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Notes: In this paper extensive measurements of magnetic equilibrium and source parameters in the m=1 helicity source spheromak experiment are described (previously called the kinked z-pinch source [Comments Plasma Phys. Control Fusion 9, 161 (1985)]). In the cylindrical entrance region connecting the stabilized z-pinch helicity source to the spheromak flux conserver, the observed equilibrium configuration is the helical azimuthal m=1 state with no net axial flux. In the flux conserver, the equilibrium is a spheromak (m=0) state with an m=1 distortion. The magnetic equilibria observed are compared to theory. The performance of the source relative to coaxial helicity sources is also examined.

Notes: Spheromaks are formed in a mesh flux conserver in the presence of an external dc bias magnetic field. The particle confinement is improved when the spheromak separatrix is put inside the metal mesh by the application of positive bias flux. The spheromaks remain stable to tilt instabilities with ratios of bias-to-spheromak flux of up to 47±7%.

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%.

Notes: Large improvements in spheromak parameters and new understanding have been obtained from the CTX experiment at Los Alamos [Phys. Rev. Lett. 51, 39 (1983); 61, 2457 (1988)]. In one experiment the global energy confinement time has been increased an order of magnitude over previous experiments to 0.2 msec and the magnetic-energy decay time increased to 2 msec. These results were achieved in a decaying spheromak by reducing the helicity dissipation in the edge. In another smaller spheromak, record electron temperatures (∼400 eV) and record magnetic field strengths (∼30 kG) have been obtained.

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: Research on forming, compressing, and accelerating milligram-range compact toroids using a meter diameter, two-stage, puffed gas, magnetic field embedded coaxial plasma gun is described. The compact toroids that are studied are similar to spheromaks, but they are threaded by an inner conductor. This research effort, named marauder (Magnetically Accelerated Ring to Achieve Ultra-high Directed Energy and Radiation), is not a magnetic confinement fusion program like most spheromak efforts. Rather, the ultimate goal of the present program is to compress toroids to high mass density and magnetic field intensity, and to accelerate the toroids to high speed. There are a variety of applications for compressed, accelerated toroids including fast opening switches, x-radiation production, radio frequency (rf) compression, as well as charge-neutral ion beam and inertial confinement fusion studies. Experiments performed to date to form and accelerate toroids have been diagnosed with magnetic probe arrays, laser interferometry, time and space resolved optical spectroscopy, and fast photography. Parts of the experiment have been designed by, and experimental results are interpreted with, the help of two-dimensional (2-D), time-dependent magnetohydrodynamic (MHD) numerical simulations. When not driven by a second discharge, the toroids relax to a Woltjer–Taylor equilibrium state that compares favorably to the results of 2-D equilibrium calculations and to 2-D time-dependent MHD simulations. Current, voltage, and magnetic probe data from toroids that are driven by an acceleration discharge are compared to 2-D MHD and to circuit solver/slug model predictions. Results suggest that compact toroids are formed in 7–15 μsec, and can be accelerated intact with material species the same as injected gas species and entrained mass ≥1/2 the injected mass.

Notes: By iteratively solving the Grad–Shafranov equation and the Mercier criterion, stable pressure profiles may be determined self-consistently with spheromak equilibria. No assumption is made about the shape of the pressure profile and an individual determination is made for that value of the pressure that drives the plasma marginally stable everywhere. These limits determine the pressure profile that provides the largest 〈β〉vol allowed by Mercier modes. Particular attention is given to the CTX spheromak [Phys. Rev. Lett. 51, 39 (1983)]. The results on spheromak Mercier stability limits leading to 〈β〉vol =1.5% for sustained spheromaks are summarized. In addition, 〈β〉vol =7.0% has been calculated for spheromaks with current holes.