Electrostatic “bounce” instability in a magnetotail configuration

To understand the possible destabilization of two-dimensional current sheets, a kinetic model is proposed to describe the resonant interaction between electrostatic modes and trapped particles that bounce within the sheet. This work follows the initial investigation by Tur et al. [Phys. Plasmas 17, 102905 (2010)] that is revised and extended. Using a quasi-parabolic equilibrium state, the linearized gyro-kinetic Vlasov equation is solved for electrostatic fluctuations with period of the order of the electron bounce period. Using an appropriated Fourier expansion of the particle motion along the magnetic field, the complete time integration of the non-local perturbed distribution functions is performed. The dispersion relation for electrostatic modes is then obtained through the quasineutrality condition. It is found that strongly unstable electrostatic modes may develop provided that the current sheet is moderately stretched and, more important, that the proportion of passing particle remains small (less than typically 10%). This strong but finely tuned instability may offer opportunities to explain features of magnetospheric substorms.