Stability analysis of Hasegawa space-charge waves in a plasma waveguide with collisional ion beam

The dispersion relation for the Hasegawa space-charge wave propagating in a cylindrical waveguide dusty plasma containing collision-dominated ion stream is derived by using the fluid equations and the Poisson equation which lead to a Bessel equation. The solution of Bessel equation is null at the boundary and then the roots of the Bessel function would characterize the property of space-charge wave propagation. We have found that the Hasegawa space-charge wave can be excited for a large axial wave number. The growth rate of excitation increases as the order of the roots of the Bessel function increases. The growth rate decreases with an increase of the radius of cylindrical waveguide as well as with an increase of the collision frequency. We found that the disturbance of wave can be damped only for small wave numbers.