The possibilities of electron acceleration by ponderomotive force of a circularly polarized laser pulse in magnetized quantum plasma have been explored. The basic mechanism involves acceleration of electron by the axial gradient in the ponderomotive potential of the laser. The quantum effects have been taken into account for a high-density plasma. The ponderomotive force of the laser is resonantly enhanced when Doppler up-shifted laser frequency equals the cyclotron frequency.

The out-of-equilibrium situation in which an initially sharp-edged cylindrical electron beam, that could, e.g., model electrons flowing within a wire, is injected into a plasma is considered. A detailed computation of the subsequently produced magnetic field is presented. The control parameter of the problem is shown to be the ratio of the beam radius to the electron skin depth. Two alternative ways to address analytically the problem are considered: one uses the usual Laplace transform approach, the other one involves Riemann's method in which causality conditions manifest through some integrals of triple products of Bessel functions.