Notes: Transient changes in polarizability during collisions between atoms and molecules give rise to interaction-induced rototranslational Raman scattering: the scalar component of the collision-induced polarizability Δα00 accounts for isotropic scattering, while the second-rank component ΔαM2 accounts for collision-induced depolarized scattering. We have evaluated the changes in electronic polarizability due to interactions between an atom and a molecule of D∞h symmetry in fixed configurations, with nonoverlapping charge distributions. We have cast the resulting expressions into the symmetry-adapted form used in spectroscopic line shape analyses. Our results are complete to order R−6 in the atom–molecule separation R. To this order, the collision-induced change in polarizability of an atom and a D∞h molecule reflects not only dipole-induced–dipole (DID) interactions, but also molecular polarization due to the nonuniformity of the local field, polarization of the atom in the field due to higher multipoles induced in the molecule, hyperpolarization of the atom by the applied field and the quadrupolar field of the molecule, and dispersion. We have analyzed the dispersion contributions to the atom–molecule polarizability within our reaction-field model, which yields accurate integral expressions for the polarizability coefficients. For numerical work, we have also developed approximations in terms of static polarizabilities, γ hyperpolarizabilities, and dispersion energy coefficients. Estimated polarizability coefficients are tabulated for H, He, Ne, and Ar atoms interacting with H2 or N2 molecules. The mean change in polarizability Δα¯, averaged over the orientations of the molecular axis and the vector between atomic and molecular centers, is determined by second-order DID interactions and dispersion. For the lighter pairs, dispersion terms are larger than second-order DID terms in Δα¯. In both Δα00 and ΔαM2, first-order DID interactions dominate at long range; other interaction effects are smaller, but detectable. At long range, the largest deviations from the first-order DID results for Δα00 areproduced by dispersion terms for lighter species considered here and by second-order DID terms for the heavier species; in ΔαM2, the largest deviations from first-order DID results stem from the effects of field nonuniformity and higher multipole induction, for atoms interacting with N2.

Notes: When the charge overlap between interacting molecules or ions A and B is weak or negligible, the first-order interaction energy depends only upon the molecular positions, orientations, and the unperturbed charge distributions of the molecules. In contrast, the first-order force on a nucleus in molecule A as computed from the Hellmann–Feynman theorem depends not only on the unperturbed charge distribution of molecule B, but also on the electronic polarization induced in A by the field from B. At second order, the interaction energy depends on the first-order, linear response of each molecule to its neighbor, while the Hellmann–Feynman force on a nucleus in A depends on second-order and nonlinear responses to B. One purpose of this work is to unify the physical interpretations of interaction energies and Hellmann–Feynman forces at each order, using nonlocal polarizability densities and connections that we have recently established among permanent moments, linear response, and nonlinear response tensors. Our theory also yields new information on the origin of terms in the long-range forces on molecules, through second order in the interaction.One set of terms in the force on molecule A is produced by the field due to the unperturbed charge distribution of B and by the static reaction field from B, acting on the nuclear moments of A. This set originates in the direct interactions between the nuclei in A and the charge distribution of B. A second set of terms results from the permanent field and the reaction field of B acting on the permanent electronic moments of A. This set results from the attraction of nuclei in A to the electronic charge in A itself, polarized by linear response to B. Finally, there are terms in the force on A due to the perturbation of B by the static reaction field from A; these terms stem from the attraction of nuclei in A to the electronic charge in A, hyperpolarized by the field from B. For neutral, dipolar molecules A and B at long range, the forces on individual nuclei vary as R−3 in the intermolecular separation R; but when the forces are summed over all of the nuclei, the vector sum varies as R−4. This result, an analogous conversion at second order (from R−6 forces on individual nuclei to an R−7 force when summed over the nuclei), and the long-range limiting forces on ions are all derived from new sum rules obtained in this work.

Notes: The nonlocal polarizability density α(r;r',ω) is a linear-response tensor that determines the electronic polarization induced at point r in a molecule, by an external electric field of frequency ω, acting at r'. This work focuses on the change in α(r;r',ω) when a nuclear position shifts infinitesimally. We prove directly that the electronic charge distribution responds to the change in Coulomb field due to the nucleus via the same hyperpolarizability density that describes its response to external fields. This generalizes a result found previously for the static (ω=0) polarizability density. The work also provides a new interpretation for the integrated intensities of vibrational Raman bands: it proves that the intensities depend on the hyperpolarizability densities and the dipole propagator.

Notes: Experimental test of the radial force balance equation was done in the Compact Helical System Heliotron/Torsatron [S. Okamura et al. Nucl. Fusion 39, 1337 (1999)]. A radial electric field is measured with a heavy ion beam probe, while plasma rotation and drift velocity of fully ionized carbon are measured with charge exchange spectroscopy. The two measurements agree with each other to within 10% of the radial electric field in a wide range of electron densities of 0.3–2.0×1019 m−3. © 2001 American Institute of Physics.

Notes: From extensive simulation of simple local fluid models of long wavelength drift wave turbulence in tokamaks, it is found that conventional notions concerning directions of cascades, locality and isotropy of spectral transfer, frequencies of fluctuations, and stationarity of saturation do not hold for moderate to long wavelengths (kρs≤1). In particular, at long wavelengths, where spectral transfer of energy is dominated by the E×B nonlinearity, energy is carried to short scale (even in two dimensions) in a manner that is anisotropic and highly nonlocal (energy is efficiently passed between modes separated by the entire spectrum range in a correlation time). At short wavelengths, transfer is dominated by the polarization drift nonlinearity. While the standard dual cascade applies in this subrange, it is found that finite spectrum size can produce cascades that are reverse directed (i.e., energy to high k) and are nonconservative in enstrophy and energy similarity ranges (but conservative overall). In regions where both nonlinearities are important, cross-coupling between the nonlinearities gives rise to large nonlinear frequency shifts which profoundly affect the dynamics of saturation by modifying the growth rate and nonlinear transfer rates. These modifications produce a nonstationary saturated state with large amplitude, long period relaxation oscillations in the energy, spectrum shape, and transport rates. Methods of observing these effects are presented.

Notes: Since the start of the Large Helical Device (LHD) experiment, various attempts have been made to achieve improved plasma performance in LHD [A. Iiyoshi et al., Nucl. Fusion 39, 1245 (1999)]. Recently, an inward-shifted configuration with a magnetic axis position Rax of 3.6 m has been found to exhibit much better plasma performance than the standard configuration with Rax of 3.75 m. A factor of 1.6 enhancement of energy confinement time was achieved over the International Stellarator Scaling 95. This configuration has been predicted to have unfavorable magnetohydrodynamic (MHD) properties, based on linear theory, even though it has significantly better particle-orbit properties, and hence lower neoclassical transport loss. However, no serious confinement degradation due to the MHD activities was observed, resolving favorably the potential conflict between stability and confinement at least up to the realized volume-averaged beta 〈β〉 of 2.4%. An improved radial profile of electron temperature was also achieved in the configuration with magnetic islands, minimized by an external perturbation coil system for the Local Island Divertor (LID). The LID has been proposed for remarkable improvement of plasma confinement like the high (H) mode in tokamaks, and the LID function was suggested in limiter experiments. © 2001 American Institute of Physics.

Notes: A self-consistent model of the low to high ("L'' to "H'') transition is derived from coupled nonlinear envelope equations for the fluctuation level and radial electric field shear, Er', as determined by ion pressure gradient, ∇Pi, and poloidal flow. These equations extend the phase transition model of the L to H bifurcation by including ∇Pi effects. In this model, the transition occurs when the turbulence drive is large enough to overcome the damping of the total E×B flow. Near the critical power for transition, poloidal flow shear dominates Er', but at high power, ∇Pi gives the main contribution. The inclusion of ∇Pi also introduces a quenched fluctuation state that is accessible at high power and may be the experimentally observed H-mode state for P(very-much-greater-than)Pcrit. In this state, the radial electric field is determined only by ∇Pi because no fluctuation energy is available to produce a turbulent Reynolds stress. © 1994 American Institute of Physics.

Notes: The emission of collective waves by a moving charged particle in a nonuniform medium is discussed. Emission occurs in a nonuniform medium when the local dispersion relation of the collective wave is satisfied. This is a form of resonance crossing. Using the Weyl symbol calculus, a local expansion of the collective wave equation driven by the particle source is derived in the neighborhood of the crossing. The collective wave dispersion manifold and the gyroballistic wave dispersion manifold can be used as a pair of local coordinates in the neighborhood of the resonance crossing, which greatly simplifies the analysis. This change of representation is carried out using a metaplectic transform (a generalization of the fourier transform). The Wigner function of the emitted wave field is then computed in the new coordinates. The Wigner function is a phase space scalar, hence the numerical value is invariant under linear canonical transformations. This invariance is invoked to finally arrive at the Wigner function in the original (physical) coordinates. The wave-action and -energy emission rates are then computed from the Wigner function. © 1995 American Institute of Physics.

Notes: Two-dimensional profiles (32×16 spatial channels) of energy spectra of x-ray emission are measured with an energy resolution of 0.16 keV using the photon counting soft x-ray charge coupled device (CCD) camera by optimizing the intensity of x ray with attenuation Be filter in the compact helical system. The energy spectra measured with the CCD camera agrees with that estimated from electron temperature and density measured with YAG Thomson scattering. © 2000 American Institute of Physics.

Notes: Absolute measurements of poloidal rotation velocity with the accuracy up to 1 km/s (2 pm in wavelength) were done using charge exchange spectroscopy in a large helical device. Radial profiles of the absolute Doppler shift of charge exchange emission with a beam are obtained from spectra measured with four sets of optical fiber arrays that view downward and upward at the poloidal cross section with and without neutral beam injection. By arranging the optical fiber from four arrays close to each other at the entrance slit, the apparent Doppler shift due to aberrations of the spectrometer and due to interference of the cold component (the charge exchange between He-like oxygen and thermal neutrals 8 pm from the charge exchange emission with a beam) can be eliminated from the measurements. The measured poloidal rotation velocity is 1–3 km/s in the electron diamagnetic direction at half of the plasma minor radius. © 2000 American Institute of Physics.