Ignition and burn criteria for D-³He tokamak and spherical torus reactors

The D-³He ignition and burn criteria for tokamaks and spherical torus reactors are examined in a global analysis with profile corrections. Particle confinement and ash buildup effects are included with the power balance, which results in an increased sensitivity of the ignition criteria to losses via bremsstrahlung and synchrotron radiation. Plasma beta scaling via an εβ_p limit provides the needed aspect ratio (A) dependence and permits an analysis in all A values of the first and second stability regimes. Energy confinement time (τ_E) associated with particle diffusion (τ_p) and energy conduction (τ_c) is used. The ignition condition for minimum nτ_E is found to be sensitive to beta but not to the magnetic field. Steady-state burn in second stability tokamaks (ξβ_p ≥ 0.6) at high A (>4) with average synchrotron wall reflectivities below 95% requires nτ_E above 5 × 10²¹ m^-3·s or strong plasma elongation (k > 3). Ignition in a spherical torus can be achieved with wall reflectivities below 80% and at nτ_E ≤ 10²¹ m^-3·s, without requiring strong plasma shaping or εβ_p > 0.6. The need to minimize nτ_E for ignition and burn strongly limits the synchrotron radiation loss to <20% of the fusion power for all values of A. Synchrotron power fractions can be increased, but only to 40%, due to an upper bound on nτ_E. Further increases of this fraction can be obtained only by assuming preferential ash removal.