Test-Particle Trajectories in a “Sheared” Stationary Field: Newton–Lorentz and First Order Drift Numerical Simulations1

We study a magnetic field distribution that is nonuniform and sheared like in tangential discontinuities. This distribution is an input parameter for the numerical integration of the equations of motion of the test-particle and of its guiding center. Two different electric field distributions are alternatively tested. In the first case, the electric field is uniform and constant like the electric field prescribed in the large-scale, steady-state reconnection models. The numerical solution shows that in this case the test-particle is trapped within the discontinuity into a region where (i) B goes to zero or (ii) the magnetic vector becomes exactly parallel to the electric field. In the second case, we consider an electric field, which is nonuniform. Its components are computed such that the zero order (or electric) drift is everywhere perpendicular to the discontinuity surface and its value is conserved throughout the simulation. In this case the numerically integrated trajectory of the test-particle penetrates the discontinuity for any angle of shear of B. Direct comparison between exact (Newton–Lorentz) and approximated (first order drift) numerical solutions shows that the mathematical singularities of the latter do not correspond to any physical singularity of the exact equation of motion of the particle.