A nonlinear theory for multidimensional relativistic plasma wave wakefields

Abstract

A nonlinear kinetic theory for multidimensional plasma wave wakes with phase velocities near the speed of light is presented. This theory is appropriate for describing plasma wakes excited in the so-called blowout regime by either electron beams or laser pulses where the plasma electrons move predominantly in the transverse direction. The theory assumes that all electrons within a blowout radius are completely expelled. These radially expelled electrons form a narrow sheath just beyond the blowout radius which is surrounded by a region which responds weakly (linearly). This assumption is reasonable when the spot size of the electron beam and laser are substantially less than the blowout radius. By using this theory one can predict the wakefield amplitudes and blowout radius in terms of the electron beam or laser beam parameters, as well as predict the nonlinear modifications to the wake’s wavelength and wave form. For the laser case, the laser spot size must also be properly matched in order for a narrow sheath to form. The requirements for forming a spherical wave form, i.e., “bubble,” are also discussed. The theory is also used to show when linear fluid theory breaks down and how this leads to a saturation of the logarithmic divergence in the linear Green’s function.