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In this paper, we introduce and discuss an exactly energy-conservingParticle-in-Cell method for arbitrary curvilinear coordinates. The flexibilityprovided by curvilinear coordinates enables the study of plasmas incomplex-shaped domains by aligning the grid to the given geometry, or byfocusing grid resolution on regions of interest without overresolving thesurrounding, potentially uninteresting domain. We have achieved this throughthe introduction of the metric tensor, the Jacobian matrix, and contravariantoperators combined with an energy-conserving fully implicit solver. Wedemonstrate the method's capabilities using a Python implementation to studyseveral one- and two-dimensional test cases: the electrostatic two-streaminstability, the electromagnetic Weibel instability, and the geomagneticenvironment modeling (GEM) reconnection challenge. The test results confirm thecapability of our new method to reproduce theoretical expectations (e.g.instability growth rates) and the corresponding results obtained with aCartesian uniform grid when using curvilinear grids. Simultaneously, we showthat the method conserves energy to machine precision in all cases.

Exactly energy-conserving electromagnetic Particle-in-Cell method in curvilinear coordinates