Volume 37, Issue 8

The material in an accretion disk moves on Kepler orbits whereas the magnetosphere of a neutron star rotates like a solid body. Therefore large velocity differences will occur at the interface between the two media. These give rise to Kelvin-Helmholtz instabilities. We present a stability analysis for a simplified geometry. The consequences of the instability for the mass flow from the disk into the magnetosphere are discussed. The resulting transfer of angular momentum to the neutron star is compared with the observed changes of the rotation periods of these stars

A sounding rocket experiment involving the injection of a barium gas jet in the upper ionosphere provided an opportunity of investigating quantitatively several aspects of the beam-plasma interaction that is the substance of Alfven’s critical velocity effect. Whereas the experimental data are presented elsewhere, this paper contains some theoretical considerations of (1) the limiting neutral density for which the ionization process can operate, (2) the interaction of the freshly injected ions with the background plasma, and (3) the microprocess which leads to collisionless electron tail formation. The observed distribution of injected ions is consistent with the Townsend condition on the beam-plasma discharge. The mass loading on the ambient plasma, although locally high, has a weak effect on the dynamics of the involved flux-tube because of the limited extent of the beam. The most likely process by which energy is transferred from the freshly generated ions to the electrons is an ion beam instability leading to the excitation of lower hybrid waves

The “anti-dynamo” theorems for toroidal magnetic fields with axisymmetry and plane symmetry are generalized to the case of a compressible, time-dependent flow in a fluid with arbitrary conductivity

A diagnostic method for the measurement of neutrons from thermonuclear plasma devices is proposed on the basis of the neutron telescope applied in neutron astronomy. The method utilizes the elastic scattering of the neutron from a proton by measuring the directions and energies of the proton and the scattered neutron. The expected count rate is estimated, and methods of suppressing the background count level are indicated

Atomic data have been obtained for the coronal ion S XII using the UCL program codes. Energy levels and radiative transition probabilities have been computed with different target descriptions allowing for configuration interaction and relativistic effects. Multi-configuration Hartree-Fock method is used to calculate the target wave functions. Collisional excitation cross sections between the 2 s 2 2 p 2 P 0 , 2s2p 2 4 P, 2 D, 2 S, 2 P and the 2p 3 4 S 0 , 2D 0 , 2P 0 eigenstates of S XII have been calculated using eight-state close coupling and distorted wave approximations with a target description employing a 3̄̄̄d̅ pseudo orbital. Collision strengths between the lowest five eigenstates of S XII have also been computed in five-state close coupling and distorted wave approximations for comparison. The results are compared with available theoretical work. It is found that the use of elaborate target wave functions and the choice of a more accurate scattering approximation may change the cross sections by more than 25% in some of the transitions

The instability of convection rolls in a fluid layer heatet from below is studied in the case where the layer rotates about an axis slightly inclined with respect to the vertical. The inclination destroys the horizontal isotropy of the layer, but the instability of rolls found by Küppers and Lortz [1] is little affected as long as the angle of inclination is small. A new effect is the generation of mean Reynolds stresses by rolls not aligned with the horizontal component of the rotation vector. The mean flow exhibits a vorticity of the same sign as the horizontal component of rotation and agrees qualitatively with the mean flow found in the numerical experiments of Hathaway and Somerville [2]

After analyzing the general linear equation of diffusion (of a substance or of energy) with source term and given influx across the boundary we describe a method for constructing explicit and implicit conservative difference schemes which also preserve nonnegativity. We call a scheme “conservative” if via a convenient sum-analogue it does exactly imitate the conservation of a substance or energy. We concretize this method for the spatially two-dimensional heat equation in a rectangle with given influx. We also present a conservative implicit scheme with alternating directions

After analyzing the general linear equation of diffusion (of a substance or of energy) with source term and given influx across the boundary we describe a method for constructing explicit and implicit conservative difference schemes which also preserve nonnegativity. We call a scheme “conservative” if via a convenient sum-analogue it does exactly imitate the conservation of a substance or energy. We concretize this method for the spatially two-dimensional heat equation in a rectangle with given influx. We also present a conservative implicit scheme with alternating directions

The equilibrium is studied of a pinched linear plasma column of “Extrap” type which is confined in a purely transverse magnetic field, partly arising from currents in a set of external conductor rods being introduced for stabilizing purposes. The axial and transverse losses are separated in a simplified theoretical model for which stability is assumed as a working hypothesis and anomalous transport as well as impurity radiation are neglected. Then, the reduction of the axial heat transport by the magnetic field will have a substantial effect on the over-all heat balance, thus leading to high temperatures at large axial lengths of the plasma column. Conditions near ignition should become possible at technically realistic linear dimensions and pinch currents

The theoretical and numerical steady-state calculation of the width of an escaping plasma stream through a magnetic mirror solves the self-consistent potential and charge distribution for a low beta plasma. The leak width is obtained as the geometric mean of the ion and electron Lar-mor radius, also called hybrid width, in agreement with some experimental measurements. If the out-streaming plasma is unstable or collisional, the leak width can only larger, contrary to earlier results in the literature

The diffusion of magnetic lines of force in a toroidal plasma is equivalent within a perturbative treatment, to the problem of turbulent convection in two space dimensions. Neglecting a triplecorrelation the diffusion coefficient D is, therefore, given as a spectral and ensemble mean of the Green’s function, and the following order of magnitude is obtained: D xx ≈ Min(L 0 |B̃x| 2 /B 0 2 , l 0 \B̃x\/B 0 ), where L 0 and l 0 are the (Eulerian) correlation lengths of the magnetic fluctuations B̃ parallel and perpendicular to the unperturbed field B 0 , respectively

The problem of passive diffusion by strong turbulence is described by equations of motions of the form dx/dt = V(t, x), V(t, x) being a stochastic velocity field with strong nonlinear dependence on x. Present-day theories are based on certain plausible approximations rather than on a systematic treatment, e.g. in form of a perturbation theory with respect to some smallnes parameters. In this paper a method is described to construct stochastic velocity fields with reasonable velocity distributions and correlations, and to obtain at the same time the exact solution of the corresponding diffusion problem. Brownien motion is a special case of such models. The models can serve to check existing approximate theories, to simulate real turbulence, and to get altogether better insight into turbulent diffusion

A study is made of the nonlinear damping of parallel propagating Alfvén waves in a high β plasma. Two circularly polarized parallel propagating waves give rise to a beat wave, which in general contains both a longitudinal electric field component and a longitudinal gradient in the magnetic field strength. The wave damping is due to the interactions of thermal particles with these fields. If the amplitudes of the waves are low, a given wave (ω 1 , k 1 ) is damped by the presence of all longer wavelength waves; thus, if the amplitudes of the waves in the wave spectrum increase with wave length, the effect of the longest waves is dominant. However, when the amplitude of the waves is sufficiently high, the particles are trapped in the wave packets, and the damping rate may be considerably reduced. We calculate the induced electrostatic field, and examine the trapping of thermal particles in a pair of waves. Finally, we give examples of modified damping rates of a wave in the presence of a spectrum of waves, and show that, when the trapping is effective, the waves are mostly damped by their interactions with waves of comparable wavelengths

A family of ideal MHD equilibria is considered introducing the concept of a driving parameter λ the increase of which beyond a certain threshold λ 0 drives the plasma from a linearly stable to an unstable state. Using reductive perturbation theory, the nonlinear ideal MHD equations of motion are expanded in the neighbourhood of λ 0 with respect to a small parameter ε. An appropriate scaling for the expansions is derived from the linear eigenmode problem. Integrability conditions for the reduced nonlinear equations yield nonlinear amplitude equations for the marginal mode. Nonlinearly, the instabilities are either oscillations about bifurcating equilibria, or they are explosive. In the latter case, the stability limit depends on the amplitude of the perturbation and is shifted into the linearly stable regime. Generally bifurcation of dynamically connected equilibria is observed at λ 0

The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f{ω 1 t, ω 2 t) is investigated numerically and graphically. For sufficiently incommensurate frequencies ω 1 , ω 2 , a doubly indexed infinite sequence of eigenvalues and eigenmodes is obtained. The equation considered is a model for the magneto-hydrodynamic “continuum” in general toroidal geometry. The result suggests that continuum modes exist at least on sufficiently ir-rational magnetic surfaces

The dynamic evolution and the saturated state of a long sheet pinch subject to growth of resistive tearing modes was investigated by numerical solution of the 2D MHD equations. Both the compressible and the incompressible equations were used, and the difference is found to be negligible. The necessity of considering a resistive equilibrium is stressed. The paper concentrates on a static equilibrium maintained by an external electric field and requiring a special distribution of the resistivity η. In addition the dynamics of the resistivity plays an important part. Assuming η to be time independent, the sheet pinch develops a number of soliton-like magnetic islands, which coalesce. The final state consists of a single soliton, while the generation of further sol-itons is inhibited by a strong shear flow allong the current sheet. When allowance is made for parallel diffusion of the resistivity such that η is essentially a flux function, the final state is quite different. Here the longest wavelength dominates, leading to a single, large island and completely destroying the original sheet pinch

Resistive ballooning modes in general three-dimensional configurations are studied on the basis of the equations of motion of resistive MHD. Assuming small, constant resistivity and perturbations localized transversally to the magnetic field, a stability criterion is derived in the form of a coupled system of two second-order differential equations. This criterion contains several limiting cases, in particular the ideal ballooning mode criterion and criteria for the stability of symmetric systems. Assuming small growth rates, analytical results are derived by multiple-length-scale expansion techniques. Instabilities are found, their growth rates scaling as fractional powers of the resistivity

The HERA MHD as been supplemented by a code for computing the perturbation energy of a vacuum field surrounding the plasma and bounded by a conducting wall. By means of a Green’s function technique the problem is reduced to the numerical solution of an integral equation. Extensive tests and convergence studies have been done to verify the code

A set of stellarator fields with magnetic surfaces of small aspect ratio is found by superposing recently introduced, easily computable field harmonics. The law of superposition is found analytically by closely approaching “helical symmetry” of these “new” fields in suitable orthogonal coordinates

A previous stellarator expansion valid for finite aspect ratio and small rotational transform ι and based on the axisymmetric toroidal vacuum field is generalized to stellarator equilibria with arbitrary closed line vacuum fields as zeroth order field. The equilibrium beta value behaves as β ~ ι 2 . The condition for the magnetic surfaces to be unaffected by β within this ordering is formulated

Properties of finite-beta stellarator equilibria are investigated which are obtained as fully three-dimensional finite-beta solutions of the magnetohydrostatic boundary value problem with the help of the code by Bauer, Betancourt, and Garabedian based on the energy method. In the case of slender l = 2 stellarator equilibria the displacement of the magnetic axis as well as its helical deformation as functions of beta are found to be close to the known theoretical predictions which were derived for slender low beta l = 2 configurations of large aspect ratio. In the case of l = 2 stellarators with moderate aspect ratio the shear has a weak effect on the displacement in contradiction to results from asymptotic theories. A class of l = 0, 1, 2, 3 configurations with reduced secondary currents could be found showing axis displacements which are at least a factor of three smaller than those in pure l = 2 stellarators. A critical equilibrium beta value of β e (0) = 0.045 has been estimated in the W VII-AS stellarator for a bell-shaped pressure profile. Extensive numerical convergence studies are presented

The magnetohydrostatic boundary value problem is investigated for the case where the magnetic field is tangential on an toroidal surface without symmetry. The first part deals wit small deviations from the homogeneous field. If the surface deviation from a cylinder with arbitrary cross-section is small of order ε, it is found that in first order a solution exists if two profile functions are properly prescribed. The solubility condition in the (n + 1)-th order determines the freedom of the n-th order. In the second part general toroidal geometry is considered for the case of a smooth pressure profile. The longitudinal current is determined so that the rotational transform vanishes

Simple axisymmetric and ripple tokamak model fields are used to compute neoclassical trans-port coefficients by Monte Carlo simulation over a wide range of mean free paths in the approximation of small gyroradius. Further assumptions are a monoenergetic particle distribution which is only subject to pitch angle scattering and a vanishing electric field. Pfirsch-Schlüter, plateau, banana and ripple transport coefficients are obtained. In the ripple regime the description is unified by introducing the concept of an effective ripple. Cases in which ripple transport is diminished due to collisionless detrapping are observed

The neoclassical diffusion losses of an l = 2 stellarator and an advanced stellarator are analysed with a modified version of the Boozer-Kuo-Petravic Monte-Carlo Code. Particle loss and confinement of a monoenergetic ion distribution are determined at arbitrary collisionality under stationary conditions. Special attention is given to the long mean free path regime. Due to the drift motion of localized particles a depopulation of the distribution function around v ∥ = 0 occurs. The confinement time is determined by pitch angle scattering in this case. It is analysed under which conditions the 1/v-scaling of diffusion losses arises. A comparison is made between the loss rate of an advanced stellarator and a classical l = 2-stellarator. Also a tokamak with ripple losses is considered

The paper describes the physics background and the design of a compact ignition and burn control experiment (ZEPHYR). It was optimized with respect to magnetic field energy and costs on the basis of a cryogenically cooled normal conducting magnet. Ohmic heating, neutral injection and adiabatic compression were chosen to produce the required temperature. Ignition and controlled thermonuclear burn for about ten energy confinement times were foreseen

An algorithm allowing a fast solution of stationary and time dependent 1-d diffusion problems for the case of finite ionization and recombination rates is presented. Results of numerical computations and an analytic stability analysis show its unconditional stability. The computational effort involved rises only linearly with the number of ionization stages included. An application to the diffusion of oxygen and iron impurities in JET is described

Collective space charge effects play an important role in intense unneutralized beams of non relativistic heavy ions, which are of interest in recently proposed high-current accelerators (such as drivers for inertial confinement fusion etc.). Of particular importance is the propagation of wave-like perturbations including the destabilizing effect of dissipation due to finite electrical conductivity in the surrounding walls. The propagation characteristics of such waves are investigated by means of 2½-dimensional computer simulation, with emphasis on dispersion, steepening (leading to solitary waves), and the problem of reflection of a growing wave at the beam tail with subsequent conversion into a damped wave propagating back into the beam. The net result on beam quality is discussed

Calculations are presented which show that the collective acceleration of ions by rings of relativistic electrons seems feasible in the polar regions of a dipolar magnetospheric field. The well known magnetic field of the earth is taken as an example and it is found that with rings of electrons of only 4 MeV initial energy, deuterons can be accelerated up to energies of about 50 MeV from rest in a distance of one third of an earth radius. Although the drift motion of the electron rings across the magnetic field lines is negligible for latitudes greater than 45°, in the equatorial plane the ring drifts at constant altitude with a speed proportional to the local magnetic field index

A synopsis of different selfsimilar spherical compression waves is given pointing out their fundamental importance for the gas dynamics of inertial confinement fusion. Strong blast waves, various forms of isentropic compression waves, imploding shock waves and the solution for non-isentropic collapsing hollow spheres are included. A classification is given in terms of six singular points which characterise the different solutions and the relations between them. The presentation closely follows Guderley’s original work on imploding shock waves