Theory of mass-discrimination effects on ion extraction from continuum flowing plasmas

448 International Journal of Mass SpectrometrJ- and Ion Physics, 16 (1975) 448-450 @I Elsevier Scientific Publishing Company, Amsterdam - Printed in The Kerherlands

Short communication

Theory of mass-discrimination effects on ion extraction from continuum flowing plaSmaS

JEN-SHIH

CHANG*

Groape de Recherches

Ionosphbiques,

C.N.R.S.

45100, Orleans-la-source

(France)

(Received 14 October 1974)

NOTATION

USED

Symbols

Normalized

D e

4

diffusion coefficient electronic charge k Boltzmann’s constant I current density n number density r radius T temperature V probe voltage U flow velocity A mean free path A,, Debye length

=

symbols

eV[kT,

Ra = U,rp

Di Subscrips i

: ion

j, 1

: ion composition

P

:electrode

C73

: infinite

Ion extraction problems are of interest both in plasma chemistry and ion sampling mass spectrometry [l]_ Stahl and Su [2] have proposed an exact numerical treatment of the subsonic flowing continuum probe theory for ionized plasmas in which ion mean free paths 1, << Debye length, 3-0 << probe radius, rp; and the diffusion Reynolds number Ra < (r-,/&J’. This situation applies for medium pressure (2 1 torr) laboratory discharge plasmas, diffusion flames, and lower ionosphere plasma ( < 80 km). * Present z@ress; York University, Center for Research in Earth and Space Science, Downsview, Ontario M3J lP3, Canada_

449 We report here an application of this theory to estimate theoretically t-le mass-discrimination effects on the ion sampling process [1, 31. The numerical results show that the current density flowing to the pIane electrode is given approximately by the expression

where

Di is the diffusion coefficient and U, Is the fiow velocity, r can be determined as a function of normalized potential +P and Ra.

I

I

Illlll~ U--r

15_

I

I

llllll~

I

I

I

Illlli

I

I rrlil

E

--------

7

I

I111111 i0

I

1 %

Free Stream

I lllrrl lo2

I

103

Fig. l_ The low-power constant a vs. the sampling electrode surface potential & for two neutral flow profiles.

The low-power constant o! vs. sampling electrode surface potential is shown in Fig. 1 for both the free stream flow profile and the Blasius flow profile solutions and from these one can estimate the neutral boundary layer [2]. If several ionic species are present, the density ratio of two ionic species j and 1 is given by

From Fig. 1 we can obtain the value of (z- $) which varies between 0.25 and 0.75. Using the simple stationary solution [I], i.e. (a-3) = 1, without taking account of the effects of viscous flow, might mean that we would be over-estimating the mass-discrimination effects.

The author wishes to express his appreciation to Dr. L. R. 0. Storey, Dr_ R. Burke, Dr. J_ G. Laframboise and Dr. P. Michaud for valuable discussions and comments.

1 H. W. Crawin, Plasma diagnoslics, Mass spectranletry of plasmas, Academir: Holland, 1968, p- 777. 2 N. Stahl and C. H. Su, Pays. Flui&, 14 (1971) 1369. 3 E. W. Becker, K. Bier and H. Burghoff, 2. N@urforsch., 10a (1955) 565.

press,

North