An analytic spherical torus plasma equilibrium model is developed from a general solution to the Grad–Shafranov equation. The analytic model allows the calculation of axisymmetric plasma equilibria with arbitrary aspect ratio, elongation, triangularity, and diamagnetism. Using a numerical method, examples of optimized analytic equilibria are presented with plasma profiles similar to those of bootstrapped spherical tokamaks. Numerical results obtained from analytic equilibrium solutions for plasmas with aspect ratios A=1.4, elongations κ=3.0, and Troyon factors g=6.7 suggest that spherical tori can achieve toroidal beta values as large as βt≈35% at poloidal beta values βp≈1.53, with stable magnetic wells, W⩾0.

Numerical simulations of the evolution of large-scale magnetic fields have been developed using a mean-field Ohm's law. The Ohm's law is coupled to a A' stability analysis and a magnetic island growth equation in order to simulate the behavior of tokamak plasmas that are subject to tearing modes. In one set of calculations, the magnetohydrodynamic (MHD) -stable regime of the tokamak is examined via the construction of an Ii-q0 diagram. The results confirm previous calculations that show that tearing modes introduce a stability boundary into the Zi-q, space. In another series of simulations, the interaction between tearing modes and the bootstrap current is investigated. The results indicate that a completely bootstrapped tokamak may be possible, even in the absence of any externally applied loop voltage or current drive.

The nonlinear response of bootstrapped tokamaks to oscillating field current drive (OFCD) is studied with the aid of a formal mathematical solution. The tokamak plasma response to OFCD is shown to be similar to that of a driven inductor–resistor (LR) circuit, but the effective plasma resistance can be negative. A physical picture is constructed in which the tokamak bootstrap effect is viewed as a nonlinear amplification of the plasma magnetic helicity. The bootstrap amplifier can rectify the toroidal plasma current. The importance of the tokamak thermal instability for peaking the plasma current and creating a plasma dynamo is stressed. Estimates are made which suggest that steady-state tokamak fusion reactors operating with OFCD may be achievable with moderate amplitude toroidal magnetic flux and loop voltage oscillations and oscillation driving frequencies significantly below the audible frequency range.

Theoretical and computational analyses of bootstrapped tokamaks with oscillating field current drive (OFCD) have been developed using a nonlinear magnetic helicity model. Assuming a rigid current profile, the conditions for optimal tokamak steady-state operation are derived and are shown to agree with the results of computer calculations. Generalized limit formulae for the toroidal plasma beta and bootstrap current fraction are also obtained. The results of the analyses indicate that steady-state bootstrapped tokamak operation with high toroidal plasma beta can best be achieved in tight aspect ratio A → 1 reactors with OFCD supplying as much as a quarter of the total toroidal plasma current.