Compact Plasma and Focused Ion Beams

175Plasma Buildup by Short-Pulse, High-Power Microwaves

Assuming a Maxwellian electron energy distribution F(E), 〈

σ

v〉 is given by

ssvE

FEdEN

E

m

g

E

i

=

∞

∫

2

()() .

(10.14)

By substituting

FE

E

T

E

T

ee

() exp

/

=−













2

32

p

(10.15)

and assuming that

σ

is almost linear near the threshold as

s

E

T

A

E

T

E

T

ee

i

e













=−













,

(10.16)

where A (= 2.5 × 10

−17

cm

2

/eV) is the slope at the threshold of the ionization

cross section, we obtain from Equation 10.14

sx

xx

vC=+













−













2

11

ex

p,

(10.17)

where

C

E

m

NA

i

g

=

22

p

(10.18)

and

ξ

= T

e

/E

i

. Substituting the values of the constants, we obtain C = 2.35 × 10

8

p (s

−1

), where p is the pressure in Torr.

The ionization rate 〈

σ

v〉 given by Equation ...