Time-centered, hence second-order, methods for integrating the relativistic momentum of charged particles in an electromagnetic field are derived. A new method is found by averaging the momentum before use in the magnetic rotation term, and an implementation is presented that differs from the relativistic Boris Push [1] only in the method for calculating the Lorentz factor. This is shown to have the same second-order accuracy in time as that (Boris Push) [1] found by splitting the electric acceleration and magnetic rotation and that [2] found by averaging the velocity in the magnetic rotation term. All three methods are shown to conserve energy when there is no electric field. The Boris method and the current method are shown to be volume-preserving, while the method of [2] and the current method preserve the E × B velocity. Thus, of these second-order relativistic momentum integrations, only the integrator introduced here both preserves volume and gives the correct E × B velocity. While all methods have error that is second-order in time, they deviate from each other by terms that increase as the motion becomes relativistic. Numerical results show that [2] develops energy errors near resonant orbits of a test problem that neither volume-preserving integrator does.

No abstract

No abstract

Abstract. Increasing the high energy electron yield from laser wakefield acceleration is crucial to its development as an electron beam source. We present a scheme for charge yield enhancement using two equal-intensity pulses-or hot spots in a single laser pulse-intersecting at a small angle. Experiments on the Texas Petawatt Laser with two well-defined hot spots yielded more than ten times as much charge as the single-hot-spot case. VORPAL particle-in-cell simulations suggest the charge yield enhancement depends on the hot-spot intersection angle and the relative phase between spots.