~~ :t I I tth. A0 A066 922 NAVAL RESEARCH LAS WASHINSTOI U C fls 20/9 PLASMA DIFFUSION IN A SPACESIMULATION BEAMPLASMA DISCHARSE. U) ~ Ff5 79 E P SZUSZCZEWICZ. U N WALKER UNCLASSIFIED IeL*3U5 SlIEADE000 276 iii. / I ~~~~~~.
w ~~~ q s ~W7, NRL Memorandum Report 3925 Plasma Diffusion in a SpaceSimulat ion BeamPlasma Discharge. 1 ~~~~ E. P. SZUSZCZEWICZ, D. N. WALKER, and J. C. HOLMES E. 0. Hulburt Center for Space Research and H. LEINBACH NOAAIERLISpa ce Environment Laboratory Boulder, Colorado 80302 1 Cm) February 12, 1979 s DDC~ III ~~~~~~~~~ 919 APR 5 III jjj ~~ 1 L UU L ~~~~ ~ ~ ~ 7:9 02 21 0 (8 ~ NAVAL RZSEA*CH LAIO~ATORY W.ikL.~ io. DC.. ~~ ~~~~~ A~ j...j j h i ubik IdIS~~ dhtilbsdon uaftai$u~... ~~~~~
1 SECURITY CLASSIFICATION OF T ~ 4IS PAGE (P7,.., 0.t. Lnf.,.d) DEDnOT IIM ~~ IITATI ~~~ l DAI READ INSTRUCT ION S E ~~~ ~~~~~~~~~~ ~~~ ~~ ~ BEFORE COMPLETIN G FORM I. REPORI NUMCER 2. GOVT ACCESSION NO 3. RECIPIENT S CATA LOG NUMUER NRL Memorandum Report 3925 4. TITLE (,d SvbISIl.) S. TYPE QF REPORT C PENIOO COVERED ILASMA DIFFUSION IN A SPACESIMULATION BEAM PLASMADISCHARGE Interim report on a continuing NRL problem. 4. PERFORMING ORG. REPORT NUMSER I. AUTNOR(.) I. CONTRACT OR GRANT NUMSER(.) E. P. Szuszczewtcz, D. N. Walker, J. C. Holmes and H. Lalnbach*. PERFORMING ORGANIZATION NAME AND ADDRESS Ia. PROGRAM ELEMENT. PROJECT. TAlE ~~ AR EA I wo rnc UNIT NUMSERS Naval Research Laboratory Washington, DC 20375 NRL Problem A02.11 Subtask RRD38.02.42 II. CONTROLLIN G OFFICE NAME AND ADDRESS 12. REPORT DATE Office of Naval Research February 12, 1979 Axilngton, VirginIa 22217 I). NUMSER OF PAGES 18 ta MONITORING AGENCY NAME I ADDRES S(Il.. dsll.c.u,,i I C.nIvWlMg OWe.) IS. SECURITY CLASS. (.5 ffis. e ~~..t J IC. Dt$TRISUTION STATEMENT (.1 ml. R.p.l) Approved for public release; distribution unllmlt.d. UNCLASSIFIED II.. OEC ~~ Al$lFICATION/OOwNGRAOING SC IAEDULE 17. OISTRISUTION STAT EMENT (.5 ft..b.,rw..,l., d I., 1S.c* 20. II dsu...l 1cS R.pocf) II. SUPPL EMENTARY NOTES *NO ~~ Jg ~~ /Space Environment Laboratory, Boulder, Colorado I. IS. ICY ROA DS (C.uiM,. io p sr ~~ old. St 0 1 11 p ud Sd.RIIfr 5, block nid.bsf) Pl ma phyuira Energetic beasm Beam.pl nua Interactions 20. S$TRACT (c. IM.. tori?..ld. at... o. p ~~ d l* ẹs St block m bcc) ~~ ~ eetrvs density and temperature proflhss have been measured In a largefacility beam.pl ~~~ a dlsch ps (V 3 ~ 1.3 IC.V, 1 3 63 ma) at low pressure (P 24(104 )Torr) and low magnetic 6.14. (B 1.2 G) ~ The issulte follow an ezpon.ntlal behavior and axe found to be In good agreement with a simple diffusion model. The favorable comparison between theory and exp.rl. meet ylside the 6.ut.stimate of crosstisid electron diffusion (D ~ (noun) 2.2(10 6 )cm2/sic) under conditions Intended to simulate Sp.celabborn. beamplasma Investigation.. Thu value for D ~ (Continues) ~~~ DO, ~~~~~~ 1473 (DI TION OF I NOV CC 5 OS$OI.ETC C/N 0102014 slo t I SECURITY CLAUIFICATION OF YNIC PAGE ( ~~~~.i, boa. ~~ IMRdJ, )..... f ~~~~~~. _ ~ L i ~~~, ~~~~ ~~~~~~~~~~~~~~~~~~~
_ SECURITY CLASSIFICATION OF TNIS PAGE (P7 ~.n D.a. Z&..d) 4bstract (Continued) )9v orders of magnitude larger than would be expected for a crossfield collisional diffusion process, a result which Is Identified with the turbulent state of collective beamplasma Interactions..L. SECURITY CLAS$IPICATION OF THIS PAOE ~~~ oa boa..u.,.d) I.. C ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,, A.... 9 ~ ~~
~~ w ~ 1 ~~. CONTENTS I. D ~ TRODI.ICTION...... 1 NTAL RESULTS............... 2 II. ~~ PERD ~. III. THEORETICAL CONSIDERATIONS....... 3 IV. COMPARISON BE1WEEN THEORY AND ~ CPERIMENT...... 6 V. SU ~ *(ARY.................... 8 AC ~~~~ LEDG ~~~ NTS.......... 10 REFERENCES................... 11 ~~~! ~ ION for White sectice W DOC 6ut SectI0i1 ~ 0 I UNANNOUN 0 ~~~ ~~~ s.i/or #. ~~~. ~~..f d, ~ ~ j :.i., ~~ al 1 ~~,p.. 11
C ~~~~~~.. c i PLASMA DIFFUSION IN A SPACES IMULAT ION BEAMPLASMADISCHARGE I. INTRODUCTION Beamplasma interactions have received increased attention in recent years largely as a result of considerations bearing on vehicle neutralization during spaceborne accelerator experiments, enhanced beamplasma ionization processes, and in general, collective phenomena initiated by beam injection into neutral gas and charged particle environments. With plans for Shuttleborne experiments directed at controlled beamplasma interactions and the use of beams to probe ionospheric/magnetospheric electric and magnetic fields, it became important to conduct laboratory simulations which supported the Shuttle plans and helped establish definitive Shuttleborne experi ments. k As part of just such a plan involving a continuing investigation of largefacility beamplasma interactions (Bernstein, et al, 1975,1977,1978) the Naval Research Laboratory (NRL )participated in a recent series of experi ments at the NASA Johnson Space Center (JSC). The NRL Note: Manuscript submitted Dsc.mber 11, 1673.. p :
~ w contribution involved the direct measurement of electron density and temperature under varying conditions of beam plasma and neutral gas parameters. Reported here are tile first large facility profiles of electron density and temperature under conditions of enhanced beamplasma ionization...conditions which have come to be known as the BPD, tile beamplasmadischarge (Getty and Smullin, 1963; Bernstein et al.,1978). The observed density profile is found to be in good agreement with a twodimensional diffusion model and this result makes possible the first estimate for the crossfield electron diffusion coefficient in a large facility BPD. In the following Sections the experiment is described, the theoretical model is defined, and the diffusion coefficient is derived. II. EXPERIMENTAL RESULTS The Experiment. The technique of the pulsedplasmaprobe (P 3 ) was employed to measure the beamplasma profile. The P 3 provides simultaneous measurements of N e ~ T e~ V 0, and ón (+P e n (k)) and is particularly useful under dynamic plasma conditions and in environments that can contaminate electrode surfaces (Holmes and Szuszczewicz, 1975 ; Szuszczewicz and Holmes, 1975,1976,1977). Both these conditions prevailed to various degrees in the JSC experi ments. The experimental configuration (similar to that de:cribed by Bernstein et ~~~ I r T TTTTTT. ~~~~~~~~~~~~~., ~~~~~~~
b W ~ Figure 1. The P 3 was mounted on a traversal mechanism positioned at approximately 8 m above the injection point of the beam. The tungsten cathode gun was operated at 63 ma and 1.3 Ky DC with the chamber pressure in the 2_4(lO _6 ) torr range. A combination of coil current and the Earth s field established vertical and horizontal component B fields at 3 z~ 1 2 gauss and B x_fo 2? gauss, respectively. Under these conditions a BPD was established and the probe traversal mechanism was exercised to determine the plasma s radial profile out to 4.6 m. The resulting measurements of T and N e e are presented in Figure 2. Following the diffusionmodel densityprofile predictions (discussed below) the experimental curves were fit with exponential distributions found to be T e [lo s KJ= 6.93 exp (r/l.99 ) (1) N e tio 6 cm 3 ] 7.01 exp (r/2.49) (2) III. THEORETICAL CONSIDERATIONS For purposes of comparison, a simple twodimensional diffusion model is developed which follows the approach used in the study of small laboratory arc plasmas by Bobm et al., (l949a). The approach suggests the consideration of a differential plasma element of thickness dr and of length h t. I.:i::. parallel and equal to the length of the beam as depicted in Figure 3. The differential element is taken outside the of the :e :nimat bb1 ~~~ : T : : ~~~ ~ ~~~~~~~~~~~~ I,
~~~~ w along its length. The equilibrium density then arises from the balance of charge accretion by differential drift across the element, i.e., j e ~ 1 ) j e (1 ~~ 1 ) ~ and end losses (ZO and h) due to axial diffusion. Requiring ~~ e 1 dt = 0 and assuming an axial diffusion loss directly proportional to density (i.e., differential end losses 2 cx N e dr), the balance between production and loss requires (dj e /dr) h 5r 2a N ~ ~ r ( ) ~~ which is rewritten as dj e /dr IIII _2a : Ne /h. (4a) Similar arguments for the plasma s ion component yield dj 1 /dr = 2 c& ~ N i /b (4b) Independent of Eqs. (3) and (4) the diffusion currents and j can be described by their respective mobility ~ equations ( dn en dv ~ ~~~~~~~~~ ~~~~~~~~ ~~ ii ~ i ~~ ~ ( dn ~ en 1 dv and j D ~ ii ~~ + ~~~ i ~ j (5a) ~~~~~~~ (5b) where V is an electric potential and D e and D 1 are the perpendicular electron and ion diffusion coefficients, I respectively. Taking the onedimensional spacederivative 4 d/dr of Eqs. (5) and substituting (4) yields I
~~ w. ~~ 2): ~~~ ~r (~~~ N e _ dv) dr 2 k dr\ e dr when N e N ~ and the terms have been rearranged. Addition of Eqs. (6) eliminates the putentialdependent term and results in d 2 N e = 2 h ~~ aeff T+ a. 1 DT. dr 2 I DDj (T ~ + T e ) N ~ 8 2 N e (7) with a solution (N exp (BR) N R ) 1 N e ~~ N. ~~ e ~ exp (8r) (exp (BR) exp(br) ~ + N exp (j3r) e e (exp (BR) exp (BR)) exp( ~ r) (8) t 4 I I In the limit R + ~~ the solution becomes N e N e exp ($r ) (9) where 2(a e D ~~~ ~l/2 ~ j T e + z D e T i ). (10) B DD ~ (T 1 + T e ) h : ~~~~~~~~~~ _ ~~~~~~~~~~~~~~. ~~~~~~~~~~ ~
~~~~ w ~~~ IV. COMPARI SON BETWEEN THEORY AND EXPERIMENT The agreement between theoretical prediction (Eq.(9)) and experimental results is found to be good (see bottom panel, Fig. 2) and provides the opportunity for determining the effective electron diffusion perpendicular to the magnetic field, i.e., the radial diffusion in the model of Fig. 3. To accomplish this, consider 1im 8 ~~ _(D ~ h/ 2.49 (11) e)1 T 1 /T ~ s O where the value on the right side is taken from the exponential in Eq. (2). In addition, consider as the effective velocity of axially diffusing electrons which have sufficient energy to overcome chamber sheath potentials and be completely lost to the system. In this case, ~ :, /; ~i;: ; exp (_ev c /i T ~ e ) (12) where V ~ is the chambersheath potential. With V ~ (4.8 ~~~~ )kt 5 /e (Chen, 1965 ; Szuazczewicz, 1972) and 3 (1O ~ ) ~~ Eq. (12) yields ~~ (nom.) 7.0 (1O ~ ) cm /500 (13a) ~ (max) 2.8 (los ) cm /sec (13b ) 8, I ~~ ~~~~~
cz (mlxi ) 4.3 (l0 ~ ) cm /sec (13c) Substituting the values into Eq. (11) provides D ~ (nom ) 2.2 (10 6 ) cm 2 /sec (14a) D (max ) 8.8 (10 6 ) e cm 2 /sec (l4b) D ~ (min ) 1.3 (10 6 ) cm 2 /sec ( 14c) as the first experimental estimate of the effective electron diffusion coefficient perpendicular to the magnetic field in a BPD. The values for D are orders of magnitude larger than would be expected for crossfield collisional diffusion. This result in itself is not surprising since a variety of observations indicate that the diffusion of plasma across magnetic lines of force can be substantially enhanced above the collisional diffusion rate when fluctuating fields are present in the plasma (Spitzer, 1962 ; Kadomtsev, 1965). This is indeed the case in a BPD which has as one of its characteristics the presence of fluctuating electric fields that are associated with large amplitude plasma waves. The enhancement of diffusion in turbulent plasmas goes back to Bohm et al. (1949b) who semiempirically doscribed the rate by what has come to be known as the Bohm diffusion coefficient ~ D 6.25 (10 6 ) T B 5 B 1 czn 2 /sec (15) k lii I ~~~~~~~~~~~~~~~~ ~~~~~~~~~ j~~~v
~~ w where LT j = e V and [B] gauss. For our nominal temperature of 3(1O ~ ) K and a total field B = 1.2 gauss ~ Eq. (13) yields D = B l.3(10 6 )cm 2 /sec. This calculation has not been intended to confirm or deny the validity of Eqs. (14) but has been presented as the only possible comparison with an existing concept of turbulent diffusion. While the Bohm formula appears to apply to a surprising number of different experiments, care must be exercised so that the illusion of universal validity does not automatically develop. It is evident that a firstprinciples derivation of the coefficient of turbulent diffusion cannot be obtained without a detailed investigation of the plasma, particularly the fluctuation power spectra and associated instability processes (Kadomtsev, 1965 ; Pap ~ adopou1os, private communication 1978). The experimental and theoretical aspects of these details, as they relate to the JSC experiments, are currently underway at NRL (Szuszczewicz and Papadopoulos, private communication 1978). V. SUMMARY The first experimental radial profiles of electron density and temperature in a large facility beamplasmadischarge are found to fit exponential functions defined by 1 and T e [ K] = 6.93 (10 ~ ) exp (r [ m] /1.99) 8 ~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ~~
. N e (cm 3 ] = 7.01 (10 6 ) exp (r( m ] /2.49). ~ While the present stage of research does not provide a theoretical basis for the temperature distribution, the electron density results do agree wit.i a two c ir. ~ e:i ~ ioiia1 diffusion model which predicts N e N e exp (2./D h) ~ r } in the limiting case of large chambers with T j /T e ~~ s.o With taken as the effective velocity of axially diffusing electrons (assigned a nominal value of 7 (1O ~ ) cm/eec) the identity of the experimental profile with the theoretical prediction yields D L (nom) = 2.2(10 6 ) c111 2 /sec for the radial electron diffusion across a superimposed magnetic field. This is the first such determination in a largefacility BPD and points to a process substantially faster than crossfield collisionil diffusion. The reason for this is identified with the presence of large amplitude plasma waves and their associated electric fields. While enhanced crossfield diffusion appears to be a characteristic of many turbulent plasma environments, the observations reported here are particularly unique in that 4 the applied magnetic field is at best. ~~~ times weaker than in any other turbulent diffusion investigation. This points to the importance of an unequivocal determination, J 9,. i._ ~ ~~, ~~., ;: ~~~~.. ~~~~~~~~~~~~~ ~~~ wa.
~~~~~~~ w. ( I of the turbulence spectra and the associated instability processes. This work is currently underway at NRL. ACKNOWLEDGEMENTS This work was supported by the Office of Naval Research under Program Element 6ll53N33 in Task Area RR03302. The authors would like to thank Drs. Owen Oarriott and H. Friedman for suggesting and making possible the NRL participation in the JSC experiments. We also wish to thank W. Bernstein and Dr. D. Papadopoulos for their review of the manuscript, their support in the activities, and their helpful suggestions. Sincere thanks are also extended to the large number of people at JSC who helped rig the P 3 configuration and the traversal mechanism. 10 j ~~~ ;i~~~~ ~~~~~~~~~. ~
~~ w ( REFE RENCES Bernstein, W., H. Leinbach, H. Cohen, P.S. Wilson, T.N. Davis, T. Hallinan, B. Baker, J. Martz, R. Zeinike, and W. Huber, Laboratory observations of RF emissions at W pe and (N + I)W CE in electron beamplasma and beamplasma interactions, J.Geophys.Res. 80, 4375, 1975. Bernstein, W., H. Leinbach, and B. Baker, Preliminary results from the electron beamplasma experiments in the very large vacuum facilities at Plum Brook and Johnson Space Center, NOAA Technical Memorandum ERLSEL 5 August 1977. Bernstein, W., H. Leinbach, P. Kellog, S. Manson, T. Hallinan, O.K. Garriott, A. Konradi, J. McCoy, P. Daly, B. Baker, and H.R. Anderson, Electron beam injection experiments : The beamplasma discharge at low pressures and magnetic field strengths, Geophys.Res. Lett. 5, 127, 1978. Bohm, D., E.H.S. Burbop, H.S.W. Massey, and R.M. Williams, in Characteristics of Electrical Discharges in Magnetic Fields, edited by A. Guthrie and R.K. Wakerling, McGraw Hill, New York l949a, Ch. 9. Bohm, D., E.H.S. Burhop, and R.S.W. Massey, in Characteristics of Electrical Discharges in Magnetic Fields, edited by 4 A. Guthrie and R.K. Wakerling, McGrawHill, New York 1949b, Ch. 2. 11 ~~ ~~~~~~~~~~~~~~
4 Chen, F.F., in Plasma Diagnostic Techniques, edited by R.H. Huddlestone and S.L. Leonard, Academic, New York 1 ~ )U5, Cli. 4. Holmes, JC. and E.P. Szuszczewicz, A versatile plasma probe, Rev.Sci.Instr. 46, 592, 1975. Kadomtsev, B.B., Plasma Turbulence, Academic Press, New York, 1965. Spitzer L. Jr., Physics of Fully Ionized Gases, John Wiley, New York, 1962. Szuszczewicz, E.P., Area influences and floating potentials in Langmuir probe measurements, J.Appl.Phys. 43, 874, 1972 ; V 4.8kT 0 e /e has been selected as a nominal value since the wall conditions are considered more appropriately identified with the thin sheath conditions in ~ Figs. 3 and 6 of this Ref. Szuszczewicz, E.P., and J.C. Holmes, Surface contamination of active electrodes in plasmaè: Distortion of conventional Laxigmuir probe measurements, J.Appl.Phys. 46, 5134, 1975.. Szuszczewicz, E.P., and J.C. Holmes, Reentry plasma diagnostics with a pulsed plasma probe, AIAA Paper No. 76393, AIAA 9th Fluid and Plasma Dynamics Conference (San Diego, CA/July 1976). Szuszczewicz, E.P. and J.C. Holmes, Observations of electron temperature gradients in midlatitude E 8 layers, J. Geophys. Res. 82, 5073, 1977. 12 a ~~~~ ~~~~~~ ~ ~~~~~~~~~~
~~~ w ( I 30m COLLECTOR SUPPRESSO PHOTOMETER R/ ~~~~~~~~~~~~~~ j ~~~~ S _ ~~~~~~~~~ _ ~~~ ITV GUN I 1 I I TRAVERSAL j 8m. AXIS I # 1 20m Fig. I Experiment configuration utilized in the largefacility beamplasma invest igationa at the Johnson Space Center.. ~~~~~~~ 13 : ~~~~~~~~ 7 ~~~~~ ~~~~~~ ~~~~~~~~~~~~~~~~~ ~~~~~~~ ; ~~~~~~~~~~~~~ d ~~
~~~ w 1 I I I I I I I I I I I I I I I 4 3. ELECTRON TEMPERATURE i. T.[1 ~ KJ =6.93 exp( ni 99) 5 4 ELECTRON 2 6 2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ RADIAL DISTA NCE FROM CENTER [MI I I I I I 2 3 4 Fig. 2 Ra dial profiles of electron density and temperature under conditions of the beamplassm discharge. I $ 1 j I 14 i S ~~~
~~~~ w ~ ~~ ANODE I ~~ Ii. ( ) j ~ (r i dr) I I! r R r+dr.1 I V I Fig. 3 Aas*~~ sd configuration for diffusionmodel calculation s. 15 ~~~~ ~~~~~~~~~~~~~~. ~. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~ ~~~~~~~ ~.