Shafranov's virial theorem and magnetic plasma confinement

Shafranov's virial theorem implies that nontrivial magnetohydrodynamical equilibrium configurations must be supported by externally supplied currents. Here we extend the virial theorem to field theory, where it relates to Derrick's scaling argument on soliton stability. We then employ virial arguments to investigate a realistic field theory model of a two-component plasma, and conclude that stable localized solitons can exist in the bulk of a finite density plasma. These solitons entail a nontrivial electric field which implies that purely magnetohydrodynamical arguments are insufficient for describing stable, nontrivial structures within the bulk of a plasma.Comment: 9 pages no figure

Magnetic Geometry and the Confinement of Electrically Conducting Plasmas

We develop an effective field theory approach to inspect the electromagnetic interactions in an electrically neutral plasma, with an equal number of negative and positive charge carriers. We argue that the static equilibrium configurations within the plasma are topologically stable solitons, that describe knotted and linked fluxtubes of helical magnetic fields.Comment: 9 pages 1 ps-figur

A comparison of incompressible limits for resistive plasmas

The constraint of incompressibility is often used to simplify the magnetohydrodynamic (MHD) description of linearized plasma dynamics because it does not affect the ideal MHD marginal stability point. In this paper two methods for introducing incompressibility are compared in a cylindrical plasma model: In the first method, the limit $\gamma \to \infty$ is taken, where $\gamma$ is the ratio of specific heats; in the second, an anisotropic mass tensor $\mathbf{\rho}$ is used, with the component parallel to the magnetic field taken to vanish, $\rho_{\parallel} \to 0$. Use of resistive MHD reveals the nature of these two limits because the Alfv\'en and slow magnetosonic continua of ideal MHD are converted to point spectra and moved into the complex plane. Both limits profoundly change the slow-magnetosonic spectrum, but only the second limit faithfully reproduces the resistive Alfv\'en spectrum and its wavemodes. In ideal MHD, the slow magnetosonic continuum degenerates to the Alfv\'en continuum in the first method, while it is moved to infinity by the second. The degeneracy in the first is broken by finite resistivity. For numerical and semi-analytical study of these models, we choose plasma equilibria which cast light on puzzling aspects of results found in earlier literature.Comment: 14 pages, 10 figure

An equilibrium model for RFP plasmas in the presence of resonant tearing modes

The equilibrium of a finite-beta RFP plasma in the presence of saturated-amplitude tearing modes is investigated. The singularities of the MHD force balance equation JXB=grad(p) at the modes rational surfaces are resolved through a proper regularization of the zeroth-order (equilibrium) profiles, by setting to zero there the gradient of the pressure and parallel current density. An equilibrium model, which satisfies the regularization rule at the various rational surfaces, is developed. The comparison with the experimental data from the Reversed Field eXperiment (RFX) gives encouraging results. The model provides an easy tool for magnetic analysis: many aspects of the perturbations can be analyzed and reconstructed.Comment: Final accepted version. 36 page

Kolmogorov-Sinai entropy in field line diffusion by anisotropic magnetic turbulence

The Kolmogorov-Sinai (KS) entropy in turbulent diffusion of magnetic field lines is analyzed on the basis of a numerical simulation model and theoretical investigations. In the parameter range of strongly anisotropic magnetic turbulence the KS entropy is shown to deviate considerably from the earlier predicted scaling relations [Rev. Mod. Phys. {\bf 64}, 961 (1992)]. In particular, a slowing down logarithmic behavior versus the so-called Kubo number $R\gg 1$ ($R = (\delta B / B_0) (\xi_\| / \xi_\bot)$, where $\delta B / B_0$ is the ratio of the rms magnetic fluctuation field to the magnetic field strength, and $\xi_\bot$ and $\xi_\|$ are the correlation lengths in respective dimensions) is found instead of a power-law dependence. These discrepancies are explained from general principles of Hamiltonian dynamics. We discuss the implication of Hamiltonian properties in governing the paradigmatic "percolation" transport, characterized by $R\to\infty$, associating it with the concept of pseudochaos (random non-chaotic dynamics with zero Lyapunov exponents). Applications of this study pertain to both fusion and astrophysical plasma and by mathematical analogy to problems outside the plasma physics. This research article is dedicated to the memory of Professor George M. ZaslavskyComment: 15 pages, 2 figures. Accepted for publication on Plasma Physics and Controlled Fusio

From 'River Cottage' to 'Chicken Run': Hugh Fearnley-Whttingstall and the class politics of ethical consumption

Lifestyle television provides a key site through which to explore the dilemmas of ethical consumption, as the genre shifts to consider the ethics of different consumption practices and taste cultures. UK television cook Hugh Fearnley-Whittingstall's TV programmes offer fertile ground not only for thinking about television personalities as lifestyle experts and moral entrepreneurs, but also for thinking about how the meanings and uses of their television image are inflected by genre. In this article we explore how the shift from the lifestyled downshifting narrative of the River Cottage series to the 'campaigning culinary documentary' Hugh's Chicken Run exposes issues of celebrity, class and ethics. While both series are concerned with ethical consumption, they work in different ways to reveal a distinction between 'ethical' and 'unethical' consumption practices and positions - positions that are inevitably classed

The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies

We develop an approach of Grad-Shafranov (GS) reconstruction for toroidal structures in space plasmas, based on in-situ spacecraft measurements. The underlying theory is the GS equation that describes two-dimensional magnetohydrostatic equilibrium as widely applied in fusion plasmas. The geometry is such that the arbitrary cross section of the torus has rotational symmetry about the rotation axis $Z$, with a major radius $r_0$. The magnetic field configuration is thus determined by a scalar flux function $\Psi$ and a functional $F$ that is a single-variable function of $\Psi$. The algorithm is implemented through a two-step approach: i) a trial-and-error process by minimizing the residue of the functional $F(\Psi)$ to determine an optimal $Z$ axis orientation, and ii) for the chosen $Z$, a $\chi^2$ minimization process resulting in the range of $r_0$. Benchmark studies of known analytic solutions to the toroidal GS equation with noise additions are presented to illustrate the two-step procedures and to demonstrate the performance of the numerical GS solver, separately. For the cases presented, the errors in $Z$ and $r_0$ are 9$^\circ$ and 22\%, respectively, and the relative percent error in the numerical GS solutions is less than 10\%. We also make public the computer codes for these implementations and benchmark studies.Comment: submitted to Sol. Phys. late Dec 2016; under review; code will be made public once review is ove

The multiple ontologies of freshness in the UK and Portuguese agri-food sectors

This paper adopts a material-semiotic approach to explore the multiple ontologies of ‘freshness’ as a quality of food. The analysis is based on fieldwork in the UK and Portugal, with particular emphasis on fish, poultry, and fruit and vegetables. Using evidence from archival research, ethnographic observation and interviews with food businesses (including major retailers and their suppliers) plus qualitative household-level research with consumers, the paper unsettles the conventional view of freshness as a single, stable quality of food. Rather than approaching the multiplicity of freshness as a series of social constructions (different perspectives on essentially the same thing), we identify its multiple ontologies. The analysis explores their enactment as uniform and consistent, local and seasonal, natural and authentic, and sentient and lively. The paper traces the effects of these enactments across the food system, drawing out the significance of our approach for current and future geographical studies of food