Plasma sheaths and boundary layers around stagnation point electrode

Chen, M. M.

English

NASA Technical Reports Server

23 Way 1966 
EXPERIMENTAL kND THEORETICAL RESSARCFI 0?7 PLAWA SHEAW-S 
AND BOUNDARY LAYERS AROUND STAGNATIOY POITW ELECTRODES 
* r  
SEMI-ANNUAL PROGRESS RIIPORT VO. 3 
1 July 1955 to  31 December 1964 5 
NASA Grant lJSG 724 
Prepared for: 
National Space and Aeronautics Administration 
Office of Grants and Research Contracts 
Prepared by: 
GPO PRICE s 
CFSTl PRICE(S) S 
I Microfiche (M F) 
?ficcEzael Ring Chen 
Project Director 
Assistant Professor 
Department of Engineering 
and Applied Science 
Yale University 
New Haven, Connecticut 
ff 653 July 65 
https://ntrs.nasa.gov/search.jsp?R=19660018248 2020-03-16T19:05:49+00:00Z
. .  
2, 
S I ? Y  
During the period covered by the report, a fairly detailed space 
resolved experimental survey of the plasma and electrode observables has 
been made, 
sustained thermionic cathode. 
tion in a temperature dependent medium, which had been described previously. 
was being continued. 
physical processes taking place in the sheath, electrode boundary layer 
A parametric macroscopic theory ham been developed for a self- 
The stability theory for electrical conduc- 
In addition, a re-examination of the microscopic 
and the electrode surface has. been undertaken. 
3. 
I. Introduction 
This report describes the work performed during the third six-month 
period (1 July 1965 to 31 December 1965) of the two-year program entitled, 
"Experimental and theoretical research on plasma sheaths and boundary lay- 
ers around stagnation point electrodes," sponsored by the Office of Grants 
and Research Contracts, National Aeronautics and Space Administration. 
technical monitor for NASA is Mr. Howard Stine, Ames Research Center. 
The 
Personnel currently engaged in this research are: Professor Michael 
M. Chen, Chief Investigator; Fessrs. Elihu Zimet and Elliot Wyner, graduate 
students. 
XI. Technical Discussions 
1. Experimental Program. 
The design, calibration, and some preliminary results of the 
stagnation point electrode experiment had previously been described in pre-  
vious Progress Reports . During the present period, detailed, systematic 
measurements of the surface temperature, electrode potential (relative to 
a reference probe), and space resolved plasma ,-temperature and electron 
concentration distribution as a function of electrode current have been com- 
pletedZy3. 
and interpretation, the data probably represents the first measurement where- 
in space resolved plasma conditions and electrode characteristics are obtained 
simultaneously. Since it is not possible at this time to make any theoretical 
calculation of the processes involved without unjustified assumptions, no 
attempt was made to compare these data with predicted results. 
1 
While much remains to be done in terms of further improvements 
These data are described in Informal Interim Report No. 3 to be 
submitted simultaneously with the present report. 
revision, this Informal Interim Report will form the basis for a Special 
It is planned that after 
4. 
Technical Report summarizing all the experimental data taken during the first 
phase of the present research program. 
A brief summary of the above report has subsequently been given 
as a technical paper3 at the AIAA Plasmadynamics Conference, llonterey, Cali- 
fornia, March 2-4, 1966. 
Appendix 1. 
An abstract of this paper is included here as 
2, Parametric HecrescoTic Theories. 
In order to bypass the overwhelming difficulties in connection 
with simultaneous solution of macroscopic and microscopic aspects of the 
problem, it was decided to decouple them through the use of undetermined par- 
ameters, leaving the evaluation of the parameters to a separate phase of the 
program. The intercoupling of the macroscopic equations through these para- 
meters was investigated in an attempt to gain insight on the basically macro- 
scopic phenomena of discharge constriction. Two different studies were made, 
to be described in two separate Informal Interim Reports. 
concerning the characteristics of self-sustained thermionic cathodes, showed 
that if a phenomenological relationship of thermionic mission is known, the 
detail of the sheath and electron impact zone are unimportant as far as the 
electrical characteristics are concerned. A linear stability analysis fur- 
ther showed that a uniform discharge is unstable with respect to transverse 
perturbation whose wave numbers are smaller than the critical value3: 
4 The first study 
3 where je, Vs, 4, GET , q, Ks, denote electron current, sheath potential, work 
function, thermal radiation, plasma conduction, and solid thermal conductivity, 
respectively. Equation (1) thus gives an explanation for the tendency of 
cathodes to revert to “spot mode operation. It is interesting to note that 
for typical laboratory conditions, the critical wave number corresponds to 
a dimension of the order of milimeters which is consistant with known cathode 
spot dimensions. 
. .  
A second study’ concerns the tendency of the plasma to constrfct 
due to a coupling between the energy equation and the electrical conduction 
equation. The study is thus more relevant in the plasma boundary layer sur- 
I re-mding the electrode. Due to the complexity of the ;aathematira?. prublem, only unrealistically simple boundary conditions have been solved to date. I 
These show that: 
(a) In general, contriction is possible if 12112>> (3 1 
r r  
UT, u and K are I d(&nal > 1, where s = d(kns) and 
Tr 
temperature dependent electrical and thermal conduc- 
tivities, j is the current density, is a characteristic I 
thickness, and subscript r denotes reference values eval- 
uated at electrode surface temperature. 
5 (b) For the simplest case, the critical wave number is 
The computed wave length for ac at typical plasma conditions were also con- 
sistant with the observed characteristic dimensions. While this agreement 
is probably fortuitous in view of the simplifications used in the analysis, 
they are nevertheless valuable in providing new insight to the problem. 
Portions of the above results have subsequently been described 
in a presentation at the Seventh Symposium on Engineering Aspects of Magneto- 
hydrodynamics . 6 An abstract of this presentation is given in Appendix 2. 
6. 
3. Microscopic Physical Processes. 
Neglecting non-uniformities and other  macroscopic features ,  a 
c r i t i c a l  examination of the atomic sca l e  physical  processes governing refrac- 
to ry  cathode operation has been carr ied out f o r  t yp ica l  laboratory conditions . 
These included t ransport  processes in the  cathode i n t e r i o r ,  on the  cathode 
surface and i n  the  p l a s m  sheath, co l l i s ion  processes i n  the  plasma and on 
the  surface,  and the  emission processes, 
mate calculat ions were used t o  judge the p l a u s i b i l i t y  and r e l a t i v e  importance 
of each competing process. 
models of cathode operation were e i the r  theore t ica l ly  inconsistent or not 
applicable t o  re f rac tory  cathode operations. I n  pa r t i cu la r ,  it was found t h a t  
(a) Cathode heat conduction is not negl ib le  as of ten assumed (b) Ion current  
cannot accodnt f o r  al l  the  electrode heating (c) Radiative t ransfer  and thus 
photoemission cannot be neglected without fu r the r  study. 
conclusions, a new model of refractory cathode is t en ta t ive ly  formulated, 
assuming t h a t  the  electron emission t o  be a combined r e s u l t  of f i e l d  enhanced 
thermal emission and photoemission, and tha t  the electrode heating t o  be 
caused by both electron impact and atomic l i n e  radiat ion.  
of t h i s  model with experimental data showed it t o  be more sa t i s f ac to ry  than 
earlier models. However, t he  model cannot be quant i ta t ive ly  evaluated u n t i l  
some key parameters, pa r t i cu la r ly  the r a t i o  of ionizing co l l i s ions  and versus 
exc i ta t ion  co l l i s ions  and the  r a t i o  of high energy photons (photoemitting) 
and low energy photons can be found e i t h e r  experimentally or theore t ica l ly .  
6 
Cm-sistency argumzts and approxi- 
The resu l t  indicated tha t  many of the  ex i s t ing  
In view of these 
Preliminary checks 
The d e t a i l s  of t h i s  analysis are t o  be described i n  a forthcoming 
7 Informal Interim Report . 
111. Financial  Report 
Since a separate f inanc ia l  report  is  being submitted, the  matter s h a l l  
not be dea l t  with here. 
, 7. 
IV. Future Plans 
In the remaining six-month period of the current program, emphasis w i l l  
be placed on the f ina l  refinement and interpretation of the results obtained 
t o  date. These w i l l  be described in  a series of four technical reports. 
A proposal for a continued research program describing the planned 
activities for the next two years, has already been submitted to  NASA. 
i 
8- 
REFEREMCES 
1. "Experimental and Theoretical Research on Plasma Sheaths and Boundary 
Layers around Stagnation Point Electrodes'*, Semi-Annual Progress Re- 
por ts  No. 1, Jan. 1965. No. 2, Aug. 1965. Grant No. NSG 724, Submitted 
by Y a l e  University t o  National Aeronautics and Space Administration. 
2 .  "Experimental Investigation of a Stagnation Point Electrode", Informal 
Interim Report No. 3 ,  NASA Grant MSG 724,  prepared by M. N. Chen and 
E. Z i n e t ,  Yale University, (April 20, 1966)- 
3. Chen, M. M. and Z i m e t ,  E., "The Stagnation Point Electrode Experiment", 
AUIA Paper No. 66-190. Presented a t  the AIAA Plasmadynamics Conference, 
Monterey, California,  March 2-4, 1966. AIAA Bulletin 3, 1, p. 25 (1966). 
(Results of these experiments are described i n  d e t a i l  i n  reference 5 above). 
4. "Characterist ics and Stab i l i ty  of Sei€--Sustained One-dimensional Ther- 
mionic Cathode", Informal Interim Report No. 1 NASA Grant NSG 724, 
(April 2 0 ,  1966). 
5 .  "Fundaasental Conditions f o r  Uniform Current Distribution in  a Medium 
with Temperature Dependent Conductivity", Informal Report No. 2, NASA 
Grant NSG 724,  prepared by M. M. men, Yale University, (April 25,  1966). 
6 .  Chen, M. M., "Some Elementary Considerations Concerning the Uniformity 
of Elec t r ica l  Conduction Through Gases", Preprint  Book of Seventh Sym- 
posium on Engineering Aspects of Yagnetohydrodynamics, Princeton, Hew 
Jersey, Piarch 30 - April  1, 1966. (Materials contained in t h i s  presen- 
tation are discussed in references 3 and 4 ) .  
7 .  "Physical Processes Governing the Operation of Refractory Cathodes in 
Dense Gases", Informal Interim Report No. 4 ,  NASA G r a n t  NSG 724,  prepared 
by N. M. Chen, Yale University, (April 25, 1966). 
APPENDIX I 
Abstract: "Stagnation Point Electrode Experiment" 
By: M. 11. Chen and E. Z h e t  - Yale University 
Paper AIAA No. 66-190 - AIAA Plasmadynamics Conference, Monterey, California,  
March 2-4, 1966. 
By placing a test electrode in the  stagnation region of an arc 
heated argon J e t ,  s t ab le  symmetric electrode operation could be achieved. 
When operated as an anode up t o  about lo2 Amp/em2. 
charac te r i s t ics  showed clear departures from the usual probe charac te r i s t ics .  
When operated as a cathode, the  electrode followed the  usua l  probe ion 
current curve u n t i l  a breakdown point is reached. 
thermionically , reaching a current density of 102A/cm2. The voltage current 
charac te r i s t ics  could be represented approximately by the  simple theore t ica l  
resul t  J(V -4) - const. spectroscopic measurements were also made, showing 
the excite8 states t o  be not in equilibrium with the plasma conditions. 
The current-voltage 
After which it behaved 
t 19. 
APPENDIX 2 
Abstract: "Some Elementary Considerations Concerning the Uniformity of 
Electrical Conduction Through Gases" 
By: M. M. Chen 
Seventh Symposium ~n Fngineertnng Aspects of Y!!eteydm&mandcs, Princatoc, 
New Jersey, March 30-April 1, 1966. 


Experimental and Theoretical Research on Plasma Sheaths and Boundary Layers Around Stagnation Point Electrodes  Semiannual Progress Report No. 3, 1 Jul. - 31 Dec. 1965

Experimental and Theoretical Research on Plasma Sheaths and Boundary Layers Around Stagnation Point Electrodes Semiannual Progress Report No. 3, 1 Jul. - 31 Dec. 1965

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