# Head-on collision of nonlinear solitary solutions to Vlasov-Poisson equations

## TL;DR

This study investigates the stability and collision dynamics of nonlinear solitary solutions to the Vlasov-Poisson equations in a plasma, revealing stability categories, instability mechanisms, and electron hole merging behaviors through kinetic simulations.

## Contribution

It provides a comprehensive kinetic analysis of solitary solution stability, categorizes solutions by Mach number, and uncovers detailed electron hole interaction mechanisms.

## Key findings

- Solutions are categorized as stable, semi-stable, and unstable based on Mach number.
- Bipolar electron flux structures seed net-neutrality instability during collisions.
- Electron holes can merge with varying degrees, exchanging phase space cores in non-integer rotations.

## Abstract

Nonlinear solitary solutions to the Vlasov-Poisson set of equations are studied in order to investigate their stability by employing a fully-kinetic simulation approach. The study is carried out in the ion-acoustic regime for a collisionless, electrostatic and Maxwellian electron-ion plasma. The trapped population of electrons is modeled based on well-known Schamel distribution function. Head-on mutual collisions of nonlinear solutions are performed in order to examine their collisional stability. The findings include three major aspects: (I) These nonlinear solutions are found to be divided into three categories based on their Mach numbers, i.e. stable, semi-stable and unstable. Semi-stable solutions indicates a smooth transition from stable to unstable solutions for increasing Mach number. (II) The stability of solutions is traced back to a condition imposed on averaged velocities, i.e. net neutrality. It is shown that a bipolar structure is produced in the flux of electrons,early in the temporal evolution. This bipolar structure acts as the seed of the net-neutrality instability, which tips off the energy balance of nonlinear solution during collisions. As the Mach number increases, the amplitude of bipolar structure grows and results in a stronger instability. (III) It is established that during mutual collisions, a merging process of electron holes can happen to a variety of degrees, based on their velocity characteristics. Specifically, the number of rotations of electron holes around each other (in the merging phase) varies. Furthermore, it is observed that in case of a non-integer number of rotations, two electron holes exchange their phase space cores.