Recent theoretical studies on the use of neutral beams (NB), rotating magnetic fields (RMF) and helicity injection (HI) to form and sustain compact toroids are reported. A Monte Carlo code was employed to study NB injection in Field Reversed Configurations (FRC) and Spheromaks. The code calculates the ionization of the neutral particles and follows the exact orbits of the ions. The magnetic field and density profiles are determined by solving a Grad-Shafranov equation that includes the beam current. RMF current drive in FRCs was studied using a fully 2D code that solves the two fluid equations with massless electrons and uniform temperature. The ion momentum equation includes viscosity and collisions with electrons and neutrals. The electrons are described using an Ohm's law with the Hall and pressure gradient terms. Ion spin up due to collisions with electrons reduces the current drive efficiency and a large fraction of neutrals is needed to keep the azimuthal ion velocity small. The principle of minimum rate of energy dissipation was employed to calculate relaxed states for a flux core spheromak sustained by helicity injection. States with large regions of closed flux surfaces and significant toroidal current were found. Changing the resistivity profile modifies the safety factor profile, which can change from one that has a maximum at the magnetic axis (for uniform resistivity) to a tokamak-like q-profile.

The conditions required for efficient current drive in a weakly resistive plasma column, subject to a double helix traveling magnetic field, are examined in detail by using a simple non-linear Ohm's law for the plasma. In agreement with previous numerical work on the subject by Bertram [5], it is shown that field penetration is indeed strongly limited when large external bias longitudinal magnetic fields are used. However, there is a range of small external bias fields that allow for significant penetration when reasonable driving fields are used. This should be of interest for sustaining reversed-field pinches and toroidal screw pinches.

We derive a system of equations to describe stationary axisymmetric MHD equilibria characterized by toroidal and poloidal flows as well as plasma anisotropy due to strong magnetic field and eventual auxiliary heating methods. The system consists of a nonlinear partial differential equation for the poloidal magnetic flux function and an algebraic Bernoulli-type equation, which relates plasma density with several surface functions. We analyse the ellipticity of the equation and the plasma density bifurcation as the Alfvén-Mach number is changed.