Library

Notes: The theory describing the effect of fluctuations in technical parameters (voltages, beam current, external magnetic fields) on the linewidth of gyrotron radiation is presented. Results of the analysis of free-running gyrotron oscillators are given. The effect of technical fluctuations on the spectrum density of the frequency noise is considered and some estimates are compared with available experimental data. © 1997 American Institute of Physics.

Notes: As the multipactor charge builds up, the mutual repulsion overtakes the focusing effect of the rf interaction, and the thin charge ribbon formed during the initial buildup expands into a wide band. Two synergistic effects lead to saturation (a) first, spreading of the impact phases into the region where the vacuum rf retards emission (b) later, and field reversal in the front end of the bunch due to the space-charge field, regardless of the rf phase. The effective secondary yield under opposing field is zero regardless of impact energy. Steady state is achieved when the ensemble-average yield δ drops to unity. The spreads in the impact energy are less important; impacts under reversed field cause saturation even at constant (independent of impact energy) secondary yield. The bunch breakup threshold is identified from bunch stability theory. It is found that near saturation both one-surface and two-surface cascades take place simultaneously; particle orbits alternate between one- and two-surface multipactors until they are finally lost to unfavorable phase/reversed field impacts. The possibility of saturation with a tight bunch, before breakup, is also discussed. © 1997 American Institute of Physics.

Notes: Inverse bremsstrahlung heating of laser-produced plasmas can result in a non-Maxwellian electron distribution function. This leads to a modification of Langmuir wave collisional and Landau damping coefficients and may result in changes in the stimulated Raman scattering threshold and scattered light frequency spectra. The importance of these effects for current laser–plasma interaction experiments is discussed. © 1997 American Institute of Physics.

Notes: A general analytical framework is developed for the nonlinear dispersion relations of a class of large amplitude one-dimensional isolated envelope solitons for modulated light pulse coupled to electron plasma waves, previously investigated numerically [Kozlov et al., Zh. Eksp. Teor. Fiz. 76, 148 (1979); Kaw et al., Phys. Rev. Lett. 68, 3172 (1992)]. The analytical treatment of weakly nonlinear solitons [Kuehl and Zhang, Phys. Rev. E 48, 1316 (1993)] is extended to the strongly nonlinear limit. © 1997 American Institute of Physics.

Notes: It is proved that (a) the solutions of the ideal magnetohydrodynamic equation, which describes the equilibrium states of a cylindrical plasma with purely poloidal flow and arbitrary cross-sectional shape [G. N. Throumoulopoulos and G. Pantis, Plasma Phys. Controlled Fusion 38, 1817 (1996)], are also valid for incompressible equilibrium flows with the axial velocity component being a free surface quantity and that (b) for the case of isothermal incompressible equilibria the magnetic surfaces necessarily have a circular cross-section. © 1997 American Institute of Physics.

Notes: One of the scientific success stories of fusion research over the past decade is the development of the E×B shear stabilization model to explain the formation of transport barriers in magnetic confinement devices. This model was originally developed to explain the transport barrier formed at the plasma edge in tokamaks after the L (low) to H (high) transition. This concept has the universality needed to explain the edge transport barriers seen in limiter and divertor tokamaks, stellarators, and mirror machines. More recently, this model has been applied to explain the further confinement improvement from H (high) mode to VH (very high) mode seen in some tokamaks, where the edge transport barrier becomes wider. Most recently, this paradigm has been applied to the core transport barriers formed in plasmas with negative or low magnetic shear in the plasma core. These examples of confinement improvement are of considerable physical interest; it is not often that a system self-organizes to a higher energy state with reduced turbulence and transport when an additional source of free energy is applied to it. The transport decrease that is associated with E×B velocity shear effects also has significant practical consequences for fusion research. The fundamental physics involved in transport reduction is the effect of E×B shear on the growth, radial extent, and phase correlation of turbulent eddies in the plasma. The same fundamental transport reduction process can be operational in various portions of the plasma because there are a number of ways to change the radial electric field Er. An important theme in this area is the synergistic effect of E×B velocity shear and magnetic shear. Although the E×B velocity shear appears to have an effect on broader classes of microturbulence, magnetic shear can mitigate some potentially harmful effects of E×B velocity shear and facilitate turbulence stabilization. Considerable experimental work has been done to test this picture of E×B velocity shear effects on turbulence; the experimental results are generally consistent with the basic theoretical models. © 1997 American Institute of Physics.

Notes: The stability of a magnetized plasma that includes a sheared transverse flow is analyzed by using both fluid and kinetic formalisms. In addition to the well known Kelvin–Helmholtz modes it is found that another branch of oscillation exists which can dominate the collective effects in a plasma if the magnitude of shear in the transverse flow is sufficiently strong. The source of free energy for the new branch is an inhomogeneity in the energy density caused by the velocity shear. Kelvin–Helmholtz modes, when examined with a fluid theory, are found to be robust and therefore have dominated the analysis of plasma systems with velocity shear in both laboratory and space plasmas. However, when a kinetic formalism is applied to Kelvin–Helmholtz modes it is found that these modes are strongly Landau damped especially when the ion temperature is comparable to or larger than the electron temperature. In addition, since the Kelvin–Helmholtz mode is dependent explicitly on the second derivative of the flow it is sensitive to the profile of the flow. On the other hand, the new branch is dependent on the localized nature of the flow and hence it is less sensitive to the details of the flow profile. The two branches of oscillation are compared using both fluid and kinetic theories and their regimes of dominance discussed.

Notes: The stability of tearing modes in the presence of a rigid toroidal rotation of the plasma is examined. The effect of rotation is modeled by a centrifugal force, which in the cylindrical limit reduces to a uniform force transverse to the plasma column. The influence of this centrifugal force on the outer region matching data Δ, which provides a measure of the energy available for driving the tearing mode, is numerically investigated. It is found that the stability properties of the mode in the presence of the flow are sensitive to the equilibrium density profile. © 1997 American Institute of Physics.

Notes: In a magnetized laboratory plasma described in the companion paper [Stenzel and Urrutia, Phys. Plasmas 4, 26 (1997)], a large positive voltage step (V(very-much-greater-than)kTe/e) is applied to electrodes. The current front propagates in the whistler mode in the parameter regime of electron magnetohydrodynamics. The topology of the current density is that of nested helices. Large transient currents in excess of the electron saturation current can be drawn. A transient radial electric field associated with the current rise, excites a compressional, large amplitude, radially outgoing sound wave, which leaves the current channel depleted of plasma. The current collapses due to the density erosion. Electric field reversal excites a rarefaction wave which leads to a partial density and current recovery. Periodic plasma inflow and outflow cause the current to undergo strong relaxation oscillations at a frequency determined by the electrode diameter and the sound speed. In addition, a broad spectrum of microinstabilities is observed in regions of high current density. For drift velocities approaching the thermal speed, the spectrum extends beyond the ion plasma frequency (ωpi) up to the electron plasma frequency (ωpe). Correlation measurements above ωpi reveal modes propagating along the electron drift at speeds above the sound speed but well below the electron drift speed. © 1997 American Institute of Physics.

Notes: A new map called the symmetric simple map is introduced to represent the chaotic trajectories of magnetic field lines in the scrape-off layer of a single-null divertor tokamak. Good surfaces of this map are very nearly axisymmetric. Therefore it gives a far better representation of the magnetic topology of a single-null divertor tokamak. The map is investigated in detail and used to analyze the generic features of the field line trajectories and their footprint on the divertor plate. The map is employed to calculate the variations in the fraction of magnetic flux from the stochastic layer diverted onto plate, in the footprint and in related parameters as the map parameter is varied. The Lyapunov exponents and the field diffusion coefficients are calculated. The low mode number map and the dipole map are introduced to include the effects of low and high mode number perturbations in the new map. © 1997 American Institute of Physics.

Notes: The energy spectra of energetic confined alpha particles are being measured using the pellet charge exchange method [R. K. Fisher, J. S. Leffler, A. M. Howald, and P. B. Parks, Fusion Technol. 13, 536 (1988)]. The technique uses the dense ablation cloud surrounding an injected impurity pellet to neutralize a fraction of the incident alpha particles, allowing them to escape from the plasma where their energy spectrum can be measured using a neutral particle analyzer. The signal calculations given in the above-mentioned reference disregarded the effects of the alpha particles' helical Larmor orbits, which causes the alphas to make multiple passes through the cloud. Other effects such as electron ionization by plasma and ablation cloud electrons and the effect of the charge state composition of the cloud, were also neglected. This report considers these issues, reformulates the signal level calculation, and uses a Monte-Carlo approach to calculate the neutralization fractions. The possible effects of energy loss and pitch angle scattering of the alphas are also considered. © 1997 American Institute of Physics.

Notes: The nonlinear behavior of the toroidal Alfvén eigenmode (TAE) driven unstable by energetic ions in the Tokamak Fusion Test Reactor (TFTR) [Phys. Plasmas 1, 1560 (1994)] is studied. The evolution of instabilities can take on several scenarios: a single mode or several modes can be driven unstable at the same time, the spectrum can be steady or pulsating, and there can be negligible or anomalous loss associated with the instability. This paper presents a comparison between experimental results and recently developed nonlinear theory. Many features observed in experiment are compatible with the consequences of the nonlinear theory. Examples include the structure of the saturated pulse that emerges from the onset of instability of a single mode, and the decrease, but persistence, of TAE signals when the applied rf power is reduced or shut off. © 1997 American Institute of Physics.

Notes: A new gyrokinetic equation is derived for rotating plasmas with large flow velocities on the order of the ion thermal speed. Neoclassical and anomalous transport of particles, energy, and toroidal momentum are systematically formulated from the ensemble-averaged kinetic equation with the gyrokinetic equation. As a conjugate pair of the thermodynamic force and the transport flux, the shear of the toroidal flow, which is caused by the radial electric field shear, and the toroidal viscosity enter both the neoclassical and anomalous entropy production. The interaction between the fluctuations and the sheared toroidal flow is self-consistently described by the gyrokinetic equation containing the flow shear as the thermodynamic force and by the toroidal momentum balance equation including the anomalous viscosity. Effects of the toroidal flow shear on the toroidal ion temperature gradient driven modes are investigated. Linear and quasilinear analyses of the modes show that the toroidal flow shear decreases the growth rates and reduces the anomalous toroidal viscosity. © 1997 American Institute of Physics.

Notes: In the presence of a high-frequency intense uniform electric field, the collisions of electrons with ions can be made more frequent or less frequent, depending on the polarization of the hf field, the direction and magnitude of particle velocity, and the ratio of the plasma Debye length to the size of the electron oscillation in the hf field. The stimulated bremsstrahlung emission is calculated for both circularly and linearly polarized fields. © 1997 American Institute of Physics.

Notes: Scattering instabilities, such as stimulated Brillouin scatter (SBS) and stimulated Raman scatter (SRS), transfer momentum to the plasma which leads to flow inhomogeneities in laser hot spots that may significantly reduce the level of SBS. Simple estimates and simulations shown that the magnitude of flow fluctuations can reach Mach numbers of order unity in a time scale of hundreds of picoseconds. © 1997 American Institute of Physics.

Notes: The nonlinear destabilization of pressure driven (ballooning) modes by internal kink modes during sawtooth cycles was found in the Tokamak Fusion Test Reactor (TFTR) [Park et al., Phys. Rev. Lett. 75, 1763 (1995)]. It is shown by a numerical parameter study, including aspect ratio and magnetic shear profile effects, that in ideal magneto-hydrodynamics (MHD), this nonlinear destabilization occurs in plasma equilibria close to marginal stability to linear sub-harmonics of the internal kink with toroidal mode number n≥3. © 1997 American Institute of Physics.

Notes: A theory of plasma response to electromagnetic perturbations has been developed based on the full solution to the Fokker–Planck equation in high Z plasmas without electron–electron collisions. For the first time the transverse electron susceptibility has been calculated for the entire range of frequencies and wave numbers including the quantitative description of the weakly collisional regime where the wave frequency is comparable to the electron–ion collision frequency and the wave number is comparable to the inverse electron mean free path. The results have been compared to approximate expressions for the electron conductivity based on the Drude model showing discrepancy by a factor of few in regions where the spatial dispersion is important. The theory is applied to the calculation of laser light absorption in solid density plasmas. © 1997 American Institute of Physics.

Notes: The kinetic theory of transport in an impure, partially ionized, edge plasma is developed. It is found that the thermal force between bulk ions and impurities is enhanced by the presence of neutral atoms, but the dynamical friction is not affected by the neutrals. When the neutral viscosity is large, an additional force on the impurities also arises. This force is parallel to the magnetic field, and is proportional to the shear of the parallel plasma velocity and the perpendicular ion density and temperature gradients. © 1997 American Institute of Physics.

Notes: For an arbitrary monotonic charging function, the dynamics of a dust grain is dissipative and energy is a Liapunov function. In an arbitrary external potential two types of equilibria exist. The first type, with uncharged grain, is always unstable. The second type of equilibrium, admitting states of both positive and negative charge, can be marginally stable; stability depends on the local potential. Under spatially uniform (constant or time-dependent) potentials, motion is free while the charge adapts to the potential. For a spatially oscillating potential, the phase space is that of the simple pendulum with one additional degree of freedom, the charge. Dissipation in the charging process forbids periodic behavior and ensures the existence of attractors: A grain is at stable equilibrium only when charged positively and trapped in a potential well, or when charged negatively on top of a hill. The small oscillations near a stable equilibrium decay weakly, and the grain charge oscillates at twice the oscillation frequency. © 1997 American Institute of Physics.

Notes: The effect of ion and electron drifts on the existence of arbitrary amplitude solitary waves is studied using Sagdeev's pseudopotential method. It is found that if the electron drift velocity u0 is finite, solitary waves may exist for relatively large values of v0/c, where v0 is the ion drift velocity and c is the velocity of light. © 1997 American Institute of Physics.

Notes: The expansion into vacuum of a one-dimensional, collisionless, negative ion plasma is investigated in the framework of the Vlasov–Poisson model. The basic equations are written in a "new time space" by use of a rescaling transformation and, subsequently, solved numerically through a fully Eulerian code. As in the case of a two species plasma, the time-asymptotic regime is found to be self-similar with the temperature decreasing as t−2. The numerical results exhibit clearly the physically expected effects produced by the variation of parameters such as initial temperatures, mass ratios and charge of the negative ions. © 1997 American Institute of Physics.

Notes: The spatiotemporal evolution of near-forward stimulated Brillouin scattering (SBS) is studied in detail. For large scattering angles SBS grows and saturates as a three-wave instability. For small scattering angles SBS begins to grow as a three-wave instability, then continues to grow and saturates as a four-wave instability. Expressions for the saturation time and steady-state gain exponent of SBS are derived for large and small scattering angles. © 1997 American Institute of Physics.

Notes: The problem of nonlinear Burger equation in a plasma contaminated with heavy dust grains has been revisited. As discussed earlier [C. B. Dwivedi and B. P. Pandey, Phys. Plasmas 2, 9 (1995)], the Burger equation originates due to dust charge fluctuation dynamics. A new alternate mathematical approach based on a simple traveling wave formalism has been applied to find out the solution of the derived Burger equation, and the method recovers the known shock-wave solution. This technique, although having its own limitation, predicts successfully the salient features of the weak shock-wave structure in a dusty plasma with dust charge fluctuation dynamics. It is emphasized that this approach of the traveling wave formalism is being applied for the first time to solve the nonlinear wave equation in plasmas. © 1997 American Institute of Physics.

Notes: Eikonal approximation is applied to investigate elastic electron-ion collisions in weakly coupled plasmas. Plasma screening effects on eikonal phase are investigated for eikonal differential elastic scattering cross sections. The electron-ion interaction potential in weakly coupled plasmas has been obtained by the introduction of the longitudinal plasma dielectric function. The semiclassical straight-line trajectory method is applied to the path of the projectile electron in order to investigate the variation of the eikonal phase as a function of the impact parameter and the plasma parameters. In the first-order eikonal approximation, the dynamic plasma screening effect is identical to the static screening effect obtained by the Debye–Hückel potential. The eikonal differential elastic cross section substantially decreases with an increase in the projectile energy and increases as the plasma screening effect decreases through the Debye length. The plasma screening effects are more significant for large impact parameters. © 1997 American Institute of Physics.

Notes: The flow resonance is concealed when the linearized equation of motion in magnetohydrodynamics is written in terms of the Lagrangian displacement vector. Its contribution to the dispersion equation of a rotating cylindrical plasma column, surrounded by a thin resistive wall, is clarified by a simple model calculation, relevant for axisymmetric modes, in the Eulerian representation. Under certain assumptions the flow resonance is shown to damp the resistive wall mode, with the damping proportional to the square of the gradient of vorticity at the resonant surface. It is shown that a flow resonance can stabilize a slightly elliptical plasma, surrounded by a thin resistive wall, against axisymmetric modes. © 1997 American Institute of Physics.

Notes: The Alfvén continuum of an asymmetric plasma configuration that is an exact solution of the equilibrium equations of ideal magnetohydrodynamics is treated. The equilibrium is parallel to an infinite straight magnetic axis about which the magnetic lines of force form closed magnetic surfaces. Properties of the governing continuum equation for small plasma beta are explored, and the associated spectrum is determined. The continuum has a localized component characterized by modes that decay to zero along magnetic field lines, and a non-localized component characterized by modes that approach non-zero constants at the plasma ends. The localized component is restricted to real frequencies, while the non-localized component covers the entire complex frequency plane. The non-localized modes can be joined generally with those on neighboring field lines to form modes that smoothly cover the entire magnetic surface. The localized modes do not occur in symmetric plasmas. © 1997 American Institute of Physics.

Notes: A variational formalism is introduced in the theory of three-wave parametric instabilities in inhomogeneous plasmas. This minimum pump strength principle (MPSP) is then applied to two model problems, the first being the Rosenbluth model equations [Phys. Rev. Lett. 29, 565 (1972)]. By choosing appropriate trial functions, the MPSP is used to solve for the complex eigenfrequency of the most unstable mode. The wave vector mismatch is assumed to be of the form κ(x)=κ(n)(0)xn/n!, where n is any positive integer. The results are compared to numerical solutions of the same eigenvalue problem. The second problem is the Liu, Rosenbluth, and White Raman sidescattering model [Phys. Fluids 17, 1211 (1974)], which is treated for any positive-integer power law density profile. The choice of trial functions, the role of symmetry, and various useful approximations are discussed.

Notes: The theory of the two-plasmon decay instability is recast in the form of a variational principle for the pump strength or intensity of the incident laser. This allows the calculation of growth rates, frequency shifts, and threshold conditions for two-plasmon decay modes that occur in integer power law density profiles, including the effects of oblique incidence of the laser and both S and P polarizations. The transition between parabolic profiles occurring at the peak of an exploding foil target and linear profiles on its flanks is treated as well.

Notes: The theory of temporally unstable modes or bound states associated with stimulated Raman scattering in inhomogeneous plasmas is recast in the form of a variational principle for the pump strength or intensity of the incident laser. This Minimum Pump Strength–Variational Principle (MPS–VP) formalism allows the unification of disparate results on growth rates, frequency shifts, and threshold conditions, which in the past relied on specific and restrictive assumptions on the density profile, scattering geometry, temperature, and damping rates. The variational approach leads to generalizations of these results in a uniform manner. Various levels of sophistication in the choice of trial and dual functions are explored. Simplifications and short cuts that will be used throughout this series of papers are tested here, and their regions of validity explored. The principle new result of some practical interest is the growth rate of Raman sidescattering occurring anywhere at the peak or on the flanks of a parabolic density profile such as can be found in an exploding foil experiment. This new calculation includes any density at or below quarter-critical, at any temperature, and at low or high damping rate limits.

Notes: The theories of the two plasmon decay (TPD) instability and stimulated Raman scattering (SRS) are unified and presented using a variational formulation. The mixed polarization high-frequency instability is the resulting generalization which has SRS and TPD as special cases. The most unstable mode's properties are derived and shown as a function of perpendicular wave number. For vanishing wave number we recover the Raman backscattering result and for wave numbers a few times larger than the square root of the homogeneous plasma growth rate normalized to the pump frequency, the two plasmon decay instability modes are recovered. This transition is accompanied by a change of polarization from a purely electromagnetic transversely polarized wave in the case of Raman to a strictly electrostatic or longitudinally polarized wave in the case of TPD, and admixtures in between. Experimental signatures of these modes are given and a method is proposed by which the density scale length and electron temperature would be simultaneously inferred from the width and height of the spectral signature corresponding to these hybrid modes in an ideal experiment.

Notes: In a recent series of publications, a new theory of electromagnetic radiation with emission frequency close to the plasma frequency and/or its harmonic (i.e., the plasma emission) was presented. In this theory, the emission of radiation takes place as a result of excitation of long wavelength modes by a nonlinear beam-plasma instability, which are converted to radiative electromagnetic waves by a nonlinear mode conversion process. Unlike standard theories, the new theory predicts high radiation growth rate. In all the previous efforts on this theory, however, effects due to the presence of constant background magnetic field were ignored. The purpose of this article is to generalize the new theory to the case of weakly magnetized plasmas. © 1997 American Institute of Physics.

Notes: The correlations in dusty plasmas in the gaseous state is considered. It is shown that the long-ranged correlations of dust particles, contrary to usual matter, start to form in a weakly correlated state, leading finally to the formation of dust crystals and dust liquids with not strong but intermediate strength correlations. The physical mechanism leading to long-ranged correlations is the dust attraction due to shadow effects of the plasma particle fluxes. An analytic theory for the long-ranged dust density correlation function is developed and the numerical results for a broad range of dust densities and plasma temperatures are presented. The long-ranged correlations induced by dust for electron densities, ion densities, and dust charges are also investigated, and the results for electron density correlations are presented in a way that permits measurement of the long-ranged correlation function in laser and radio-wave scattering experiments. © 1997 American Institute of Physics.

Notes: The test-field model is shown to be potentially nonrealizable in the presence of linear waves such as those frequently encountered in models of plasma and geophysical turbulence. A new statistical closure, the realizable test-field model (RTFM), is proposed as a remedy. Both the damping rate and frequency are renormalized to account for nonlinear damping and frequency shifts. Like the realizable Markovian closure (RMC), the RTFM is based on a modified fluctuation-dissipation ansatz. Numerical solutions of the RTFM, RMC, and direct-interaction approximation for the Hasegawa–Mima equation are presented; rough agreement with direct numerical solution is found. The number of retained Fourier modes is dramatically reduced with an anisotropic generalization of a recently developed wave-number partitioning scheme. © 1997 American Institute of Physics.

Notes: The relativistic nonlinear self-consistent equations for a strongly rarefied plasma with stationary ions is considered. The resulting system of equations is reduced to a single sinh-Gordon equation. Using the Bäcklund transformations technique and Painlevé analysis, a set of exact soliton solutions is obtained for stationary and nonstationary equations that describes the charge density equilibrium configuration. © 1997 American Institute of Physics.

Notes: The corrugation instability of magnetic shock waves in a relativistically hot plasma with photon gas has been investigated. Conditions under which spontaneous amplification of surface corrugations on the discontinuity occurs are obtained. The corrugation instability may cause the condensation of the plasma number density, as well as the magnetic field behind the shock wave. © 1997 American Institute of Physics.

Notes: When the ratio μ1i/μ1e is of the order of unity, electron transport fluxes such as bootstrap current can be affected by the ion orbit squeezing. Here, μ1e is the electron viscous coefficient, and μ1i is the ion viscous coefficient with the effects of ion orbit squeezing included. The condition μ1i/μ1e∼1 can be satisfied for plasmas, such as those in enhanced reversed shear (ERS) mode, with ion temperature greater than electron temperature and orbit squeezing factor S(very-much-greater-than)1. Transport fluxes for both standard squeezed banana orbits and for squeezed orbits close to the magnetic axis are calculated for a large aspect ratio tokamak. It is found that ion heat flux and bootstrap current are reduced in ERS-like plasmas. Furthermore, the bootstrap current density does not vanish on the magnetic axis for a parabolic pressure profile in minor radius r due to the finite value of the fraction of trapped particles. This makes it possible to operate tokamaks in steady state. © 1997 American Institute of Physics.

Notes: The oscillation of ion bunches around a strongly negative grid in a double plasma device is studied with one–dimensional particle–in–cell simulation. The system exhibits feedback amplified virtual anode oscillations in the target chamber. The undriven system is shown to perform relaxation processes which can be described by the van der Pol equation for high nonlinearity. The periodically driven system exhibits nonlinear phenomena like mode locking and periodic pulling, which are in quantitative agreement with theoretical predictions for the driven van der Pol oscillator. For large driver amplitudes period doubling and weak chaos are found. © 1997 American Institute of Physics.

Notes: The problem of translation symmetric stationary magnetohydrodynamic (MHD) flow is analyzed with respect to the different permitted flow regimes. A minimal set of equilibrium functions is constructed facilitating the complete explicit solution in the case of self-similar flow. It is found that limiting line and Alfvén singularities leads to a division in four distinct velocity regimes which cannot be connected by continuous flows. Instead, the three types of MHD shocks appear, enabling the system to pass from the high to the low speed regimes. © 1997 American Institute of Physics.

Notes: The sudden release of magnetic free energy, as occurs in spectacular solar flare events, tokamak disruptions, and enigmatic magnetospheric substorms, has long defied any acceptable theoretical explanation. Usual attempts at explaining these explosive events invoke magnetic reconnection and/or ideal magnetohydrodynamic (MHD) instability. However, neither of these two mechanisms can explain the fast time scales without nonlinear destabilization. Recently, Cowley et al. [Phys. Plasmas 3, 1848 (1996)] have demonstrated a new mechanism for nonlinear explosive MHD destabilization of a line tied Rayleigh–Taylor model. In this paper, this picture is generalized to arbitrary magnetic field geometries. As an intermediate step, the ballooning equation in a general equilibrium is derived including the effects of magnetic field curvature, shear, and gravity. This equation determines the linear stability of the plasma configuration and the behavior of the plasma displacement along the magnetic field line. The nonlinear equation which determines the time and spatial dependence, transverse to the equilibrium magnetic field, of the plasma displacement is obtained in fifth order of the expansion. The equations show that explosive behavior is a natural and generic property of ballooning instabilities close to the linear stability boundary. © 1997 American Institute of Physics.

Notes: A general method for including various collisional effects, such as the drag and diffusion of test particles due to background plasmas, the effect of particle source and sink, and the like-particle Coloumb collisions, is presented. The marker density g is generally unknown along the particle trajectory, and its evaluation depends on the way particles are initially loaded and new particles are injected into the simulation. The method is demonstrated for the problem of the nonlinear evolution of the toroidicity induced Alfvén eigenmode, driven by energetic α particles. The saturation amplitude is found to scale with the collision rate in a way as predicted by theory.© 1997 American Institute of Physics.

Notes: A miniature magnetic probe array, consisting of 10 spatially separated coils, has been used to obtain profile information on the time varying magnetic field within the 2.54 cm wide flow channel of the coaxial plasma source experiment (CPS-1) [R. M. Mayo et al., Plasma Sources Sci. Technol. 4, 47 (1995)]. The magnetic field data have been used, together with a resistive, Hall magnetohydrodynamic (MHD) model of applied field distortion by the flowing plasma, to obtain estimates of the microturbulent enhancement to electron collisionality within the CPS-1 flow channel. These measurements provide direct experimental evidence of anomalous electron collisionality, a previously predicted effect in these devices. The anomaly parameter, a=νan/νcl, determined both from the distortion of contours of constant magnetic flux, and from local Bθ and Bz measurements scales with the classical electron magnetization parameter (Ωcl=ωce/νecl), indicating that collisionality plays a strong role in determining the level of anomalous transport in the plasma. When this anomaly parameter scaling is cast in terms of the ratio νecl/ωlh, it is found that the resistivity enhancement scales with νecl/ωlh, and becomes significant at νecl/ωlh≤1, suggesting that a lower hybrid drift instability may be the responsible mechanism for enhanced transport. © 1997 American Institute of Physics.

Notes: The electron temperature response of a tokamak to rapid edge cooling has characteristics difficult to reconcile with local transport analysis. The initial observations in the Texas Experimental Tokamak [K. W. Gentle, Nucl. Tech. Fusion 1, 479 (1981)] have been extended to a wider range of plasma and perturbation parameters, including auxiliary heating, and the associated turbulence changes have been measured across the plasma radius. The fast edge temperature drops and core temperature increases are quantified by more extensive analysis. A perturbation complementary to edge cooling, edge heating by a fast current ramp, evokes a completely complementary plasma response. © 1997 American Institute of Physics.

Notes: Local, time-resolved measurements have been made of the response of the internal magnetic-field distribution to large changes in the total plasma current. Measurements were made by the motional Stark effect (MSE) polarimeter on the Tokamak Fusion Test Reactor (TFTR). [R. J. Hawryluk et al., Proceedings of the 11th International Conference on Plasma Physics and Controlled Nuclear Fusion (International Atomic Energy Agency, Vienna, 1987) Vol. I, p. 51.] A direct test of the classical and neoclassical resistivity models was made by comparing the predicted field evolution using either model to that measured. It was found that the neoclassical resistivity model was a better predictor of the local magnetic-field temporal evolution than was the classical model. © 1997 American Institute of Physics.

Notes: Low and improved confinement modes in the H-1 heliac [M. G. Shats et al., Phys. Rev. Lett. 77, 4190 (1996)] are studied experimentally in rf-sustained (〈100 kW, 7 MHz) argon discharges at low magnetic fields (〈0.15 T). Surprisingly high ion temperature, measured using a retarding field energy analyzer, is found which increases across the transition to improved confinement mode from 40 to 80 eV, while the electron density increases by about 50%. Both toroidal and poloidal plasma flow velocities do not change across the transition. The increase in a radial electric field in high mode is balanced on average by a corresponding increase in the ion pressure gradient. © 1997 American Institute of Physics.

Notes: Electrostatic and electromagnetic fluctuations generally cause cross-field particle transport in confined plasmas. Thus core localized turbulence must be kept at low levels for sufficient energy confinement in magnetic fusion plasmas. Reversed-field pinch (RFP) equilibria can, theoretically, be completely stable to ideal and resistive (tearing) magnetohydrodynamic (MHD) modes at zero beta. Unstable resistive interchange modes are, however, always present at experimentally relevant values of the poloidal beta βθ. An analytical quasilinear, ambipolar diffusion model is here used to model associated particle transport. The results indicate that core density fluctuations should not exceed a level of about 1% for plasmas of fusion interest. Parameters of experimentally relevant stationary states of the RFP were adjusted to minimize growth rates, using a fully resistive linearized MHD stability code. Density gradient effects are included through employing a parabolic density profile. The scaling of particle diffusion [D(r)∝λ2n0.5T/aB, where λ is the mode width] is such that the effects of particle transport are milder in present day RFP experiments than in future reactor-relevant plasmas. © 1997 American Institute of Physics.

Notes: Reversed magnetic shear is associated with large negative surface averaged parallel current densities that increase in magnitude towards the plasma edge and guarantee stability at large β in tokamaks. The surface averaged parallel current density is smaller and decreases in magnitude radially in conventional shear tokamaks. This results in much lower magnetohydrodynamic (MHD) stable β. The parallel current density in torsatrons is dominated by the Pfirsch–Schlüter currents, the global shear contributes negligibly to the local shear and the β limits are comparable to that of a conventional tokamak. A simplistic evaluation of the local sign of the driving terms in the energy principle does not provide a useful guide to even qualitatively describe the MHD stability of a device. Ballooning instabilities concentrate in regions where the curvature is most destabilizing. Their localization does not appear to depend on the sign of the interaction between the parallel current density and the local magnetic shear contribution to the driving term. © 1997 American Institute of Physics.

Notes: A three-dimensional (3-D) global gyrokinetic particle code in toroidal geometry has been used for investigating the transport properties of ion temperature gradient (ITG) drift instabilities in tokamak plasmas. Using the isotopes of hydrogen (H+), deuterium (D+) and tritium (T+), it is found that, under otherwise identical conditions, there exists a trend for favorable isotope scaling for the ion thermal diffusivity, i.e., χi decreases with mass. Such a trend, which exists both at the saturation of the instability and also at the fully nonlinear stage, can be understood from the resulting wave number and frequency spectra. © 1997 American Institute of Physics.

Notes: Ion drift surfaces in the presence of applied rotating magnetic perturbations in the Compact Auburn Torsatron (CAT) [Fusion Technol. 18, 281 (1990)] have been studied. A compact, monoenergetic ion gun was used to launch a continuous beam of 6Li+ ions in the vacuum magnetic fields of the CAT. The ions are detected on a paddle probe that is swept though a poloidal cross section of the torsatron. The applied magnetic perturbation was produced using helical magnetic perturbation coils capable of generating rotating magnetic islands. Using a fixed energy ion beam the effects of constant frequency perturbations on ion drift orbits were studied as a function of the direction of rotation, amplitude, and frequency of the perturbation. A drift Hamiltonian model was developed to simulate ion trajectories in the presence of constant frequency rotating islands. The results of this experiment agree well with the predictions of the Hamiltonian model. Preliminary results of ion orbit modification by swept-frequency, rotating magnetic perturbations are also presented. © 1997 American Institute of Physics.

Notes: An interface current balance (ICB) method for neutral particle transport is presented and specialized to the calculation of neutral atom transport in background plasmas. A multigroup extension of the ICB methodology is presented which enables the direct calculation of neutral atom energy distributions and energy and momentum transport, as well as particle transport. Extension of the ICB methodology to multidimensions recovers the transmission/escape probability method. © 1997 American Institute of Physics.

Notes: The design of high power, continuous wave (cw), 170 GHz gyrotron cavities is considered. The anticipated degradation of efficiency with beam velocity spread places a premium on the optimization of efficiency. For parameters of interest achievement of high efficiency requires utilization of a high quality cavity. Two options are considered: a barrel cavity and a long simple tapered cavity operating at low voltage. The cavities are examined for their sensitivity to velocity spread, their mode competition, and their maximum Ohmic power dissipation. © 1997 American Institute of Physics.

Notes: Structure of the periodic accelerator orbits of the Harper map is investigated in detail from the viewpoint of underlying scenario of chaos in the area preserving nontwist map. Since the twist function of the Harper map is free from the polynomial local approximation, it admits rigorous treatment for the entire range of phase variable. The results obtained in the present analysis describes generic novel phenomena, which are outside of the applicability of the Kolmogorov-Arnol'd-Moser theory. © 1997 American Institute of Physics.

Notes: A systematic way for deriving the parameter renormalization group equation for one-dimensional maps is presented and the critical behavior of periodic doubling is investigated. Introducing a formal potential function in one-parameter cases, it is shown that accumulation points correspond to local potential maxima and universal constants are easily determined. The estimates of accumulation points and universal constants match the known values asymptotically when the order of potential grows large. The potential function shows scaling in the parameter space with the universal convergent rate at the accumulation point similar to the Feigenbaum universal function. For two-parameter cases, a parameter reduction transformation is found to be useful to determine some important fixed points. A locally defined potential function is introduced and its scaling property is discussed. © 1997 American Institute of Physics.

Notes: The dynamics of a thermal pulse combustor model are examined. It is found that, as a parameter related to the fuel flow rate is varied, the combustor will undergo a transition from periodic pulsing to chaotic pulsing to a chaotic transient leading to flameout. Results from the numerical model are compared to those obtained from a laboratory-scale thermal pulse combustor. Finally the technique of maintenance (or anticontrol) of chaos is successfully applied to the model, with the result that the operation of the combustor can be continued well into the flameout regime. © 1997 American Institute of Physics.

Notes: We review a simple recursive proportional feedback (RPF) control strategy for stabilizing unstable periodic orbits found in chaotic attractors. The method is generally applicable to high-dimensional systems and stabilizes periodic orbits even if they are completely unstable, i.e., have no stable manifolds. The goal of the control scheme is the fixed point itself rather than a stable manifold and the controlled system reaches the fixed point in d+1 steps, where d is the dimension of the state space of the Poincaré map. We provide a geometrical interpretation of the control method based on an extended phase space. Controllability conditions or special symmetries that limit the possibility of using a single control parameter to control multiply unstable periodic orbits are discussed. An automated adaptive learning algorithm is described for the application of the control method to an experimental system with no previous knowledge about its dynamics. The automated control system is used to stabilize a period-one orbit in an experimental system involving electrodissolution of copper. © 1997 American Institute of Physics.

Notes: A thermodynamic study of nonlinear dynamical systems, based on the orbits' return times to the elements of a generating partition, is proposed. Its grand canonical nature makes it suitable for application to both maps and flows, including autonomous ones. When specialized to the evaluation of the generalized entropies Kq, this technique reproduces a well-known formula for the metric entropy K1 and clarifies the relationship between a flow and the associated Poincaré maps, beyond the straightforward case of periodically forced nonautonomous systems. Numerical estimates of the topological and metric entropy are presented for the Lorenz and Rössler systems. The analysis has been carried out exclusively by embedding scalar time series, ignoring any further knowledge about the systems, in order to illustrate its usefulness for experimental signals as well. Approximations to the generating partitions have been constructed by locating the unstable periodic orbits of the systems up to order 9. The results agree with independent estimates obtained from suitable averages of the local expansion rates along the unstable manifolds. © 1997 American Institute of Physics.

Notes: The dynamical properties of the ring wave solutions of the model ψtt−∇n2ψ+sin ψ+ε sin (ψ/2)+αψt=0 (0≤ε(very-much-less-than)1,0≤α(very-much-less-than)1) are studied analytically and numerically for spatial dimension (n=2,3). The model is obtained as a continuum approximation of a multidimensional Frenkel–Kontorowa lattice. We will show that in the case ε〉0, α=0 (or α〉0) the return effect of the ring wave does not occur only for well defined values of ε. It will be shown numerically that the dissipative perturbation αψt (α〉0) stabilizes both the velocity and the wave profile of the ring wave when the return effect does not occur. © 1997 American Institute of Physics.

Notes: In this paper the vibration and the traveling wave in a coupled magneto-elastic beam system are discussed experimentally. The vibration excited by the periodical forcing at the beam system propagates to another as a wave through the coupling elastic beams. Each magneto-elastic beam shows the variety of vibrations caused by the nonlinearity of the potential well and the wave propagation with time delay. The temporal vibration of the magneto-elastic beam is explained with relations to the spatial state transition based on the experimental results. © 1997 American Institute of Physics.

Notes: We review the convergence of chaotic integrals computed by Monte Carlo simulation, the trace method, dynamical zeta function, and Fredholm determinant on a simple one-dimensional example: the parabola repeller. There is a dramatic difference in convergence between these approaches. The convergence of the Monte Carlo method follows an inverse power law, whereas the trace method and dynamical zeta function converge exponentially, and the Fredholm determinant converges faster than any exponential. © 1997 American Institute of Physics.

Notes: Since the seminal remark by Pecora and Carroll [Phys. Rev. Lett. 64, 821 (1990)] that one can synchronize chaotic systems, the main example in the related literature has been the Lorenz equations. Yet this literature contains a mixture of true and false, and of justified and unsubstantiated claims about the synchronization properties of the Lorenz equations. In this note we clarify some of the confusion. © 1997 American Institute of Physics.

Notes: The time delay embedding for the reconstruction of a state space from scalar data introduces strong folding of the smooth manifold in which a chaotic attractor is embedded, which is absent in some more natural state space. In order to observe the deterministic nature of data, the typical length scale related to this folding has to be resolved. Above this length scale the data appear to be random. For a particular model class we prove these statements and we derive analytically the dependence of this length scale on the complexity of the system. We show that the number of scalar observations required to observe determinism increases exponentially in the product of the system's entropy and dimension. © 1997 American Institute of Physics.

Notes: An analysis of stationary and nonstationary cellular patterns observed in premixed flames on a circular, porous plug burner is presented. A phenomenological model is introduced, that exhibits patterns similar to the experimental states. The primary modes of the model are combinations of Fourier–Bessel functions, whose radial parts have neighboring zeros. This observation explains several features of patterns, such as the existence of concentric rings of cells and the weak coupling between rings. Properties of rotating rings of cells, including the existence of modulated rotations and heteroclinic cycles can be deduced using mode coupling. For nonstationary patterns, the modal decomposition of experimental data can be carried out using the Karhunen–Loéve (KL) analysis. Experimental states are used to demonstrate the possibility of using KL analysis to differentiate between uniform and nonuniform rotations. The methodology can be extended to study more complicated nonstationary patterns. In particular, it is shown how the complexity of "hopping states" can be unraveled through the analysis. © 1997 American Institute of Physics.

Notes: In branching theory of solutions of nonlinear equations group analysis methods [Ovsyannikov, Group Analysis of Differential Equations (Nauka, Moscow, 1978); Lectures on the Theory of Group Properties of Differential Equations (Novosibirsk University, Novosibirsk, 1966)] give the general approach for the construction of the complete form of branching equation and its subsequent investigation. These methods are applied here to the general situation of Andronov-Hopf bifurcation when there are some multiple semisimple eigenvalues on imaginary axis. © 1997 American Institute of Physics.

Notes: For a volume-preserving map, we show that the exit time averaged over the entry set of a region is given by the ratio of the measure of the accessible subset of the region to that of the entry set. This result is primarily of interest to show two things: First, it gives a simple bound on the algebraic decay exponent of the survival probability. Second, it gives a tool for computing the measure of the accessible set. We use this to compute the measure of the bounded orbits for the Hénon quadratic map. © 1997 American Institute of Physics.

Notes: We introduce the mathematical concept of multifractality and describe various multifractal spectra for dynamical systems, including spectra for dimensions and spectra for entropies. We support the study by providing some physical motivation and describing several nontrivial examples. Among them are subshifts of finite type and one-dimensional Markov maps. An essential part of the article is devoted to the concept of multifractal rigidity. In particular, we use the multifractal spectra to obtain a "physical'' classification of dynamical systems. For a class of Markov maps, we show that, if the multifractal spectra for dimensions of two maps coincide, then the maps are differentiably equivalent. © 1997 American Institute of Physics.

Notes: Interaction of charged particles with various types of one-dimensional pulses is investigated systematically. Gaussian pulses of arbitrary velocity and polarization, both electrostatic and electromagnetic, are considered. The pulses range from ordinary wave packets to impulses. Analytic expressions are obtained for velocities of charged particles interacting with those traveling pulses, and are compared with numerical counterparts. Dependence of the interaction on pulse size, initial particle velocity, and external magnetic field is investigated. For many nonrelativistic pulses traveling along an external magnetic field, the interaction can be divided into two types, i.e., transit-time acceleration and reflection in the wave frame. In the absence of the magnetic field, transit-time acceleration is significant only for impulses with sizes of less than one wavelength. On the other hand, with a magnetic field (transit-time) cyclotron acceleration becomes possible for pulses of sizes greater than one wavelength. With larger amplitudes the wave-frame reflection becomes increasingly important, typically occurring at the pulse head or tail. However, it tends to be suppressed by external magnetic fields. Compact expressions are obtained for final velocities of the particles for the two types of interaction. Both types of acceleration mechanism may be important in dissipating relatively large-amplitude waves. © 1997 American Institute of Physics.

Notes: The problem of multiple time scales in modeling plasmas by dynamical particle simulation methods, such as the particle-in-cell (PIC) method, is well known. One important cause is the large ratio of the ion and electron mass. Ways to overcome this problem are the implicit PIC, or simply, the use of a reduced ion–electron mass ratio. However, these methods are not acceptable in modeling dc glow discharges by the PIC-Monte Carlo hybrid simulation technique. Therefore, a new method called asynchronous cycling was developed, which manipulates the synchronization of the electron and ion simulation cycles. It allows a 50 times faster convergence due to direct reduction of the different time scales for situations in which the changes of macroscopic quantities are slower than the ion movement. This is demonstrated by the modeling of a complete one-dimensional dc glow discharge including cathode fall, plasma bulk, and anode fall. © 1997 American Institute of Physics.

Notes: The relativistic Fokker-Planck collision term in Braams and Karney [Phys. Fluids B 1, 1355 (1989)] is expanded using Cartesian tensors (equivalent to associated Legendre spherical harmonics) retaining all non-linear terms and an arbitrary zeroth order distribution background. Expressions are given for collision terms between all harmonics and the background distribution in terms of the j and y functions in Braams and Karney. The results reduce to Braams and Karney for the first order harmonic term with a Maxwellian background and to those given by Shkarofsky [Can. J. Phys. 41, 1753 (1963)] in the non-relativistic limit. Expressions for the energy and momentum transfer associated with relativistic Coulomb collisions are given. The fast two dimensional Fokker-Planck solver in Shoucri and Shkarofsky [Comput. Phys. Commun. 82, 287 (1994)] has been extended to include the second order harmonic term. © 1997 American Institute of Physics.

Notes: Thomson scattering was used to measure the Langmuir wave spectrum driven by stimulated Raman scattering. The Thomson scattering signals measured in the experiment showed Langmuir waves with components both parallel and antiparallel to the incident laser's wave vector, k0. The parallel component was attributed to stimulated Raman scattering. However, the Langmuir waves with components antiparallel to k0, which cannot be explained by stimulated Raman scattering, were attributed to the Langmuir decay instability (LDI). The relative amplitude of the two Langmuir wave features and their angular width supported the conclusion that the Langmuir waves traveling antiparallel to the incident laser's wave vector were driven by the Langmuir decay instability. © 1997 American Institute of Physics.

Notes: An intense short pulse laser of finite spot size propagating through a gas produces plasma via tunnel ionization on a femtosecond time scale. The radial profile of plasma density is strongly peaked on the axis and has a defocusing property. As electron density grows with time, the trailing part of the laser pulse suffers stronger divergence than the leading front, causing severe temporal distortion of the pulse. A self-consistent paraxial ray theory of electron density evolution and defocusing of the laser reveals that a square (in time) laser pulse, after propagating one Rayleigh length, has an order of magnitude difference in the axial intensity at the front and the tail of the pulse. © 1997 American Institute of Physics.

Notes: The transport of radiation in anisotropic, weakly inhomogeneous and spatially dispersive media with internal sources is considered on the basis of the relevant geometric optics far-field as a function of position and frequency. The second rank radiation intensity tensor is obtained directly from the autocorrelation of the electric far-field in terms of a second rank emissivity tensor and accounts for coherent as well as incoherent emission, along with the effects of generalized Faraday rotation. The case of Cerenkov radiation is considered in detail. © 1997 American Institute of Physics.

Notes: Present status and understanding of the principal plasma-performance determining physics issues that affect the physics design and operational capabilities of the International Thermonuclear Experimental Reactor (ITER) [ITER EDA Agreement and Protocol 2 (International Atomic Energy Agency, Vienna, 1994)] are presented. Emphasis is placed on the five major physics-basis issues—energy confinement, beta limit, density limit, impurity dilution and radiation loss, and the feasibility of obtaining partial-detached divertor operation—that directly affect projections of ITER fusion power and burn duration performance. A summary of these projections is presented and the effect of uncertainties in the physics-basis issues is examined. ITER capabilities for experimental flexibility and plasma-performance optimization are also described, and how these capabilities may enter into the ITER physics program plan is discussed.

Notes: The interaction between two neighboring laser beams focused in a hot underdense homogeneous plasma is investigated using the non-paraxial wave coupling code KOLIBRI [S. Hüller et al., Phys. Scr. T63, 151 (1996)] in two and three spatial dimensions. Both the plasma hydrodynamic evolution and the stimulated Brillouin scattering (SBS) aspects are studied in the case of strongly damped ion sound waves. The hydrodynamic effects consist in ponderomotively driven density perturbations located between the beams which may, in turn, influence strongly the light propagation through the plasma. The two beams are found to merge whenever the distance between them is smaller than or of the order of their diameter. Concerning the SBS aspect, it is found that due to interference effects between the beams, the spatial amplification of the backscattered light is asymmetric with respect to the laser axis. SBS can also enforce the hydrodynamic effects and the beam merging. © 1997 American Institute of Physics.

Notes: This paper presents a quasilinear analysis of the relativistic electron cyclotron maser instability in which the self-consistent set of equations governing the evolution of the particle distribution function and the energy spectra of unstable waves is numerically solved for parameters typical of the Earth's auroral zone plasma, taking into account both resonant and non-resonant diffusions. The results obtained show that only 0.1%∼0.2% of the particle energy is converted into wave energy by the loss cone instability, and also show that the saturation amplitude for the extraordinary mode increases in proportion to the ratio between electron cyclotron frequency and electron plasma frequency, in agreement with previous results obtained with numerical simulations. © 1997 American Institute of Physics.

Notes: The dynamic form factor for Thomson scattering with a non-Maxwellian (super-Gaussian) electron velocity distribution is analytically and numerically studied for the first time. Both the ion and electron features of the spectra for α〉1 are found to be affected strongly. For the ion feature, the use of the usual theoretical spectra with the assumption of a Maxwellian distribution for fitting the measured Thomson scattering spectra may have resulted in some errors in calculating the plasma parameters in high-Z plasmas irradiated with high intensity light. However, it is impossible to use the ion feature of the measured spectra alone to deduce the form of the electron distribution. For the electron feature, the spectral shape (in particular the peak amplitude) changes sensitively with the distribution index. It would be possible to detect the super-Gaussian distribution by simultaneously measuring the ion and electron features of the spectra. © 1997 American Institute of Physics.

Notes: Analytical results are presented for laser beam deflection rate due to plasma flow when the ponderomotive force (PMF) is static and given. Explicit expressions are obtained in various parameter regimes including that of weak PMF for the case of a coherent (diffraction limited) beam and a beam whose fluctuations are spatially homogeneous, as in the case of a model random phase plate beam. When the Landau damping coefficient, γ0, is negligible and the beam is either coherent and cylindrically symmetric, or random with isotropic fluctuations, the deflection rate is obtained as a closed form function of plasma flow Mach number, M. For finite damping, results are expressed in terms of a universal, one dimensional integral parameterized by M and γ0. For arbitrary PMF and M small, the problem is identified with one in the theory of random dielectric media. © 1997 American Institute of Physics.

Notes: The effect of poloidally mode coupled, ballooning type electrostatic drift waves on a magnetic island has been studied both analytically and numerically. It has been shown quantitatively that particle orbits become stochastic and their behavior can be a possible candidate for the radial plasma transport across a magnetic island of a tokamak. The transport is significant in that it takes place even when the flux surface is not destroyed. The mechanism of the stochasticity generation is understood as an overlapping of secondary islands caused by resonance between periodic particle motions in the magnetic island and Fourier modes of E×B drift due to the electrostatic drift waves. The diffusion process perpendicular to magnetic surface has been analyzed by approximating the distribution to the Gaussian type. In addition, local diffusion process in the vicinity of Kolmogorov, Arnold, and Moser surfaces has been discussed. © 1997 American Institute of Physics.

Notes: On the basis of quasilinear kinetic theory, the electron heating of rf discharges is treated for characteristic scale lengths of the heating field much shorter than the electron mean free path. The analysis considers plasmas bounded by walls providing specular reflection. The expressions for the coefficients of electron diffusion in energy space are obtained and analyzed for inductively and capacitively coupled plasmas. Accounting for the oscillatory spatial structure of the penetrating electric field in the regime of anomalous skin effect leads to a decrease of the diffusion coefficient for high, and an increase for low, energy electrons. It is shown that the presence of a second boundary in the case of collisionless plasma slabs results in a similar effect. The formation of energy distribution functions in various regimes of collisionless heating is discussed. The diffusion coefficients are presented taking into account ambipolar electric fields. © 1997 American Institute of Physics.

Notes: A drift-Alfvén magnetoturbulence model that augments reduced magnetohydrodynamics with evolution of electron density under parallel compression and fluid advection has been studied numerically. In the Alfvénic regime, measurement of spectral transfer rates, frequency spectra, energy partitions, and the ensemble-averaged turbulent response reveals both Alfvénic and hydrodynamic characteristics. The rms turbulent frequency is Alfvénic, the energies are equipartitioned, and there is a fast, Alfvén-time scale relaxation in the turbulent response. The mean frequency is hydrodynamic, with diamagnetic and eddy straining signatures, and there is an eddy straining decorrelation appearing as a distinct, long time scale branch in the turbulent response. The decay rates and relative fluctuation strengths associated with fast and slow time scale decorrelation are in good agreement with theoretical predictions that posit a Kolmogorov spectrum in the Alfvénic regime. © 1997 American Institute of Physics.

Notes: A formalism for the construction of energy principles for dissipative systems is presented. It is shown that dissipative systems satisfy a conservation law for the bilinear Hamiltonian provided the Lagrangian is time invariant. The energy on the other hand, differs from the Hamiltonian by being quadratic and by having a negative definite time derivative (positive power dissipation). The energy is a Lyapunov functional whose definiteness yields necessary and sufficient stability criteria. The stability problem of resistive magnetohydrodynamic (MHD) is addressed: the energy principle for ideal MHD is generalized and the stability criterion by Tasso [Phys. Lett. 147, 28 (1990)] is shown to be necessary in addition to sufficient for real growth rates. An energy principle is found for the inner layer equations that yields the resistive stability criterion DR〈0 in the incompressible limit, whereas the tearing mode criterion Δ′〈0 is shown to result from the conservation law of the bilinear concomitant in the resistive layer. © 1997 American Institute of Physics.

Notes: It is found that a dusty plasma with inertial dust fluid and two-temperature isothermal ions admits both compressive and rarefactive solitary waves, as well as compressive and rarefactive double layers (depending on the concentration of low-temperature ions). In this paper, Korteweg-de Vries equation (KdV-type equations) with cubic and fourth-order nonlinearity at the critical density of low-temperature isothermal ions are derived to discuss properties of dust-acoustic solitary waves. In the vicinity of critical density of low-temperature ions, KdV-type equation with mixed nonlinearity is discussed. By using quasipotential analysis, critical Mach numbers M1c and M2c are obtained such that rarefactive dust-acoustic solitons exist when 1〈M〈M1c and compressive dust acoustic solitons exist when 1〈M〈M2c. © 1997 American Institute of Physics.

Notes: Chaos and a strange attractor were found in time-dependent solutions of the full magnetohydrodynamic equations for a Faraday disc in an applied magnetic "seed" field. These were treated by the Galerkin method, truncated at five modes. The seed field is amplified several hundredfold. There are also aperiodic "partial pole reversals." © 1997 American Institute of Physics.

Notes: In the limit where a strong parallel electric field has short parallel scale lengths, the parallel electron motion becomes nonadiabatic and highly nonlinear, and the usual ponderomotive treatment of the slow time scale behavior of electrons is invalid. Here, a new nonadiabatic model for describing the resulting heating and expulsion of electrons from regions of a strong electric field is developed. The model shows that a typical electron is heated to a value characterized by the "quiver" velocity in the applied field. A nonlinear density expulsion still occurs in this nonadiabatic strong rf field limit, but exhibits an algebraic dependence on the wave amplitude in contrast to the exponential dependence that occurs in conventional ponderomotive theory. Results are applied to electrons in the edge plasma, near a high-power Ion Bernstein Wave heating antenna. © 1997 American Institute of Physics.

Notes: A linear theory for a free electron laser with a one-dimensional helical wiggler and axial magnetic field in the collective regime is presented. The configuration consists of a cylindrical waveguide with arbitrary ratio of electron beam radius a to waveguide inner radius R. Parametric decay of the wiggler pump wave, in the beam frame, into a space-charge wave and an electric–magnetic (EH) waveguide mode is analyzed in three dimensions. A nonlinear wave equation for the three-wave interaction is derived and employed to obtain a formula for the spatial growth rate of the excited eigenmodes. It was found that the relativistic treatment of the electron oscillations in the wiggler field destroys the cyclotron resonance which appears in the nonrelativistic case. Nevertheless, appreciable amplification was found. Numerical analysis is conducted to study the growth rate, radiation wavelength, and required relativistic factor as functions of axial magnetic field B0 and radius ratio a/R. The suitable value for a/R was found to be around 0.65 for our choice of parameters. © 1997 American Institute of Physics.

Notes: The influence of various kinetic effects (e.g., Landau damping, diffusive and collisional dissipation, and finite Larmor radius terms) on the nonlinear evolution of finite amplitude Alfvénic wave trains in a finite-β environment is systematically investigated using a novel, kinetic nonlinear Schrödinger (KNLS) equation. The dynamics of Alfvén waves is sensitive to the sense of polarization as well as the angle of propagation with respect to the ambient magnetic field. Numerical solution for the case with Landau damping reveals the formation of dissipative structures, which are quasi-stationary, S-polarized directional (and rotational) discontinuities which self-organize from parallel propagating, linearly polarized waves. Parallel propagating circularly polarized packets evolve to a few circularly polarized Alfvén harmonics on large scales. Stationary arc-polarized rotational discontinuities form from obliquely propagating waves. Collisional dissipation, even if weak, introduces enhanced wave damping when β is very close to unity. Cyclotron motion effects on resonant particle interactions introduce cyclotron resonance into the nonlinear Alfvén wave dynamics. © 1997 American Institute of Physics.

Notes: The stability of the scrape-off layer to high toroidal mode number ballooning-type instabilities is considered. The equilibrium includes a simple model of the X-point geometry, and parallel (as well as cross-field) equilibrium variations of temperature, density, and potential. The latter are computed numerically from the Braginskii form for Ohm's law. The stability analysis includes the effects of curvature, resistivity, parallel variation of the E×B drift frequency, and sheath boundary conditions at the divertor plate. Importantly, the equilibrium model assures consistency among the possible instability drives; i.e., the pressure weighting of the curvature, the plasma potential (E×B drift), and the conditions at the divertor plate are coupled by the equilibrium model. Numerical solutions indicate two modes: (i) the curvature-driven mode with growth rate enhanced by the sheaths; and (ii) the E×B shear mode driven by equilibrium variations in the region between the X point and the plate. The latter mode is shown to be partly driven by the X-point geometry. The effect of finite Larmor radius, resistivity, and electron inertia on these modes is investigated. © 1997 American Institute of Physics.

Notes: The time-dependent flux-surface-averaged Fokker–Planck equation for the distribution function of minority ions during ion cyclotron resonant heating introduced by Stix in a classic paper [T. H. Stix, Nucl. Fusion 15, 737 (1975)] is solved keeping two dimensions (2-D) in velocity space (speed and pitch-angle). An analysis of the applicability of the method of expansion of the distribution function f in Legendre polynomials of the pitch-angle, a method suggested by Stix and subsequently used by others, is given. A full numerical 2-D solution is also calculated. It is shown that the convergence of the Legendre polynomial expansion is very slow and non-uniform with respect to both particle energy and pitch-angle, making the method impractical when f is required at energies much higher than the background plasma thermal energy. However, the iterative sequences for the moments of f are found to converge very fast. In particular, a good approximation to the pitch-angle average of the distribution function is obtained already with two terms kept in the expansion, for a wide range of heating parameters. The validity of Stix's analytical one-dimensional approximations is analysed in detail. © 1997 American Institute of Physics.

Notes: The stabilization of cylindrical plasmas by resistive walls combined with plasma rotation is analyzed. Perturbations with a single mode rational surface q=m/n in a finitely conducting plasma are treated by the "resistive kink" dispersion relation of Coppi et al. [Sov. J. Plasma Phys. 2, 533 (1976)]. The possibilities for stabilization of ideal and resistive instabilities are explored systematically in different regions of parameter space. The study confirms that an ideal instability can be stabilized by a close-fitting wall and a rotation velocity on the order of resistive growth rates [J. M. Finn, Phys. Plasmas 2, 3782 (1995)]. However, the region in parameter space where such stabilization occurs is very small and appears to be difficult to exploit in experiments. The overall conclusion from the cylindrical plasma model is that resistive modes can readily be wall stabilized, whereas complete wall stabilization is hard to achieve for plasmas that are ideally unstable with the wall at infinity. © 1997 American Institute of Physics.

Notes: A generalized Fokker–Planck equation is developed in the pattern of a well-known collision operator [Beliaev and Budker, Sov. Phys. Dokl. 1, 218 (1957)] and solved for a relativistic singly charged electron–ion plasma under the impact of crossed electric and magnetic fields. Using the differential form of the collision operator and the modified Rosenbluth potentials appropriate for the relativistic plasma various cross-field transport coefficients are derived analytically in the limit of nonrelativistic, moderately relativistic and ultrarelativistic temperatures. © 1997 American Institute of Physics.

Notes: Starting from the Braginskii fluid equations, a set of nonlinear reduced equations are derived which describe the low frequency dynamics of electron and ion energy and density in a toroidal plasma. The equations have an energy integral. The equations are appropriate for studying the relation between electron and ion thermal transport and particle transport in low temperature plasma near the edge of plasma confinement devices. © 1997 American Institute of Physics.

Notes: Due to the high heat flux to the target plates of present day divertor tokamaks, the use of thermally robust flush mounted Langmuir probes becomes more and more important. The surface normal of the probe defines a direction in space which is generally neither parallel nor perpendicular to the magnetic field, and the angle between these two vectors plays an important role for the physics in front of the probe. An analytic description of the sheath physics in front of a target plate is presented, and a model for the analysis of the I–V characteristics of such probes is derived therefrom. The model includes, on the one hand, considerably more physics than previous descriptions, and is, on the other hand, much simpler and more practical than numerical solutions and simulations. Subsequently the application of this model to triple probes is discussed. It will become evident that flush mounted probes can be used as reliably as domed probes to determine the plasma parameters in front of the target plates. © 1997 American Institute of Physics.

Notes: The behavior of a passive particle in a flow that exhibits bifurcations in the transition to a turbulent regime is investigated. The flow considered is a variant of the Charney–Hasegawa–Mima equation. The scalar particle dynamics is considered for different regimes of the main flow. A regime of anomalous diffusion (hypodiffusion) is observed when the field has few harmonics whereas normal diffusion occurs in the strange attractor regime. The analysis of the singular orbit reveals the presence of traps and flights that control the transport. ©1997 American Institute of Physics.

Notes: Formation of a wave-front pattern accompanied by an electrostatic ion-cyclotron instability driven by electrons drifting along a magnetic field is investigated by two-and-half dimensional particle simulations. A clear spatial wave-front pattern appears as the ion cyclotron wave grows due to the instability. When the electron stream is uniform in the system, an obliquely intersected stripe wave-front pattern is formed. When the stream has a bell-shaped pattern across the magnetic field, a V-shaped stripe wave-front pattern appears. The wave fronts have small angles with the magnetic field lines and propagate from the high-stream region to the low-stream region. © 1997 American Institute of Physics.

Notes: The simplest nontrivial model of transport across a magnetic island chain in the presence of collisionless streaming along the magnetic field is solved by a Wiener–Hopf procedure. The solution found is valid provided the boundary layer about the island separatrix is narrow compared to the island width. The result demonstrates that when this assumption is satisfied the flattened profile region is reduced by the boundary layer width. The calculation is similar to the recent work by Fitzpatrick [Phys. Plasmas 2, 825 (1995)] but is carried out in the collisionless, rather than the collisional, limit of parallel transport, and determines the plasma parameters on the separatrix self-consistently. © 1997 American Institute of Physics.

Notes: The effectiveness of using localized current drive or heating to suppress the formation and growth of neoclassical magnetohydrodynamic (MHD) tearing modes is addressed. The most efficient way to use an auxiliary current source is to cause current to flow in the same direction as the equilibrium bootstrap current and phase the current relative to the magnetic island such that the current is deposited on the O-point of the island. Theoretical estimates for the amount of required current to suppress the formation of a large magnetic island is of order a few percent of the equilibrium current. If the suppression is successful, the magnetic island will saturate at a width of order the radial localization width of the current source. Localized heating at the O-point of the magnetic island can also produce stabilizing effects relative to magnetic island growth. The effects of the driven current or heating can be illustrated by using a phase diagram of the island growth. © 1997 American Institute of Physics.

Notes: Magnetic coordinates are singular on a separatrix. A method is given for transforming to nonsingular coordinates that are closely related to magnetic coordinates and can be used in the canonical coordinates of the Hamiltonian for particle drifts. The case of a magnetic separatrix with a single X point is emphasized and approximate expressions are given for the functions that appear in the drift Hamiltonian. © 1997 American Institute of Physics.

Notes: The wavelet bicoherence technique is used to examine floating potential fluctuations in ADITYA tokamak edge plasma, which have shown vortex-like coherent structures on statistical basis [Proceedings of the 15th International Conference on Plasma Physics and Controlled Nuclear Fusion, Seville (International Atomic Energy Agency, Vienna, 1995), Vol. 1, p. 583]. On a single discharge basis, the data exhibit intermittent episodes of quadratic interaction in which low and high frequency components are coupled. The broadband nonlinear phase coupling is used as a diagnostic signature of localized coherent structure. It is observed that the wavelet bicoherence is high in the presence of sparse structures and small when the structures are closely packed. The turbulent edge plasma has regions of packed Gaussian structures and sparse non-Gaussian structures. © 1997 American Institute of Physics.

Notes: An analytic solution to the problem of strongly magnetized plasma flow past a smooth, conducting sphere is considered. The magnetic field is taken to be uniform at very large distances and the sphere is assumed to be unmagnetized. In addition, the flow speed is assumed to be subsonic and super-Alfvénic. It is shown that a steady state solution is possible only if the frozen-in condition can be relaxed near the surface of the sphere. By inclusion of a small resistivity, the presence of two, nested boundary layers near the surface is demonstrated. The magnetic field is shown to drape about the sphere with a scale size of the order of the square root of the resistivity. © 1997 American Institute of Physics.

Notes: A special class of Pierce diodes, that consists of a pair of grounded coaxial cylindrical electrodes, with electrons streaming radially between them, is studied. The full set of roots of the dispersion relation of the Pierce instability is obtained by solving the dispersion relation numerically. The nonlinear behaviour of the system is then investigated using particle simulation. It is shown that the behaviour of cylindrical systems depends on two nondimensional parameters. Linear and nonlinear properties are different for convergent and divergent configurations. Several remarkable differences between cylindrical and planar Pierce diodes are reported. © 1997 American Institute of Physics.