Investigation of cubic non‐linearity‐driven electrostatic structures in the presence of double spectral index distribution function

Abstract

In this article, modified Korteweg-de Vries equation (which involves cubic non-linearity) was derived to study non-linear ion acoustic waves in a plasma in which electrons follow the double spectral index distribution function. The double spectral index distribution successfully apes the distribution functions that have been frequently observed in space plasmas. The spectral index r moulds the distribution function at low energy and by increasing its value, flatness of the distribution enhances. The spectral index r can also have negative values due to which distribution becomes spiky at low energies. The index q, on the other hand, controls the shape of the tail of distribution function. It has been shown that propagation of the solitary structures gets significantly altered by the choice of the double spectral indices, namely, r and q. A comparison was also made, using the parameters of the auroral zone, between the quadratic and cubic non-linearities-driven non-linear structures and it was shown that the solitary structures form on a much shorter scale for cubic non-linearity compared to their quadratic counterpart. K E Y W O R D S(r, q) distribution, KdV equation, modified KdV, nonlinear ion acoustic waves, nonthermal electrons

Ion‐acoustic solitary waves in e‐p‐i plasmas with (r, q)‐distributed electrons and kappa‐distributed positrons

“…The effect of the electron to positron temperature ratio has also been investigated, and we found that maximum amplitudes of compressive and rarefactive solitons increase with the decrease and increase in the temperature ratio, respectively, although the changes are not very large. We also numerically solved the Sagdeev potential (25) and obtained the solitons by following the conditions (26) and (27). Our numerical results showed that solitons can be obtained for subsonic and supersonic regimes in kappa-distributed plasmas.…”

“…where Φ m is the maximum value of potential. From the above Equation 26, Mach number M must fulfil the following condition to obtain a soliton solution from Equation (25).…”

“…Several studies on non-Maxwellian plasmas have shown that wave characteristics change significantly due to the presence of non-thermal distributions and provided a better insight into the underlying physical processes. [22][23][24][25][26] Kappa distribution has been used extensively to study various electrostatic and electromagnetic non-linear waves in astrophysical and space plasmas and is characterized by the spectral index , which basically models the particles with velocities greater than the thermal velocity. A smaller value of signifies a larger number of high-energy particles in the distribution and vice versa.…”

“…[23][24][34][35][36] In recent years, a more general distribution function has successfully been used to model the observed non-thermal particle distributions known as the generalized (r, q) distribution function. [25][26]37] In the last decade, Qureshi et al, [38] in their pioneering work, empirically formulated this distribution function to fit the observed flat top in the particle velocity distribution profiles, which could not otherwise fit, by using other non-Maxwellian distribution functions. The (r, q) distribution not only gives flat tops but also models spikes at low energies along with the modelling of high-energy particles.…”

Nonlinear structure and growth rate of solitary waves for extended Zakharov-Kuznetsov equation in plasma having (r, q) distribution electrons

“…The generalized ( ) r q , distribution has recently been used to explain data in the Earth's magnetosphere [33,34], and its impact on wave propagation in plasmas has also been studied [35,36]. However, the ( ) r q , distribution function's generalized version is [37]…”