Bifurcation of space-charge wave in a plasma waveguide including the wake potential effect

The wake potential effects on the propagation of the space-charge dust ion-acoustic wave are investigated in a cylindrically bounded dusty plasma with the ion flow. The results show that the wake potential would generate the double frequency modes in a cylindrically bounded dusty plasma. It is found that the upper mode of the wave frequency with the root of higher-order is smaller than that with the root of lower-order in intermediate wave number domains. However, the lower mode of the scaled wave frequency with the root of higher-order is found to be greater than that with the root of lower-order. It is found that the influence in the order of the root of the Bessel function on the wave frequency of the space-charge dust-ion-acoustic wave in a cylindrically confined dusty plasma decreases with an increase in the propagation wave number. It is also found that the double frequency modes increase with increasing Mach number due to the ion flow in a cylindrical dusty plasma. In addition, it is found that the upper mode of the group velocity decreases with an increase in the scaled radius of the plasma cylinder. However, it is shown that the lower mode of the scaled group velocity of the space-charge dust ion acoustic wave increases with an increase in the radius of the plasma cylinder. The variation of the space-charge dust-ion-acoustic wave due to the wake potential and geometric effects is also discussed. Published by AIP Publishing.This paper is dedicated to the late Professor P. K. Shukla in memory of exciting and stimulating collaborations on physical processes in complex dusty plasmas. One of the authors (Y.-D.J.) gratefully acknowledges Professor W. Roberge for useful discussions and warm hospitality while visiting the Department of Physics, Applied Physics, and Astronomy at Rensselaer Polytechnic Institute. This research was initiated while one of the authors (Y.-D.J.) was affiliated with Rensselaer as a visiting professor. The work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MISP) (No. 2016R1A2B4011356)