A simple model of current ramp-up and ramp-down in tokamaks

Abstract A simple model of the ramp-up and ramp-down of the toroidal current in a tokamak plasma is developed. Faraday’s law of electric induction is found to limit how rapidly the current can be safety ramped up or down. It is estimated that the minimum completely safe ramp-up/down times for the JET, SPARC, ITER, and DEMO tokamaks are 4.2, 2.0, 14.7, and 38.4 s, respectively. These estimates are obtained for ohmic ramp phases with relatively low flat-top temperatures. The JET ramp time is in accordance with operational experience. The SPARC, ITER, and DEMO minimum safe ramp times are less than the ramp times in the respective designs. Hence, there is no indication that the design ramp times are infeasible, as was recently suggested in Boozer (2025 arXiv: 2507.05456v1 ). The typical ratios of the inductive electric field to the Connor–Hastie field in SPARC, ITER, and DEMO during current ramps are found to be less than those in JET. Thus, the fact that the JET tokamak was able to operate successfully without encountering runaway electron problems during current ramps suggests that the future SPARC, ITER, and DEMO tokamaks should also be able to avoid such problems.