Oscillating Two-Stream Instability of a Plasma Wave in a Plasma Channel

A long wavelength Langmuir wave (uio, ko), propagating through a parabolic plasma density channel, can decay into a low-frequency mode (*v,k) and two short wavelength Langmuir wave sidebands (̂ '1,2, &i,2), via two-stream instability where w l i2 = u =p uio and fci 2 = k =p ko. Depending on the mode number n, the growth rate maximizes in the range 7max — O.lu-'pj —QAuip, for the range of k from ().l(ujpi/cs) to ().2(ujpl/c8) for co ~ (th where VQ and eth are the oscillatory and thermal velocities of electrons, ^p; is the ion plasma frequency on the axis, and cs is the sound speed. The growth rate increases with the width a of the plasma density channel. It decreases with the mode number. The instability may be relevant to laser based charged particle accelerators.