The relativistic motion of an electron is calculated in the combined fields of a transverse helical wiggler field (axial wavelength is ${\lambda }_0=\frac{2\pi }{k_0}$) and the constant-amplitude, circularly polarized primary electromagnetic wave ($\hat{\delta }{B}_T,\omega ,k$) propagating in the $z$ direction. For particle velocity near the beat-wave phase velocity $\frac{\omega }{(k+k_0)}$ of the primary wave, it is shown that the presence of a second, moderate-amplitude longitudinal wave ($\hat{\delta }{E}_L,\omega ,k$) or transverse electromagnetic wave ($\hat{\delta }{B}_2,{\omega }_2,k_2$) can lead to stochastic particle instability in which particles trapped near the separatrix of the primary wave undergo a systematic departure from the potential well. The condition for onset of instability is calculated, and the importance of these results for free-electron-laser (FEL) application is discussed. For development of long-pulse or steady-state free-electron lasers, the maintenance of beam integrity for an extended period of time will be of considerable practical importance. The fact that the presence of secondary, moderate-amplitude longitudinal or transverse electromagnetic waves can destroy coherent motion for certain classes of beam particles moving with velocity near $\frac{\omega }{(k+k_0)}$ may lead to a degradation of beam quality and concomitant modification of FEL emission properties.

The response of an atomic or molecular system to an external perturbation is studied within the framework of time-dependent Hartree-Fock theory. Quadratic response functions are defined and analyzed with regard to their poles and residues, from which an expression for matrix elements of an arbitrary operator between excited states is deduced. For one-particle operators the matrix elements $〈m\left|A\right|n〉$ are correct through first order in correlation and the hypervirial relation $(E_n-E_m) 〈m\left|A\right|n〉=〈m\left|\mathrm{}\right[A,H\left]\mathrm{}\right|n〉$ is satisfied. Spurious poles, which have no counterpart in an exact theory, are encountered in the quadratic response functions. Their appearance is attributed to well-known deficiencies in the time-dependent Hartree-Fock approximation.

We present a quantum electrodynamic calculation of the gain associated with the stimulated emission and absorption of photons by high-energy electrons in the presence of a spatially periodic, static magnetic field. The calculation is relevant to the description of a high-energy electron laser in the long-interaction-length low-density (single-particle) regime. The different kinematic constraints imposed on the photon-emission and -absorption processes are shown to produce the effect of population inversion in an energetic electron beam which allows for a net gain in the number of photons produced per unit path length. The spectral dependence of the gain on the wave vector of the emitted photon has a width determined by the incident electron momentum distribution and a maximum in the vicinity of a $k$ value [$2{\left(\frac{W_{10}}{m{c}^2}\right)}^2\left(\frac{2\pi }{{\lambda }_0}\right)$] determined by the central electron momentum $\frac{W_{10}}{c}$ and the spatial period of the magnetic field. Derived formulas for the gain and gain-minus-loss coefficients are compared with formulas obtained on the basis of the stimulated Comptonscattering model. While the separate gain and loss coefficients diverge in the limit $\hslash \to 0$, the gain-minus-loss coefficient is shown to have a finite value in this limit which agrees with the result of a classical derivation.

A theory of the multicomponent wiggler free-electron laser is formulated in the small-signal regime. Analytical expressions for the spontaneous spectrum and the corresponding small-signal gain are derived. The expressions are valid for an arbitrary wiggler configuration consisting of any number of constant or tapered sections and drift spaces. Thus, optical klystrons are included as a particular case of the two-component devices. As a natural result of the derivation, it is proved that Madey's theorem holds for any multicomponent wiggler configuration including the optical klystron. As particular cases, several two-component wiggler schemes are discussed in detail. Based on the simple-gain expression an upper limit is obtained for the small-signal gain. It is shown that this cannot exceed the maximum gain of a constant wiggler of the same effective length by more than 25%.

A formalism for applying path integrals to certain problems in nonlinear optics is considered. The properties of a coherent-state propagator are discussed and a path-integral representation for the propagator is presented. This representation is then employed in evaluating the propagator for general single-mode and multimode Hamiltonians which are at most quadratic in the creation and destruction operators of the field. Some examples involving parametric processes are given.

Calculated Rayleigh-Taylor growth for perturbations on ablation fronts may be reduced by an order of magnitude due to thermal smoothing. Because studies of the development of perturbations on ablation layers have generally derived growth rates by assuming that conditions are quasisteady in a reference frame moving with the front, they neglect this stabilizing effect. If confirmed experimentally, this will allow substantial improvements over present designs for inertial confinement fusion implosions. Using a combined Galerkin perturbation technique, we develop analytic models for the propagation of a rippled thermal front into a uniform medium. We find that the mean front advances slightly more rapidly than a uniform front, and the perturbation on the front rapidly dies off.

A nonrelativistic theory of charged-particle scattering by a background potential $V\left(r\right)\mathrm{}$ in the simultaneous presence of a magnetic and a laser field is developed. The particle motion in the magnetic and laser field in dipole approximation is treated exactly. Transitions between exact quantum-mechanical states of the charged particle are considered to lowest-order Born approximation in $V\left(r\right)\mathrm{}$. Conservation laws and selection rules for the scattering are derived for the case of laser light circularly polarized in the plane perpendicular to the magnetic field direction. It is shown that nonlinear bremsstrahlung may occur accompanied by a corresponding change of the electron's angular momentum component along the magnetic field axis. Transition amplitudes for these cases are presented in closed form and their electric and magnetic field dependences are discussed in the limiting cases of weak and strong magnetic and laser fields. The connection of this approach to previous work is established.

A motivated protocol for the construction of a Hamiltonian density for continuum systems in an Eulerian coordinate system is presented and applied to the case of magnetohydrodynamics. The gauge invariance (i.e., invariance under unphysical transformations) is investigated and the structure of the gauge group evaluated.

The width and the profile of the strongest line in the visible spectrum of hydrogenlike carbon broadened by electric fields from ions and electrons are calculated for plasmas with electron densities from ${10}^{17}$ to ${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and temperatures near 100 eV. Most of the broadening is due to ion-produced fields whose effect is evaluated with the use of the quasistatic approximation. The electron broadening both from elastic and inelastic collisions is calculated with the use of the impact approximation. Corrections for dynamical Stark effects due to relative ion-ion motion are also discussed.

We report measurements of the transmission of 1 - 6-keV energy positrons through films of Al, Cu, and Si up to 3000 Å thick. When the thickness is expressed in terms of mass per unit area, the transmission of Cu and Al is found to be the same within ±10%. Within a ±20% precision we observe no effect having to do with the crystallinity of the materials. The median penetration depth of positrons in Al and Cu is found to vary with the energy $E$ as $E^n$, with $n={1.60}_{-0.08\mathrm{}}^{+0.15\mathrm{}} \mathrm{and} {1.43}_{-0.11\mathrm{}}^{+0.07\mathrm{}}$, respectively. Our measured median penetration depths are significantly less than one would have expected from the calculation of Nieminen and Oliva [R. M. Nieminen and J. Oliva, Phys. Rev. B 22, 2226 (1980)] which seems to indicate the importance of large-angle scattering effects. Our measurements can be combined with independent measurements of the energy dependence of the yield of positronium at a surface [K. G. Lynn, Phys. Rev. Lett. 44, 1330 (1980) and K. G. Lynn and D. O. Welch, Phys. Rev. B 22, 99 (1980)] to obtain values for the positron diffusion constant $D_{+}$ in single-crystal metal samples. For example, we find $D_{+}\left(\mathrm{Al}\right)=(0.76\mathrm{}\pm 0.14)$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$ and $D_{+}\left(\mathrm{Cu}\right)=(1.06\mathrm{}\pm 0.20)$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$. The former is in agreement with the deformation-potential calculation of Bergersen et al. B. Bergersen, E. Pajanne, P. Kubica, M. J. Stott, and C. H. Hodges, [Solid State Commun. 15, 1377 (1974)] if the positron effective mass in Al is $m_{+}=(1.59\mathrm{}\pm 0.12)m_e$. Finally, we use our measurements to calculate the optimum thickness of transmitting positron moderators for enhancing the brightness of slow positron beams.

The $2s^{2}2p^5-2s2p^6$ transitions in ${\mathrm{Sr}}^{29+}$ and ${\mathrm{Y}}^{30+}$ have been observed by means of a laser-produced plasma and a 2.2-m grazing-incidence spectrograph. Comparison of the observed $2s^{2}2p^5{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}-\frac{1}{2}}^{}{}_{}{}^{}$ fine-structure intervals with values calculated by the Dirac-Fock method allows accurate wavelengths to be predicted for the $2s^{2}2p^5{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}-{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ magnetic-dipole transitions in the isoelectronic series of ions ${\mathrm{Kr}}^{27+}$${-\mathrm{M}\mathrm{o}}^{33+}$.

A one-dimensional, one-parameter-map model for dissipative systems with translational symmetry is studied. The map possesses confined periodic and chaotic solutions which form an infinite array on the real line, periodic or chaotic running solutions which propagate coherently to the left or right, and a variety of diffusive motions where iterates wander over the entire interval like a random walk. The onset of diffusion in various regions of parameter space is studied in detail and simple dynamical models for the behavior of the diffusion coefficient near bifurcation points are constructed.

An examination of the physics of the reversible-energy-fluctuations (REF) converter shows that the addition of the energy-transducing first layer and the thermal-barrier second layer for the REF converter enables the REF circuit to control the voltage levels of the input energy transferred to the diodes in the third layer. This enables the maximum efficiency of the Carnot cycle to be approached both for power conversion and for reversible operations as a heat pump or refrigerator. When the energy from the first layer is transferred to the third layer in the near field, the input energy to the rectifying layer can be increased by several orders of magnitude over the maximum input energy that can be transferred by the radiation field and can be rectified by smaller discrete diodes or thinner rectifying films than can be used in solar cells. Power-conversion performance equations for quantum-effect diodes in a REF circuit show a power-conversion efficiency of 82% for one model. Thin-film designs are given without discrete components with a 1-kW/${\mathrm{cm}}^2$ output power. It is shown that the theoretical potential for maximum efficiency and at temperatures ranging from cryogenic to incandescent, can, in principle, be extended to detecting minimum signal powers and counting single photons in the quantum limit. It is also shown that, in principle, for the conversion of solar energy, the limiting efficiency of 93% for this irreversible thermodynamic cycle can be approached using crystal-lattice temperatures for the first layer much lower than the electron temperature and, thereby, minimizing the thermal gradient across the thermal barrier.

We suggest an interpretation of the spin-orbit interaction as an electrostatic effect, involving the Lorentz-transformation properties of the center of mass and center of charge.

The formation of orderly, steady, spatial structures in rf-heated plasmas that have metastable states is studied as the development of an instability of the solution to the reaction-diffusion equations for the plasma species. Plasma-species (electrons, ions, and metastable atoms) source functions are given in terms of the electron energy distribution in strong electric fields and of the various collision cross sections. The methods of two-time expansions and bifurcation theory are used to calculate the nonuniform states that bifurcate from the unstable uniform steady state for straight and toroidal tubes. The sinusoidal density variations give the discharge the appearance of glowing balls of gas. This pattern formation is analogous to the morphogenesis found in certain chemical reactions and biological processes.

A liquid-gas system at temperatures below criticality and densities between the liquid and the gas density at the coexistence curve exhibits equilibrium between a spherical liquid domain and the surrounding gas. This two-phase state is studied for the three-dimensional lattice-gas model, with the use of Monte Carlo methods. In sampling the chemical potential of lattices which are finite but much larger than the correlation length for various densities, the radius $R$ of the liquid cluster is derived from the excess density without any ambiguities in the cluster definition. From the relation between cluster radius and excess chemical potential, information on the universal scaled interface free energy of clusters as a function of $\frac{R}{\xi }$ is obtained, in the range $3\lesssim \frac{R}{\xi }\lesssim 10$, which is also the range of experimental interest. The resulting free-energy barriers against nucleation deviate distinctly from the capillarity approximation in most parts of this regime. At temperatures far below criticality, the present method is shown to agree with the standard approach where a cluster is defined in terms of the contour around occupied lattice sites. Finally, the consequences of our results for experiments and phenomenological droplet models are briefly discussed.

The heating of and the force acting on the electrons of the magnetic plasma by the externally launched electromagnetic wave are investigated from first principles. The quantum-mechanically extended Vlasov equation is first derived to treat properly the inverse bremsstrahlung, and then a quasilinear equation is derived from this Vlasov equation to consider properly the electron velocity-space diffusion by the turbulence induced by the electromagnetic wave. The heating rate of and the force acting on the electrons are explicitly expressed in the forms of hydrodynamic energy and momentum equations derived from the quasilinear equation. The heating is shown to be due to the collisional and collisionless inverse bremsstrahlen of the electromagnetic wave in the magnetic field under the influence of the plasma field, and the Landau and cyclotron resonance damping of the plasma waves induced by the electromagnetic wave while the force is due to only the former. It is shown that the force is negligible in the vicinity of the electron cyclotron frequency except for the ordinary wave propagating in the direction perpendicular to the magnetic field.

A modified trial solution of Roberts's function, depending on two parameters, is chosen in such a way that it can satisfy the boundary conditions and the subsidiary condition that the electron density be normalized. The proposed solution is used to calculate the total ionization energy of atoms, and also the repulsive interaction energy between rare-gas atoms. The results obtained by the proposed function are better than those obtained from Csavinszky's function and from Kesarwani and Varshni's function for medium-atomic-number elements, and the numerical values of the parameters are easier to optimize.

After modifying Davydov's original equations for the $\alpha$-helix soliton to include ten additional dipole-dipole coupling terms and to represent helical symmetry, a numerical study predicts that such solitons should appear under normal physiological conditions. This conclusion is supported by the assignment of a recently measured laser-Raman spectrum of a metabolically active cell to internal vibrations of the soliton. Analytical studies of continuum approximations to the numerical model provide additional insight into the soliton dynamics.

The two-particle wave function is used to study the diffraction pattern resulting from a double-slit experiment and to describe quantum $\frac{1}{f}$ noise from a beam of charged particles in vacuum. The density-matrix approach is also used to examine the case of $\frac{1}{f}$ noise resulting from a beam of scattered particles and to compare with the results we obtained with the two-particle wave-function method. The autocorrelation function was found analytically for the three cases mentioned above. The form of the autocorrelation function which we have obtained for $\frac{1}{f}$ noise is consistent with previous calculations of quantum $\frac{1}{f}$ noise, and is bilinear in the wave function, as required by the principles of quantum mechanics.