Application of the Virial Theorem to Equilibria of Toroidal Plasmas

Necessary conditions for equilibrium of a current-carrying toroidal plasma are derived under the assumption of azimuthal symmetry. It is demonstrated that an azimuthally symmetric toroidal plasma can be in equilibrium only if an additional transverse magnetic field is present, which absorbs the expanding force of the plasma. An expression of parabolic pressure distribution is obtained, when the plasma minor radius is much smaller than the major radius. Stability criterion of the plasma ring against displacement is discussed. The weak focusing can be employed to stabilize the plasma ring.