  This paper is a first step toward understanding the effect of toroidal
geometry on the rigorous stability theory of plasmas. We consider a
collisionless plasma inside a torus, modeled by the relativistic Vlasov-Maxwell
system. The surface of the torus is perfectly conducting and it reflects the
particles specularly. We provide sharp criteria for the stability of equilibria
under the assumption that the particle distributions and the electromagnetic
fields depend only on the cross-sectional variables of the torus.
