The effects of unstable modes, connected with the presence of impurity ions in a magnetically confined high-temperature plasma column and not dependent on wave-particle resonances that involve only a small portion of velocity space, are discussed for two significant regimes: a collisional one corresponding to relatively short mean free paths of the main ion population and a collisionless one in which a significant fraction of this population is magnetically trapped.

Helium films are explored in the temperature range 1-2.8 K for thicknesses of 3-11 atomic layers. Sharp heat-capacity peaks for the thinnest films appear to indicate melting of the second-layer solid. Thicker films display coverage-dependent truncations of the $\lambda$-point specific-heat anomaly, and cell thermal conductivity shows abrupt changes near these truncation points. Comparison with mass-flow measurements leads to the discussion of a possible intermediate superfluid phase.

An argument is given that a model field theory with an $n$-component order parameter has a nonzero critical temperature for large $n$ in two dimensions. A simple dependence of the depression of the $\lambda$ point below $T_{\lambda }$ (bulk) on film thickness is found which correlates with properties of the heat capacity for multilayer He films on graphite observed by Bretz.

The influence of a turbulent spectrum of high-frequency, short-wavelength electron plasma waves on the linear dispersion relation for low-frequency, long-wavelength drift waves has been analytically investigated.

A drift instability due to electrons trapped in a series of shallow magnetic troughs has been observed and compared to theoretical estimates. The instability, identified as Kadomtsev's trapped-electron mode, is maximum at a density lower than estimated from the theory.

Data analyses reveal that the Mahan form of the x-ray absorption threshold law, ${\epsilon }_2\left(\omega \right)=A{\left[\frac{(\hslash \omega -\hslash {\omega }_T)}{\xi }\right]}^{-{\alpha }_0}$, can describe $L_{2,3}$ edge data of Al, Mg, and Na, with the empirical rule ${\alpha }_0\approx 0.068{\mathcal{r}}_s$. However, the many-electron interpertation of the Li $K$ edge cannot be reconciled with this rule, and the exponents ${\alpha }_0$ can be calculated from the Nozières-De Dominicis expression only if the electron-hole interaction exhibits unusual properties.

It is shown that the ideas of effective-medium theory can be applied to the evaluation of the ac behavior of a random system. The results for systems of which the components have no dispersion, show dispersion. In particular, it is found that the ${\omega }^s$ behavior of the ac conductivity of many disordered systems is reproduced to a good approximation over a limited frequency range.

We present a first-principles calculation of the lattice dynamics of Be. The dynamical matrix is set up by evaluating the total electron energy up to third order in the electron-ion pseudopotential. In this way we are able to describe the three-body forces, which are essential for reproducing the experimental data.

The Wilson-Fisher $\epsilon$ expansion is used to calculate critical exponents in a semi-infinite Ising model to first order in $\epsilon$. It is found that potentials renormalize just as in the bulk, and all surface information is contained in the wave-function renormalization. $\nu$ is $\frac{1}{2}+\frac{1}{12}\epsilon$ and $\eta$ is 0, just as in infinite systems. ${\eta }_{\perp }$ and ${\eta }_{\parallel }$ are, respectively, $1-\frac{1}{6}\epsilon$ and $2-\frac{1}{3}\epsilon$ and the surface gap exponent ${\Delta }_1$ is $\frac{1}{2}-\frac{1}{12}\epsilon$ if scaling is assumed.

We have measured the de Haas-van Alphen effect in a single crystal of Gd, refined by solid-state electrolysis, observing four frequencies (in the range ${10}^5$-3×${10}^7$ G) near the $c$ axis and three frequencies in the basal plane. The faster oscillations identify with orbits on the third-zone sub-band Fermi surfaces of the relativistic augmented plane-wave calculations, if the sub-band energies are displaced by ± 0.57 eV by the ferromagnetic internal field.

Conversion from $E$ to $A$ proton spin symmetry of methyl groups undergoing tunneling rotation at 4.2 K is observed by means of nuclear magnetization induced by resonant processes which, besides symmetry conversion, involve simultaneous flips of nuclear and impurity electronic spins. Nonequilibrium populations of spin symmetries, frozen in at 4.2 K, relax when electronic Larmor and tunneling frequencies are close. A spread of tunneling frequencies inhomogeneously broadens the resonance which exhibits "hole burning" and similar distortion effects.

A shear-mode quartz-crystal microbalance measures only the nonsuperfluid component of the helium film adsorbed on it. From this effect detailed curves of the superfluid content in such films are obtained as functions of the total film mass adsorbed per unit area and of temperature. Besides the characteristic linear growth region of superfluid with thickness, these curves reveal the quantitative details of the onset region. Our results are presented together with some characteristic helium parameters deduced from them.

It is shown that a charged particle moving in a strong nonuniform electromagnetic wave suffers a net acceleration in the direction of the negative intensity gradient of the wave. Electrons will be expelled perpendicularly from narrow laser beams and various instabilities can result.

We report the first observations of the small temperature oscillations which accompany the nearly isothermal oscillations in the levels of two reservoirs of He II which are connected only by the mobile superfluid film. We show that our experimental results are in accord with a nearly isothermal approximation to the general theory first elucidated by Robinson for capillary flow. The amplitude of the temperature oscillations is in agreement with expectations based on the measured thermal conductance and time constant for our apparatus.

We present a Bäcklund transformation operating on solutions of the Kortweg-de Vries equation. It provides a unifying approach to the theory of solitary waves (solutions). Recursive application of the transformation to any solution of the Korteweg-de Vries equation generates a hierarchy of solutions for which an algebraic recursion relation is obtained. Every such hierarchy (one of which is the known family of pure multisoliton solutions) thus admits a nonlinear superposition principle.

We report nonlinear studies of the Weibel instability of a relativistic electron beam in a plasma. If $n_b\ll n_p$, the beam splits into self-pinched filaments at density $n_p$. These filaments then recombine into a single dense beam, from which the return current is expelled. The ratio of final magnetic to final streaming energy is $O(\frac{\nu }{\gamma )}$, and significant plasma heating occurs.

Superconducting tunneling experiments on double-hexagonal close-packed La show that the ratio $\frac{2{\Delta }_0}{k{T}_c}$ increases with pressure. The low-frequency part of the phonon density of states shifts to lower energies. Phonon softening is thus, at least partially, responsible for the strong increase of the superconducting $T_c$ with pressure.

A formula for the electrical resistivity expressed in terms of a projection operator is derived and discussed. It is argued that the correct evaluation of the resistivity to the lowest order in the strength of the scattering interaction on the basis of this formula requires, as do other formal expressions, the summation of an infinite number of terms. This re-establishes the standard theory of electrical conductivity, based on the integral transport equation for the distribution function.

We present a method of calculating the band structure of layer compounds that combines the transmission and reflection matrices from individual atomic layers. The computing time increases linearly with the number $p$ of layers in the repeat unit, compared with $p^3$ for other methods, thus rendering the method suitable for layer compounds with complicated stacking sequences. Results for Mo${\mathrm{S}}_2$ are described.

We consider phonon-electron interactions in highly doped III-V and II-VI semiconducting compounds, including nonparabolicity of the conduction band and the spin-orbit interaction. Absorption coefficients are calculated for monochromatic phonons produced by superconducting Sn and Al tunnel junctions, and we predict the possibility of observing directly an interaction of conduction electrons with slow and fast transverse modes, and phonon-induced spin-flip transitions.