  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
$\infty$.
