Two-dimensional studies of relativistic electron beam plasma instabilities in an inhomogeneous plasma

Relativistic electron beam propagation in plasma is fraught with several micro instabilities like two stream, filamentation, etc., in plasma. This results in severe limitation of the electron transport through a plasma medium. Recently, however, there has been an experimental demonstration of improved transport of Mega Ampere of electron currents (generated by the interaction of intense laser with solid target) in a carbon nanotube structured solid target [G. Chatterjee et al., Phys. Rev. Lett. 108, 235005 (2012)]. This then suggests that the inhomogeneous plasma (created by the ionization of carbon nanotube structured target) helps in containing the growth of the beam plasma instabilities. This manuscript addresses this issue with the help of a detailed analytical study and 2-D Particle-In-Cell simulations. The study conclusively demonstrates that the growth rate of the dominant instability in the 2-D geometry decreases when the plasma density is chosen to be inhomogeneous, provided the scale length 1/ks of the inhomogeneous plasma is less than the typical plasma skin depth (c/ω0) scale. At such small scale lengths channelization of currents is also observed in simulation.