The impedance and energy efficiency of a coaxial magnetized plasma source used for spheromak formation and sustainment

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 2 9, 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