Electrostatic probe characteristics for a spherical probe in a slightly ionized continuum plasma

...~.~.. International $ounud of Mau Spectrometry and Ion Physics, 24 (1977) 359--361 • ) _Et~vier Scientific Pab]~l,;,~ Company, Am,d ~ l a m - - P r i n t e d in The Netherlands

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ELECTROSTATIC PROBE CHARACTERLqTICS F O R A SPHE.I~,TCAL PROBE IN A SLIGHTLY IONIZED CONTINUUM PLASMA F.H_ D O R M A N

and J.A.

HAMILTON

C.qlRO Divfzion o f M i n ~ Chemistry. 1).0. Baz 124. Port Melbounw, V~c. 3207

(Am~tr~i~)

(Received 11 October 1976)

ABSTRACT C u n ~ n t - ~ o t e n t i a l characteristics have been calculated for sphefie.al probes in a slightly ionized continuum p t ~ m , with the parameter ranges o f e (ion/electzon temperature)

0.01, 0.1, 0.5, 1.0; pp (probe radius/pla.~n~ Dehye ]~n~h) 5, 10, 20, 30; and 0 < yp< 7 where yp is the normalized probe potential.

The nomenclature has been given in a previous paper [1]. R~pedmentally it is relatively easy to obtain currant--potential curves for electrostatic probes o f spherical, cylindrical or planar configuration when they am immersed in a sufficiently quiescent plasma. However, the theoretical dezivation of the charged particle concentration from these e x p e x i m e n t a l r e s u l t s h a s b e e n conti~versial, p a t ~ ~ at .the higher pressures (p ~ 1 tozr) o f interest to p l~L~a chemi~s. We have shown previously [1] that only Cohen's continuum theory [2] ~,Alows a zeasonably accurate calculation to be made for p > 1 t o z r and spherical probes. All other theozies, such as that o f Su and T=m [3] based on highly negative probe appro~m~tions, are not in agreement with the physics

of ion--molecule zeactions. Cohen's theoretical current potential characteristics were calc-lAted-, [2] using asymptotic approximstions valid only for a • sufficiently large p p ~ 50. F o r low pp; yp and e -~ 0.01 there are no c h ~ avaflable, whilst the extrapolation of Cohen's curves to pp ~. 5 - 1 0 iS u n ~ . _:." We report here the theoretical ch~actexistics for 5 < pp:~ 30 obtained • b y using an electronic analogue computer [4_]. T h e full description of the

method.used is somewhat lengthy..[5]. B d .efly,it:c~nsisted _in solving the c 0 n t i n ~ n " e q u a t i p n s [2] for p~ticular.values o f y p and pp"todetermine J± •and So obtaining a set of points, from which a characteristic, cu~rent~-POtent~! curve:could-be draWn;--.The c0mputer-curve for"..-.::n~".-.~-"-". and~. ' y:. . ; .did-not cross the .'!:.:-~::.=-i-'-:.'"." " - : " - . ~ : ~ . . . " . :~ : " ~ - ' - " - = ~ ' : . : ' " - ! . " ~ . . - . . ' : : ~ ' " - . " : : . . .'...~"-"':'- ..... •,

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Fig. 2. The,difference A(eJ+) between the eJ÷ o f our Fig. l(a) and Su and Lam's [31 Fig. 7 plotted against the nomlalized probe potential Yw

quasineutral curves o.£ n± and y' Versus 1/~. The accuracy foz~d . and J_ was estimated at about 0.01. Figure 1 shows the results for pp ~ 5. Below pp = 5 the asymptotic approach of the computer n± curves to the q-~;neutral solution became less d~finite for reasons z~zted to the electronics 0arge dynamic range requizvd in the divider in the computer time base). Figure 2 shows the error i n c u n ~ it Su and Lam's [3] theory is used for e = 0 . 0 1 a n d 1 0 <~ pp <~ 3 0 . W e n o t e t h a t t h e i r t h e o r y is a c c u r a t e o n l y f o r yp>6. REFEREN~ 1 2 3 4 5

F.H. Dormau and J.A. I4~mUton, InL J. Mass Spectrum. Ion Fhys., 20 (1976) 411. TM. Cohen, PhyL Fluid~ 6 (1963) 1492. CJ~I. Su and S~L Lain, Phy~ Fluid~ 6 (1963) 1479. J ~ . l~pmflton, J. Chem. Educ., 52 (1975) 341. F.H. Dorman and J.A. I ~ m i l t o n , An iterati~ method for determ;n;-~ the curr~t-potential curves o f a spherical probe in s alightly ionized continuum plasma, with 5 ~ pp ~ 50, yp ~ 7, CompuL Fluid~ in p.-v~

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