Turbulent spectrum of Alfvén waves excited by a kinetic instability for explaining the modulations with multi-timescales in solar flares

Abstract

A low-frequency wave is treated as a local oscillation to modulate the guiding center of electrons beam, which is considered as free energy to excite Alfven waves by a kinetic plasma instability under low-frequency approximation. The nonlinearity of the model is shown by a critical value of the amplitude of the low-frequency wave, and Alfven waves are growing in a broad turbulent spectrum with fractional harmonics, which strongly depend on the criterion. The instability is limited in the direction nearly perpendicular to the ambient magnetic field. The growth rates are very sensitive to the beam speed that perpendicular to the magnetic field, the propagational angle, and the magnetic field strength, but not sensitive to the beam speed parallel to the magnetic field. This model is used to explain the modulations with multiple timescales in the flare light curves at radio, hard X-ray and H-alpha bands.