Equilibrium of a toroidal plasma in a magnetic field

Equilibrium conditions are obtained for an axisymmetric toroidal plasma column by expanding in terms of a/R (where a and R are the bore radius and the radius of the torus), without specifying any particular form for the distribution of the current and longitudinal magnetic field over the cross section of the plasma. The only assumption made is that in the zero-order approximation ( R = ∞ the plasma possesses cylindrical symmetry. Improved formulae are given for the displacement of the plasma column in a conducting shell; these formulae are valid in the second approximation, i.e. taking into account terms of the form b 2 / R 2 , where b is the radius of the shell.