On the plasma-sheath transition in low temperature plasmas: on the existence of a collisionally modified Bohm criterion (CMBC)

Table of Contents

1 Theorists view the Bohm criterion as approximately true, holding only for collisionless plasmas: the question is whether there exists a collisionally modified Bohm Criterion (CMBC). Here we are thinking only of single ion species plasmas
- 1.1 many theoretical works are devoted to this question–most theorists believe that there is no CMBC
- 1.2 R.P. Brinkmann's 2011 paper compares many theoretical models, all of which show that `the Bohm speed' falls further below the ion sound speed as λ_D/λ grows
  - 1.2.1 the meaning of the Bohm speed here is not the usual one
  - 1.2.2 I don't know whether there are similar liberties taken in the other theories
2 My proposal is to take up the question experimentally, purposely varying λ_D/λ over the range 2x10^-2 < λ_D/λ < 1, measuring
3 Previously results from this group suggests that increased collisionality may be achieved by going to lower density as well as higher density discharges
4 Results from this week–tentatively–we seem to have found a low pressure case of enhanced collisionality, in which < v > < C_s at the sheath edge.

1 Theorists view the Bohm criterion as approximately true, holding only for collisionless plasmas: the question is whether there exists a collisionally modified Bohm Criterion (CMBC). Here we are thinking only of single ion species plasmas

1.1 many theoretical works are devoted to this question–most theorists believe that there is no CMBC

1.2 R.P. Brinkmann's 2011 paper compares many theoretical models, all of which show that `the Bohm speed' falls further below the ion sound speed as λ_D/λ grows

Brinkmann's main result:
The Bohm speed is that ion speed at which ``diffusive, ambipolar dynamics'' gives way to ``unipolar flow''... but not exactly the same thing as v_i where space charge appears.

Some references:

Brinkmann's 2011 paper: J. Phys. D: Appl. Phys. 44 (2011) 042002 <\li>
his ref#6: Godyak V A 1982 Phys. Lett. A 89 80
his ref#8: Valentini H-B 1996 Phys. Plasmas 3 1459
his ref#9: Chen X P 1997 Phys. Plasmas 5 804

1.2.1 the meaning of the Bohm speed here is not the usual one

1.2.2 I don't know whether there are similar liberties taken in the other theories

2 My proposal is to take up the question experimentally, purposely varying λ_D/λ over the range 2x10^-2 < λ_D/λ < 1, measuring

2.1 ivdf(z) (LIF measurments, Argon)

2.2 phi(z) (emissive probe measurements, including identification of sheath edge)

2.3 Δ phi(z), potential drop across the presheath

with the goal of assessing what the average flow speed is at the location that space-charge becomes apparent.

3 Previously results from this group suggests that increased collisionality may be achieved by going to lower density as well as higher density discharges

From Oksuz & Hershkowitz¹

p(mtorr)	λ_D/λ
1	2.33x10^-2
0.8	1.96x10^-2
0.65	1.85x10^-2
0.48	4.18x10^-2
0.44	5.7x10^-2
0.44	3.6x10^-2
0.44	3.6x10^-2
0.3	5.45x10^-2

4 Results from this week–tentatively–we seem to have found a low pressure case of enhanced collisionality, in which < v > < C_s at the sheath edge.

Initial measurements, P_n~0.1mTorr Ar, n_e~4e8cm^-3, T_e~3 eV indicate that the ions do not reach the Bohm speed at the sheath edge, as predicted by theory; which theory is best? This is the open question.

We also tried P_n~0.1mTorr Ar, n_e~1e9cm^-3, T_e~3.9 eV;² results indicate that the ions do reach the Bohm speed at the sheath edge, for this case of finite collisionality. What is the ratio of λ_D/λ? That depends on our interpretation of the emissive probe profile!

[1.] Table 1, L. Oksuz & Noah Hershkowitz, PSST vol.14 (2005) 201
[2.] We used 120V on the plasma demon to get the higher electron temperature

Date: 2013-07-19 07:09:54 Central Daylight Time

Author: gds

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