Computing Ideal Magnetohydrodynamic Equilibria

Nuclear fusion research promises to harvest the excess energy carried by energetic neutrons when Deuterium and Tritium hydrogen isotopes are fused together to form (alpha)-particles. Pressure and density conditions needed for these fusion reactions ensure that these charged constituents, together with the free electrons, form a fully ionized plasma at temperatures of about 100 million Kelvin. Any contact with material walls would instantaneously cool the plasma and must be avoided. In the axisymmetric toroidal vessel of a tokamak, a hot plasma is confined primarily by magnetic Lorentz forces. Strong helical magnetic fields that trace out nested toroidal surfaces help to thermally insulate the plasma from the walls and support it against its own pressure gradient. To lowest order, a fluid model of the equilibrium considers only this force balance in the poloidal cross-section of the tokamak, as expressed analytically by the Grad-Shafranov equation