We considered a homogeneous, collisionless two species plasma consisting of electrons and ions (H+ ions) in the simulation model. The ambient plasma parameters for ions and electrons are given in Table 2. The ions and electrons are considered to be fluid and their dynamic is incorporated into the simulation model using the following model equations viz., the continuity, momentum, and pressure equations of each species, and the Poisson equation (Kakad et al. 2014) given by
1



∂nj∂t+∂(njvj)∂x=0,



2



∂vj∂t+vj∂vj∂x+1mjnj∂Pj∂x−qjmjE=0,



3



∂Pj∂t+vj∂Pj∂x+γjPj∂vj∂x=0,



4



∂E∂x=∑jqjnj/ϵ0.

Here, the electric field E = −∂ϕ/∂x and the variables n

j
, P

j
, and v

j
 are the plasma density, thermal pressure, and velocity of species j, respectively. The subscripts j = e and j = i are, respectively, used for electrons and ions. m

j
 and q

j
 represent the mass and the charge of species j, respectively. For electrons q

e
 = −e and ions q

i
 = e., ϵ
0 is the electric permittivity. In Equation (3), electrons and ions are treated as adiabatic with the same adiabatic index γ

e
 = γ

i
 = 3. The above set of equations is solved numerically. The spatial derivatives in these equations are solved using the fourth order central finite difference method and time derivatives are integrated using the leap-frog method to achieve second order accuracy. The details of the development of the simulation model are given in Kakad et al. (2013). We used a compensated filter to eliminate the small wavelength modes linked with such numerical noise (Lotekar et al. 2016; Kakad et al. 2016b). These numerical schemes are highly stable, and in the past, several electrostatic solitary wave structures have been modeled using such fluid simulations in multispecies plasmas (Kakad et al. 2014, 2016a). Δx and Δt are respectively considered as the grid size in spatial and time domain, and their values are taken in such a way that it fulfills the Courant–Friedrichs–Lewy condition, i.e., 



cΔtΔx≤1

, which is necessary for the convergence of the explicit finite difference method. Here, c is the speed of light. We performed two simulation runs in a one-dimensional system with the periodic boundary conditions by considering the observed ambient parameters as (i) T

e
 = 60 eV, T

i
 = 300 eV, n

i0 = 15/cc, n

e0 = 15/cc, V
di = V
de = −50 km s−1 (2) T

e
 = 30 eV, T

i
 = 300 eV, n

i0 = 15/cc, n

e0 = 15/cc, V
di = V
de = −50 km s−1 (see Table 2 for more details). In the simulations, we considered the real mass ratio, i.e., m

i
/m

e
 = 1836. The background electron and ion densities satisfy the quasi-neutrality, i.e., n

e0 = n

i0 = n
0. For electron temperature, two values are considered based on the observations, i.e., 60 and 30  eV (see Figure 6(d)). The values of ω
pi, ω
pe, λ

i
, and λ

e
 for the considered parameters are 5.1 × 103 rad s−1, 2.18 × 105 rad s−1, 33.3 m, and 14.9 m, respectively. To initiate the simulations, we used a localized Gaussian-type initial density perturbation in the equilibrium electron and ion densities given by
5



δn=Δnexp−x−xcl02.

Here, Δn and l
0 are the amplitude and width of the initial density perturbations, respectively. Thus, the perturbed density at t = 0 is n

j
(x) = n

j0 + δn. We consider the simulation system length as L

x
, and x

c
 = L

x
/2 is the center of the simulation system. We performed two simulation runs for the parameters given in Table 2. For these simulation runs, we consider the time interval dt = 1 × 10−3, the grid spacing dx = 0.2, system length L

x
 = 7000, l
0 = 1, and Δn = 0.1. Here, time is expressed in units of ω
pi
−1, space is in λ
di, and density is in units of n

i0.
Citation: Lotekar et al. 2016
Citation function: Uses