Continuous Family of Equilibria of the 3D Axisymmetric Relativistic Vlasov-Maxwell System

We consider the relativistic Vlasov-Maxwell system (RVM) on a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, assuming axisymmetry in the problem. We construct continuous global parametric solution sets for the time-independent RVM. The solutions in these sets have arbitrarily large electromagnetic field and the particle density functions have the form $f^{\pm }={\mu }^{\pm }(e^{\pm }(x,v),p^{\pm }(x,v))$, where $e^{\pm }$ and $p^{\pm }$ are the particle energy and angular momentum, respectively. In particular, for a certain class of examples, we show that the spectral stability changes as the parameter varies from $0$ to $\mathrm{\infty }$.