeetry of fignre 4 ia naad.

Der:lvat:lves and vel~:lty coaponents in y and z direettoa are nealected.

It is assuaed that the effect of frietiou. and eonduetive heat loss is

preseu.t only u.ear the wslls. These effects are seeared out over the

periphery C of the cross section À. Af ter integration over i the crosa section the conservetion equatione of maaa, aoaentua and entbalpy read

[6]

d: (puA) • 0 dn

pu di

pu!!!!. eb

s l 2 [ 1 with H • 2 RT + 2 u • The shear stress Tw ia given bY 6

24

(11)

(12)

(13)

With

at'ld

R

Fig 4. Geornetey used in the

quari-one-di1113nsionaZ mode Z.

c -0.058 &e-0•2 f x

.,_ x+ i1 ""'x • pu-ll--

(14)

(15)

(16)

Bere cf is the friction coefficient. Rex is the loca1 Reyno1ds nuaber

and i1 is the distance between the throat of the nozzle and the channe1

inlet. Tbe vlscosity n is taken from [7]. The heat flux to the walls ~ is given by [ 6]

(17)

wlth

25

(18)

au.d

Nu • o.023 ae0•8 x x (19}

Here ax is the heat transfer eoeffielent and Nux is the loeal Husselt m~~aber. The theX'IIIIll eonduetivity À ls taken froa [7 j. The set of equs-tlons is eoap1eted with the equstlon of state

(20)

The averapd eurrent denslty jy is deterained froa the 11eaaured e1eetrl-

cal. current. The electrlcal power dens:l.ty JYJ.Y is eale~tlated froa the

power dlsslpated in the load reslstors, Pel,l • "r_,l I~. The. resllltlus set of differentlal equtlons la solved n-rleally

startlus froa the condltlona at the ehannel lnlet. These eondltlons are

ealcolated froa equatlons 11, 12, 13 and 20, wlth zero electrleal cor-

rent, startlus at x • xl which is l ca downstreillil of the nozzle throat.

To avold n-rical prob1ell8 around M • l, the firat eentiaeter la re-garded lsentropic,and the flow properties at x • xl are cale~tlated froa

the properties in the tbroat (index t) ~tslus

(21)

wl tb !!; • 4 I (M!1 + 3} • The Mach m111.ber Mxl at x • xl is ca1culated . froa the cross aeetlon ratio

2 Axl 1 Mx1+ 3 2 Ç ~ Mxl (--4-} (22)

The eonditions ln the throat are determined froa the stagnation condl-

tlons using the lsentropic relatlons

(23)

26

witb Y • S/3.

The produced electdeal power Pel is caleulated from tbe measured

electrode currents

The tbermal input power Pth is given by

where the mass flow à is

Hence the (enthalpie) efficiency is calculated froa

lleferences

[1] A. Veefkind, et al., AIAA J.l4 {1976) p. 1118.

[2] H. Oertel, Stossrohre, Springer Verlag, Vienna (1966).

\ (24)

(25)

{26)

(27)

[3] A.r.c. Sens, et al., 20th Symp. on Eng. Aap. of MBD, lrvine, CN (1982) P• 10.6.

[ 4] A. Veefkind, et al., 19th Syap. on Eng. Asp. of MBD, Tullahou, TN

(1981) P• 7.3.

(5] J.M. Wetzer, IEEE Trans. PS.-11 (1983) P• 72.

[6] J.B. Blom, Relezation Phenoaena in an MBD generator With pre-ionis-

er, Ph.D. thesis, Eindhoven Univarsity of Technology (1973).

[7] VDI-wlrmeatlas, VDI-Yerlag (1974) DUsseldorf.

27

CHAPTEB. 3

PLASMA DIAGNOSTICS

3.1. Introduetion

In this ehspter the optica! plaSlila diaposties thst hsve been used in

thia worlt, eonsisttoa of spectroscopie teehniques and a achlieren teeh- .

nique, will be preaented. The spectroscopie teehniques iuvolve abaorp-

tion, line intenaities and line profile&, and contin- elliasion. The

meehsnill!lla wUl be described and the evalustion of plana psraaetera

will be diaeussed. Purther, sinee these methode provide line integrated

data, attention ia psid to reconstruetion techniquea to obtain apatially

resolved inforaation. A qusntitative achlieren -thod called. the laser

beaa defleetion metbod will bè deseribed.

An hlportant part of this chspter ia contained in three publies-

tions which will be referred to as Pl, P2 aod P3. They are included at

the end of thia chspter. The titles are:

[Pl] Electron density deterlllination in arson eest .. HBD plasaas

( P2] Aa:v-etrical Abel inversion of HBD senerator diachsqes

[P3] Kaasurement of arson deneity nonuniforalties in argon cesium MBD

plasaaa.

3.2. Spectroscopie technisues

3.2 .1. !&.A!!ll~l!!!!!!! The spectroscopie techniquea are based on the speetral properties of the

cesium sta. whieh is the only optically active coqponent in the plasaa.

The temperaturea involved are too low (Te ~ 5000 K) for significsnt

excitation or tonization of argon stoms. The followiq meehanisaa are

used to obtain inforaation on plasaa parameters: absorption of resonant

light by ground state atoms, emisaion by apontaneous radiative transi-

28

tions between excited states, and continuum emission originatins froa

the recombination of electron& with cesium atoms.

Absorption

The absorption messurement is performed b1 irradiation of the plasma and aeasurement of the tranamitted light. The light souree is a xenon laap

with a continuons spectrum in the near intra-red. The radlation is de-

tected in the red wing of the 8521 A line which corresponds to the 6s112

- 6P312 transition of cesium. The energy diagr- is shown in ligure 1.

s I P I D I F I G 4 1-

E leV)

3 ___.!!_ &&

------z - &D

lP 312

1 p••m - ,.. !11$

0 IS 1/2

Fig 1. Ene1!'(JY diagram of the cesium atom.

The aeasu.red light is analyzed with the one-diaenaional equatioa of

radiative transfer

(1)

Bere IA is the intensity, eA is the plasaa emissivity and ltA is the

absorption coefficient. The geometry of figure 2 is used.

29

, .....

8 1 x

l?ig 2. Geometry ueeil in the eva"tuation of

the equation of m.diative tronafeP.

The so1ut1on of equation (1) with t 1 (o) as the boundary eondition

yle1ds

with

and

1 Ir(1)- I CA(x) ezp {-TA(x)}dx

0

1 T1(x) • I k1(x')dx' x

(2)

(3)

(4)

. Ir(1) ls the eontrlbution of the plasma emiaslon to the measured lnten-

sity. By chopping the incident beam, the plasma intensity is determined

and tben subtraeted from the total llîeasured intensity yleldlng tbe

transmltted part of the incident intensity. I 1(o) is measured separate-

ly. Renee the transmission of the plasma is determined from:

(5)

30

In case of a hoaogeneous plasma -r,_(o) • k,_l with k,_ • n~ q,_. Then tbe cesium ground state denaity n~s can be obtained froa thestransaisaion if the cross section for absorption at wavelength A, Q,_, is known. This cross section is given by

(6)

where f is the absorption oscillator strength and P(A) is the normalized

line profile. The profile of the 8521 A line of cesium is doainsted by

van der Waals broadening and bas a Lorentzian shape near tbe line centre

[1]. In the wings however large deviationa froa the Lorentzian profile

aay occur. Chen and Phelps' [2] observed that tbe absorption coeffieient

k,_ ia proportional to both argon and cesiua dens1ty. Therefore t,. • k,_lnArnCs is a funct1on of wave-length and tempersture only. In the near

wing t,_ is independent on teapersture [3). In tbe far wing the profile shows a moderate tempersture dependenee exeept near satellites wbere tbe

dependenee is strong. These aatellites are due to rotationsl and Vibra-

tional transitiona of tbe CsAr molecule which is formed [3 ]. Sucb a

satellite occurs in the blue wing of the 8521 A line at 200 A froa tbe line centra. The present experiaents have baen perforaed in the red

wing, and the tempersture dependenee haa been negleeted. The profile of

t,. bas baen measured in a homogeneons argon cesioa af.xture with saturat-ed vapor,. using tbe vessel described in chapter 4. Tbe reaalt is given

in figure 3 together with the profile obtained by Chen and Pbelps [2].

Both experiaents have been performed at temperatures batween 400 and

500 K, and tbe agreeaent is good.

The evalustion of equation (5) presented bere is valid only if tbe

plasma is boaogeneous. The aeasure .. nt is carried out in the stagnation

region of the shock tuba. The set-up used is given in f1gure 4. Tbe

wavelength is 8621 A whieh is 100 A from tbe line centre. For this

choice the transaf.ssion is in tbe order of o.s.

Line eaf.saion

Line eaf.ssion originetea froa the spontaneoos transition of an atoa.froa

an excited state u to a lower state 1. The eaf.ssivity is given by

31

trf trf kA

8Cs

8Ar 1!1 HEB N.INO ( .. s, C!) BLUF N.INO

...... 10

1 Hf .. I • •

~~ ~--~~~~LU~~~~~~~~~;~ 10

1 A- A

0 I ll (j'

Fig 3. Reduced absoPption coefficient ve%'6UB 14a!Je-Zength

7l'IM8UZ'6d a;t; a t61l'fplarature of 400 - 600 K. Dots: this ûlOZ'k

D:M.lm Une: Chen and Phelps [2].

crass Metion llttcktube

Fig 4. Set up used in the absoPption meas'UI'ement.

32

(7)

where n11 la the populatlon denaity of exeited state u, P(A) la the nor-

malized line profile and A111 ia the transition probability

(8)

Bere f 111 is the absorption oscillator atrength. Valnes for f 111 are taken

from Fabry [ 4 J. Measureaent of line emiasion usually concerns the line profile or

the total line intenaity, integrated over the profile. In the plasu

under eonaideration the line profile is governed by preesure broadening.

The perturbing partieles may be neutral cesium atoma (reaonant broaden-

ing), neutral argon atoma (van der Waals brnadening) or ebarged parti-

cles (Stark broadening). These 111eehanisu are described in [Pl ]. For

uny linea of cesiWII the linewidth ia not very amall c0111pared with the

monochromator profile. Therefore meaaure111ent of the total line intenaity

involvea a correction for thia instraental profile. The following for-

III.Ola ia derived (see figure 5)

k_ 2 2A~ 1 A\ { A~ 2} 1tot • ; aretau ( A\) - 211 A~ ln 1 + (2 "\) (9)

Bere Itot ia the total line intenaity, Iexp is the maxiqua intensity

obaerved, AAM is the halfwidth of the monochromator profile and "\ is

the halfwidth of the line profile. The correction involves not only the

effect of the cutting off of the line wings (like in [ 5 ]>, but also the ahape of the instrnmental profile. For the latter a triangular shape is

aSaUIIled, and for the line profile a Lorentzian abape is uaed. The eor-

reetneas of the asaWIIptions on ahape bas been verified experimentally.

When the speetral linea are absorbed the evalustion of line inten-

aities and line profiles beeomea more elaborate, eapeelally in case of

inhomogeneons plaamas. The eaiasion experiaenta described in this work

are reatrieted to tranaitlona for whieb the plasma is optieally tbtn.

33

10 2

l !!!1 ~ t,., 7.5 t.75 M 5 t.5

Fig. 6. Cor:r.oeation fatrl;or for Une intensities due

to instrumentat profile (Lorentz.ia:n U.ne

proflte. triangu'Lar monochromator profile).

Continuum emission

Contionum eadssion originates aainly. from the reeoabination of electrous

with cesium ions. Thia meehan1B11l, and its applieation to tbe electron

density deteraination is discuseed in detail in [Pl].

3. 2. 2. !!!!!!!~..!!!..!!!!!!U!!!!!!!!:!!! The cesium denaity is evaluated from the abaorption aeasureaent in tbe

stagnation region as described in the previous seetion. In the analysis

it ia assumed that tbe seed ratio a • nC8

/nAr. established in the stagna-

tion region is maintained tbraughout the generator.

The eleetl'on denaity ia evaluated from tbe eontinuum intenaity

aethod. In [ Pl] tbia metbod bas been eompared experimantally witb a

metbod invalving the Stark broadening of speetral linea. Tbis experiment

bas been performed witb a atationary are and agreement within 20% is

found. Furtber it bas been sbown that near the wave-lengtbs of measure-

ment tbe eontinuum is not affeeted by molecular eontributiona.

34

Three metbods of electron tempersture determination have been com-

pared: tbe relative continuum intensity metbod, the relative line inten-

sity metbod and tbe line to continuum ratio. In the relativa contionum

intensity metbod recombination radlation is meaaured at two wavelengtbs

and the tempersture is evaluated from [Pl]

(10)

The wavelengtbs naed are A1 • 4900 A . and A2 • 4100 A. Above 5010 A the

contionum intensity drops sharply because there recombination to the

first excited state (6P) ia no longer involved. Below 3190 A the inten-

sity rises sharply beeause of recombinstion into the ground state (68).

Messurement in the ultra-violet bowever requirea special techniques. Por

this reason measurements are carried out at wavelengtbs above 3190 A.

Because tbe intenaity decrellees strongly with decreasing w•velength,

4100 A is chosen as tbe lower value. Purtber, by tbis choiee of w•ve-

lengtbs line radlation is avoided. Prom equation (10) it follows thllt

tbis metbod is not very sensitive to tbe electron temper•ture.

In tbe evalustion of line intenstties PLTE is assumed, hence the

populations of different excited statea are related llecording to the

Boltzmann f•ctor

(11)

Tbe tempersture is usually obtained from tbe plot of ln(~/~) versus

Ek' the slope of whicb gives the tempersture (an exsmple is presented in

chapter 4, tigure 9). Also this metbod ia not very aensitive to the

electron tempersture aince the range of useful ~ valnes is limited.

Transitions from excited statea with low ~ are subject to a substantial

absorption and may not be in partlal equilibrium. Transitions from lev-

els with high Ek combine • low intensity and a large broadening. Both

effects reduce the accuracy of the excited state density determination.

A complication in c•se of generator experimenta is that all transitions

involved have to be measured simnltllneously.

The metbod used 1n'4~his ~rk to determine the electron temperat:ure is tbe line to eont:inuua ratio. Also tbia metbod involves tbe aaaumpt:ion

on PLTE througb

35

(12)

This metbod is signifieantly more sensitive to the electron temperature

tban the other methode discussed, yie1dins better accuracies. When de-

termining Te fro• the ratio of two intensities e12 • e1te2, a aaesure for the sensitivity is + given by

dT d812 dT 812 + '" 1 • d8 e • Te

e 12 12

.----------..------,--. 1

z 0 .... 1-u z :::I .... >- .s 1- .s .... > -1-.... CD :z

·W m. Ht.f CD

• llCJ'

• LCH

0 ~-----~------~0 0 2500 5000

ELECTRON TEMPERATURE (KI

Pig 6. Relative eensitivity funation 1/J for> Pelative

Une inteneity method (RLI)~ r>elative aontinuum

inteneity method (RCI) and line to aontinuum

Ntio (LCR). Note that the eeneitivity gete

better> as 111 deaNaaes.

Data: RLI: Eu 3. 6 eV; 'Ez = 3.2 eV. RCI: À1 = 4900 R; Àz 4100 R. LCR: À(aont) = 4900 i;

À(line) = 5664 i (6P112

-sv312J.

36

(13)

Note that tbe sens1t1vity (or accuracy) gets better as + decreases. For tbe relative continuum 1ntensity metbod and for the relativa line inten-

sity metbod we find + • Te/c wbere c ia a constant depeoding on the wavelengtbs or transitloos involved. Por the line to continuum ratio + • Te/(1.5 Te+ c). Typtcal curves of +versus T

8 are given in figure 6.

Above 1500 K the line to continuum ratio provides an essentia11y better

aecuracy.

The assumption on PLTE bas been eheeked with the criterion of

Thorne [ 6]

-3 111 (14)

Bere AE ia the energy differenee in eV between the state in qnestion aod

any neighbouring state to whieh it cao make transitions. For tbe exe1ted

statea involved in tbe teapersture determ1nat1on AE is smaller than 0.25

eV. For temperatures up to 5000 K we find as PLTE require.ent that n8

>>

2 x 1018 m-3, whieb is easily fulfilled. Also the eharaeteristic time

for estsbUshing PLTE eood1t1one (• 10 1,111) is short e011pared to tbe

transit time (• 1 ma) of the flow in the MBD-generator as bas been shown

by Borghi, Veefkind and Wetzer [7]. Further inhomogeneities might affect

tbe validity of the PLTE assumption. This however oeeurs aainly for the

lover levels.

3.2. 3. !!'!!!!!!!!!!!~L!~~~!!I!!.!:!~-!!!!!L~.-!!! All spectroscopie measurements presented provide line integrated infor-

mation. Reeonstruction teehniques are used to obtain the loeal valnes

inside the are. Apart from the homogeneons situation the simplest case

is a eylindrieally symmetrie diseharge, like the one investigated in

ehapter 4. In that case the well known Abel inversion metbod cao be

applied to reeoostmet radial profiles (see for example [8]). An exten-sion of tbis metbod is the asymmetrie Abel inversion presented by Yasn-

tomo [ 9] whicb sllows for an asymmetry perpeodicular to the line of

sigbt. A limitation of tbis teehnique is that at increasing distance

from tbe are eentre the solution relaxes to a cylindrical solution. KHD

generator discharges bovever exbibit a 110re or leas elliptieal cross

section [ 10]. Silllilar ahapas have been found for balsneed discharges iu

presenee of a flow aod a aagnetie field by Uhlenbuseh [11] and by lloun

and Myers [12]. In [P2] the metbod of Yasutomo is generalized and ap-

plled to reeonstruet the spattal distributton of MBD generator dis-

charges from stereoscopie radlation measurements.

7

3. 3. Laset beam deflect:1on metbod

A quantitative achlieren metbod called the laser beam deflection metbod

bas been developed and applied to meaaute the argon deuity profiles

that are associated with streamers. Th1s metbod and its app11cat1on is

described in [P3].

[1] H.R. Gdem, Speetral 11ne btoaden1ng by pla811111s, Academie Prees

(1974) New Yorlt.

(2] C.L. Chen and A.V. Phelps, Phya. Rev. A7 (1973) P• 470.

[3] w. Behllenbu.rg, Line shapes, froa: Progtess in atOirlc speetroscopy, put B, ed. by w. Banle and H. lCleinpoppen, PlenUIII Publishing Corp. (1979) Hew Yorlt.

[4} M. Fabry, J. Quant. Spectr. Radiat. Transfer 16 (1976) P• 127.

[5] W.L. Wieae, Line broadening, from: Plana diagnoetic techn1quea, ed. by R.H. Huddlestone and

S.L. Leonard, .Acade8dc Prees (1965) New Yorlt.

[6] A.P. Thone, Spectropbysics, Chapman and Hall (1!174) London.

[7] C.A. Borcbi, et al., Pbysica 121C {1983) P• 269.

(8] W.L. Barr, J. Opt. Soc. Am., 52 (1962) p. 885.

[9] Y. Yasutoao, et al., IEEE Trans., PS-9 (1981) p. 18.

[10] A.r.c. Sens, et al., Proc. 20th Symp. on Eng. Asp. of MBD. lrvine,

CN (1982) P• 10.6.

[11] J.F. Uhlenbu.scb, Pbysica 82C (1976) p. 61.

{12] w.c. Roman and T.w. Myers, AIAA J.,5 (1967) P• 2011.

38

3.4. Publications

The following publications are included in this section:

[Pl] Electron density determination in argon cesium MBD plasaas

[P2] Asymmetrical Abel inversion of MBD generator discharges

[P3] Maasurement of argon density nonuniformities in argon cesium MBD

plasmas.

39

Pbysica 123C (1984) 247-256 North-Holland, Amsterdam

Pl

ELECTRON DENSITY DETERMINATION IN ARGON CESIUM MJID.PLASMAS

J.M. WETZER Divisitm Direct Enetgy Cotwenion, Universily 11/ Tedmology, P.O. &x 513, 561.2 AZ Eilldlw!>en, Tlle Nedwrlaruls

The metbod of electron density determination from contimtu.m emission is often used In the nonstalionaiy plàSma of an ~ becausc of üs simpllcity. An assumptiOperimentaBy with the metbod of Stark broacleoing meaourement of speçtra1 Hnes, using a stalionazy atgon eesinm clisdwp. Both teclmiqnes invólve eorreelions for plasma lnhomogeneities. Agreement withln 20% is found. The contribulion of Cs, molecules to the continuurn emissîon, wbidt is signi6cant in satuJ:ated vapor at moderate tempelatures (500-1000 K), is eslimated io he of minor imporlanee m the generator plasma.

1. IDtrodudiGD

Measurement of plasma parameters in an MHD-generator is usually complicated because the discharge structure is nonstationary, in-hornogeneous and not accurately reproducible [1-3]. This is a serious restrietion to the ap-plicability of more or less advanced diagnostic techniques like line profile measurement or in-terferometric techniques, because these methods require either a homogeneaus plasma or a well-defined inhomogeneity. When one is interested in the spatial distribution of plasma parameters, also scattering techniques becorne cornplicated because the discharge structure is both non-stationary and not reproducible. This restricts the possibility of scanning or repeated measurement. Thus relatively simple continuons diagnostic techniques are required, logether with analysing techniques, in order to reconstruct the spatial distribution of plasma parameters. One such diagnostic technique, which is often used in MHD-generator plasmas, is the determination of electron density from continuurn emission [1-3]. This metbod however carries with it some un-certainties. In this work the ability of the metbod for application in MHD-generator plasmas is discussed. An analysing technique to reeoostmet spatlal distributions from line integrated inten-

sities in generator plasmas will be presenled elsewhere (4}.

To analyse continuurn emission, informatinn is requîred on the origin of the radiation. In the MHD plasma considered, consisting of cesium in an argon bulfer gas, radiative recOmbinatinn is the dominant process contributi;ng to the con-tinuurn einission. In an argon ·cesium plasma without impurities the most likely souree of ad-ditional radiation, atomie lines being avoided, is formed by cesium diatomîc molecules. It has been shown by Lapp and Jiar,is [SJ that in saturated vapor a considerable mlction of cesium

. is present in molecular form. In this work the -effect of cesium molecular emission and ab-sorption on the continuurn is estimated.

ID general argon cesium plasrqas will include impurities which wil! give rlse to contributions to the continuurn emission. Another possible source. of error is the uncertainty of the cross section data of radiative recombination. In our analysis the data obtained by Norcross and Stone [ 6] are used. When camparing their valnes with the results of Agnew and Summers [7), Gridneva and Kosabov [8] and Burgess and Seaton [9], discrepancies of more than 30% occur. These uncertainties demand an experimental com-parison with a metbod that is independent of both additional radiative contributions and

0378-4363/841$03.00 © Elsevier Science Publishers B.V. Reprinted with permission (North·Holland Physics Publishing Division)

40

P1

J.M. Wetzer I Elec- density determin

-n 18

." 10 !;-..L.~~~""--:-:!::::-'--'---'-~-=

Tt lltl

Fig. 1. Temperattue dependenee of lhe radiative _.,.- trom leOOIIlbinalion of ekclroDs witb cesium ions at wavelengtbs 4100 and 4900 A.

electron tempenture is known. The latter is derived frorn the ratio of intensities at different wavelengtbs

e(A,)/e(A.} = f(A,, T.)lf(A2, T.)

= (~)' exp{~ (t-i;)}- (8) Fig. 2 shows this ratio as a tunetion of tem-perature for A1 = 4900A and A2 =4100Ä.

As can be seen from figs. :!. and 2 this diag-

-~-;.so .. .. "'"'

18

'o!:-~-'--'---'~~~-L~~~I~OOOG T•IKl

F~g. 2. Ratio of recombinative emission power values at wavelengtlis 4900 and 4100 Ä.

P1

42

nostics is not very sensitive to electron tem-perature in tbe regime wbere T. > 4000 K. The determination of the electron density, bowever, is rather accurate because the; radiative power depends on the square of n., · wbile tbe inac-curacy in electron temperature only weakly affects f(A, T.), or n.. The accuracy of tbe elec-tron density is prlmarily determined by the ac-curacy of tbe measured intensities.

2.2. Molecular contribution to thi continuum

The cesium molecules present in tbe plasma can botb emit or absorb radiatidn. To delermine tbe effect on the measured continuurn intensity, apart from plasma parameters information is needed about tbe molecular fra

'""'.-----.-----,..-----..,.., El~~ • !,;

-3 10

....

1501 tOOG K

Fig. 3. Molecular oesium fraction as a furu:tion of atomie oesium density for different gas temperatures.

tbe Jayer itself, the transmission is given by

I(x =I)= exp(-n.. .. Q ·I) I(x=O) . ....., ' (10)

where x = 0 and x l are the bonndarles of the layer and Q is the abso!'J)tion cross section of Cs, molecules at A = 4900 À. Calculations have been perlonned in the range of cesium atomie den-sities between 1020 m-3 and ton m·3 and gas tem-peratures between 500 and 1000 K for I = 5 cm. For these conditions, which are characteristic for MHD-generator plasmas, the transmission is lar-ger than 97o/o. Heoce the elieet of cesium mole-cules can be neglected.

The emission of cesium molecules bas been calculated using tbermodynamic equilibrium, and bas been compared with recombinative emission. In equilibrium the molecular emissive power per unit volume per unit solid angle per wavelengtb interval is related to tbe absorption coefficient k(v) = nc., • Q tbrough

e(v)= k(v)B(v, Tc.,), (11)

where B(v, Tc.,) is Planck's function. Evaluation in tenns of wavelengtbs yields

P1

43

(12)

With eqs. (9) and (12) it is now possible to calculate the molecular emission once the tem-peratures involved are known. To estimate the maximal molecular contributioo that might occur it is assumed tbat the dissociation process is ruled by the heavy partiele translational tem-pcrature wbile the emission is assumed to be ruled by a vibrational temperature equal to the electron temperature. The recombinative emis-sion is calculated using eqs. (4), (5) and (6}.

The ratio of molecular and recombinative emission is given in fig. 4 as a tunetion of elec-tron temperature for equiHbrium conditions at a heavy partiele temperature of 1000 K and cesium atomie densities in the range between 1020 m·> and 1()22 m·3• It can be concluded that in the MHD generator discharge, where tbe electron temperature exceeds 4000 K, the molecular con-tribution is negligible. In practical experiments the measured intensity wiJl be line-integrated, and will thus contain contributions of tbe colder plasma around tbe discharge, wbere molecular emission might play a role. The total intensity of these colder parts, however, will be smaller than tbe intensity trom the discharge by orders of

F".g. 4. Ratio of molecular and reoombinative emission power of an equilibrium plasma as a fuoction of eleetroo tem· perature fur diffem~t atomie oesium densities at a li8S tem· perature of 1000 K.

Pl

JM. W•tz.,. I E,.._ Mruity ddmninalion in Ar-Cs p/asmas 251

magnitude, and usually will be below the delec-tion limit considering the dynamic range of the photomultiplier. In reality the situation as it emerges from fig. 4 wiU be even more pronounced because the molecular emission will be governed by a temperature lower than the electron temperature.

2.3. Stark broadening of speetral lines

The speetral lines of cesium in an argon cesium MHD plasma are broadened primarily by pressure broadening. The perturbing particles may be neutral (Van der Waals broadening, resonance broadening) or charged particles (Stark broadening). For many speetral lines of cesium, especially for the fundamental series, the main contribution to the linewidth is produced by the Stark effect because the free electrous interact rather efficiently with the weakly bound optica! electron. These Stark dominaled speetral lines are very attractive for diagnostical purposes because over a wide range the width is propor-tional to the electron density, and almost in-dependent of the electron temperature.

In our work the theory of Griem [10] bas been used to relate linewidths to electron densities. In this theory the ion contribution is described in the quasi-static approximation while the electron contribution is described in the impact ap-proximation. The profile is finally obtained by averaging over the different ion field contribu-tions, taking into account the effect of ion-ion correlations and the Debye shielding by elec-trons. Over a wide range of conditions the result-ing profile is Lorentzian with the fuU halfwidth given by

w• = {1 + 1.75a(1~)"'(1-0.75R)}

x2w.(1~) (13)

with n. in m·3• a and w. are weak functions of temperature and are tabulated by Griem [10], while R is the ratio of the mean ion-ion separa-tion Pi= (41171./3]113 and the Debye radius Po= (n.e2/,;0k7)"112• A= a(nJ1022)'14 represents the

44

ion contribution and w.(nJ1~) is half the half-width due to the electron contribution. Eq. (13) is valid when the following requirements are fulfilled:

A :s0.5, R :s0.8, u= w.p/v > 1, (14)

where v is the relative velocity between the perturbing ion and the pertorbed atom. In all the experiments these requirements have been checked a posteriori. In fig. 5 i the linewidth of some fundamental lines of cesium is plotled as a function of electron density for a Saba-plasma with a total cesium· density of 5 x 1021 m·3• Also the conesponding electron temperature is shown. Although the latter varles from 2000 K at n. = 1.3 x 1019 m·3 to 6000 K at n. = 5 x 1()21 m·3 the width remains proportional to the electron density in the whole range. Since the fundamen-tal lines are more sensitive to electron density than the memhers of any other series, these lines have been selected for the experiment&.

The remaining pressure broadening mechanisms, Van der Waals broadening and

513/2- •Fi/Z 5000 ...

.... ...

31100

~

Pl

252 J.M. Wetter I Bkctron density detvminaótm in Ar-0 plasmar

resonance broadening, usually have a small effect on the Iinewidth of above-mentioned Iines, though not always negligible. Also for these mechanisms Griems description is used [10]. Resonance broadening results in unshifted Lorentzian profiles (except in tbe far wing) wbose full halfwidth is given by

(15)

where g1 and g. are the degeneracies ol' lower and upper level of the conesponding transition, A and f are the wavelength and absorption oscil-lator strengtbs of this transition and nc. is the neutral cesium density. The oscillator strength data are taken from Fabry [12]. Van der Waals broadening results in Lorentzian profiles with a full halfwidth given by

(16)

Here E. is the energy ol' the first excited level of argon, and tbe matrix element R'! is well esti-maled by

(17)

EH and Em are the ionization energies of hydragen and the radiating cesium atom, Ea is the excitation energy ol' the upper· state of the line, and 1" is its orbital quanturn number. z is the effective charge acting on the radiating elec-tron.

All pressure broadenîng mechanisms discussed cause Lorentzian profiles. Therefore tbe result-ing profile is Lorentzian and the linewidth is given by the sum of the different contributions. In tableI valnes are given for the Van der Waals contribution and the resónance contribution to the linewidth ol' some fundamental lines ol'

45

TableI linewidtb contn'butiOIIS of Van der Waals· and teSOrumCe broadening to some fundamental lines of cesium at n..v = Sx 10"'m·>, na.• 5x 10" m·• and T•2000K

Transition Wavelengtil w• w" (A) (A) (Al

SD,a-nFm n• 6 7:t29 3.2x 1o-1 1.2x to-3

7 6825 3.8x to-1 5.6X to-4 8 6586 4.5X to-1 3.2X 10"4

9 6432 5.2X to-1 2.0x to-4 10 6326 6.0X 1o-1 1.4xto-'

SD,a-nF",.,n '!:- 6 7280 3.3X to-1 1.4X to-3

7 6870 3.8x to-1 6.8x 10"" 8 6629 4.5X to-1 3.8X 10"" 9 6473 5.3X 1o-1 2.4X 10""

10 6366 6.1 x to-1 1.6X 1o-4

cesium. The condinons are typical for MHD-plasmas, nAr= 5 x 1

, ....... riltUol ..

Pl

Fig. 6. Set·up used in lhe present cxperiments

FQ~. 7. Discharge tube used in the pJeSellt experiments.

discharge current. In order to improve the signal-to-noise ratio for measurement of the weak fun. damental l.ines that show the ·largest width, the monochromator slit bas been imaged in a plane perpendicular to the axis of the t11be. Since no spatial resolution ean be obtained in this way, corrections for inhomogeneity have been per-formed using the radial profiles measured by · Borghi (11) in the same discharge tobe. The correction concerns both the profile messure-ment and the continuurn emission lneasurement. A1so the monochromator profile bas been cor-rected for.

Since the fundamentallines (SD;,.rnFm. 5Dsa-nFm 7a) exhibit the strongest dependenee on electron density, these lines have been choscn in the experiments. The linewidth increases with principal quanturn number of the upper level. However, becausc of both the lower population of this level and the larger width of the line, the signal-to-noisc ratio decreases. The best results

46

under the present conditions have been found using the 6326Á line of cesium (SD31rlOFm). The absorption of this line can be neglected, and near the centre the profile is not disturbed by adjacent lines.

In lig. 8 the prqliles of the fundamental lines 5D~F•a (6432Ä) and 50m-10F512 (6326Ä), measured at a discharge current of 2 A, are plotted. Fig. 9 shows the measured profiles of the line 50m-10F512 at two different discharge cur-rents. In all cases the profiles are litted with Lorentzian curves. Since we are mainly inter-esled in the line centre, this part bas been given a larger weight in the fitting procedure. It can be concluded that Lorentzian profiles coincide with the measured profiles in the centre and the near red wing of the lines, but underestimate the

P1

I.M. Wmu I Elecrron tknsiJy tktumlnation In Ar-Cs p/asmM

·-·'"" ------'----.--1 >->,!À I a

Fig. 8. Normalized Une profiles of the !ines SD,n-nF512 for n • 9 (6432 A) and n = 10 (6326 A) at a discharge cummt of 2 A. Drawn liruos lndkate Lorentzian fittings, dasbed Unes indicate the measured profilea. For clarity - aU experimen-tal points have heen plotted.

Fig. 9. Norma!ized !ine profiles of the tinc SO",..lOFS/2 (6326 A) at discharge omrents of 1 and 2 A. See also the caption of fig. 8.

measured profiles in the blue wing. From the line SD31rlOFm electron densities have been derived using Griem's theory. These val u es are plotted in fig. 10, curves 1, as a lunetion of a discharge current. tagether with the values obtained from continuum emission. Agreement is found to be within 30%.

In the analysis so far inhomogeneities have not been taken into account. However, as is proven by excited state density measurements of Borghi

47

0 0~_,__.....__......__2!-.......

I !Al

Fig. 10. The electron density at the centre of !he discbarge tube as a fnnction of discharge current. obtained fmm .,..... tinuum emission and Stark broadening. (1) Homogeneity assumed. (2) Corrected lor inhomogeneity.

(11] in the same discharge tube, the plasma parameters show a strong radial dependence. Fig. 11 shows the population density dis-tribution of the 70312 level of cesium, at a discharge current of 2 A. From this densîty the n. and T. distributions are calculated using the Saha-Boltzmann equilibrium. Two cesium den-sity profiles have been used yielding the same

.5

•~:-----~----~ 0 !.S 'I••J 5.8 F~g. 11. Radial distribution of !he 7D ex

results. One is a homogeneons profile, the other is a parabolle profile which results from a simpte energy balance between ohmic healing and con-ductive loss. The obtained radial distributioos, given in fig. 12, enable us to obtain the electron density at the centre of the discharge (r = 0) from both continuurn emission and Iine profile measurement.

8 oL----------~2.7i--~-,-,.-.-~~5~

Fig. 12. Radial disttibulion of electron density and electron lemperature obtalned froln lig. 11.

In the case of continuurn emission the electron density, found wben ·assuming homogeneity, bas to be multiplied by a correction factor g. Since the continuurn emission depends on the square of tbe electron density, but only weakly on the electron temperature, and beeause the latter shows only a weak radial dependence, the factor e can be well estimated by

- [ J' {!!A.el}2 ]-1/2 l- 2 n.(O) pdp (18) 0

with p = r/ R where R is the discharge diameter. In the case of the Iine profile measurement the electron density in the centre of tbe discharge is determined from a computational model. With this model the linewidtb of tbe emitted profile is calculated as a function of n. (r = 0), using the obtained radial profiles of n. and T .. The cor-rected electron densities are plotled in fig. 10, curves 2. The two methoos now agree witbin

Pl

48

20%, wbicb is satisfactory for tbe application under consideration. The difference is not due to experimental errors. The error in tbe continuurn intensity measurement is estimated to be less

· than 5%, yielding an error in the corresponding electron density of less than 2.5%. The error in tbe Iinewidth determination is estimated to be 6% at low discharge current and less at bigher discharge current. The error in the electron den-sity obtained from this linewidtb, is the same.

An error in tbe Van der Waals broadening by a factor of two would result in an error of only 5% in the electron density obtained from line profile measurement. The remaining possible sourees of error are the Stark coëfticients used, the recombination cross sections, in particular their temperature dependence, and the elfeet of other contributions to tbe continuurn than recombinative emission. Of these the latter two are the most likely sources. It should be noted, however, that if the discrepancies are due to Cs, molecular radiation, the effect will be much smaller for plasma conditions as they occur in an actual MUD-generator because of the higher temperatures of both heavy p~icles and elec-trons, enhancing botb the dissociation process and the recombinative emission (see fig. 4).

5. Ceaelusion

It is showo that tbe metbod of electron density determination from continuurn en:usston measurement is applicable to argon cesium plasmas. Possible sourees of error like additional radiative contributions, especially from cesium molecules, or the inaccuracy in the recom· bination cross sections do not heavily affect the resulting electron density. The accuracy obtained in a simulated MHD plasma, a{ter corrections for inbomogeneity, is 20%. Th41 accuracy ex-pected in an actual generator plasma is better because of the higher temperatures involved.

Ackaowledgement

This work bas been performed as a part of the

Pl

I.M. W11zer I Electron density detmninalion in Ar-Cs plasmas

research program of the Shock Tube MHD project of the Direct Energy Conversion Group of the Eindhoven University of Technology. The author wishes to express bis gratitude to C.A. Borghi, P.H.M. Feron, J.F. Uhlenbusch and A. Veefkind for their contribution and fruittul dis-cussions.

[11 W.M. Hellebre.."., lnstabiüty analysi< in a nonequlli· brium MHD .-tor, !'b.D. Thesis, Eindhoven Uni· v~ty of Tedmology (1980).

[2] A.F.C.Sens, V.A.Bityurin,J.M. Wetzer,A. Veelkindood J.F.O. Bra...., 2Dth Symp. on Eng. Asp. of MHD, Irvine, CN (1982) p. 10.6.

(3) A. Veelkind, J.W.M.A. Houben, J.H. Blomand L.H.T. Rietjens, AlAA J. 14 (1976) 1118.

49

(4] J.M. Wetzer,IEEE, PS-11, 2 (June 1983). [SJ M. Lapp and LP. Harris, J. Quant. Spectr. Radiat.

Tr.msfer 6 (1966) 1@. [6] O.W. Norcross and P.M. Stone, J. Quant. Spectr.

Radial. Transfer 6 (1966) m. [7] L. Agnew and C. Summers, Prne. 7th Int. Cnnf. on

Pbenomena in Jonized Oases. Beograd, Vol. 2 (1966) p. 574 Oratievinska Kujip Pub!. House, Beograd.

181 S.M. Oridneva and O.A. Kosabov, Prne. 3rd Int. Cnnf. on MHD, Vol. 1 (1966) p. 73. S.M. Oridneva and O.A. Kosabov, High. Temp. 5 (1967) 334.

(9] A. Burgoss and HJ. Seaton, Mon. NO!. Roy. Astr. Soc. 120 (1959) 121.

(10] H.R. Oriem, Speetral Une Broadening by Plasmas (Aeademic Press, New Y ork, 1974).

[111 C.A. Bocpl. DiochatgeS in the inlet region of a noble gas MHD generator, !'b.D. Thesis. Eindhoven Uul· versity of Teebnolngy (1982).

(121 M. Fabry, J. Quant. Spectr. Radiat. Transfer 16 (1976) 127.

Copyright (§) 1983 IEEE P2 72 Reprinted, .wi th permiss ion, from: IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL I'S-11, NO. 2, JUNE 19113

Asymmetrical Abel Inversion of MHD Generator Discharges

J.M. WETZER

Ab.tnlct-ne melllod or Y- et 111. fo< 1$)'-lrical Abel imonÎOII is •ieaded. 1lle od&laal solutioa COI18ÏIItl of • radio! part 1811 a Molglit fucli

WETZER: ASYMMET!liCAL ABEL INVE!lSJON

J(y) = lo(y) +J, (y)

/o(y) = ! {l(y) + /(-)')} I,(y)=} {l(y)- /{-y)}.

P2

(5)

lt is important to note tbat tbe choice of tbe y-coordinate according to P"tg. I implies tbàt the boundaries are symmetrie with respect toy = 0.

Combination of (I) and (4) yields

i.Jii'-YT

/(y)= g(y)no(r)dx ~

i.JR'-y' = 2g(y) 0 n0{r)dx =g(y)J0 (y). (6) From (5)and (6) we see thatg(y) can be derived directly from tbe observed data using

g{y)= {t + J,{y)} (7) lo{y)

while n0(r) follows from Abel inversion of / 0(y)

73

Applying tbe inversion metbod for N = JO and N = 20, good rest~lts are found (agreement within 0.25 percent) eXl:ept for k = N- I and k = N, where errors of more than I 0 percent are found. These errors have been reduced drastically by imposing

no(rN)=O

(13)

To compare tbe resulting distribution with the measured inten-sity profiles norrnalized on !heir maximum values, it is inte· grated over both axes of observation, and then norrnalized

J{y)= J: n(x,y)dx!I: n(x,y..,)dx

11"'Xcos-ysin. (IS)

no(r) = M .!.JR dlo{y) . -.....!!.!...._, 11' ' dy ...r;r:;r

and Y m and t" denote the y and ~ values wbere the integrals (8) take on their maxima.

Finally, J{y) and P(t) are compared witlt the measured profiles /(y) and t•. From (7), it follows that . The metbod described so far has been apPiied to an intensity

g(y) + g(-y) = 2. (9} measurement of MHD generator discharges. The calculated profile J'~>(t), however, does not match the measured profile J•(t). The reason for this is tbàt the distribution n(x,y) is Uke in {2) , Barr's metboa of Abel inversion is used which as-sumes a smooth function no(r) for which

I dNo(r) no(r)=- 21Tr ~

with

No(r)=2 J. R J{y)ydy. r ..;yr::rr

(tOa)

(tOb)

Least square fitting is introdw:ed after inlegration (lOb) but before differentlation (I Oa). In this way, the numerical metbod becornes rather lnsensitive to small random erron. In· cludlng all these steps the inversion takes the form

(11)

wherey,. •nA, rt =kA,R =NA, and ~kn is tabulated by Barr [1) forN(t).

111 EXPERIMENTAL ARRANGEMENTS· The expedments are perforrned with the shock-tunnel MHD

generator described.in (SJ. The argo~um plasmaisheated by cornpression and expanded through a nozzle into a diverg. lng MHD channel. The channel height is constant and equal to 10.8 cm, the width eliverges from 3.7 to 8.7 cmoveralength of 110 cm. The walls cousist of G-1 0 ep(>xy laminate or Jexan and contain quartz windows for spectroscopie measurements. CyUndrical stalnless-steel electrodes are mounted halfway countersunk in tbe parallel walls. All electrode pairs are loaded with 1-sl resistors. Top view and side view of the channel are schematically shown in Fig. 2 and Fig. 3. Typical experimen-tal conditions are: flow velodty u"' 1000 m/s, magnetic in-duction B = 2.5 T, stagnation temperature T. = 3500 K; stag·

P2 74 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. l'S-I I, NO. ~. JUNE 1953

\Ct I

!'jg. 2. Top view of pnoraror ellamlel ..., experimental sel-up. CL= caliblllioD lamp, L • kml, QW ··quartz willdow, M =minor, D = diapllracm, BS = beamspllttet, MC = monoehromator, PM = photl>-

. Jllultipller, VF • voltap rouower, o • oaciJioscopt.

F~g. 3. Sido view of pnorator

P2 WETZER: ASYMMETRICAL ABEL INVERSION

Fig. 6, Radial part n0 (T) of the solution of the generator discharge distribution.

-I +I Yt•J

f"~g. 7. Weigilt functlon g(y) of the solution of the generator discharge distnbution.

;'Jr---,---~-r----~r---; .; .

..

f"1g. 8. Emisslvlty distrlhutlon of the generator discharge for x = 0. The error ban indicate the ina=racy due the erron in the measuftld proliles.

force. The long axis of the elliptical part is parallel to the magnetic field lines. Similar results were obtained by Uhlen· buscli [3) and Roman and Myers [4) for balanced discharges in a flow wîth a magnetic field, for large values of u and B.

The different parts of the solution, the radial part n0 (r) and the weiglit functiong(y), are plotted in Fig. 6 and Fig. 7. The effect of the inaccuracy in !he measured profiles is indicated by error bars. The inaccuracy of the radial part n0 (r) is of the sameorder as the inaccuracy of J(y). The inaccuracy ofg(y) becomes large near !he boundaries. From (7) it follows:

A -(y) ; J(y) à/(y) ..... Jj(y)

(17)

when IJ.J(y) is the error in /(y), and t:.g(y)is thecorresponding

53

75

error in g(y). This, however, does nol seriously restriet the method of reconstruction because near the boundaries the value of n0 (r) approaches zero. The effect of the inaccuracies in n0 (r) and g(y) on the reconstructed distribution n(x,y) is shown in Fig. 8 for x "0. lt can be concluded that the inaccu-racy in n(x,y) does nol significantly exceed the errors in the measured profiles.

Another possible souree of error should be discussed. As mentioned before, the intensity versus place profiles have been derived from the intensity versus time profiles using the .gas velocity. In fact, the discharge velocity should be used which is somewhat lower, the relative velocity causing the drag force exerted on the discharge. This means that the real dilltribution of emissivity is somewhat smaller, but retains its sbape. The relative velocity between discharge and gas is estimated to be less than I 0 percent of the gas velocity.

V. CONCLUSION

The metbod of Yasutomo et al. [2) for asymmetrical Abel inversion is extended to cases in which the distribution is con· fined withln an elliptical boundary with arbitrary ellipticily, inslead of a circular boundary. To delermine the elllpticity from experiments, an additional simultaneons mensurement from a different direction of observation is required. The extended method is successfully applied to MHD generator experiment&, reproducing fairly well the measured intensities. The resultlng distribution is in qualilalive agreement with experimental and theoretica! investigations performed by Uhlenbusch [3) and Roman and Myers [4) for similar condi· tions. lt exhiblts a nearly elliptical sbape with asymmetry in flow direction due toa dragglng force exerted on the discharge. The long axis of the elliptical part of the solution is parallel to the magnetic field llnes.

AcKNOWLEDGMENT

This work was performed as a part of the research program of the Shock Tube MHD project of the Group Direct Energy Conveesion of the Eindhoven Unlvecsity of Technology. The assistance of A. W. M. van lersel, H. F. Koolmees, H. F. Lin· ders, H. P. Maréchal, and Ms. M.H. A. J. van Rlxtelisgratefully acknowledged. The author wishes to express his gratilude to Prof. J. Uhlenbusch and Dr. A. Veelkind fortheir contribu· t!on and fruitful discusslons.

REFllRENCES

(11 W. L. Ban, "Method for computirlg the radial distnl>ut!on of emitten in a cyliruiJk:al source," J. Op/. Soc. Am., voL 52, no. 8, pp. 885-888, Aug. 1962.

121 Y. Yasutomo e/111., "A new numerical metbod for asymmetrical Abel inversion~fi IEEE Trans. Plarma Sci,. voL PS-9. no. 1, pp. 18-21, Mar.l98l.

131 J. Uhlenbusch, "Miscel!aneous aro devlce$," l'llysial, vol. 82{', pP. 61-85,1976.

(41 W. C. Roman and T.W. Myers, "Experimental investiption ofan electrit are in transverse 11erodynamic and magnotie foelds," A/AA J., voL 5, p. 2011, 1967.

ISI A. Veelkind et 111., ••High power density experimentsin a shocls et ttL, in Proc. 201/r Symp. ltllg. Alp. MHD (!moe, CN), pp. 10.6.1-10.6.7, 1982.

P3

MEASUI!MEliT OP AlGON DENSITY NONUNIPOli.MITIES

Abstract

!!.

AlGON CBSlOM MBD PLASliAS

J,M. Wetzer

Direct Energy Conversion Group

Eindhoven Univarsity of Technology

P.O. Box 513, 5600 KB EINDHOVEN

The Netherlands

The heavy partiele density nonuniformties eorrelated with the

observed are atructure of closed cyele MBD generators are ..asured with

a quantitative achlieren teehnique called the laser be&ll. deflection

method. The uperiments are performed with a shock tube MBD generator

worlting with an atmoapberie eesium-seeded argon plS&ll.&. The evalustion

of argon density and tempersture profiles from the experiments is dis-

cuseed and the results are presented. It is shown that an argon density

nonuniformity is assoeiated with every are, and that the argon density

within the are is about 25% lower than the density outside.

1. Introduetion

The investigation of are properties in atmospherie alltali-seeded noble

gas plasus is iaportant in the field of elosed cycle MBD eonversion.

The MBD generator exhibita an are structure whieh is strongly nonuni-

form, and moves with approdmately the flow velocity (1 - 3 ]. ICnowledge

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of the are properties and their spattal distributton is required in the

study of transport properties and of the mechanisma for energy aud mo-

mentum transfer from the surrounding flow to the are. The electron prop-

erties and seed coneentration of such area have been examined intensive-

ly using spectroscopie techniques [ 4 - 5], however maasurement of the

noble gas density nonuniformities associated with area bas not yet been

performed in closed cycle MBD experiments.

In this work a qusntitative achlieren technique is described which

makes use of the deflection of a thin HeNe laser besm by gradients in

refractive index perpendicular to the direction of propagstion of the

beam. The metbod has been applied to a shock tube MBD generator using

argon as the noble gas. The argon is seeded with 0.05% cesiua. At the

BeNe laser wave-length (6328 A) the refractive index of the plasma con-

sidered is primsrily determined by the argon density. Hence tbe .. asured

deflection yields informstion on the argon density nonuniformities.

In section 2 the refractive index of atmospberic argon-cesium plaa-

maa will be discussed. Section 3 deals with the evalustion of argon

density nonuniformi ties from the measured deflection. The expel'iaental

set up will be described in section 4, wbile in section 5 tbe results

will be presented and discussed.

2. B.efractive index

The refractive index N of a plasma ia compoaed of the contributtons of

the different species s as followa

N • 1 + E (N - 1) s s

(l)

In an argon-cesium MBD plasma the contributing species are argon and

cesium neutral atoas, cesium ions and eleetrons. lontzation of argon is

not regarded ainee the electron taperature remeins below 5000 It. Tbe

neutral atom contributton of species n, Nn' is given by the Cauchy equa-

tion [6]

B (N - 1) • A (l + -ll2} n n A

(2)

provided that irradiation ia off-resonsnce. The wave-length dependenee

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ia weak. The factor An is related to the neutral atoa polarizability Bn

accordiq to

(3)

where nn is the neutral atom density. At tbe BeRe laser wsve-leogth

(6328 A) we flnd at standard conditions (p • 1 ata, T • 273 K) that

(NAr - 1) • 2.8 x 10-~ and

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to the refraetive index is mueh larger tban the gradients of the neutral

eesiua or eharged partiele eontributions. Renee tbe deflection is gov-

erned by argon density nonuniformities. In the subsequent sections tbe

heavy partiele properties are given without subscript&, and refer to

argon.

3. Beam defleetion anslysis

We eonsider a light beam passing through an area of inh0111ogeneous re-

fractive index (see figure 2). The beam widtb is zmall c0111pared to the

characteristic dimension of the nonuniforad.ty. The angle between the

ineoming and the outgoing beam is gi ven by [ 6]

y2 tan {a(x)} • f s! {ln (H(x,y)j} dy

yl (6)

Since N - 1 • Kn is of tbe order 10-4 the deflection is 8111411 and equa-tion (6) can be written aa

12 Sn a(x) • K f 6X dy

yl

Under tbe aasuaption of constant pressure p we may write

* 12 6 1 ll(X) • K f Gx (f) dy yl

(7)

(8)

witb K* • Kp/k wbere k is Boltzmann's .constant. In the generator experi-

ment tbe laser beam is fixed at a eertsin position x, wh11e tbe are

moves with respect to this position with a