On the Complex-Valued Distribution Function of Charged Particles in Magnetic Fields

In this work, we revisit Boltzmann's distribution function, which, together with the Boltzmann equation, forms the basis for the kinetic theory of gases and solutions to problems in hydrodynamics. We show that magnetic fields may be included as an intrinsic constituent of the distribution function by theoretically motivating, deriving and analyzing its complex-valued version in its most general form. We then validate these considerations by using it to derive the equations of ideal magnetohydrodynamics, thus showing that our method, based on Boltzmann's formalism, is suitable to describe the dynamics of charged particles in magnetic fields.

Automated summary

In this work, the authors revisit Boltzmann's distribution function and show that magnetic fields can be included as an intrinsic constituent of the distribution function by theoretically deriving its complex-valued version in its most general form. They validate these considerations by deriving the equations of ideal magnetohydrodynamics, demonstrating the suitability of their method for describing the dynamics of charged particles in magnetic fields.