Experimental determination of the conservation of magnetic helicity from the balance between source and spheromak

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Abstract
The conjecture that magnetic helicity (linked flux) is conserved in magnetized plasmas for time scales that are short compared to the resistive diffusion time is experimentally tested in the CTX spheromak [Phys. Rev. Lett. 4 5, 1264 (1980); 5 1, 39 (1983); Nucl. Fusion 2 4, 267 (1984)]. Helicity is created electrostatically by current drawn from electrodes. The magnetized plasma then flows into a conducting flux conserver where the energy per helicity of the plasma is minimized and a spheromak is formed on a relaxation time scale of many Alfvén times. The magnetic field strength of the equilibrium is subsequently increased and sustained. The amount of helicity created by the magnetized coaxial plasma source, the helicity content of the spheromak equilibrium, and the resistive loss of the helicity are measured to determine the balance of helicity between source and spheromak with a ±16% uncertainty. In CTX the amount of energy that must be rapidly dissipated within the conducting boundary while conserving helicity in the process of sustaining the spheromak is experimentally controllable, and has varied from 1.8 times the spheromak magnetic energy to greater than 10 times. The relaxation, or minimization of the energy‐to‐helicity ratio, determines the gross structure (the normalized spatial profile) of the spheromak, while the conservation of helicity itself determines the magnitude and time dependence of the magnetic fields of the spheromak equilibrium. Helicity balance tests are done by individually varying the sign and magnitude of the source voltage and flux, and by observing sustainment of spheromaks with fields opposing those of the source. A threshold for helicity injection from the source is measured and related to the source and entrance region size. During times short compared to resistive diffusion time scales the helicity is shown to be conserved with a ±12% uncertainty using no free parameters. For longer times the resistive dissipation Its value is independently measured and appears to be related to the expected classical resistive decay. Absolutely calibrated bolometer measurements are consistent with excess source energy heating the spheromak plasma during the sustainment by electrostatic helicity injection.