Relativistic distribution functions, fluid equations and equations of state for magnetized electron streams

A class of anisotropic relativistic distribution functions for magnetized electron streams and the corresponding fluid equations are proposed, supposing a dominant Lorentz force and weak collisions between particles. Equations of state and the relativistic second law of thermodynamic quantities are derived that are not limited to small temperatures. The proposed form of the distribution function and thermodynamic relations were developed to model the energetic population in electron cyclotron current drive experiments, but may also be applied to other laboratory and space plasma science problems.