Whistler mode waves for ring distribution with A.C. electric field in inner magnetosphere of Saturn

Whistler mode waves can propagate upstream without collision impact. They are generated in these areas of vibration. They are known to play a crucial role in thermodynamics and electron acceleration. Sometimes, in some cases, they are seen as waves that strike the wavefront. Mercury, Earth, Venus and Saturn are the planets where whistlers have been recorded in the upstream regions. They are right handed waves and can be left-hand polarized in the frame of spacecraft due to the strong negative Doppler shift. The weaker Doppler shift owes to the large angle between magnetic field vectors at 10 AU (Astronomical unit) and the solar wind velocity. These waves propagate with an angle between 10 to 60 degrees to background magnetic field. In the present paper, we took an advantage of Cassini present in the Saturnian magnetosphere to explore the whistler mode wave’s importance. A dispersion relation for obliquely as well as for whistler waves propagating perpendicular to the magnetic field, has been applied to Saturnian magnetosphere. Using the observations made by Voyager and Cassini, growth rate has been determined for non-relativistic plasma. Whistler waves are excited by temperature anisotropy, where the vertical temperature is higher than the parallel temperature. The effect of electron density, temperature anisotropy, energy density with some other parameters on the growth of whistler mode emission is studied. The result is found to be in good agreement with observations. Whistler mode wave interaction with particles basically emphasizes on the increase (decrease) in the energy of resonant particles and this variation is related to the transfer of energy to (from) other resonant particle group where the wave is the mediator of the energization process. Due to the non-monotonic nature of the ring distribution, at vertical velocities, the magnification produced by this instability is larger than the typical bi-Maxwellian anisotropy distribution because the wave can maintain resonance over a longer portion of its orbit.