Relaxation-time measurement via a time-dependent helicity balance model

A time-dependent helicity balance model applied to a spheromak helicity-injection experiment enables the measurement of the relaxation time during the sustainment phase of the spheromak. The experiment, the Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI), studies spheromak formation and sustainment through inductive helicity injection. The model captures the dominant plasma behavior seen during helicity injection in HIT-SI by using an empirical helicity-decay rate, a time-dependent helicity-injection rate, and a composite Taylor state to model both the helicity content of the system and to calculate the resulting spheromak current. During single-injector operations, both the amplitude and the phase of the periodic rise and fall of the toroidal current are predicted by this model, with an exchange of helicity between the injector states and the spheromak state proposed as the causal mechanism. This phenomenon allows for the comparison of the delay between the current rises in the experiment and the numerical model, enabling a measurement of the relaxation time. The measured relaxation time of 4.8 μs ± 2.8 μs is shorter than the toroidal Alfvén timescale. These results validate Hall MHD calculations of the Geospace Environmental Modeling challenge.