arXiv subjects
Publications and source records attributed to M. J. Hole.
We show the stepped-pressure equilibria that are obtained from a generalization of Taylor relaxation known as multi-region, relaxed MHD (MRXMHD) are also generalizations of ideal MHD. We show this by proving that as the number of plasma regions becomes infinite, MRXMHD reduces to ideal MHD. Numerical convergence studies demonstrating this limit are presented.
We describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which we call MRXMHD. The model is compatible with Hamiltonian chaos theory and allows the three-dimensional MHD equilibrium problem to be formulated in a well-posed manner suitable for computation. The energy-functional is discretized using a mixed finite-element, Fourier representation for the magnetic vector potential and the equilibrium geometry; and numerical solutions are constructed using the stepped-pressure equilibrium code, SPEC. Convergence studies with respect to radial and Fourier resolution are presented.
A radio frequency (RF) field solver based on Maxwell's equations and a cold plasma dielectric tensor is em- ployed to describe wave phenomena observed in a cylindrical non-uniform helicon discharge. The experiment is carried out on a recently built linear plasma-material interaction machine: the MAGnetized Plasma In- teraction Experiment (MAGPIE) [B. D. Blackwell, J. F. Caneses, C. Samuell, J. Wach, J. Howard, and C. S. Corr, submitted on 25 March 2012 to Plasma Sources Science and Technology], in which both plasma density and static magnetic field are functions of axial position. The field strength increases by a factor of 15 from source to target plate, and plasma density and electron temperature are radially non-uniform. With an enhancement factor of 9.5 to the electron-ion Coulomb collision frequency, 12% reduction in the antenna radius, and the same other conditions as employed in the experiment, the solver produces axial and radial profiles of wave amplitude and phase that are consistent with measurements. Ion-acoustic turbulence, which can happen if electron drift velocity exceeds the speed of sound in magnetized plasmas, may account for the factor of 9.5 used to match simulated results with experimental data. To overcome the single m vacuum solu- tion limitations of the RF solver, which can only compute the glass response to the same mode number of the antenna, we have adjusted the antenna radius to match the wave field strength in the plasma.(not finished because of the limited number of characters, please see the full paper)
In this paper, current profiles for plasma discharges on the Mega-Ampere Spherical Tokamak (MAST) are directly calculated from pickup coil, flux loop and Motional-Stark Effect (MSE) observations via methods based in the statistical theory of Bayesian analysis. By representing toroidal plasma current as a series of axisymmetric current beams with rectangular cross-section and inferring the current for each one of these beams, flux-surface geometry and q-profiles are subsequently calculated by elementary application of Biot-Savart's law. The use of this plasma model in the context of Bayesian analysis was pioneered by Svensson and Werner on the Joint-European Tokamak (JET) [J. Svensson and A. Werner. Current tomography for axisymmetric plasmas. {\em Plasma Physics and Controlled Fusion}, 50(8):085002, 2008]. In this framework, linear forward models are used to generate diagnostic predictions, and the probability distribution for the currents in the collection of plasma beams was subsequently calculated directly via application of Bayes' formula. In this work, we introduce a new diagnostic technique to identify and remove outlier observations associated with diagnostics falling out of calibration or suffering from an unidentified malfunction. These modifications enable good agreement between Bayesian inference of the last closed flux-surface (LCFS) with other corroborating data, such as such as that from force balance considerations using EFIT++ [L. Appel et al., Proc. 33rd EPS Conf., Rome, Italy, 2006]. In addition, this analysis also yields errors on the plasma current profile and flux-surface geometry, as well as directly predicting the Shafranov shift of the plasma core.
We describe a magnetohydrodynamic (MHD) constrained energy functional for equilibrium calculations that combines the topological constraints of ideal MHD with elements of Taylor relaxation. Extremizing states allow for partially chaotic magnetic fields and non-trivial pressure profiles supported by a discrete set of ideal interfaces with irrational rotational transforms. Numerical solutions are computed using the Stepped Pressure Equilibrium Code, SPEC, and benchmarks and convergence calculations are presented.
A two-fluid model developed originally to describe wave oscillations in the vacuum arc centrifuge, a cylindrical, rapidly rotating, low temperature and confined plasma column, is applied to interpret plasma oscillations in a RF generated linear magnetised plasma (WOMBAT), with similar density and field strength. Compared to typical centrifuge plasmas, WOMBAT plasmas have slower normalised rotation frequency, lower temperature and lower axial velocity. Despite these differences, the two-fluid model provides a consistent description of the WOMBAT plasma configuration and yields qualitative agreement between measured and predicted wave oscillation frequencies with axial field strength. In addition, the radial profile of the density perturbation predicted by this model is consistent with the data. Parameter scans show that the dispersion curve is sensitive to the axial field strength and the electron temperature, and the dependence of oscillation frequency with electron temperature matches the experiment. These results consolidate earlier claims that the density and floating potential oscillations are a resistive drift mode, driven by the density gradient. To our knowledge, this is the first detailed physics model of flowing plasmas in the diffusion region away from the RF source. Possible extensions to the model, including temperature non-uniformity and magnetic field oscillations, are also discussed.
Recently, a new probabilistic "data fusion" framework based on Bayesian principles has been developed on JET and W7-AS. The Bayesian analysis framework folds in uncertainties and inter-dependencies in the diagnostic data and signal forward-models, together with prior knowledge of the state of the plasma, to yield predictions of internal magnetic structure. A feature of the framework, known as MINERVA (J. Svensson, A. Werner, Plasma Physics and Controlled Fusion 50, 085022, 2008), is the inference of magnetic flux surfaces without the use of a force balance model. We discuss results from a new project to develop Bayesian inversion tools that aim to (1) distinguish between competing equilibrium theories, which capture different physics, using the MAST spherical tokamak; and (2) test the predictions of MHD theory, particularly mode structure, using the H-1 Heliac.
We calculate the stability of a multiple relaxation region MHD (MRXMHD) plasma, or stepped-Beltrami plasma, using both variational and tearing mode treatments. The configuration studied is a periodic cylinder. In the variational treatment, the problem reduces to an eigenvalue problem for the interface displacements. For the tearing mode treatment, analytic expressions for the tearing mode stability parameter $Δ'$, being the jump in the logarithm in the helical flux across the resonant surface, are found. The stability of these treatments is compared for $m=1$ displacements of an illustrative RFP-like configuration, comprising two distinct plasma regions. For pressure-less configurations, we find the marginal stability conclusions of each treatment to be identical, confirming analytic results in the literature. The tearing mode treatment also resolves ideal MHD unstable solutions for which $Δ' \to \infty$: these correspond to displacement of a resonant interface. Wall stabilisation scans resolve the internal and external ideal kink. Scans with increasing pressure are also performed: these indicate that both variational and tearing mode treatments have the same stability trends with $β$, and show pressure stabilisation in configurations with increasing edge pressure. Combined, our results suggest that MRXMHD configurations which are stable to ideal perturbations plus tearing modes are automatically in a stable state. Such configurations, and their stability properties, are of emerging importance in the quest to find mathematically rigorous solutions of ideal MHD force balance in 3D geometry.
The celebration of Allan Kaufman's 80th birthday was an occasion to reflect on a career that has stimulated the mutual exchange of ideas (or memes in the terminology of Richard Dawkins) between many researchers. This paper will revisit a meme Allan encountered in his early career in magnetohydrodynamics, the continuation of a magnetohydrodynamic mode through a singularity, and will also mention other problems where Allan's work has had a powerful cross-fertilizing effect in plasma physics and other areas of physics and mathematics.
The concept of plasma relaxation as a constrained energy minimization is reviewed. Recent work by the authors on generalizing this approach to partially relaxed three-dimensional plasma systems in a way consistent with chaos theory is discussed, with a view to clarifying the thermodynamic aspects of the variational approach used. Other entropy-related approaches to finding long-time steady states of turbulent or chaotic plasma systems are also briefly reviewed.