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

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 of plasma parameters of a noble gas linear MHD

generator. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR141532

DOI:

10.6100/IR141532

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Published: 01/01/1984

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Spatially resolved determination

of plasma parameters of a

noble gas linear

MHD

generator

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

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

The éMarf eeee fa1'theP tha:n the giant, when he has the giant '8 e'houlder to mount on.

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

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

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 interacdescrip-tion 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. I t 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-croscopie and mami-croscopie 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.

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 (T 2). 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 advsneobtain-ed 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.

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:

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.

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

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 % 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

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.

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.

[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~)·

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 _exp • 5 • • 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

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 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<~~~pariaon with earlter uperiMnta [4, 5] the aeeond half of the channel ia equiped with eylindrieal electrode& half-way counteraunk in the parallel walla. The Mach nuaber at 'the f1rat electrode pair poaitioned 15 cm downstraam of the nozzle ia 1.9 and the cbannel diversea linearly froa 2.9 x 11 ca2 in the throat to 12 x 11 em2 at the outlet over a length of 95 ca. The channel ia •de of G-10 upoxy laainate and containa large windowa, coverins tbe whole heiabt of the channel over a lensth of 19 ca. liear the firat and laet elactrodea

pres-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 p

8 and stagnation t~erature

T

8• 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 t i • 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

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 i

8 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

u2 and P2 are caleulated from the measured values for T 1' _{p2 end} i 8 (or K 8). 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 M

8• This is echieveel by varying the f1111ng pressure p 1 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

i

8 is deterained froa tbe time delay between the

stepvisa presaura increments at two different poaitions. Purther tbe

pressure bebind the rafleeteel shoCk (p

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 a t - r - l i k e 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

(11)

(12)

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 • p u l l -(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)

(18)

au.d

Nu •

_x

o.023 ae0

_x

•8 (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 relacondl-tlons

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.

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

transi-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 6s

112 - 6P

312 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.

,

...

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 T 1(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. I₁(o) is measured separate-ly. Renee the transmission of the plasma is determined from:

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 describsaturat-ed 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

trf

trf

kA 8 Cs 8Ar 1!1 HEB N.INO

( .. s,

C!) _{BLUF N.INO} ... 101

Hf

..

I

•

_•

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

101 A- A₀ 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

(7)

where n

11 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 f111 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

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 • nC

8/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.

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 A_{1 •} 4900 A . and A_{2 •} 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

(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

e

₁₂ • e₁te₂, a aaesure for the sensitivity is

+

given by

dT d812 dT 812

+ '"

<-:/->1<-e.:::> •

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

(6P

112

-sv

312

J.

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 n

8 >>

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 inverexten-sion 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.

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.

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

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 assumptiO<l in the analysls is that recombinalive radlalion fonns ibe main

conlribation to the continuum. Next to this the metbod oarries with it some other uncertalnlies. In this work the metbod is oompated e>perimentaBy 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)

P1

J.M. Wetzer I Elec-density determin<Uion in A!'-Cs plasmas

recombination cross sections. For this purpose the line broadening of speetral lines of cesium is used. Unes have been selected whose width is primarily determined by Stark broadening. From the line profile the electron density bas been determined using Griem's theory [10], and bas been compared with the results of continuurn emtssiOn analysis. To avoid experimental difticulties, a stationary diseharge, witb a diameter of 10 mm, bas been used in an argon cesium plasma with a composition comparable to that of the actual MHD-generator plasma. Cor-rections for radial inbomogeneity have been performed using the measurements of radial profiles of Borgbi [11] in the same discharge tube.

2.1. Radiative recombination

Radiative recombination occurs wben a free electron and an ion recombine to form a neutral atom in a state j, according to

The energy equation of this process yields

h.E.= h .E..+.!m v2

À À; 2 • .,

(1)

(2)

where hel A is the energy of the released photon,

hel A1 is the binding energy of atomie state j and

m.v'U'l

is the free electron's kinetic energy. The continuurn arising trom tbis process thus shows an edge at A = Ar The radiative power per unit volume and per unit solid angle in a wavelengtb interval dA around wavelength A is given by

wbere Q(v.) is the cross section of radiative recombination into atomie state j, f(v,) is tbe electron velocity distribution and dv. is the elec-tron velocity interval corresponding to the wavelengtb interval dA througb eq. (2). Eq. (3) is

41

furtber evaluated assuming charge neutrality and a Maxwellian electron distribution function. The validity of the latter assumption bas been verified for argon cesium MHD plasmas by Borghi [U]. Moreover, tbrougbout tbe analysis tbe plasma is assumed to be optically thin at wavelengtb A, and argon is assumed not to contribute to the con-tinuum, considering the temperatures involved. Combination of eqs. (2) and (3) and elaboration of tbe assumptions yields

with

A1 =

(L.!.)o{v,(A)}exp{-k/L.!.)}.

_{A A}

(5)

1 . kT, \A

A1

Summation of all eontributions gives the total radiative power per unit volume and per unit solid angle in the wavelength interval dA

(6)

(Al a: A).

According to Agnew and Summers [7] most of tbe radiative power in tbe visible originates from recombination into the 6P and 5D stales of cesinm. In our analysis also recombination into the 7P and 6D states is taken into account. The correspondin_g edges occor at 5010, 5825, 10 552 and 11135 A. Therefore. measurements have been performed at wavelengtbs smaller than 5010Á.

The continuurn intensity bas been measured at 4100 and 4900

A.

At these wavelengtbs the con-tinuurn is not affected by line radiation. For the evaluation of the measured intensities tbe radia-live power is divided into an n.-dependent part and a T.-dependent part

e(A)= n~ ·/(A, T.). (7) The ternperature-dependent ~ is shown in fig. 1, forA = 4100

A

and A = 4900

A.

Expression (7) is used to obtain the electron density once tbe

-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<:tion aud about tbe absorption and emission ooefficlents at the wavelengtbs of interest. The molecular concen-tration is calculated using chemica! equilibrium,

nc., =

n~

· 8(T) · exp(&), (9) where nc. is the atomie concentration and D is tbe dissoclation energy (D = 0.45 eV). Since

li (T) depends relatively weakly on temperature, and only a small temperature, range is

con-sidered, 8(T) can be approximated by a

con-stant. The value used is 3.43 x 10-29 _m3 , and is determined from tbe saturated yapor pressores at T = 700 K, Pc.= 27.6 Torr and Pc.,= . 0.625 Torr. D, Pc. and Pc., are taken frorn Lapp · and Harris [5]. Fig. 3 shows the molecular

trac-tion for conditrac-tions which are typical for

MHD-generator plasmas.

Tbe absorptinn cross section of cesium mole-cules bas been measured by Lap~ and Harris [5]. They report that around 4100 À no significant molecular band is present, while around 4900 Ä

a band exists witb a maximum at 4800 Ä. Tbe absorption cross section at 4900 Ä is 5 x

to-

21 _m'. In the subsequent part of this StlCtion the effect of this band on the absorption and emission at 4900 Ä will be estimated separately.

We consider a homogeneaus plasma layer witb tbickness I. Only tbe absorption of light by molecules is regarded. Neglecting the emission of

'""'.---.---,..---..,..,

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.