Algorithms for electron dynamics in a Lorentz plasma – a case study of algorithmic plasma physics

Standard algorithms, such as the RK4, symplectic RK4, and Euler-Maruyama, have been developed for solving generic deterministic and stochastic differential equations. However, these methods are not most suitable for applications in plasma physics. Using the example of electron dynamics in a Lorentz plasma, we demonstrate that it is necessary to develop custom structure-preserving geometric algorithms that preserve the symmetries and conservation laws specific to the system, including space-time symmetry and energy-momentum conservation, covariance, gauge symmetry, and symplecticity. These desirable features ensure the accuracy in physics generated by the algorithms, but also limit their applicability as general algorithms for generic differential equations. These bespoke algorithms belong to plasma physics. They make up a subset of plasma physics that can be appropriately called algorithmic plasma physics. The proposition that plasma physics has intrinsic algorithmic components should not be surprising. For example, to model the physics of electron pitch angle scattering, the governing stochastic differential equation cannot be correctly formulated without choosing an algorithm first, be it the Ito integral, Stratonovich integral, or others.