Mark A. Heald

Magnetic braking: Improved theory

An alternative analysis is presented for the magnetic braking experiment of Wiederick et al., taking into account the fringing streamlines of eddy currents for a rectangular ‘‘footprint’’ of the magnetic field.

Time‐dependent generalizations of the Biot–Savart and Coulomb laws

Strictly, Coulomb’s law and the Biot–Savart law determine the electric and magnetic fields for static sources only. Time‐dependent generalizations of these two laws, introduced by Jefimenko, are used here to explore the applicability of Coulomb and Biot–Savart outside the static domain. The fact that Biot–Savart holds for some classes of time‐dependent currents has led to much confusion in the literature, which this paper endeavors to dispel. To illustrate Jefimenko’s equations, the standard Lienard–Wiechert fields of a point charge are derived.

Electric fields and charges in elementary circuits

In an effort to clarify the role of surface charges on the conductors of elementary electric circuits and the electric fields in the space around them, we present a quantitative analysis of (two‐dimensional) circular current loops. It is also noted that, in general, lines of Poynting flux lie in the equipotential surfaces of quasistatic systems.

EXPERIMENTS ON THE OHMIC HEATING AND CONFINEMENT OF PLASMA IN A STELLARATOR

The basic concepts of confinement and ohmic heating in a figure‐eight stellarator are briefly reviewed and experimental data in these areas summarized. The production of energetic x‐rays by runaway electrons, up to ten milliseconds after the disappearance of the accelerating field, has indicated effective single‐particle confinement by magnetic fields of 20 000 to 30 000 gauss. However, the plasma confinement time during ohmic heating appears to be limited by unknown processes to approximately 100 microseconds for hydrogen, more than three orders of magnitude shorter than predicted from classical collisional diffusion. The ionization level in a helium discharge, with an initial pressure of about 1 μ of Hg, becomes virtually complete during the heating pulse, and the electric resistivity corresponds to a kinetic temperature of about 100 volts, or 106 degrees. After the heating pulse, the electron density decays with a time constant as great as 6 milliseconds under some conditions. The hydromagnetic kink in...

Where is the “Wien peak”?

Electronic mail: john.field@cern.ch A. Alaniz, ‘‘A simple special relativistic perturbation scheme for yielding the general relativistic behavior of point particles and photons in the gravitational field of stars,’’ Am. J. Phys. 70, 498–501 ~2002!. H. Goldstein, Classical Mechanics ~Addison–Wesley, Reading, MA, 1980!, 2nd ed., Chap. 3. G. Herzberg, Atomic Spectra and Atomic Structure ~Dover, New York, 1944!, p. 19. R. Ferraro, ‘‘The equivalence principle and the bending of light,’’ Am. J. Phys. 71, 168–170 ~2003!. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity ~Wiley, New York, 1972!, Chap. 8, Sec. 5. L. B. Okun, K. G. Selivanov, and V. L. Telegdi, ‘‘On the interpretation of the redshift in a static gravitational field,’’ Am. J. Phys. 68, 115–119 ~2000!.

Microwave Scattering from Unstable Electron Plasma Waves

An analysis is presented of an experimental study of the scattering of microwaves by the density fluctuations due to electron plasma‐wave instability in a beam‐plasma system. Reasonably good agreement with the general predictions of the Shapiro and the Drummond and Pines nonlinear theories of plasma oscillations is obtained. In particular, at the “quasilinear” steady state, the experimentally measured values of the scattering cross sections, the angular spread of the scattered radiations, the functional dependence of the scattering cross sections on the wavenumber of the most unstable plasma wave mode, and the increase in the thermal energy of the plasma electrons were all in reasonably good agreement with the corresponding theoretically expected values. In a few cases, a rather weak satellite line corresponding to scattering at the “bounce frequency” was seen. In these cases, the satellite line appeared only on the low‐frequency side of the main plasma line.

Energy flow in circuits with Faraday emf

Several elementary models are analyzed to clarify the essential features of energy flow in circuits involving electromagnetic induction.

Least Squares Made Easy

A very practical method for hand calculation of least-squares-adjusted slopes, acceleration coefficients, etc., is presented and compared with better known but less-satisfactory algorithms. Particular attention is given to easy methods for estimating the precision of the adjusted constants. The method, based on weighted successive differences, applies to the special case of equal increments in the independent variable.

Microwave propagation in a plasma with a sheared magnetic field

The propagation of a plane electromagnetic wave through a Lorentz plasma in a sheared magnetic field is considered. The characteristic waves in a uniformly sheared, but otherwise homogeneous, medium are found, and their properties presented graphically. Some effects introduced by the presence of shear are investigated by means of elementary applications of the uniform-shear theory. By suggested extensions of the analysis, refinements may be made in the interpretation of microwave diagnostic experiments with controlled-fusion containment devices having complicated sheared fields.

Computation of Fresnel diffraction

A review and commentary is given of practical methods for computing the Fresnel diffraction patterns of circular and linear apertures. The general problem of approximating transcendental functions is also considered.