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ABSTRACT  We describe a new scheme for evolving the equations of force‐free electrodynamics, the vanishing‐inertia limit of magnetohydrodynamics. This pseudo‐spectral code uses global orthogonal basis function expansions to take accurate spatial derivatives, allowing the use of an unstaggered mesh and the complete force‐free current density. The method has low numerical dissipation and diffusion outside of singular current sheets. We present a range of one‐ and two‐dimensional tests, and demonstrate convergence to both smooth and discontinuous analytic solutions. As a first application, we revisit the aligned rotator problem, obtaining a steady solution with resistivity localized in the equatorial current sheet outside the light cylinder.

Introducing phaedra : a new spectral code for simulations of relativistic magnetospheres