Electron acceleration by a plasma wave in a sheared magnetic field

Using a relativistic two-dimensional single particle code, the acceleration of electrons by a plasma wave, in the presence of a sheared magnetic field (a slab model for the azimuthal magnetic field) is studied. The plasma wave propagates along z-axis while its amplitude profile in the transverse x-direction is Gaussian, E=-∇φ, φ=A/ke-x2/r0'2 sin(ωt-kz+θ). The magnetic field is taken as Bs=-(Bs0x/r0)ye-x2/r02. The electrons that originate off the axis with finite velocity execute oscillatory trajectories in the x-z plane, due to the magnetic field. As they pass through the axial region, the plasma wave accelerates them. The electrons that originate at x0=2, z=0, with vx0=0.1, vz0=0.9, attain maximum energy Emax≅35 MeV for dimensionless plasma wave amplitude ap=eA/m0ωc≅0.6, b0=eBs0/m0ωc≅0.6 , where -e and m0 are the electronic charge and rest mass, respectively