H. Hurwitz

Large‐Amplitude Magnetic Compression of a Collision‐Free Plasma. II. Development of a Thermalized Plasma

Numerical calculations are made of a strong one‐dimensional disturbance traveling perpendicular to a magnetic field in a fully ionized and collisionless plasma. When the Alfven‐Mach number Mh is greater than 2, orbit crossings of the ions occur, which rapidly leads to thermalization perpendicular to the magnetic field if the crossings are extensive (Mh > 3). The thermalization approximates the behavior of a classical hydromagnetic shock, with a shock‐front thickness roughly equal to the distance the shock front travels in one‐half an ion gyration time. This length is somewhat greater than the ion gyration radius. The structure of the front is found to be strongly time dependent, and undergoes large fluctuations in an ion gyration period. It is argued that when the ion‐electron mass is large, the magnetic forces tend to suppress electron orbit crossings. This results in relatively cold electrons in the shocked region, with the ions obtaining nearly all of the thermal energy. A relationship between the longitudinal electrostatic potential difference across the shock front and mass flow in the plane of the front is derived on the basis of a simplified model and is found to be in qualitative agreement with the numerical results. The range of applicability of the calculations to real plasmas is discussed.

On the Bayesian approach to image reconstruction

A new iterative method is proposed for finding the optimal Bayesian estimate of an unknown image from its projection data (experimentally obtained integrals of its grayness over thin strips). Convergence of the method is proved and its performance is illustrated. The method compares favorably with previously proposed procedures.

Low Mach Number Magnetic Compression Waves in a Collision‐Free Plasma

The development of a strong hydromagnetic disturbance traveling perpendicular to an initially uniform magnetic field in a cold plasma is investigated by numerical integration of the equations of motion. The disturbance is driven by an electric field applied at a fixed plane surface which coincides with the initial boundary of the plasma. If the Mach number of the resulting disturbance is less than two, no crossing of particle orbits occurs. The disturbance then consists of a growing train of almost independent hydromagnetic pulses progressing into the undisturbed plasma at a speed somewhat in excess of the shock velocity which would be calculated from classical theory. The magnitudes of the vacuum magnetic field and the vacuum‐plasma interface velocity are, however, almost identical to the predictions of classical theory. These results, as well as the observed pulse spacing, can be understood in terms of a two‐region model of the disturbed portion of the plasma together with the assumption that the pulses...

COLLECTIVE OSCILLATIONS IN A COLD PLASMA

The collective motions of a fully ionized cold plasma in a uniform external magnetic field are treated by standard small amplitude theory. Finite temperature and collision effects are neglected. Specializing the analysis to a neutral plasma of uniform unperturbed density containing electrons and ions of one species, one obtains a dielectric tensor and dispersion relation which is a special example of results previously given by Astrom. A detailed discussion of the exact dispersion relation is given for the entire frequency spectrum, and completeness theorems are presented with the aid of scalar potentials representing the electromagnetic field quantities. It is found that when the Alfven dielectric constant α = 4πn(m + M)c2/B02 becomes comparable in magnitude to the ion‐to‐electron mass ratio, the plasma space charge may play an important role in determining the nature of collective oscillations. In particular, if the axial wavelength of the perturbation is sufficiently large, the singularities of the eff...

Electrical and pressure losses in a magnetohydrodynamic channel due to end current loops

End electrical and pressure losses are calculated for d-c magnetohydrodynamic (MHD) power generators, accelerators, or induction pumps having a geometry of a rectangular parallelopiped with the electric field, magnetic field, and fluid flow mutually perpendicular. For an MHD generator, having a cubic geometry, the maximum conversion efficiency is only 29%. This can be improved by increasing the length of the generator, inserting vanes, and extending the magnetic field, so that efficiencies of 90% should be attainable.

Electron Conductivity at Cyclotron Resonance

The electron conductivity of an ionized gas for electromagnetic radiation of frequency omega circularly polarized in the right-handed sense propagating along a uniform mag netic field is estimated for a plasma of nonzero temperature. Collisions are included. It is also shown that in the limit where the collision frequency becomes small and omega = omega /sub c/ there remains a nonvanishing real part of the form sigma = (ne/sup 2//km) (1/v/sub th/) alpha where k is the propagation constant, v/sub th/ is the speed which characterizes the thermal spread of the electrons velocity component in the longitudinal direction and alpha is a number of order unity relatively insensitive to the actual form of the electron distribution in longitudinal speeds. (auth)

CALCULATIONAL TECHNIQUE FOR STABILITY INTEGRAL GRADIENTS

A technique for obtaining stability integral gradients in plasma equilibrium studies is presented. The technique is based on the introduction of an artificial hamiltonian whose associated action integral may be identified with integrals along magnetic field lines. (C.E.S.)

Suppression of ∇B Drift in Curved Theta Pinch

Introduction of a conducting ring transverse to the axis of a curved theta pinch and inside the vacuum tube creates an equilibrium position for the plasma on the curved thetapinch axis.

Present Status of the Fusion Problem

Publisher Summary The prospects of developing a fusion reactor with net power output have been given an unexpected boost by the recent advances in the field of superconductivity. The fact that it now appears technically feasible to construct superconducting coils which produce magnetic fields in the 100-kgauss range introduces the possibility of obtaining net power output under conditions in which the ratio of plasma pressure to magnetic pressure is low—possibly not much higher than the one that has already been explored in the Coensgen experiment. On the other hand, it is by no means assured that such low pressure devices would be economically attractive. Hence, the motivation for exploring configurations in which the plasma pressure is not small compared to the magnetic pressure is as strong as ever. Indeed, even though the high pressure devices may not provide the quickest path to developing a machine with net energy output, they may well prove to be more practical in the long run.