A Simple Model of Current Ramp-Up and Ramp-Down in Tokamaks

TL;DR

This paper presents a simple model based on Faraday's law to estimate safe current ramp-up and ramp-down times in tokamaks, showing that future devices like SPARC and ITER can operate safely without runaway electrons.

Contribution

It introduces a straightforward model linking electric induction to current ramp times and evaluates safety limits for JET, SPARC, and ITER, challenging recent concerns about ramp time feasibility.

Findings

JET's ramp time aligns with operational data.

SPARC and ITER have feasible ramp times according to the model.

Successful JET operation suggests future tokamaks can avoid runaway electrons.

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 safe ramp-up/down times for the JET, SPARC, and ITER tokamaks are 4.2, 2.0, and 14.7 seconds, respectively. The JET ramp time is in accordance with operational experience. The SPARC and ITER 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 arXiv:2507.05456 (2025). The typical ratios of the inductive electric field to the Connor-Hastie field in SPARC and ITER 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 and ITER tokamaks should also be able to avoid such problems.