Relative Merits of Size, Field, and Current on Ignited Tokamak Performance

A simple global analysis is developed to examine the relative merits of size (L = a or R₀), field (B₀), and current (I) on ignition regimes of tokamaks under various confinement scaling laws. Scalings of key parameters (nτ_E, β, P_aux, P_fus, etc.) with L, B₀, and I are presented at several operating points, including (a) optimal path to ignition (saddle point), (b) ignition at minimum beta, (c) ignition at 10 keV, and (d) maximum performance at the limits of density (n_max ∼ B₀/R₀) and beta (β_crit ∼ I/aB₀). Expressions for the saddle point and the minimum conditions needed for ohmic ignition are derived analytically for any confinement model of the form τ_E ∼ n^xT^y. For a wide range of confinement models, the “figure of merit” parameters and I are found to give a good indication of the relative performance of the devices, where q_* is the cylindrical safety factor. As an illustration, the results are applied to representative “CITs” (a class of compact, high-field ignition tokamaks) and “Super-JETs” [a class of large-size (few × JET), low-field, high-current (≳20-MA) devices].