Effect of magnetization and magnetic field variation on stationary axisymmetric equilibrium
The inclusion of plasma magnetization in the equations of stationary equilibrium is derived, and its effect on the determination of axisymmetric equilibrium calculated. A factor of 2 on the pressure gradient arises in the equilibrium equation from the force felt by the dipole moment density. The algebraic and differential equation formulations are compared both with and without consideration of magnetization, revealing the effects of both magnetization and magnetic field variation on the equilibrium, which become more pronounced for high pressures in a weak external field. The equivalence of the magnetized equilibrium equation with the standard equilibrium equation in the limit of vanishing magnetization is demonstrated.