Spiraling ion beam driven electrostatic ion cyclotron wave instabilities in collisionless dusty plasma

The numerical calculations of the growth rate in long parallel wavelength are made for a spiraling ion beam propagating through a collision less magnetized dusty plasma cylinder that drives electrostatic ion cyclotron waves to instability via cyclotron interaction. It is found that the growth rate of the instability of the electrostatic ion cyclotron waves increase in the long parallel limit with the density ratio of negatively charged dust grains to electrons. The growth rate of the unstable mode has the maximum value for the modes whose Eigen functions peak at the location of the beam and varies as the one-third power of the beam current in both the limits.