Effect of ion temperature on modulational instability and envelope solitons of ion acoustic waves in nonthermal electron–positron–ion plasmas

Abstract

The modulational instability and envelope solitons of ion acoustic waves in an unmagnetized nonthermal electron-positron-ion (epi) plasma are investigated. The ions are taken to be dynamic and warm while electrons and positrons are assumed to be inertialess and hot which follow the kappa (or Generalized Lorentzian) distribution. The Krylov-Bogoliubov-Mitropolsky method is used to derive the nonlinear Schrödinger equation for nonlinear amplitude modulation of ion acoustic waves in nonthermal epi plasmas with warm ions. The dispersive and nonlinear coefficients are obtained for ion acoustic waves in nonthermal epi plasmas which depend on spectral indices of kappa distributed electrons and positrons, ion temperature and positron density. The modulationally stable and unstable regions are studied for a wide range of wave numbers and it is found that the finite ion temperature, positron density and spectral indices of kappa distributed electrons and positrons play a significant role in the formation of bright and dark envelope solitons in nonthermal epi plasmas with adiabatically heated ions. Our findings are applicable to explain some aspects of nonlinear propagation of envelope solitons in astrophysical plasma situations such as neutron stars or pulsars where nonthermal epi plasmas with warm ions can exist

Gardner Solitons in Electron-Positron-Ion Plamsa Featuring Cairns-Tsallis Electrons

“…Where β 1 is a constant depending on the parameter q and µ. Here,|q-q c |is the small and dimensionless parameter and can be given as expansion parameter ε i.e.,|q-q c | ≅ ε and s=1 for q >q c and s= -1for q < q c . So, ρ (2) can be expressed as…”

“…Motivated by these events, Cairns et al(1995) showed that the presence of nonthermal electrons changes the nature of the ion sound solitary structures and allows the existence of both positive and negative ion-acoustic (IA) solitary structures, like those observed by Freja and Viking. Various observations of fast ions and electrons in interplanetary space environments clearly indicate that these particles have velocity distribution functions that deviate from the Maxwellian behaviour (Asbridge et al,1968;Divine and Garret, 1983;Krimigis et al, 1983;Lundlin et al, 1989;Futaana et al, 2003;Shan et al, 2014;Akhtar et al, 2014). Therefore, the Maxwellian distribution may be inadequate to describe the long range interactions in plasmas in the presence of nonequilibrium stationary states because the Maxwellian distribution is valid only for the macroscopic ergodic equilibrium state.…”

“…Thus, the stretched coordinates for these higher order equations which take us to the third order calculations to derive the modified mK-dV equation and hence Gardner equation are ξ=ε (x-v p t) and τ=ε 3 t. Now, on substituting the values of ξ and τ into equations (1)-(3) and using equation 5, we will obtain the same values of n (1) , u (1) and v p as attained during the derivation of the K-dV equation (6). Further, one can utilizes n (1) , u (1) and v p and the next higher order coefficient of ε to have a set of expressions as u (2) = (ϕ (1) ) 2 /2v p 3 +ϕ (2) /v p , n (2)…”

“…ρ (2) = -A(ϕ (1) ) 2 /2 = 0 respectively.It should be noted that the above equation is satisfied identically owing to the criticality condition, i.e., A = 0. After replacing ϕ (1) with ϕ for the sake of simplicity and rearranging the terms we get the following…”

Solitons collision and freak waves in a plasma with Cairns-Tsallis particle distributions

“…Motivated by these events, Cairns et al [3] showed that the presence of nonthermal electrons changes the nature of the ion sound solitary structures and allows the existence of both positive and negative ion-acoustic (IA) solitary structures, like those observed by Freja and Viking. Various observations of fast ions and electrons in interplanetary space environments clearly indicate that these particles have velocity distribution functions that deviate from the Maxwellian behavior [4][5][6][7][8][9][10]. Therefore, the Maxwellian distribution may be inadequate to describe the long range interactions in plasmas in the presence of nonequilibrium stationary states because the Maxwellian distribution is valid only for the macroscopic ergodic equilibrium state.…”