Microtearing modes in reversed field pinch plasmas

In the reversed field pinch RFX-mod strong electron temperature gradients develop when the single-helical-axis regime is achieved. Gyrokinetic calculations show that in the region of the strong temperature gradients microtearing instabilities are the dominant turbulent mechanism acting on the ion Larmor radius scale. The quasilinear evaluation of the electron thermal conductivity is in good agreement with the experimental estimates.     

Vortex-induced diffusivity in reversed field pinch plasmas

Coherent structures identified in two reversed field pinch experiments are interpreted as a dynamic balance of dipolar and monopolar vortices growing and evolving under the effect of the ExB flow shear. For the first time their contribution to the anomalous transport has been estimated in fusion related plasmas, showing that they can account for up to 50% of the total plasma diffusivity. The experimental findings indicate that the diffusion coefficient associated with the coherent structures depends on the relative population of the two types of vortices and is minimum when the two populations are equal. An interpretative model is proposed to explain this feature.     

Transport processes in magnetically confined plasmas in the nonlinear regime

A field theory approach to transport phenomena in magnetically confined plasmas is presented. The thermodynamic field theory (TFT), previously developed for treating the generic thermodynamic system out of equilibrium, is applied to plasmas physics. Transport phenomena are treated here as the effect of the field linking the thermodynamic forces with their conjugate flows combined with statistical mechanics. In particular, the Classical and the Pfirsch-Schluter regimes are analyzed by solving the thermodynamic field equations of the TFT in the weak-field approximation. We found that, the TFT does not correct the expressions of the ionic heat fluxes evaluated by the neoclassical theory in these two regimes. On the other hand, the fluxes of matter and electronic energy (heat flow) is further enhanced in the nonlinear Classical and Pfirsch-Schluter regimes. These results seem to be in line with the experimental observations. The complete set of the electronic and ionic transport equations in the nonlinear Banana regime, is also reported. A paper showing the comparison between our theoretic results and the experimental observations in the JET machine is currently in preparation.     

On the origin of rotation in magnetically confined plasmas

The main part of this paper surveys the mechanisms that can lead to rotation of plasma in an electrodeless discharge (commonly called a theta pinch) and in a mirror machine. Eight proposed mechanisms are examined, of which two are found to be incorrect in some way. Another mechanism, in which the reaction is purely electromagnetic, applies only to the tenuous plasma of a mirror machine. The remaining five theories apply to the highly compressed plasma of a theta pinch. These all rely fundamentally on the large difference in mass between an ion and an electron, i.e. either on Hall currents or the correction for finite ion Larmor radius in the stress tensor. The mechanisms which incorporate the Hall effect cause an equal and opposite mechanical reaction either on the wall (Roberts and Taylor), or on external conductors (Haines), or on the plasma at each end of the discharge axis (Bostick). The mechanisms which use the collisionless stress tensor predict either radial division into oppositely rotating plasma (Velikhov) or a transfer of angular momentum to the walls by collisions during the initial stage of physical contact (Haines). This last theory is new and arose as a result of a critical examination of an earlier theory (Jensen and Voorhies).

Experimental evidence for rotation has been confined mainly to high speed photographic techniques, and methods of obtaining a more definite measurement of the rotation and its origin are suggested.

The paper distinguishes carefully between the angular motions associated with the centre of mass, the guiding centres and the diamagnetic current, and also considers the stability of a rotating plasma including the Hall effect and the collisionless stress tensor.     

Momentum transport from current-driven reconnection in the reversed field pinch

We calculate momentum transport from tearing fluctuations in a reversed field pinch with sheared flow, considering both the effect of a single tearing mode (through quasilinear theory and MHD computation) and multiple tearing modes (through nonlinear MHD computation). A single tearing mode transports momentum, via Maxwell and Reynolds stresses, more rapidly than classical viscous forces. Moreover, the transport is enhanced by nonlinear coupling of multiple modes.     

Size scaling of turbulent transport in magnetically confined plasmas

Transport scaling with respect to device size in magnetically confined plasmas is critically examined for electrostatic ion-temperature-gradient turbulence using global gyrokinetic particle simulations. It is found, by varying device size normalized by ion gyroradius while keeping other dimensionless plasma parameters fixed, that fluctuation scale length is microscopic in the presence of zonal flows. The local transport coefficient exhibits a gradual transition from a Bohm-like scaling for device sizes corresponding to present-day experiments to a gyro-Bohm scaling for future larger devices.     

Nonequilibrium thermodynamics and the transport phenomena in magnetically confined plasmas

The neoclassical theory of transport in magnetically confined plasmas is reviewed. The emphasis is laid on a set of relationships existing among the banana transport coefficients. The surface-averaged entropy production in such plasmas is evaluated. It is shown that neoclassical effects emerge from the entropy production due to parallel transport processes. The Pfirsch-Schlüter effect can be clearly interpreted as due to spatial fluctuations of parallel fluxes on a magnetic surface: the corresponding entropy production is the measure of these fluctuations. The banana fluxes can be formulated in a quasithermodynamic form in which the average entropy production is a bilinear form in the parallel fluxes and the conjugate generalized stresses. A formulation as a quadratic form in the thermodynamic forces is also possible, but leads to anomalies, which are discussed in some detail.     

Observation of velocity-independent electron transport in the reversed field pinch

Confinement of runaway electrons has been observed for the first time in a reversed field pinch during improved-confinement plasmas in the Madison Symmetric Torus. Energy-resolved hard-x-ray flux measurements have been used to determine the velocity dependence of the electron diffusion coefficient, utilizing computational solutions of the Fokker-Planck transport equation. With improved-confinement, the fast electron diffusivity drops by 2 orders of magnitude and is independent of velocity. This suggests a change in the transport mechanism away from stochastic magnetic field diffusion.     

Dominant electrostatic nature of the reversed field pinch dynamo

The origin of the dynamo velocity field of the reversed field pinch within the visco-resistive MHD modeling is uncovered. The main component of this field is an electrostatic drift. The corresponding electrostatic field is related to a small charge separation which is consistent with the quasineutrality approximation, and which should be present in real plasmas, too. While quite natural in the stationary single helicity state, this analysis is shown to extend also to the nonstationary multiple helicity regime. Numerical simulations provide the spatial distribution of fields and of charge separation.     

Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas

Implicit algorithms are essential for predicting the slow growth and saturation of global instabilities in today’s magnetically confined fusion plasma experiments. Present day algorithms for obtaining implicit solutions to the magnetohydrodynamic (MHD) equations for highly magnetized plasma have their roots in algorithms used in the 1960s and 1970s. However, today’s computers and modern linear and non-linear solver techniques make practical much more comprehensive implicit algorithms than were previously possible. Combining these advanced implicit algorithms with highly accurate spatial representations of the vector fields describing the plasma flow and magnetic fields and with improved methods of calculating anisotropic thermal conduction now makes possible simulations of fusion experiments using realistic values of plasma parameters and actual configuration geometry. This article is a review of these developments.     

Bifurcation in viscoresistive MHD: the hartmann number and the reversed field pinch

A scaling approach to the simplest viscoresistive MHD model reveals that the Prandtl number acts only through the inertia term. When this term is negligible the dynamics is ruled by the Hartmann number H only. This occurs for the reversed field pinch dynamics as seen by numerical simulation of the model. When H is large the system is in a multiple helicity state. In the vicinity of H = 2500 the system displays temporal intermittency with laminar phases of quasi-single-helicity (SH) type. For lower H's two basins of SH are shown to coexist. SH regimes are of interest because of their nonchaotic magnetic field.     

Observation of the alpha particle "Knock-On" neutron emission from magnetically confined DT fusion plasmas

Suprathermal fuel ions from alpha-particle knock-on collisions in fusion DT plasmas are predicted to cause a weak feature in the neutron spectrum of d+t-->alpha+n. The knock-on feature has been searched for in the neutron emission of high ( >1 MW) fusion-power plasmas produced at JET and was found using a magnetic proton recoil type neutron spectrometer of high performance. Measurement and predictions agree both in absolute amplitude and in plasma-parameter dependence, supporting the interpretation and model. Moreover, the results provide input to projecting alpha-particle diagnostics for future self-heated fusion plasmas.     

A model for the shell current in a reversed field pinch

A model for the shell current in a reversed field pinch which includes the current induced by the motion of the plasma is discussed. This model gives a good approximation to the magnitude and time dependence of a shell current measured experimentally     

Observations of multiple magnetic islands in the core of a reversed field pinch

We describe in this Letter the first measurement of multiple islands in the core of a reversed field pinch (RFP). These islands appear with current profile modification leading to magnetic fluctuation reduction in the Madison symmetric torus RFP. Magnetic island widths decrease to an unprecedented level, reducing the overlap of adjacent islands and allowing distinct islands to appear. The structures are observed in multichord measurements of soft-x-ray emissivity. The soft-x-ray data is validated with Poincaré reconstructions of the magnetic field structure in the core.     

Observation of high-field-side crash and heat transfer during sawtooth oscillation in magnetically confined plasmas

High resolution (temporal and spatial), two-dimensional images of electron temperature fluctuations during sawtooth oscillations were employed to study the crash process and heat transfer in magnetically confined toroidal plasmas. The combination of kink and local pressure driven instabilities leads to a small poloidally localized puncture in the magnetic surface at both the low and the high field sides of the poloidal plane. This observation closely resembles the "fingering event" of the ballooning mode model with the high- mode only predicted at the low field side.     

Experimental observation of anisotropic magnetic turbulence in a reversed field pinch plasma

In this Letter we report an experimental study of fully developed anisotropic magnetic turbulence in a laboratory plasma. The turbulence has broad (narrow) spectral power in the perpendicular (parallel) direction to the local mean magnetic field extending beyond the ion cyclotron frequency. Its k[see symbol] spectrum is asymmetric in the ion and electron diamagnetic directions. The wave number scaling for the short wavelength fluctuations shows exponential falloff indicative of dissipation. A standing wave structure is found for the turbulence in the minor radial direction of the toroidal plasma.     

Vanishing magnetic shear and electron transport barriers in the RFX-mod reversed field pinch

We define the safety factor q for the helical plasmas of the experiment RFX-mod by accounting for the actual three-dimensional nature of the magnetic flux surfaces. Such a profile is not monotonic but goes through a maximum located in the vicinity of the electron transport barriers measured by a high resolution Thomson scattering diagnostic. Helical states with a single axis obtained in viscoresistive magnetohydrodynamic numerical simulations exhibit similar nonmonotonic q profiles provided that the final states are preceded by a magnetic island phase, like in the experiment.