Influence of Non -thermal Electron Parameter on Heavier Masses of Negative Ion Plasma

In presence of non-thermal electrons, theoretical investigations on ion-acoustic solitary waves are made in a collisionless unmagnetized warm plasma consisting of positive and negative ions by the well known pseudopotential technique. The influence of non-thermal electron parameter(β) on heavier masses (Q) of negative ion plasma for Sagdeev potential function[ψ(φ)], first (φ1)and second (φ2)order solitary wave solutions are mainly analysed and discussed here properly.

of positron. Regarding this non-thermal electron plasma, earlier authors did not take the heavier masses of negative ion plasma and also did not show the effect of non-thermal electron ( )on heavier negative ion masses(Q). The present author thus tried to take the heavier negative ion plasma(Q) and studied the influence of non-thermal electron parameter(β) on heavier masses of negative ion plasma.
The working plan of the present paper is arranged in the following way: In sec.2 we investigate the exact form of the Sagdeev potential function ψ(φ) in warm and cold ion plasma with an analytical calculation of the max. Value of the electrostatic potential ( ) i.e. amplitude where ψ( ) = 0 , first ( 1 ) and second

FORMULATION
We consider a collisionless unmagnetized plasma consisting of warm non-thermal electrons, positive and negative ions with drifts. The governing normalised basic set of equations along x-axis for such types of unbounded plasmas are Equation of continuity: (1) Pressure equation: Poisson's equation: In this case where is the temperatures of ion and is the temperature of electron, Where β =

1+3
[with ≥ 0 and 0≤ < For solitary wave solution we assume that the dependent variables depend on a single independent variable η defined by where V is the velocity of the solitary wave .The boundary conditions are Following Chattopadhyay 19 and using the above transformation (8) & boundary conditions (9) we get finally from equations (1) to (4) (11a) By equation (7) we get from equation (11a) For n  to be real the following restrictions on  is From equations (1) to (4) after using the boundary conditions (9), the above transformation relation (8) and by the equation (7) we can write finally equation (11b) as Where The above function (ф) can also be written in the following form: Also the form of the said function (ϕ) for cold positive and negative ion plasma is given by The function (ф) in (15) is called the sagdeev potential and it will be reduced to that form of potential which Cairns et al 14

Condition for solitary wave solution and its consequences
The first order soliton solution ( 1 ) will be real and finite only when It is also evident from (18) that the first order solution may be compressive or rarefactive.
Again the second order soliton solution ( 2 ) will be real and finite only when 1 > 0 and 4 2 2 -18 1 3 > 0 The condition for the existence of solitary wave solution will be obtained from 1 > 0 [i.e. In absence of cold negative ion ( 0 = 0, = 0) and for 0 → 1, inequality (20a) supports Ref. 16 . Again in another words for absence of non-thermal electron (β = 0), inequation (20a) supports Ref. 19 . For cold non-thermal plasma [ = 0, = 0], the above condition (20a) reduces to the form This gives the condition for real second order ( 2 ) soliton solution along with (20a). For cold non-thermal plasma the above condition (21a) reduces to the following form For cold positive ion non-thermal plasma (i.e. in absence of cold negative ion = 0), inequality (21b) reduces to the following inequality The max.value of the electrostatic potential (ϕ= ) for second order solitary wave solution so obtained may be either positive (i.e. compressive in nature) or negative (i.e. rarefactive in nature), satisfied all the three cases (21a), (21b) and (21c).
In case of non-drifting positive and negative ion plasma (i.e. = 0, = 0) with nonthermal electron (β ≠ 0), inequality (21b) reduces to the following form:  Figure 1 represent the respective Sagdeev potential (ψ) function at β = 0, 0.09 and 0.2 with Q = 35.5. It is also seen from those figures that 1 < 2 < 3 due to increase of β for a higher mass ratio Q. This is the effect of β on Q.
Moreover a comparison between a non-thermal and an isothermal electron plasma is also observed.  In figure 3, the profiles of Sagdeev potential function ( ) verses electrostatic potential ( ) with the variation of the concentration of heavier negative ion (nj0) plasma are shown.