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Notes: 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. 45, 1264 (1980); 51, 39 (1983); Nucl. Fusion 24, 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 resistivediffusion 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.

Notes: Electrostatic (dc) helicity injection has previously been shown to successfully sustain the magnetic fields of spheromaks and tokamaks. The magnitude of the injected magnetic helicity balances (within experimental error) the flux lost by resistive decay of the toroidal equilibrium. Hence the problem of optimizing this current drive scheme involves maximizing the injected helicity (the voltage-connecting-flux product) while minimizing the current (which multiplied by the voltage represents the energy input and also possible damage to the electrodes). The impedance (voltage-to-current ratio) and energy efficiency of a dc helicity injection experiment are studied on the CTX spheromak [Phys. Fluids 29, 3415 (1986)]. Over several years changes were made in the physical geometry of the coaxial magnetized plasma source as well as changes in the external electrical circuit. The source could be operated over a wide range of external charging voltage (and hence current), applied axial flux, and source gas flow rate.A database of resulting voltage, helicity injection, efficiency, electron density, and rotation has been created. These experimental results are compared to an ideal magnetohydrodynamic theory of magnetic flux flow. The theory is parametrized by the dimensionless Hall parameter, the ratio of electric to mass current. For a constant Hall parameter the theory explains why the voltage depends quadratically on the current at constant flux. The theory also explains the approximately linear dependence of the impedance-to-current ratio on the current-to-flux ratio of the source. The current-to-flux ratio itself (the energy-per-unit helicity of the source) is bounded below by considerations of force balance. While the rotation of the flow is not understood, the density of the sustained spheromak is shown to be related to the mass flow in the source, supporting the constant Hall parameter assumption. The overall efficiency of sustainment through dc helicity injection is limited by the usual Ohmic resistive decay, by the force-balance limits on the current-to-flux ratio, by the losses of the external electrical circuit, and by the fundamental limitations on the achievable impedance of flux flow in a magnetized plasma. Even so, ratios of spheromak magnetic energy to capacitor bank energy of over 17% have been achieved on CTX. Ignoring external circuit losses the efficiency of electrostatic helicity injection for converting energy received by the coaxial source to the energy of the spheromak magnetic field has exceeded 70%.