Ion Bernstein Mode Instability in Presence of Ion Cyclotron Turbulence Associated with Particle Heating

This study aims to investigate the ion Bernstein mode instability through nonlinear resonant interaction process of particles with ion cyclotron turbulence and subsequent transfer of accelerated particle energy for the onset of Bernstein mode instability. We consider a particle distribution function for non-uniform plasma involving density gradient parameter. The ion cyclotron wave turbulence is considered to be present in the system and the fluctuating parts of this quasi-steady plasma state corresponding to this turbulence is evaluated on the basis of weak turbulence theory. In this quasi-steady state of plasma, we have considered the ion Bernstein mode wave as perturbation to the system. Non-linear interaction of ion Bernstein mode with turbulence field is described by Vlasov-Poisson system of equations and the various linear and non-linear fluctuating parts of distribution functions are evaluated. By using Poisson’s equation, we acquire the non-linear dispersion relation of ion Bernstein mode with the involvement of ion cyclotron turbulent energy. An expression of growth rate of Bernstein mode is obtained by the influence of turbulent energy as well as the gradient parameters which can be analysed for the onset of instability.