Upconversion of whistler waves by gyrating ion beams in a plasma

A gyrating ion beam, with a ring-shaped distribution in velocity, supports negative energy beam modes near the harmonics of beam gyro-frequency. An investigation of the non-linear interaction of high-frequency whistler waves with the negative energy beam cyclotron mode is made. A non-linear dispersion relation is derived for the coupled modes. It is shown that a gyrating ion-beam frequency upconverts the whistler waves separated by harmonics of beam gyro-frequency. The expression for the growth rate of whistler mode waves has been derived. In Case 1, a high-amplitude whistler wave decays into two lower frequency waves, called a low-frequency mode and a side band of frequency lower than that of pump wave. In Case 2 a high-amplitude whistler wave decays into two lower frequency daughter waves, called the low-frequency mode and whistler waves. Generation mechanism of these waves has application in space and laboratory plasmas.