Page 43 - swp0000.dvi

At equilibrium, we have the neutrality condition,

 0 =  0 +    0 +    0  (2.2)

where   and   are the charge numbers for negatively charged hot and

cold dust, respectively.   and   are the cold and hot dusty plasma ve-
locities, respectively. The quantities,  ,   ,  ,and   are the number

densities of the plasma species and  0,  0,  0,and  0 are the corre-

sponding equilibrium number densities.

As the ions are assumed to be nonthermaly distributed, we chose a
more general class of distributions; the velocity distribution function with

a population of fast energetic particles [120] given by

1 1
4
2
  ()= √ (1 +  )exp(−  ) (2.3)
(1 + 3) 2 2

where the velocity  is normalized by the mean ion thermal speed  
and  is a parameter governing the population of nonthermal ions in our

plasma model. The effect of electrostatic disturbances of the equilibrium
2
ion distribution can easily be introduced by replacing  in the exponent
in equation (2.3) by  +2. Integrating the resulting distribution function
2
over the entire velocity space yields

∙ ¸
  
  =  0 1+  +  ( ) 2 exp(− )
     
4
 =  (2.4)
1+3

2.3 Nonlinear Analysis

According to the derivative expansion method [?], the independent vari-

ables in equation (2.1) are stretched as [138]:

31