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.
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