Magnetic stresses in ideal MHD plasmas

The concept of magnetic stresses in ideal MHD plasma theory is reviewed and revisited with the aim of demonstrating its advantages as a basis for calculating and understanding plasma equilibria. Expressions are derived for the various stresses that transmit forces in a magnetized plasma and it is shown that the resulting magnetic forces on a finite volume element can be obtained by integrating the magnetic stresses over the surface of the element. The concept is used to rederive and discuss the equilibrium conditions for axisymmetric toroidal plasmas, including the virial theorem and the Shafranov shift.

The method had pedagogical merits as it simplifies the calculations, improves the physical understanding and facilitates an assessment of the approximations made in the calculations.