Order in very cold confined plasmas

The study of the structure and dynamic properties of classical systems of charged particles confined by external forces, and cooled to very low internal energies, is the subject of this article. An infinite system of identical charged particles has been known for some time to form a body-centered cubic lattice and is a simple classical prototype for condensed matter. Recent technical developments in storage rings, ion traps, and laser cooling of ions, have made it possible to produce such systems in the laboratory, though somewhat modified because of their finite size. In this article I discuss what one may expect in such systems [1] and also show some examples of experiments.     

Melting of crystalline confined plasmas

The melting of cold, ordered arrays of up to 10 000 charges, confined in external fields, has been studied in simulations. The latent heat associated with melting and the behavior of the specific heat were obtained, along with the spatial correlation function g(r) with respect to neighbors and the diffusion rates, both as a function of temperature. The melting temperatures of finite arrays of ions are found to be lower than that for infinite Coulombic matter, by an amount that depends on the number of charges and on the fraction of ions in the surface layer, in particular.     

Prediction of net energy gain in deuterium-beam interactions with an inertially confined plasma

It is shown that deuteron beams incident on compressed, tritium-based plasma targets can undergo beam-fusion reactions at a rate greater than Coulomb scattering for a wide range of beam energies and target temperatures. As a result, energy gains of about 5 are possible. The analysis is carried out by treating the beam ions, target ions, and the electrons as separate fluids. Essential to the attainment of high gain is the inclusion of the contribution to the fusion yield from deuterons that gain scattered energy at the expense of directed energy. The results are confirmed by Monte Carlo simulations equivalent to a Fokker-Planck treatment.     

Fluid-like instability of trapped electrons in confined plasmas

An instability, which does not depend on mode-particle resonances, can be driven by the drift of trapped electrons in the unfavorable curvature region of the confining magnetic field for selected values of the relevant mode transverse wavelengths.     

Stability of plasmas confined by magnetic fields

In this paper, we examine the question of the stability of plasmas confined by magnetic fields. Whereas previous studies of this problem have started from the magnetohydrodynamic equations, we pay closer attention to the motions of individual particles. Our results are similar to, but more general than, those which follow from the magnetohydrodynamic equations.     

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.     

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.     

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.     

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.     

Observations of an ion-driven instability in non-neutral plasmas confined on magnetic surfaces

The first detailed experimental study of an instability driven by the presence of a finite ion fraction in an electron-rich non-neutral plasma confined on magnetic surfaces is presented. The instability has a poloidal mode number m=1, implying that the parallel force balance of the electron fluid is broken and that the instability involves rotation of the entire plasma, equivalent to ion-resonant instabilities in Penning traps and toroidal field traps. The mode appears when the ion density exceeds approximately 10% of the electron density. The measured frequency decreases with increasing magnetic field strength, and increases with increasing radial electric field, showing that the instability is linked to the E x B flow of the electron plasma. The frequency does not, however, scale exactly with E/B, and it depends on the ion species that is introduced, implying that the instability consists of interacting perturbations of ions and electrons.     

Evolution of particle clouds around ablating pellets inmagnetically confined hot plasmas

Cryogenic hydrogen isotope pellets are being used for introducing fuel particles into the plasma interior in magnetic confinement fusion experiments. The spatial and the time evolution of the initially low-temperature, high-density particle clouds forming around such pellets are considered, with particular attention given to such physical processes as heating of the clouds by the energy fluxes carried by incident plasma particles, gas-dynamic expansion with j× B-produced deceleration in the transverse direction, finite-rate ionization and recombination processes, and magnetic field convection and diffusion. While the dynamic processes associated with the ionization and radial confinement processes are characterized by the relatively short Alfven time scale (μs range), the subsequent phase of axial expansion is associated with a notably larger hydrodynamic time scale defined by the heat input and gas-dynamic expansion rates (ms range). Data stemming from experimental measurements in toroidal confinement machines are compared with results of model calculations. Some similarities with extraterrestrial plasma scenarios, such as the earlier magnetospheric barium release experiments, are discussed     

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.     

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.     

Generality of deterministic chaos, exponential spectra, and Lorentzian pulses in magnetically confined plasmas

The dynamics of transport at the edge of magnetized plasmas is deterministic chaos. The connection is made by a previous survey [M. A. Pedrosa et al., Phys. Rev. Lett. 82, 3621 (1999)] of measurements of fluctuations that is shown to exhibit power spectra with exponential frequency dependence over a broad range, which is the signature of deterministic chaos. The exponential character arises from Lorentzian pulses. The results suggest that the generalization to complex times used in studies of deterministic chaos is a representation of Lorentzian pulses emerging from the chaotic dynamics.