Experimental spheromak magnetic equilibria are measured which differ significantly from the minimum-energy state, and are well described by a numerical model where jw/Bhas a linear dependence on the poloidal flux function. Equilibria are determined in a nonperturbing manner by the combination of measurements of flux-conserver image currents with calculations from this model. These equilibria are corroborated by the observation of nondisruptive rotating internal kink distortions (with toroidal mode numbers n = 1, 2, and 3), coupled with theoretical MHD thresholds for the onset of these modes. PACS numbers: 52.55.Hc, 52.35.Py, 52.70.Ds In a spheromak, the magnetic fields are generated primarily by internal currents rather than by external coils. Once established, these fields are conjectured 1 to relax towards a state of minimum energy subject to the constraint that the magnetic helicity 2 is conserved. In a closed system the minimum-energy equilibrium satisfies VxB = XB with X^/xoJ 11/5 = const. Since competing effects are certainly present in any experiment, small deviations from a uniform, constant X can be expected. However, these departures from the minimum-energy or "Taylor" state are expected 1 to relax towards this lowest-energy configuration on a time scale shorter than the resistive diffusion time.We report results from the compact toroid experiment 3 ' 4 (CTX) which give spheromak equilibria (determined in a nonperturbing manner) not with X = const, but with X = X(iJ/), where t// is the normalized poloidal flux function [t|/ = (poloidal flux value)/ (total poloidal flux)]. The departures in magnetic energy of these equilibria with respect to the minimumenergy state is small. Coherent oscillations are seen, generated by rotating kink modes within the equilibria. The onset of the modes is shown to be consistent with the slope of X(i|/) from the equilibrium measurement.Other spheromak experiments 5,6 have measured the magnetic fields with internal probes, and have found experimental agreement with a zero-pressure, constants model. Hart et al? obtained for their data better agreement by including a finite-plasma-pressure correction to a constant-X model,In CTX, the X(i/i) profile is inferred from external measurements of induced image currents flowing in a mesh flux conserver 8 (MFC) surrounding the plasma, combined with results from numerical calculations of the equilibrium. This general technique is in principle similar to that used before to establish the MHD equilibrium in noncircular-cross-section tokamaks [see, e.g., Luxon and Brown, 9 and references therein]. Application of the technique to the CTX spheromak benefits from increased sensitivity to equilibrium changes since the spheromak is a small-aspect-ratio system; changes in the equilibrium affect the position of the magnetic axis and have a large effect on toroidal MFC image currents near the symmetry axis. Arrays of small Rogowski loops (5% relative calibration) measure the MFC currents, with the ratios of the currents (filtered to remove osci...
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 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.
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The paper presents experiments and analysis of energy confinement on the CTX spheromak. Compared to previous published results from 0.4 m radius flux conservers, in a 0.67 m radius mesh flux conserver (with the current density kept constant), the magnetic field increases while the plasma density is kept the same. However, the electron temperature does not rise, and hence ⟨β⟩vol drops. The plasma resistivity remains constant (the resistance drops as the size increases), and the energy confinement time stays the same. Plasma energy content results from spheromaks during sustainment by helicity injection are also presented and show confinement equivalent to that during the decay phase. Increased magnetic field in the same size experiment produces very little improvement in electron temperature and a decrease in confinement time. The resistive decay time is found to be empirically independent of the core electron temperature. It is, instead, proportional to the strength of the magnetic field at constant plasma density, while the ratio of magnetic field to decay time depends on plasma density, consistently with ionization breakdown at the edge of the spheromak dominating helicity dissipation. The possible causes of this observed confinement are examined separately in detailed quantitative and qualitative studies. Absolutely calibrated multichord bolometry shows that impurity radiation is not the cause of the low electron temperatures. The particle confinement time has increased with size, but does not show an increase with increasing magnetic field. At the lower ⟨β⟩vol of the larger experiment, the particle replacement power cannot explain the unaccounted energy losses. Any important role of pressure driven modes in the CTX energy balance is shown to be inconsistent with the available CTX data. The possibility that rotating coherent current driven kink modes can seriously degrade energy confinement is evaluated and discounted owing to the lack of improvement when the modes are absent. The role of anomalous ion heating is examined, and the available data are presented. Finally, a hypothesis explaining these results is presented, suggestions for future work are made, and the results are summarized.
A nonaxisymmetric stable magnetohydrodynamic (MHD) equilibrium within a prolate cylindrical conducting boundary has been produced experimentally. It has m=1 azimuthal symmetry, helical distortion, and flat lambda profile, all in agreement with the computed magnetically relaxed minimum magnetic energy Taylor state. Despite varied initial conditions determined by two helicity injectors on the device, this same equilibrium consistently emerges as the final state. These results therefore describe a new example of self-organization in an MHD plasma.
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