Leaf Turner

Anisotropic magnetohydrodynamic turbulence in a strong external magnetic field

A strong external dc magnetic field introduces a basic anisotropy into incompressible magnetohydrodynamic turbulence. The modifications that this is likely to produce in the properties of the turbulence are explored for the high Reynolds number case. The conclusion is reached that the turbulent spectrum splits into two parts: an essentially two‐dimensional spectrum with both the velocity field and magnetic fluctuations perpendicular to the dc magnetic field, and a generally weaker and more nearly isotropic spectrum of Alfven waves. A minimal characterization of the spectral density tensors is given. Similarities to measurements from the Culham–Harwell Zeta pinch device and the University of California, Los Angeles Macrotor tokamak are remarked upon, as are certain implications for the Belcher and Davis measurements of magnetohydrodynamic turbulence in the solar wind.

Force free equilibria in toroidal geometry

The equation ∇×B−λB=0, where B is the magnetic field and λ is constant, is solved analytically in toroidally curved cylindrical coordinates, assuming a large aspect ratio torus.

Collective effects on equilibria of trapped charged plasmas

A fluid model is used to study analytically the equilibria of charged plasma in traps. Several geometries are explored: a one‐dimensional slab equilibrium of a finite‐temperature plasma mechanically confined by two plates that are externally maintained at fixed potentials, and both spherical as well as spheroidal equilibria of a zero‐temperature plasma confined in traps distorted from the standard Penning‐trap configuration by virtue of the multipole moments of the trapped plasma. Although this study was motivated by the necessity of understanding possible collective effects in charged‐plasma traps for the design and future diagnosis of the ambitious antiproton‐gravity experiment being undertaken by the Los Alamos Collaboration [Proceedings of the Second Conference on the Intersections between Particle and Nuclear Physics (American Institute of Physics, New York, 1986), AIP Pub. No. 150, p. 436], this study is also relevant to current and future attempts at producing strongly coupled plasmas and ionic cry...

Driven, steady-state RFP computations

The pseudospectral three-dimensional MHD code of Dahlburg et al. (1986 and 1987) is used to compute the dynamical behavior of a channel of magnetofluid carrying an axial current and magnetic flux. This situation contains the essential MHD behavior of the reversed-field pinch (RFP). An externally imposed electric field is applied to an initially current-free magnetofluid and drives currents that rise and eventually fluctuate about values corresponding to pinch ratios Theta of about 1.3, 2.2, and 4.5. A period of violent turbulence leads to an approximately force-free core, surrounded by an active MHD boundary layer that is not force-free. A steady state is reached that can apparently be sustained indefinitely (for several hundred Alfven transit times or longer). The turbulence level and time variability in the steady state increase with increasing Theta. The average toroidal magnetic field at the wall reverses for Theta = 2.2 and 4.5, but not for Theta = 1.3. Negative toroidal current filaments are observed. The Lundquist numbers are of the order of a few hundred.

Analytic solutions of ∇ × B=λB having separatrices for geometries with one ignorable coordinate

Analytic solutions of ∇×B=λB are presented for PS‐1 and CTX types of spheromaks, and for the proposed Wisconsin reversed‐field pinch. Inherent in the spheromak solutions is a separatrix that separates a region of closed magnetic field lines from a surrounding region of open ones. Such a structure enhances the plausibility of maintaining steady‐state spheromak operation by driving a steady current along the open field lines.

Turbulent relaxation of a confined magnetofluid to a force-free state

Three-dimensional, pseudo-spectral computation is used to follow the evolution of a resistive, incompressible magnetofluid. The magnetofluid is confined by rigid, free-slip, perfectly-conducting square boundaries in the x, y directions (‘poloidal’ boundaries), and periodic boundary conditions are assumed in the z direction (‘toroidal’ direction). A constant, uniform d.c. magnetic field B 0 is assumed in the z direction and a non-uniform current density j flows along it initially. Starting from a non-equilibrium hollow current profile, the evolution is followed for several tens of Alfven transit times. Considerable small-scale turbulence develops, which causes energy to decay more rapidly than magnetic helicity. The average toroidal magnetic field at the ( x, y ) boundary reverses sign spontaneously. The near spatial constancy of the ratio j B/ ( jB ) ≡ cos θ, in the relaxed state at late times, suggests that the state is nearly force-free. However, the ratio j . B /B 2 ≡ α is considerably less uniform than is cos θ suggesting more residual disorder than a pure minimum-energy state would display.

Incomplete relaxation of pinch discharges

Solenoidal field linkage is explained and its application to magnetic helicity is discussed. A Green’s tensor function for the magnetic vector potential of a plasma current distribution bounded by a perfect conductor is derived. A hypothesis of incomplete relaxation of a turbulent discharge is then used to establish reversed‐field pinch configurations with finite beta.

Fokker‐Planck equation for a plasma in a magnetic field

A convergent Fokker‐Planck equation is derived for an electron plasma in a strong dc magnetic field. Conservation laws and an H theorem are proved. The equation is manipulated into a form in which it is straightforward to evaluate magnetic‐field‐dependent relaxation times in terms of a series of modified Bessel functions.

Production and application of dense Penning trap plasmas

A new paradigm for producing well‐confined, dense‐thermonuclear plasmas is described. The convergence of a radial beam distribution of a Penning‐trap‐confined plasma produces a dense inertially confined non‐neutral plasma. The equilibrium, stability, classical transport, and particle‐handling properties of such a concept are developed. The application of this approach to controlled fusion using a pure electron plasma to form a central virtual cathode in which ions are electrostatically confined is discussed. On one hand, extreme plasma control is required, placing the major uncertainty on issues of machine precision. On the other hand, development is characterized by the manufacture and testing of extremely small and inexpensive systems. Thus, it would seem that a timely experimental test of this concept would be ineluctable. Success at such experiments might indicate an alternate path to practical fusion applications.

Statistical mechanics of a bounded, ideal magnetofluid

A statistical model of a three-dimensional, incompressible, cylindrically bounded, current-bearing magnetofluid is presented for the purpose of gaining insight into the nonlinear relaxation process routinely observed in reversed-field-pinch experiments. An absolute equilibrium ensemble is utilized that incorporates energy, magnetic helicity, and magnetic flux constraints. Results are extracted only after an extensive mathematical treatment of the properties of poloidal and toroidal fields. The model predicts the presence of magnetic fluctuations about a cylindrically symmetric, Bessel-function-model, mean magnetic field, which satisfies ▽ × 〈B〉 = μ〈B〉. As Taylors ∵-parameter approaches 1.56, the model predicts that the significant region of the fluctuation spectrum narrows down to a single (coherent) m = 1 mode. An analogy between the Debye length of an electrostatic plasma and μ−1 suggests the physical validity of the models prediction of the magnetic-field-fluctuation autocorrelation tensor 〈δB(r) δB(r′)〉, when |;r − r′| ≥ μ−1.