Geoscience Reference

In-Depth Information

Fig. 5.24

An approximation of the form of a protuberance (
a
); dependence from Eq.
5.30
at

b

D

1(
b
)

Here
b
is the radius of the basis of the ellipsoidal asperity and
a
is its height. The

dependence given by Eq.
5.30
is shown in Fig.
5.24
b.

Having applied for simplicity the known approximation of the ionization and the

dissociative attachment sum of frequencies (Mayhan
1971
):

E

E
cr

1
!
; ˇ

ˇ

i
a
D
a

5:34;

(5.31)

and using Eq.
5.27
, we estimate the speed of the asperity development in the

coordinates of the front:

r
E
cr
Q.a;b/
ˇ

0

1

1

@

A

da

dt
D
V
fr

r
E
cr
ˇ

1

:

(5.32)

1

For small values of
a
the approximation is fair:

2

a

b
; a

Q.a;b/
1
C

b:

(5.33)

Taking Eq.
5.33
into account, it is easy to determine the increment of the asperity

development:

V
fr

b

ˇ

4
.E=E
cr
/
ˇ
:

max

(5.34)