S. Woodruff

Sustained Spheromak Physics Experiment (SSPX): design and physics results

The Sustained Spheromak Physics Experiment (SSPX) was a high-temperature (Te up to 0.5xa0keV) spheromak formed by coaxial helicity injection (CHI) and with plasma duration of a few milliseconds following the high-current formation stage. Clean walls and low impurity operation were obtained by a combination of baking, discharge cleaning and titanium deposition on the walls, allowing the generation of high-quality plasmas. Resistive-magnetohydrodynamic simulations, benchmarked to the experiment, were used to elucidate the physics. The detailed characteristics of the nφxa0=xa01 toroidal mode associated with CHI were determined as was the physics of the nonlinear current drive and magnetic reconnection that formed and sustained the spheromak. If the helicity injection rate was reduced following formation the plasma became relatively quiescent and magnetic surfaces formed. The measured thermal diffusivity in the core was as low as ∼1xa0m2xa0s−1. However, reconnection events during buildup or sustainment of the plasma current by CHI were found to open magnetic surfaces throughout the plasma allowing rapid energy loss to the walls. As a result, experiments and simulations in SSPX found no path to simultaneous sustainment by CHI and good energy confinement. Additional physics results are also presented in this review.

Simulation of spheromak evolution and energy confinement

Simulation results are presented that illustrate the formation and decay of a spheromak plasma driven by a coaxial electrostatic plasma gun, and model the plasma energy confinement. The physics of magnetic reconnection during formation is also illuminated. The simulations are performed with the three-dimensional, time-dependent, resistive magnetohydrodynamic NIMROD code [C. R. Sovinec, A. H. Glasser, T. A. Gianakon, D. C. Barnes, R. A. Nebel, S. E. Kruger, D. D. Schnack, S. J. Plimpton, A. Tarditi, and M. S. Chu, J. Comput. Phys. 195, 355 (2004)]. The simulation results are compared to data from the Sustained Spheromak Physics Experiment (SSPX) [E. B. Hooper, L. D. Pearlstein, and R. H. Bulmer, Nucl. Fusion 39, 863 (1999)]. The simulation results are tracking SSPX with increasing fidelity (e.g., improved agreement with measured magnetic fields, fluctuation amplitudes, and electron temperature) as the simulation has been improved in its representations of the experimental geometry, the magnetic bias coils,...

Magnetic Reconnection During Flux Conversion in a Driven Spheromak

During buildup of a spheromak by helicity injection, magnetic reconnection converts toroidal flux into poloidal flux. This physics is explored in the resistive magnetohydrodynamic code, NIMROD [C.R. Sovinec, A.H. Glasser, T.A. Gianakon, D.C. Barnes, R.A. Nebel, S.E. Kruger, D.D. Schnack, S.J. Plimpton, A. Tarditi, and M.S. Chu, J. Comp. Phys., 195, 355-386 (2004)], which reveals negative current sheets with {lambda} = {mu}{sub 0}j {center_dot} B/B{sup 2}reversed relative to the applied current. The simulated event duration is consistent with magnetic diffusion on the sheet thickness and is accompanied by cathode voltage spikes and poloidal field increases similar to those seen in the Sustained Spheromak Physics Experiment, SSPX [E. B. Hooper, L. D. Pearlstein, and R. H. Bulmer, Nucl. Fusion 39, 863 (1999)]. All magnetic fieldlines are open during reconnection and their trajectories are very sensitive to their starting points, resulting in chaos. The current sheets are most intense inside the separatrix near the X-point of the mean-field spheromak, suggesting that the reconnection occurs near fieldlines which are closed in the azimuthal average.

Transport and fluctuations in high temperature spheromak plasmas

Higher electron temperature (Te>350eV) and reduced electron thermal diffusivity (χe<10m2∕s) is achieved in the Sustained Spheromak Physics Experiment (SSPX) by increasing the discharge current=Igun and gun bias flux=ψgun in a prescribed manner. The internal current and q=safety factor profile derived from equilibrium reconstruction as well as the measured magnetic fluctuation amplitude can be controlled by programming the ratio λgun=μ0Igun∕ψgun. Varying λgun above and below the minimum energy eigenvalue=λFC of the flux conserver (∇×B=λFCB) varies the q profile and produces the m∕n=poloidal/toroidal magnetic fluctuation mode spectrum expected from mode-rational surfaces with q=m∕n. The highest Te is measured when the gun is driven with λgun slightly less than λFC, producing low fluctuation amplitudes (<1%) and 1∕2<q<2∕3. Transport analysis shows a reduction in χe as Te increases, differing from Bohm or open field line transport models where χe increases with Te. Detailed resistive magnetohydrodynamic sim...

Controlled and spontaneous magnetic field generation in a gun-driven spheromak

In the Sustained Spheromak Physics Experiment, SSPX [E. B. Hooper, D. Pearlstein, and D. D. Ryutov, Nucl. Fusion 39, 863 (1999)], progress has been made in understanding the mechanisms that generate fields by helicity injection. SSPX injects helicity (linked magnetic flux) from 1 m diameter magnetized coaxial electrodes into a flux-conserving confinement region. Control of magnetic fluctuations (delta B/B similar to 1% on the midplane edge) yields T-e profiles peaked at > 200 eV. Trends indicate a limiting beta (beta(e)similar to 4%-6%), and so we have been motivated to increase T-e by operating with stronger magnetic field. Two new operating modes are observed to increase the magnetic field: (A) Operation with constant current and spontaneous gun voltage fluctuations. In this case, the gun is operated continuously at the threshold for ejection of plasma from the gun: stored magnetic energy of the spheromak increases gradually with delta B/B similar to 2% and large voltage fluctuations (delta V similar to 1 kV), giving a 50% increase in current amplification, I-tor/I-gun. (B) Operation with controlled current pulses. In this case, spheromak magnetic energy increases in a stepwise fashion by pulsing the gun, giving the highest magnetic fields observed for SSPX (similar to 0.7 T along the geometric axis). By increasing the time between pulses, a quasisteady sustainment is produced (with periodic good confinement), comparing well with resistive magnetohydrodynamic simulations. In each case, the processes that transport the helicity into the spheromak are inductive and exhibit a scaling of field with current that exceeds those previously obtained. We use our newly found scaling to suggest how to achieve higher temperatures with a series of pulses.

Magnetic helicity balance in the Sustained Spheromak Plasma Experiment

The magnetic helicity balance between the helicity input injected by a magnetized coaxial gun, the rate-of-change in plasma helicity content, and helicity dissipation in electrode sheaths and Ohmic losses have been examined in the Sustained Spheromak Plasma Experiment (SSPX) [E. B. Hooper, L. D. Pearlstein, and R. H. Bulmer, Nucl. Fusion 39, 863 (1999)]. Helicity is treated as a flux function in the mean-field approximation, allowing separation of helicity drive and losses between closed and open field volumes. For nearly sustained spheromak plasmas with low fluctuations, helicity balance analysis implies a decreasing transport of helicity from the gun input into the spheromak core at higher spheromak electron temperature. Long pulse discharges with continuously increasing helicity and larger fluctuations show higher helicity coupling from the edge to the spheromak core. The magnitude of the sheath voltage drop, inferred from cathode heating and a current threshold dependence of the gun voltage, shows that sheath losses are important and reduce the helicity injection efficiency in SSPX.

Theoretical investigation of field-line quality in a driven spheromak

Theoretical studies aimed at predicting and diagnosing field-line quality in a spheromak are described. These include nonlinear three-dimensional MHD simulations and analyses of confinement in spheromaks dominated by either open (stochastic) field lines or approximate flux surfaces. Three-dimensional nonlinear MHD simulations confirm that field lines are predominantly open when there is a large-amplitude toroidal-mode-number n = 1 mode. However, an appreciable volume of good flux surfaces can be obtained either during the drive-off phase of a scheme with periodic pulsed drive or for an extended period under driven conditions, with oscillating volume, when the odd-n modes are suppressed. If a configuration with radially localized perturbations can be achieved, a scaling analysis for a Rosenbluth?Bussac spheromak equilibrium indicates a favourable (1/Lundquist number) scaling to larger, higher-field devices. A hyper-resistivity analysis, which also assumes small-scale perturbations, reproduces well magnetic probe data in the sustained spheromak physics experiment, while an analysis of the same experiment based on one-dimensional transport along open field lines contradicts experimental observations in several key ways. The scaling analysis is also applied to reversed-field pinches and indicates that a completely determined scaling can be obtained with less approximation to the resistive MHD equations than indicated in the previous literature.

Sustained spheromak coaxial gun operation in the presence of an n=1 magnetic distortion

The Sustained Spheromak Physics Experiment (SSPX) uses a magnetized coaxial gun to form and sustain spheromaks by helicity injection. Internal probes give the magnetic profile within the gun. Analysis of these data show that a number of commonly applied assumptions are not completely correct, and some previously unrecognized processes may be at work. Specifically, the fraction of the available vacuum flux spanning the gun that is stretched out of the gun is variable and not usually 100%. The n=1 mode that is present during sustained discharges has its largest value of {delta}B/B within the gun, so that instantaneously B within the gun is not axisymmetric. By applying a rigid-rotor model to account for the mode, the instantaneous field and current structure within the gun are determined. The current density is also highly non-axisymmetric and the local value of {lambda} {triple_bond} {mu}{sub 0}j{sub {parallel}}/B is not constant, although the global value {lambda}{sub g} {triple_bond} {mu}{sub 0}I{sub g}/{psi}{sub g} closely matches that expected by axisymmetric models. The current distribution near the gun muzzle suggests cross-field current exists, and this is explained as a line-tying reaction to plasma rotation.

Particle control in the sustained spheromak physics experiment

In this paper we report on density and impurity measurements in the sustained spheromak physics experiment (SSPX) which has recently started operation. The SSPX plasma is sustained by coaxial helicity injection for a duration of 2 ms with peak toroidal currents of up to 0.5 MA. Plasma-facing components consist of tungsten-coated copper to minimize sputtering. The surfaces are conditioned by a combination of baking at 150°C, glow discharge cleaning, titanium gettering, and pulse-discharge cleaning with helium plasmas. In this way we achieve density control with n c ∼1-4 x 10 20 m -3 . However, gas input has only a weak effect on plasma density; injector current is the dominant factor. Conditioning reduces the impurity radiation to the point where it is no longer important to the energy balance, so that the lifetime of the spheromak discharge is ultimately governed by MHD activity, which grows rapidly about 1.5-2.0 ms after helicity injection ends.

Characterization and conditioning of SSPX plasma facing surfaces

Abstract The Sustained Spheromak Physics Experiment (SSPX) will examine the confinement properties of spheromak plasmas sustained by DC helicity injection. Understanding the plasma-surface interactions is an important component of the experimental program since the spheromak plasma is in close contact with a stabilizing wall (flux conserver) and is maintained by a high current discharge in the coaxial injector region. Peak electron temperatures in the range of 400 eV are expected, so the copper plasma facing surfaces in SSPX have been coated with tungsten to minimize sputtering and plasma contamination. Here, we report on the characterization and conditioning of these surfaces used for the initial studies of spheromak formation in SSPX. The high pressure plasma-sprayed tungsten facing the SSPX plasma was characterized in situ using β-backscattering and ex situ using laboratory measurements on similarly prepared samples. Measurements showed that water can be desorbed effectively through baking while the removal rates of volatile impurity gases during glow discharge and shot conditioning indicated a large source of carbon and oxygen in the porous coating.