The dispersion characteristics and the resonant instability mode of the space-charge wave are investigated in a streaming Lorentzian dusty plasma column by using the normal mode analysis. The result shows that the non-thermal character of the Lorentzian cylindrical dusty plasma enhances the unstable property of the space-charge wave due to the beam–plasma interaction. It is found that the resonant growth rates of the space-charge wave increase with an increase of the harmonic-order of the root of the Bessel function. It is also found that the influence of the self-gravitation enhances the resonant growth rate of the space-charge wave of the Lorentzian cylindrical dusty plasma. In addition, it is found the resonant growth rate decreases with an increase of the radius of the dusty plasma column. The variation of the resonant instability mode due to the non-thermal character and geometric effects is also discussed.
Cyclotron damping of the space charge wave of a beam in a nonuniform magnetic field region