ALBERT

Notes: It is shown that the equations governing the dynamics of weakly interacting medium-frequency electrostatic waves in a nonuniform magnetoplasma with a fixed ion background can have localized vortex chain solutions.

Notes: A mechanism of communication through plasma sheaths which surround vehicles traveling at hypersonic velocities is proposed. The idea is to place a source of an intensive, high frequency electromagnetic pump wave on the vehicle and to use the nonlinearity of the medium to create a backscattered Stokes wave through the interaction of the pump wave with the signal-carrying wave sent by a ground transmitter. Such an interaction will be mediated by the plasma oscillations generated in the process of the resonant absorption of the signal-carrying wave. The advantages of this mechanism for information transfer are that the high frequency pump wave only is present in a small region near the vehicle and that the signal wave can have relatively low frequency.

Notes: Analytic solutions are derived from one-dimensional fluid equations with arbitrary shear viscosity for the free and bounded presheaths in the strongly magnetized flowing plasma. Plasma density and flow velocity are obtained analytically in terms of position along the field line, Mach number (M∞), normalized viscosity (α), and size of bounded presheath. Simple analytic relations between the ratio (R) of sheath current and the flow Mach number [M∞ ≡ Vd/(square root of)(ZTe+Ti)/mi] are derived as R=exp(M∞/Mc), where Mc = 1/[1 +(square root of)α2/1+α arctan(square root of)1+α], with less than 5% accuracy for 0≤M∞≤0.5. By generating two free and two bounded presheaths by two Mach probes within two free presheaths generated by a larger object than Mach probes, one can measure α and M∞ simultaneously. The allowed range of α in terms of M∞ is obtained, and comparisons with previous numerical analyses are also made.

Notes: Experiments have been performed on the Extrap T1 reversed-field pinch [Phys. Scr. 44, 358 (1991)] where the detailed radial structure of the mean profiles, together with associated edge field fluctuation spectra, have been studied at different values of the pinch parameter 1.6≤aitch-theta≤2.5. It is found that the parallel current density is strongly suppressed inside the resonances of the most active m=1 modes, resulting in hollow μ profiles near the axis. This effect introduces a spectral shift in n space between the dominant m=1 modes and the leading linear growth rates. At high aitch-theta a local flattening of μ around the reversal (m=0 resonance) surface becomes apparent. As a result a second set of m=1 modes resonant near the off-axis peak in μ becomes linearly unstable. In this case, the resulting m=1 spectrum is double peaked for the internal modes. The experimental results show several characteristic similarities with recent numerical magnetohydrodynamic simulations of the reversed-field pinch dynamo.

Notes: It is analytically proved that the self-generated magnetic fields in the static limit have the self-collapse behavior. Numerical results show that in the nonstatic limit magnetic fields self-generated by transverse plasmons with frequency ωP≈ωpe may collapse.

Notes: Corresponding to the experiment done with the JIPPT-II-U device [Phys. Rev. Lett. 54, 2339 (1985)], the cyclotron subharmonics resonant (CSR) heating mechanism is studied using particle simulation codes with an emphasis on the relationship between CSR and the nonlinear Landau damping.

Notes: The interaction of high energy particles with an Alfvén eigenmode is investigated self-consistently by using a kinetic dispersion relation. All important poloidal mode numbers and their radial mode profiles as calculated with the nova−k code [C. Z. Cheng, Phys. Rep. 211, 1 (1992)] are included. A Hamiltonian guiding center code is used to simulate the alpha particle motion. The numerical simulations include particle orbit width, nonlinear particle dynamics, and the effects of the modes on the particles. Modification of the particle distribution leading to mode saturation is observed. Particle loss depends on the radial extent of the mode and the ratio of the alpha particle gyroradius to the minor radius.

Notes: Edge plasma fluctuations are studied with inserted triple Langmuir probes and magnetic coils in the TPE-1RM20 reversed-field pinch [Y. Yagi et al., in Plasma Physics and Controlled Nuclear Fusion Research 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. 2, p. 611]. Two-point measurements show that density and potential fluctuations have relatively low mode numbers (m〈3, n〈40). High coherence (γ=0.5) with magnetic field fluctuations and similar mode spectra suggest that density and potential fluctuations are mainly caused by electromagnetic turbulence. Broadband magnetic fluctuations are dominated by m=0, low-n modes and internally resonant m=1 and m=2 modes. A coherent (f=20–30 kHz) m=0, low-n mode is also observed. Particle flux driven by electrostatic electric field fluctuations is 50%–100% of total flux obtained from Dα line intensity measurement. Low-frequency fluctuations (f〈100 kHz) give the main contribution to the total flux. Electrostatic fluctuation driven electron energy flux is only of the order of 10% of total nonradiative power loss.

Notes: Experiments were conducted to confirm that the Rayleigh–Taylor instability is the main process controlling the burnthrough time in imploding spherical experiments. In these experiments the laser irradiates targets overcoated with a parylene layer, in which one or more thin signature layers of moderate- to high-Z material are embedded to signal the penetration of the heat front. Target parameters were varied to study the effect on the burnthrough time of changes to target acceleration, Atwood number, and ablation velocity. The effects of improved laser uniformity through the introduction of smoothing by spectral dispersion are also presented. The results agree well with those obtained from a multimode mix model. This suggests that burnthrough experiments can be used to measure improvements in laser-irradiation or target-fabrication uniformity and to test methods to mitigate the growth of the Rayleigh–Taylor instability.

Notes: A modified Langmuir–Child equation, including both temperature and relativistic effects, is derived and studied using kinetic theory. The current densities of charged particles are analyzed numerically, and the results clearly show that the temperature and relativistic effects can be easily determined through the parameters δ=T/2mc2 and α=q(Vp−V)/2mc2.

Notes: Particle-in-cell (PIC) simulations of electromagnetic (EM) pump wave propagation into an overdense, strongly magnetized plasma with a linear density gradient are investigated. A localized three-wave interaction is observed involving the pump decaying into upper and lower hybrid waves. The upper hybrid (UH) wave converts on pump induced density depletions into an electromagnetic wave which exits the plasma. When the pump wave frequency equals an electron cyclotron harmonic plus lower hybrid (LH) frequency, all excited waves vanish, implying a magnetic field strength remote diagnostic capability. These results are relevant to stimulated electromagnetic emissions (SEE) and also to electron heating in a strongly magnetized plasma.

Notes: Wave breaking of electron plasma waves in an unmagnetized, cold, collisionless plasma with a parabolic density profile is considered when the plasma resonance is situated near the top of the profile. For this case, wave breaking takes place at a density lower than the resonant one and limits the growth of the plasma wave. The dynamics of wave breaking in such conditions are studied as a function of position of resonance in the profile and of amplitude of the driver field.

Notes: Two-dimensional simulations of the electron-beam plasma instability with large system size are carried out and are compared with recent one-dimensional simulations for plasma parameters appropriate to the electron foreshock. It is found that wave propagation and diffusion perpendicular to the beam drift are significant at all times. Because a plateau cannot be maintained in this case, the wave level decreases much more rapidly than in one-dimensional simulations. The nonlinear wave scattering process which occurs at late times also differs in that it generates a broad secondary spectrum rather than a condensate. The two-dimensional model, in addition, allows the investigation of the effects of increasing magnetic field strength (e.g., along auroral field lines). For intermediate magnetic fields Langmuir waves and a highly oblique spectrum belonging to the lower hybrid branch are simultaneously excited. The oblique wave spectrum for strong magnetic fields can be explained by mapping from the magnetic field direction.

Notes: Lattice gas and lattice Boltzmann methods are recently developed numerical schemes for simulating a variety of physical systems. In this paper a new lattice Boltzmann model for modeling two-dimensional (2-D) incompressible magnetohydrodynamics (MHD) is presented. The current model fully utilizes the flexibility of the lattice Boltzmann method in comparison with previous lattice gas and lattice Boltzmann MHD models, reducing the number of moving directions from 36 in other models to 12 only. To increase computational efficiency, a simple single time relaxation rule is used for collisions, which directly controls the transport coefficients. The bidirectional streaming process of the particle distribution function in this paper is similar to the original model [H. Chen and W. H. Matthaeus, Phys. Rev. Lett. 58, 1845 (1987), S. Chen et al., Phys. Rev. Lett. 67, 3776 (1991)], but has been greatly simplified, affording simpler implementation of boundary conditions and increasing the feasibility of extension into a workable three-dimensional (3-D) model. Analytical expressions for the transport coefficients are presented. Also, as example cases, numerical calculation for the Hartmann flow is performed, showing a good agreement between the theoretical prediction and numerical simulation, and a sheet-pinch simulation is performed and compared with the results obtained with a spectral method.

Notes: The nonlinear behavior of low- and large-wave number tearing modes is studied. The emphasis is laid on diamagnetic effects. A kinetic equation, including transport processes associated with a background of microturbulence, is used to describe the electron component. Such transport processes are shown to play a significant rôle in the adjustment of density and temperature profile, and also in the calculation of the island rotation frequency. The fluctuating electric potential is calculated self-consistently, using the differential response of electrons and ions. Four regimes are considered, related to island width (smaller or larger than an ion Larmor radius) and transport regime (electron–ion collisions or electroviscosity dominated). It is shown that diamagnetism does not influence the island stability for small island width in the viscous regime, as long as the constant Ψ constraint is maintained. It turns out that the release of this constraint may strongly modify the previously calculated stability thresholds. Finally, it is found that diamagnetism is destabilizing (stabilizing) for island width smaller (larger) than an ion Larmor radius, in both resistive and viscous regimes. A typical island evolution scenario is studied which shows that even large-scale tearing modes with positive Δ' could saturate to island width of order of a few ion Larmor radii. Illustrative Δ' threshold and island saturation size are calculated.

Notes: The ion and neutral densities and temperatures in the edge region of a diverted plasma can vary over two or more orders of magnitude causing atomic physics processes to modify the usual short mean-free path transport descriptions of magnetized plasmas. The short-mean-free path ordering is particularly relevant to the rather cold, moderately dense plasmas of interest in gas target divertor operation. Under such conditions, charge-exchange, ionization, and recombination couple the ions to the neutrals and alter the transport coefficients of both species. The coupling modifications to the ions are evaluated in the short mean-free path limit by a minor adjustment in standard procedures when neutral–neutral collisions are negligible. The short-mean-free path coupling modifications to the neutrals are evaluated by assuming the charge-exchange rate coefficient is velocity independent. A closed neutral-ion fluid description is obtained by assuming temperatures sufficiently high that ion energy and momentum exchange with the electrons is unaffected by atomic processes and densities sufficiently low that electron–neutral collisions may be neglected.

Notes: This paper examines the use of gas targets to create low- and mid-Z plasmas ≈3 mm in size at 5% to 10% critical density for green and blue light (ne≈2×1020 to 1021 cm−3) with an electron temperature of several keV. At sufficiently high intensities (≈1014 W/cm2) the gas is ionized and heated by a laser absorption wave propagating faster than the sound speed. For pulses under 2 ns, the bulk of the plasma remains stationary, resulting in efficient heating minimizing density and velocity gradients, which are particularly important for instability thresholds in nonuniform plasmas. The propagation of a laser absorption wave in a preionized plasma is derived analytically. Ionization resulting from multiphoton and electron avalanche processes is studied by numerical methods and dimensional analysis. This establishes the length and time scales over which an absorption wave can be observed. Computer simulations, using the lasnex code, are presented for several implementations of this concept, applicable to the relevant regime for inertial confinement fusion. These examples include a gas jet (≈3×1 mm in cross section), 3 to 4 mm diameter gas balloons, and gas puffs generated by exploding a foil with a low-energy prepulse (≈200 J).

Notes: A curvature-driven flute instability will be excited in the magnetized plasmas if the magnetic field lines curve toward the entire plasma boundary. Conditions under which it can be effectively stabilized in axisymmetric geometry have been experimentally studied in a gas-dynamic trap (GDT) at Novosibirsk. Flexible design of the experimental device and the availability of neutral beams and ion cyclotron heating enabled the pressure-weighted curvature to be varied over a wide range. The stability limits were thus measured and compared with those predicted by the modified Rosenbluth–Longmire criterion. Characteristics of unstable curvature-driven flute modes were also measured and found to conform to a theory including finite ion Larmor radius (FLR) effects. Stable operation during neutral beam injection was achieved with a cusp end cell, resulting in an increase in Te to 45 eV, limited by end losses rather than anomalous power losses.

Notes: The final hardware modifications for tritium operation have been completed for the Tokamak Fusion Test Reactor (TFTR) [Fusion Technol. 21, 1324 (1992)]. These activities include preparation of the tritium gas handling system, installation of additional neutron shielding, conversion of the toroidal field coil cooling system from water to a FluorinertTM system, modification of the vacuum system to handle tritium, preparation, and testing of the neutral beam system for tritium operation and a final deuterium–deuterium (D–D) run to simulate expected deuterium–tritium (D–T) operation. Testing of the tritium system with low concentration tritium has successfully begun. Simulation of trace and high power D–T experiments using D–D have been performed. The physics objectives of D–T operation are production of ≈10 MW of fusion power, evaluation of confinement, and heating in deuterium–tritium plasmas, evaluation of α-particle heating of electrons, and collective effects driven by alpha particles and testing of diagnostics for confined α particles. Experimental results and theoretical modeling in support of the D–T experiments are reviewed.

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: A brief review is given of the potential applications of laser ablation in the automotive and electronics manufacturing industries. Experiments are presented on KrF laser ablation of three materials relevant to manufacturing applications: aluminum metal vs aluminum–nitride (AlN) and alumina (Al2O3) ceramics. Plasma and neutral-atom diagnostic data are presented from resonant-holographic-interferometry, dye-laser-resonance-absorption photography, and HeNe laser deflection. Data show that plasma electron densities in excess of 1018 cm−3 exist in the ablation of AlN, with lower densities in Al and Al2O3. Aluminum neutral and ion expansion velocities are in the range of cm/μs. Ambipolar electric fields are estimated to be 5–50 V/cm.

Notes: Improvement of laser irradiation uniformity in the Gekko XII system [IEEE J. Quantum Electron. QE-17, 1639 (1981)], both single beam pattern and power balance, is discussed. Substantial reduction of laser absorption nonuniformity is obtained for spherical harmonic modes greater than 15 by introducing spectrally dispersed amplified spontaneous emission. No perturbation growth is observed in flat foils accelerated by spectrally dispersed amplified spontaneous emission. Dependences of laser absorption uniformity on beam pattern and power imbalance are investigated in detail. The design goal of the power imbalance in the precision Gekko XII system is 3% in peak to valley, and laser absorption nonuniformity is estimated to be a few percent. Growth of hydrodynamic instabilities is analyzed for high convergence ratio implosions in the precision Gekko XII system.

Notes: The magnetized, million-degree solar corona evolves in cycles of about 11 years, in dynamical response to newly generated magnetic fluxes emerging from below to eventually reverse the global magnetic polarity. Over the larger scales, the corona does not erupt violently all the time. Violent events like the flares and episodic ejections of material into interplanetary space occur frequently, several times a day, but they often originate in long-lived magnetic structures that form continually throughout the solar cycle. In this paper, the creation, stability, and eventual eruption of these structures are discussed from basic principles, drawing on recent advances in observation and theory. A global view is offered in which different pieces of observation relate physically, with distinct roles for the conservation of magnetic helicity and the release of magnetic energy in dissipated and ordered forms.

Notes: Gyrotrons and free electron lasers have recently increased both the power and tunability of, respectively, millimeter wave and infrared sources by several orders of magnitude. As radiation at these wavelengths interact strongly with atmospheric aerosols and trace impurities, these sources have a great potential as atmospheric sensors. They open the possibility of increasing by at least an order of magnitude both the range and sensitivity of these atmospheric sensors.

Notes: The dispersion relation of a fast wave in a thermal (minority) hydrogen–deuterium plasma is investigated near the ion cyclotron frequency of hydrogen. It is found that the plasma shield for waves between the two-ion hybrid resonance and the minority fundamental resonance may be reduced by the thermal effects of plasma. By using zero Larmor radius approximations, the condition for cutoff layer vanishing due to the thermal effects of plasma is obtained analytically. The formula derived is compared with the numerical results from the full thermal-plasma dispersion relation, and excellent agreement is found. The results show that the cutoff layer may disappear in practical minority hydrogen–deuterium heating experiments.

Notes: The effect of rotation on the magnetohydrodynamic stability of m=1 modes in spheromaks is calculated to reveal a threshold for rotational instability at ΩτA≈0.2, where Ω is the angular rotation frequency and τA is the Alfvén transit time. This result may explain the appearance of m=1 modes in spheromak experiments in which the flux conserver aspect ratio L/R lies well below the threshold for the tilt instability (m=n=1). For flux conservers with aspect ratios above the tilt instability threshold, rotational instability dominates when ΩτA exceeds the rotational threshold.

Notes: The nonlinear particle transport arising from the convection of nonadiabatic electron density by ion-temperature-gradient-driven turbulence (i.e., ion-mixing mode particle transport) is examined for trapped electron collisionality regimes. The renormalized dissipative nonadiabatic trapped electron phase-space density response is derived and used, along with an ansatz for the turbulently broadened frequency spectrum, to calculate the nonlinear particle flux. In the lower-temperature end of this regime, trapped electrons are collisional and all components of the quasilinear particle flux are outward (i.e., in the direction of the gradients). Nonlinear effects can alter the phase between the nonadiabatic trapped electron phase-space density and the electrostatic potential, producing inward components in the particle flux. Specifically, both turbulent shifting of the peak of the frequency spectrum and nonlinear source terms in the trapped electron response can give rise to inward components. However, in the dissipative regime these terms are small, and the trapped electron response remains dominantly laminar. When the trapped electrons are collisionless, there is a temperature threshold above which the electron-temperature-gradient-driven component of the quasilinear particle flux changes sign and becomes inward. For finite-amplitude turbulence, however, turbulent broadening of both the electron collisional resonance and the frequency spectrum removes this threshold, and the temperature-gradient-driven component remains outward.

Notes: Classical models of magnetic reconnection consist of a small diffusion region, which is bounded by two pairs of slow shocks. In these models, the plasma is accelerated across the shocks. It has long been postulated that violation of symmetry across the current sheet will lead to the formation of intermediate waves in the current sheet. These asymmetries are important properties of space plasma current sheets. Equally important in space plasmas is the presence of sheared flow across current sheets. In this study, the structure of steady-state reconnection is investigated in the presence of a shear flow across the current sheet with symmetric density and magnetic field strengths using two-dimensional magnetohydrodynamic (MHD) simulations. The results show that for sheared flow above the Alfvén velocity of the inflow regions no steady-state magnetic reconnection occurs. For sheared plasma flow below this critical velocity steady-state reconnection is obtained. A detailed examination of the Rankine–Hugoniot jump conditions reveals that each pair of slow shocks is replaced by a strong intermediate shock and a weak slow shock in the presence of shear flow.

Notes: The results of an analytical description and of a particle-in-cell simulation of the interaction of an ultrashort, relativistically intense laser pulse, obliquely incident on a nonuniform overdense plasma, are presented and several novel features are identified. The absorption and reflection of the ultraintense electromagnetic laser radiation from a sharp-boundary plasma, high harmonic generation, and the transformation into low-frequency radiation are discussed. In the case of weak plasma nonuniformity the excitation of nonlinear Langmuir oscillations in the plasma resonance region and the resulting electron acceleration are investigated. The vacuum heating of the electrons and the self-intersection of the electron trajectories are also studied. In the case of a sharp-boundary plasma, part of the energy of the laser pulse is found to be converted into a localized, relativistically strong, nonlinear electromagnetic pulse propagating into the plasma. The expansion of the hot electron cloud into the vacuum region and the action of the ponderomotive force of the laser pulse in the localized longitudinal electric field of the Langmuir oscillations lead to ion acceleration. The energy increase of a minority population of multicharged ions is found to be much greater than that of the ambient ions.

Notes: Electron–ion bremsstrahlung radiation from high-temperature plasmas is investigated. The first- and second-order Coulomb corrections in the nonrelativistic bremsstrahlung radiation power are obtained by the Elwert–Sommerfeld factor. In this paper, two cases of the electron distributions, the thermal and nonthermal power-law distributions, are considered. The inclusion of Coulomb corrections is necessary in deducing correctly the electron distribution function from radiation data. These results provide the correct information of electron distributions in high-temperature plasmas, such as in inertial confinement fusion plasmas and in the astrophysical hot thermal and nonthermal x-ray sources.

Notes: The mechanism for confinement improvement in the toroidal-rotation-induced very high mode (VH mode) may be the turbulence suppression due to the shear of the toroidal angular frequency associated with parallel flow. This explanation is in contrast to the plausible hypothesis that high-mode (H-mode) confinement improvement may be caused by the turbulence suppression due to the shear of the poloidal angular frequency associated with E×B and parallel flows. Here, E is the electric field and B is the magnetic field. A theory for VH mode, based on the rapid change of the radial gradient of the toroidal flow, is presented.

Notes: Tilting instability is an instability of convective motion in two-dimensional (2-D) ideal fluid transforming convection into sheared flow. An analytical model of the tilting instability is proposed that clearly exhibits inverse cascade phenomenon, conserving both energy and enstrophy. Obtained solution describes the evolution of the nonlinear stage in which initial fluid convection is transformed completely into the large-scale flow.

Notes: The magnetohydrodynamic stability of force-free plasma–vacuum systems (curl B=μB in the plasma, with constant μ) is studied in circular cylinders with identified ends (topological torus). A necessary stability criterion is derived by considering large poloidal mode numbers. This takes a simple form (the magnetic rotation numbers at the axis and plasma–vacuum interface must have opposite signs) if the magnetic field lines in the interface are not closed. If they are closed, then violation of this simple condition does not imply instability unless the aspect ratio exceeds some value which depends on both the numerator and denominator of the rational magnetic rotation number at the interface. For aspect ratios greater than unity, combination with the criterion for stability to internal kinks implies that the inhomogeneity parameter ||μ|| must be above the threshold for reversal of the toroidal current density, but below that for reversal of the poloidal one. This condition is independent of the wall radius, in contrast to the well-known necessary and sufficient stability criterion in the limit of infinite aspect ratio, which remains sufficient for arbitrary aspect ratios, and which requires that ||μ|| be in a smaller interval that does depend on the wall radius.

Notes: Monte Carlo operators for the orbit-averaged Fokker–Planck equation describing collisions and wave–particle interaction are constructed. Special emphasis is put on ion-cyclotron-resonance heating of tokamaks, but the results are applicable to general quasilinear processes in arbitrary magnetic configurations in which particle motion is integrable. All effects of nonstandard orbit topology, such as large orbit widths, are fully taken into account. The Monte Carlo operators may be used for simulating, e.g., radio-frequency heating, wave-driven spatial diffusion, and alpha particle slowing down.

Notes: Among heterogeneously catalyzed chemical reactions, the CO oxidation on the Pt(110) surface under vacuum conditions offers probably the greatest wealth of spontaneous formation of spatial patterns. Spirals, fronts, and solitary pulses were detected at low surface temperatures (T〈500 K), in line with the standard phenomenology of bistable, excitable, and oscillatory reaction-diffusion systems. At high temperatures (T(approximately-greater-than)540 K), more surprising features like chemical turbulence and standing waves appeared in the experiments. Herein, we study a realistic reaction-diffusion model of this system, with respect to the latter phenomena. In particular, we deal both with the influence of global coupling through the gas phase on the oscillatory reaction and the possibility of wave instabilities under excitable conditions. Gas-phase coupling is shown to either synchronize the oscillations or to yield turbulence and standing structures. The latter findings are closely related to clustering in networks of coupled oscillators and indicate a dominance of the global gas-phase coupling over local coupling via surface diffusion. In the excitable regime wave instabilities in one and two dimensions have been discovered. In one dimension, pulses become unstable due to a vanishing of the refractory zone. In two dimensions, turbulence can also emerge due to spiral breakup, which results from a violation of the dispersion relation.

Notes: Two types of transitions from the time-periodic spatiotemporal patterns to chaotic ones in the spatially one-dimensional ionic reaction-diffusion system forced either with direct or alternating electric field are described and analyzed by numerical techniques. An ionic version of the Brusselator kinetic scheme is considered. The Karhunen–Loève decomposition technique is shown to be a possible tool for the global representation of dynamic behavior, but fails as a tool in the identification of the route of transition to chaos in the case of direct current forcing. Higher dimensional chaos with two positive Lyapunov exponents has been identified for the case of alternating current forcing. Results of the Karhunen–Loève analysis are compared to results of classical analysis of local time series (attractor dimensions, Lyapunov exponents).

Notes: The accuracy of standard finite Larmor radius (FLR) models for wave propagation in the ion cyclotron range of frequencies (ICRF) is compared against full hot plasma models. For multiple ion species plasmas, the FLR model is shown to predict the presence of a spurious second harmonic ion–ion type resonance between the second harmonic cyclotron layers of two ion species. It is shown explicitly here that the spurious resonance is an artifact of the FLR models and that no absorption occurs in the plasma as a result of this "resonance.'' © 1994 American Institute of Physics.

Notes: The effect of an external rhythm on rotating spiral waves in excitable media is investigated. Parameters of the unperturbed medium were chosen, such that the organizing spiral tip describes meandering (hypocyclic) trajectories, which are the most general shape for the experimentally observed systems. Periodical modulation of excitability in a model of the Belousov–Zhabotinsky (BZ) reaction forces meandering spiral tips to describe trajectories that are not found at corresponding stationary conditions. For different modulation periods, two types of resonance drift, phase-locked tip motion, a spectrum of hypocyclic trajectories, and complex multifrequency patterns were computed. The computational results are complemented by experimental data obtained for periodically changing illumination of the photosensitive BZ reaction. The observed drastic deformation of the tip trajectory is considered as an efficient means to study and to control wave processes in excitable media.

Notes: The dynamics of an assembly of cardiac cells is modeled by a simple cellular automaton that reduces to a single variable the two variable competition of the standard models of excitable media. Furthermore, a short superexcitability period is introduced, as suggested by the dynamics of the single cardiac miocyte. The model reproduces several pathological cardiac behaviors as, e.g., the fast transition from normal behavior to fibrillation, showing how this latter one can either occur over the whole spatial domain or can be confined within a limited region.

Notes: Exponentially small splitting of the separatrix has been calculated for a high frequency large amplitude perturbation and the correspondent correction to the width of the stochastic layer is obtained. The result can be applied to the large amplitude perturbation.

Notes: Experimental evidence is presented that a lateral instability of a wave front, as described earlier in a chemically active medium with the Belousov–Zhabotinsky reaction with decreased excitability, can also occur in a medium with any degree of excitability provided that a high-frequency wave train travels through the medium. The interaction of chemical waves with the boundary of the medium can result in the appearance of wave breaks and spiral waves.

Notes: Classical theory of potential distribution in cardiac muscle (cable theory) postulates that all effects of electric field (internally or externally applied) should decay exponentially with a space constant of the order of the tissue space constant (∼1 mm). Classical theory does not take into account the cellular structure of the heart. Here, we formulate a mathematical model of excitation propagation taking into account cellular gap junctions. Investigation of the model has shown that the classical description is correct on the macroscopic scale only. At microscopic scale, electric field is modulated with a spatial period equal to the cell size (Plonsey and Barr), with the zero average. A very important new feature found here is that this effect of electric field does not decay at arbitrary big distances from the electrode. It opens the new way to control the excitation propagation in the cardiac muscle. In particular, we show that electric field can modify the velocity of propagation of an impulse in cardiac tissue at arbitrary big distances from electrode. In 2-dimensions, it can make rotating waves drift. To test these predictions, experiments with cardiac preparations are proposed.

Notes: The phenomenon of intermittency, which arises near a point of degeneracy of an unperturbed Hamiltonian under the influence of a discontinuous perturbation function, is studied in the example of a two-dimensional (2-D) model of a kicked oscillator. This example describes the dynamics of a particle in a cylindrically symmetric potential well subjected to radial kicks which occur periodically in time. The problem is reduced to a Hamiltonian system with N=3/2 degrees of freedom, whose unperturbed Hamiltonian has a degeneracy point. The intermittency is studied numerically and analytically.

Notes: In the context of planetary atmospheres and oceans, it is natural to define "coherent structures'' as "long-lived,'' or "solitary,'' Rossby vortices. These can be described by the generalized Charney–Obukhov equation (in fluid dynamics) or the analogous generalized Hasegawa–Mima equation (in plasma physics). These two equations contain KdV-type nonlinearities which (together with the compensating dispersive spreading) determine the formation of the coherent structures and explain the clear-cut cyclonic/anticyclonic asymmetry observed experimentally in long-lived planetary Rossby vortices. Examples are given of natural vortices which are (and which are not) coherent structures.

Notes: The dynamical properties of convection in rotating cylindrical annuli and spherical shells are reviewed. Simple theoretical models and experimental simulations of planetary convection through the use of the centrifugal force in the laboratory are emphasized. The model of columnar convection in a cylindrical annulus not only serves as a guide to the dynamical properties of convection in rotating sphere; it also is of interest as a basic physical system that exhibits several dynamical properties in their most simple form. The generation of zonal mean flows is discussed in some detail and examples of recent numerical computations are presented. The exploration of the parameter space for the annulus model is not yet complete and the theoretical exploration of convection in rotating spheres is still in the beginning phase. Quantitative comparisons with the observations of the dynamics of planetary atmospheres will have to await the consideration in the models of the effects of magnetic fields and the deviations from the Boussinesq approximation.

Notes: Let S10, S11,...,S1n−1 be n circles. A rotation in n circles is a map f:∪i=0n−1S1i→∪ i=0n−1S1i which maps each circle onto another by a rotation. This particular type of interval exchange map arises naturally in bifurcation theory. In this paper we give a full description of the symbolic dynamics associated to such maps.

Notes: A nonlinear stage in the development of the tearing mode instability is studied analytically using a two-fluid plasma description. A coherent nonlinear solution is constructed in the form of a moving single chain of magnetic islands, coupled with a double chain of hydrodynamic vortices. The adiabatic theory of the chain evolution in the presence of finite electron viscosity indicates its finite lifetime and the possibility of intermittency, which provides a new mechanism for the magnetic field stochastization within a layer of a collisionless skin depth scale. This process occurs before the magnetic island overlapping and the global stochastization takes place.

Notes: The behavior of finite-pressure-induced magnetic islands is numerically analyzed for three-dimensional magnetohydrostatic equilibria of the Helias configuration by using a three- dimensional equilibrium code. It is found that an island chain is generated on the 5/6 rational surface, when such a surface appears in the plasma region of the finite-β equilibrium. The island chain, however, is not so dangerous as to destroy the plasma confinement even if it appears in a vanishingly small shear region. Thus, a high β equilibrium with clear magnetic surfaces can be realized. Moreover, it is definitely confirmed that the finite pressure effect sometimes exhibits an unexpectedly good aspect, namely, that the vacuum islands are removed as β increases, which can be called ‘self-healing' of islands. This property can be explained by the numerically discovered fact that the phases of islands induced by the finite-pressure effect are always locked in the same phase regardless of β.

Notes: Some representative potentials of the anharmonic-oscillator type are constructed. Some corresponding spectra-shift operators are also constructed. These operators are a natural generalization of Fok creation and annihilation operators. The Schrödinger problem for these potentials leads to an equidistant energy spectrum for all excited states, which are separated from the ground state by an energy gap. The general properties of the dynamic system generated by spectral-shift operators of third degree are analyzed. Several examples of such anharmonic oscillators are discussed. The relationship between the eigenvectors of the Schrödinger problem and a certain type of nonclassical orthogonal polynomials is established.

Notes: The chaotic dynamics of sound rays in a near-bottom waveguide channel is studied on the basis of the Hamiltonian dynamics of nonparaxial rays in inhomogeneous moving media. The bottom is assumed to have a two-dimensional roughness. The mapping of the coordinates of the rays upon reflection from the rough bottom is derived through a solution of the corresponding ray equations in an unperturbed waveguide with a horizontal bottom. A numerical analysis of the mapping reveals that a chaotic instability of rays which start out at small angles from the horizontal develops at short distances from the source. Because of this instability, the path segments of a ray along the horizontal coordinates and the signal passage time along a ray are random functions of the angle at which the ray emerges from the source. Upon a further reflection of rays from the rough bottom, there is a diffusion of rays in a stochastic ring which forms in the plane of horizontal ray directions as a result of the overlap and intersection of resonance curves. A qualitative analysis of this effect is carried out. This effect leads to a nearly isotropic distribution of ray directions.

Notes: Pattern selection at medium and high nonlinearity is investigated. While in the former the transient time levels off for large system sizes, in the latter it diverges exponentially giving rise to supertransients. In both cases, the final attractors are quite stable with as a consequence that even at high nonlinearity an attractor can easily be reached by means of a parameter sweep.

Notes: The transition to turbulence via spatiotemporal intermittency is investigated for coupled maps defined on generalized Sierpinski gaskets, a class of deterministic fractal lattices. Critical exponents that characterize the onset of intermittency are computed as a function of the fractal dimension of the lattice. Windows of spatiotemporal intermittency are found as the coupling parameter is varied for lattices with a fractal dimension greater than two. This phenomenon is associated with a collective chaotic behavior of the fractal array of coupled maps.

Notes: The temporal evolution of the plasma sheath in small cylindrical bores and planar gaps is calculated for zero-rise-time voltage pulses. The ions are modeled as a cold, collisionless fluid, and the problem is reduced to the solution of two coupled, first-order, ordinary differential equations. These equations are solved analytically for the planar case, and numerically for the cylindrical case. The maximum ion impact energies are 50% and 36.8% of the maximum potential drop in the planar and cylindrical cases, respectively. Ion impact energy decreases with the square of the radius of the bore.

Notes: In a recent publication [Phys. Fluids B 5, 3864 (1993)], a study has been presented on the absorption mechanisms of whistler waves in cool, dense, cylindrically bounded plasmas. The dispersion relation obtained was used to explore the transition from Landau dominated damping to cyclotron dominated damping. Although the frequencies of these waves are well below the electron cyclotron frequency, the cyclotron resonance terms were retained in full since for high density plasmas, the density dependent parallel wave number can be large enough to bring thermal electrons into cyclotron resonance. It is the purpose of the present Comment to show that, within the approximations used in the article above, off-diagonal terms, which were neglected, can give an important contribution to the dispersion and damping of the waves for the parameters considered, and therefore should be retained in the calculation.

Notes: The closed set of relativistic hydrodynamical equations describing strongly magnetized collisionless plasma with an anisotropic pressure tensor is offered. This model is the generalization of Chew–Goldberger–Low [Proc. R. Soc. London Ser. A 236, 112 (1956)] theory for the relativistic case. It is shown that at high temperatures the equation of state differs significantly from the ones used earlier.

Notes: An analytical and numerical study is presented herewith to get an insight into the excitation of forward and backward waves caused by an intense relativistic electron beam in a rippled wall plasma filled waveguide with weak modulation. The numerical results of growth rate are derived in the case of weak modulation at kz=π/z0 (the π point). Numerical results also show that no excitation of waves takes place if relativistic factor of the beam γ〈(1+μ20s/R20k20)1/2. For γ(approximately-greater-than)(1−μ20s/R20k20)−1/2, the beam excites both forward and backward waves, and only forward waves if (1+μ20s/R20k20)1/2〈γ〈 (1−μ20s/R20k20)−1/2. The dependence of the frequency of the generated forward waves on beam energy is also studied numerically and the results are compared with those of the experiment [IEEE Trans. Plasma Sci. PS-18, 490 (1990)]. The effect of corrugation depth of rippled wall plasma filled backward wave oscillator (BWO) on minimum frequency generated is also studied.

Notes: Effects of radio-frequency (RF)-induced radial diffusion on triton burnup are studied for D(3He) plasmas with an ion cyclotron range of frequencies heating in the fundamental minority regime. The triton distribution is determined from a Fokker–Planck equation including a radial diffusion term. Provided that the RF power is extremely localized in the plasma center, tritons are driven out from the center because of RF-induced diffusion in the second harmonic resonance and the emission profile of the 14 MeV neutrons due to deuterium tritium (D–T) reactions can possibly be flattened appreciably. This may lead to verification of RF-induced radial diffusion of the ions only through neutron detection.

Notes: When in a double plasma machine (DP-machine) plasma is produced solely in the source chamber, not only ions but also electrons can leak through the separating grid into the target chamber, so that a low-density plasma forms there. The electrons are trapped by the traveling ion space charge and can thereby overcome the strongly negative grid bias. The investigations presented here show that a positive space-charge forms behind the grid in the target chamber and a deep potential well is formed around the grid. When the anode of the target chamber is biased positively, under certain conditions a low-frequency instability is observed in the target chamber, the properties of which indicate a potential relaxation oscillation, somewhat similar to the potential relaxation instability in a quiescent plasma machine (Q machine). The frequency of the instability is determined by the ion transit time through a thin layer of the target chamber plasma. In addition, resonant coupling occurs between this frequency and the bounce frequency of ions in the potential well around the grid.

Notes: The effect of the background drift wave turbulence on the evolution of the low-m tearing modes has been studied, in the quasilinear regime, in various limiting cases. It is found, in the cases of the m=1 classical, collisionless, and drift-tearing modes, that the turbulence introduces finite real frequencies to these modes, which are otherwise purely growing ones, but reduces their instability activity. In the case of the m≥2 classical modes, in a limit ||α||1/2(very-much-greater-than)ρi, the turbulence enhances the frequencies as well as the growth rates of these modes; and in the case of the m≥2 collisionless modes, in the same limit, it enhances the frequencies of these modes, but reduces their instability activity, where ||α||1/2 is the current channel width and ρi is the ion Larmor radius.

Notes: It is shown that the Grad–Shafranov equation for toroidally symmetric ideal-magnetohydrodynamic (MHD) equilibria is a conventional albeit nonlinear eigenvalue problem. That this has been generally overlooked with limited consequences has been made possible by the existence of a scale-invariant transformation of the equation. If the safety factor q is chosen in place of the toroidal field as one of the free flux functions specifying the source (numerical Grad–Shafranov solvers with this capability are called "q solvers''), the eigenvalue is 1 and the scale-transformation factor drops out of the problem. It is shown how this is responsible for the numerical problems that have plagued a class of q solvers, and a simple remedy is suggested. This has been implemented in Livermore's toroidal equilibrium code (TEQ), and as an example, a quasistatically evolved vertical event is presented.

Notes: Parametric decay of an upper hybrid/electron Bernstein pump wave into an upper hybrid/electron Bernstein sideband wave and a lower hybrid decay wave in the long-wavelength regime is studied. It is found that the process associated with the electron Bernstein pump wave has a lower threshold field than that of a similar decay process of the upper hybrid pump wave when the instability is excited in the region away from the double resonance layer. Near the double resonance layer, where the upper hybrid resonance frequency equals a harmonic of the electron cyclotron frequency, the upper hybrid wave and the electron Bernstein wave become linearly coupled, and the threshold field of the parametric decay process changes back to a similar functional dependence as that of the upper hybrid decay process. Thus, their threshold fields approach each other. When incorporated with appropriate nonlinear scattering processes, this instability process along with its cascading is proposed to be the generation mechanism for the downshifted maximum (DM), 2DM, 3DM, ... etc. features as well as the upshifted maximum (UM) feature in the stimulated electromagnetic emission spectrum observed in ionospheric heating experiments.

Notes: Sideband excitation near the carrier determines the minimum spectral width for steady-state free-electron laser oscillators fed by continuous electron beams. A sideband separated by δω from the carrier resonates with harmonics of the upshifted bounce frequency for trapped particles, δω=n2γ2zΩ. The analysis focuses on sidebands excited in the immediate vicinity of the carrier δω→0, in resonance with particles trapped near the separatrix, Ω→0. For electrons distributed uniformly around their orbits, the growth tends to zero as δω, Ω→0, despite the infinite number of contributing harmonics. However, the distributions produced by injected electron beams are nonuniform around the trapped orbits, yielding finite growth rates Γ. Stability depends on the nonlinear shift δk0(a0,ω0) of the carrier wave number from the empty cavity value, where the carrier amplitude a0 and frequency ω0 parametrize the free-electron laser (FEL) operation point. The curve δk0(a0,ω0)=0 divides the FEL parameter space into areas stable and unstable to sidebands. If δk0 is negative, near-the-carrier sidebands are stable, and the linewidth is limited only by quantum effects. If δk0 is positive an unstable frequency band can emerge around the carrier, of width Δω(approximately-equal-to)8γ2zv0 δk0, and maximum growth rate Γmax/k0(approximately-equal-to)(1/6)[2πN(δk0/k0)]2, where N is the number of wiggler periods. The minimum linewidth is Δω if the frequency separation between cavity modes is less than Δω. "Single mode'' operation in the unstable region is still possible if the cavity mode separation exceeds the unstable bandwidth Δω. The above stability conclusions do not apply to sidebands "far'' from the carrier Δω∼2γ2zΩ0. The latter poses less of a threat to FEL operation, since they are easier to filter out.

Notes: An action principle for the Maxwell–Vlasov (MV) equation is formulated in terms of the Maxwell fields and the generating function, w(z,t) for deviations from a reference distribution function, f0(z), which labels a symplectic leaf. New formal fields suitable for variations are defined. These fields give rise to a symplectic and Poisson structure. The Hamiltonian formulation of the equations is found in terms of the new formal fields, and it is found how to derive Larsson's action principle [J. Plasma Phys. 48, 13 (1992); ibid. 49, 255 (1993)] and generalized versions of it on a Lagrangian constraint manifold in a double symplectic space. It is also shown how the relativistic Maxwell–Vlasov system and the Maxwell–Vlasov system with a time-dependent reference state can be formulated as an action principle and Hamiltonian system in terms of eight-dimensional particle phase space coordinates.

Notes: A quasihydrodynamic description of ion acoustic waves (IAW) has been developed in the entire range of particle collisionality. It is shown that a frequency dependent 21-moment Grad closure to ion fluid equations and phenomenological delocalized electron heat transport formulation can be used for an accurate analytical description of ion acoustic wave dispersion and damping. This description is in good agreement with the results of Fokker–Planck simulations. The authors' new model has been derived with the practical motivation of improving IAW description in large scale numerical modeling of ion wave instabilities. This theory has been also applied to the linear analysis of heat flux driven plasma instabilities. In particular, a new IAW instability in the regime of collisional electrons, which is induced by the density dependence of the electron thermal transport coefficient, has been found.

Notes: New Eulerian action principles for the linearized gyrokinetic Maxwell–Vlasov equations and the linearized kinetic-magnetohydrodynamic (kinetic-MHD) equations are presented. The variational fields for the linearized gyrokinetic Vlasov–Maxwell equations are the perturbed electromagnetic potentials (φ1,A1) and the gyroangle-independent gyrocenter (gy) function Sgy, while the variational fields for the linearized kinetic-MHD equations are the ideal MHD fluid displacement ξ and the gyroangle-independent drift-kinetic (dk) function Sdk (defined as the drift-kinetic limit of Sgy). According to the Lie-transform approach to Vlasov perturbation theory, Sgy generates first-order perturbations in the gyrocenter distribution F1≡{Sgy, F0}gc, where F1 satisfies the linearized gyrokinetic Vlasov equation and { , }gc denotes the unperturbed guiding-center (gc) Poisson bracket. Previous quadratic variational forms were constructed ad hoc from the linearized equations, and required the linearized gyrokinetic (or drift-kinetic) Vlasov equation to be solved a priori (e.g., by integration along an unperturbed guiding-center orbit) through the use of the normal-mode and ballooning-mode representations. The presented action principles ignore these requirements and, thus, apply to more general perturbations.

Notes: The Coulomb logarithm is a fundamental plasma parameter which is commonly derived within the framework of the binary collision approximation. The conventional formula for the Coulomb logarithm, λ=ln Λ, takes into account a pure Coulomb interaction potential for binary collisions and is not accurate at small values (λ〈10). However, a more exact Fokker–Planck equation was recently presented by Li and Petrasso which is accurate at small Coulomb logarithm values (λ(approximately-greater-than)2) [Phys. Rev. Lett. 70, 3063 (1993)]. This theory and computer simulations which are accurate for small Coulomb logarithm values provide the motivation for a more precise evaluation of the Coulomb logarithm. In the present work, the Coulomb logarithm is evaluated more precisely by using a cutoff Coulomb interaction potential. The result is compared to an exact numerical evaluation of the Coulomb logarithm which considers a screened Coulomb interaction potential. Fits to the numerical results are also provided. The fitted formula λ=ln(0.6 Λ) is recommended for most applications providing values within 4% of the exact numerical values for λ(approximately-greater-than)2. This formula is easily implemented by using 0.6λD in place of λD (the Debye length) in the conventional formula for the Coulomb logarithm.

Notes: A full set of Vlasov–Maxwell equations describing a stationary perpendicular collisionless shock has been solved in the asymptotic case x→±∞, where x is the spatial coordinate of the one dimensional (1-D) shock geometry. The perpendicular magnetic field in the upstream region has been found to vary asymptotically as Bz(x)−Bz(−∞)∼exp(−bx/Rp), where b(MA,βp,βe)〈0 is a function of the Alfvén Mach number, MA, and the proton and electron betas; Rp is the proton Larmor radius. The electron and proton distribution functions are expressed as one-dimensional integrals to be evaluated numerically. Two general results are derived: (i) there occurs an instability, in the sense that the distribution functions are not unique, for −b/MA=(mp/me)1/2, where mp and me are the proton and the electron mass, respectively. Numerical computations show that the lowest value of MA fulfilling this instability condition is Mc≈6.5. (ii) The perpendicular shock cannot develop if MA≤(1+βp+βe)1/2. Moreover, it was found that for MA, βp, and βe from a certain range, the proton distribution function exhibits a peak of reflected particles, with vx≈0 and vy≈2.33v0, i.e., with an energy of about 5.4 times that of the incident flux.

Notes: The space and time behavior of parametric backscattering instabilities is computed analytically in the so-called modified decay regime. The plasma is assumed to be homogeneous and of finite length. The propagation of the pump wave and its finite pulse duration both are taken into account, its depletion is ignored. The parametric growth is solved in terms of fluctuating initial and boundary conditions corresponding to thermal noise at equilibrium. Fluctuating source terms, representing spontaneous emission of waves, are accordingly retained in the coupled mode equations. The initial stage of the instability is investigated in detail; the time from which the time asymptotic concept of absolute or convective instability applies is computed. Approximate expressions for the fluctuations of the waves, that are uniformly valid for any gain factor and any time, are derived.

Notes: A general method for constructing Monte Carlo collision operators is formulated based on the introduction of a stochastic Liouville equation. The approach is applied to the investigation of a suitable discretized gyrokinetic equation describing the dynamics of a strongly rotating multispecies plasma, in a toroidally axisymmetric configuration. Improved expressions are obtained for the Monte Carlo collision operators for general non-normal (in v space) coordinate systems. As an application, the important case of the bounce-averaged gyrokinetic equation is discussed, in various cases of interest. Finally, using an approximate collision operator, the friction coefficients are evaluated and expressed in terms of energy and momentum restoring coefficients, thus yielding for the Monte Carlo operators a representation convenient for their numerical implementation.

Notes: The theory of atomic-process driven microinstabilities in the tokamak edge plasma is reexamined. It is found that these instabilities, as they are usually presented, do not exist. This assertion applies both to ionization-driven modes and to radiative condensation, or thermal-driven modes. The problem is that there exists no separation of time scales between the approach to equilibrium and the growth rate of the purported instabilities. Therefore, to describe the perturbation of an inhomogeneous plasma, it is essential either to establish an equilibrium that includes both perpendicular transport and the proposed source, or, alternatively, to follow the background evolution simultaneously with the growth of the modes. Neither has been done in theoretical or numerical studies of microinstabilities driven by atomic effects in tokamaks. Very near the density limit, macroscopic modes may be unstable, leading to marfes or disruptions, but perturbations of the equilibrium transport fluxes, when taken into account, are sufficient to stabilize the microscopic modes. If the equilibrium fluxes are not included a priori, the ordering breakdown persists into the nonlinear regime. Since the atomic driving terms are the same as in the linear limit, radial decorrelation lengths would have to approach background scale lengths to yield transport of significant magnitude. Under ordinary tokamak conditions, therefore, atomic processes are unlikely to provide an important driving mechanism for the microturbulence that is presumed to cause anomalous transport.

Notes: The issue of transport on open field lines is addressed using a fluid approach invoking anomalous inertia and viscosity. The emphasis of the model is on the transport of the toroidal momentum, which is notoriously anomalous. The model suggests that tokamaks with divertors may benefit from a significant amplification of the electric field. It is shown that biasing of the scrape-off layer (SOL) with respect to the grounded first wall results in fundamental phenomena, affecting the performance of a divertor. The theoretical model appears to be consistent with experimental results obtained on Tokamak de Varennes [Phys. Plasmas 1, 1485 (1994)].

Notes: The electrostatic and kinetic energies available in the longitudinal electron plasma wave created in the wake of an ultraintense laser pulse are obtained analytically. The analysis is one dimensional and assumes a square-shaped pulse that propagates in a highly underdense plasma with the velocity of light in vacuum. The length scale for laser depletion is given as a function of the laser irradiance and the electron density.

Notes: Braginskii's two-fluid equations, with collisional effects neglected and electron fluid assumed to be isothermal along the magnetic field lines, are employed to obtain the singular mode equations. While the ordering analysis in the paper indicates that, in the intermediate frequency regime (i.e., that with the frequency of the modes higher than the ion acoustic frequency along the magnetic field lines, but lower than the electron one), the stabilizing finite Larmor radius (FLR) effect on the modes dominates over other collisionless, two-fluid effects, the paper is devoted to the investigation of the comparable frequency regime (i.e., that with the frequency of the modes comparable to the ion acoustic frequency along the field lines). It is found that, in such a regime, the parallel electric field is excited and the plasma behaves nonadiabatically. The singular mode equations consist of two coupled second-order partial differential equations, in which the FLR, the plasma compression, and the parallel electric field effects are present. The results are discussed, and a comparison with the ideal magnetohydrodynamic formalism is given.

Notes: The role of the electron nonlinearity on saturation levels and particle transport in collisionless trapped electron mode turbulence is examined numerically using a two-dimensional fluid model. It is found that the removal of the electron nonlinearity results in an order of magnitude increase in fluctuation and particle transport levels. In addition, the qualitative behavior of the saturated state changes distinctly, including a decrease in RMS wave number in both cross-field directions, deviations from isotropy, changes in transport scalings, and changes in the spectral flow of energy. These results indicate that the electron nonlinearity is responsible for an efficient transfer of internal energy to small dissipation scales, thus resulting in lower fluctuation levels than predicted by ion mode coupling alone. The electron nonlinearity also decreases the phase angle between the density and potential leading to a decrease in the driving source. These results underscore the importance of the cross-correlation on saturation and demonstrate that numerical or theoretical use of "iδ'' models to describe weakly collisional or collisionless trapped-electron mode turbulence is not appropriate.

Notes: A one-dimensional (1-D) model is used to investigate the effect of a high neutral density on the divertor plasma via charge exchange. A regime characterized by a strong plasma pressure decrease along the field line is obtained above a critical neutral density. The bifurcation is characterized by the location of the ionization front, which reaches 70% of the distance from the divertor plate to the X point at the threshold. At this position, the Mach number is large, which has a beneficial aspect on impurity control. The weak dependence of the bifurcation control parameter on the heat outflow from the core allows one to extrapolate this regime to the ignited plasma in the next step devices without requiring large modification of the divertor geometry with respect to that of present experiments.

Notes: Low-entropy, cylindrical implosion of cryogenic hydrogen is simulated to explore the equation of state (EOS) close to the transition from molecular to atomic structure. The simulations are based on the Los Alamos EOS library. Concerning isentropic compression, optimum time-shaped pulses are derived analytically and are used in numerical simulations. Small cylinders of cryogenic hydrogen, suitable for laser experiments, are considered with 100 μm radius and about a millimeter long; the energy to be invested into such cylinders to reach the transition is about 1 J. Multiple-shock compression by an imploding liner is also considered; the liner velocity has to be close to 1 km/s. Liner compression produces more uniform compressed configurations with longer lifetime (about 10 ns), though at somewhat higher entropy. Rarefaction shocks occur in the expansion stage and might be useful as a diagnostic.

Notes: The morphology of the 33.8 A(ring) emission from laser-irradiated targets was studied using a concave mirror with a W/B4C multilayer coating. The mirror had peak normal-incidence reflectance of 1.8% at a wavelength of 33.8 A(ring). The emissions from a variety of targets were imaged on film with a spatial resolution of 30 μm in the target plane. Radiatively heated, low-density plastic and silica foams, x-ray laser targets, and a gas-filled enclosure were imaged. Several targets were simultaneously imaged at wavelengths of 33.8 and 130 A(ring) using two normal-incidence microscopes.

Notes: A sheath helix loaded waveguide supports a slow electromagnetic wave which can act as a wiggler for a millimeter-wave free-electron laser (FEL). A nonlocal theory of FEL interaction in the Compton regime reveals that the radiation frequency and growth rate are sensitive functions of the phase velocity of the pump (wiggler) wave and increase with increasing pump frequency. The FEL radiation frequency can be tuned by an additional parameter, viz., the pitch angle of the helix in this configuration.

Notes: Universal voltage-current characteristics are presented for a planar diode, showing the general transition from the Fowler–Nordheim relation to the Child–Langmuir law. These curves are normalized to the intrinsic scales that are constructed from the Fowler–Nordheim coefficients A, B. They provide an immediate assessment of the importance of the space charge effects, once the gap voltage, gap spacing, and the Fowler–Nordheim coefficients are specified. An example in the parameter regime of vacuum microelectronics is presented.

Notes: The influence of the large-scale radial electric field, E(0)r on the frequency of shear-Alfvén-type instability is analyzed. A frozen-in-flux constraint and the moderate-β ion gyrokinetic equation are used in the derivation. The present analysis indicates that the frequency predicted by a theory without E(0)r effect should be Doppler shifted by k⋅VE for comparison to the experimentally observed frequency. A specific example of the practical relevance of the result is given regarding possible identification of the edge-localized-mode-associated magnetic activity recently observed in PBX-M [Plasma Physics and Controlled Nuclear Fusion Research (International Atomic Energy Agency, Vienna, 1989), Vol. 1, p. 97] tokamak experiment.

Notes: Theory predicts that perfectly azimuthally symmetric non-neutral plasma traps should confine plasma forever. Unintentional trap asymmetries are believed to limit plasma confinement times to less than 〈105 s. Deliberately applied electrostatic fields break the azimuthal symmetry and affect the plasma confinement time. While small, deliberate asymmetries do not significantly reduce the trap's confinement properties, large asymmetries significantly degrade the plasma confinement. The scaling laws of this degradation are studied herein. The mechanism of plasma loss appears to change when deliberate asymmetries are applied.

Notes: Power partition and energy dissipation rates are examined for a self-sustained stationary turbulence of a high-n ballooning mode in a tokamak plasma. It is found that the power to excite fluctuations is almost equally transferred to perpendicular ion motion and to parallel electron motion. The ratio of the thermalized power, which excites and sustains the turbulence, to the total power lost by energy diffusion is found to be of the order of the broken symmetry parameter, i.e., the inverse aspect ratio, a/R. The dissipation rates of the fluctuations due to the thermal conductivity, the electron viscosity, and the ion viscosity are also calculated separately. The dissipation is dominated by that associated with the thermal conductivity. The relation between the induced global flux and the microscopic dissipation is also derived. It is found that a fractional part of order a/R of the dissipated power is effective in sustaining the turbulent modes.

Notes: The effect of the radial electric field on neoclassical orbits in a tokamak using the integrals of drift motion is considered. It is shown that for the most interesting case of high radial electric field shear, due to a dramatic change of the particle orbit topology at a distance of the order of one particle orbit width, it is not correct to apply local theory to describe neoclassical transport processes. For step-like electrostatic potentials typical for the tokamak plasma periphery in the high (H) mode, the trajectories of the particles can be either squeezed or expanded depending on the location of the potential jump with respect to the unperturbed particle trajectories. The widening of the orbits decreases the threshold energy of suprathermal particles which can be promptly lost and enhances the ion prompt losses which might increase the amplitude of the potential step. It is shown that these effects are more pronounced for a diverted tokamak with the X point located at the inner side of the torus. Simultaneous growth of prompt losses and potential magnitude might be the reason for the fast formation of the narrow electrostatic barrier during the "low''–"high'' (L–H) transition. Toroidal plasma rotation induced by the radial electric field can strongly enhance the destabilizing effect of the step-like potential.

Notes: Low-frequency turbulence has been studied in a plasma embedded in a pure toroidal magnetic field. A study of the variation of the spectral characteristics of the low-frequency turbulence with the variation in νin/Ωi has been carried out with two different sets of density and potential profiles. The spectral relation between density and potential fluctuations indicates that the Rayleigh–Taylor instability excites fluctuations in the long wavelength region, while the Rayleigh–Taylor driven drift instability is responsible for the short wavelength regime for νin/Ωi(very-much-less-than)1. Spectral characteristics observed in regions where density gradients are parallel to gravity are similar to the case where density gradients are antiparallel to the gravity and support the view that the fluctuations generated in the bad curvature region are transported to the good curvature region. The results are in agreement with theoretical predictions, numerical simulations, in situ measurements, and other laboratory experiments on drift and Rayleigh–Taylor instabilities. For νin/Ωi≥1, the spectral characteristics change and may correspond to the collisional gradient drift instability or the cross-field instability.

Notes: In response to the comment on theory and simulation of light filamentation in laser-produced plasma the authors believe that the criticism overstates the outcome of choosing one form of thermal conduction over another. (AIP)

Notes: The energy density expression Best presents is not (when integrated) equal to the energy of a linear perturbation in Vlasov theory. The exact expression is given by either Eq.(42) or Eq.(48) of Ref.2. The authors comment on this and other discrepancies. (AIP)

Notes: The hypothesis of stabilization of turbulence by shear in the E×B drift speed successfully predicts the observed turbulence reduction and confinement improvement seen at the L (low)–H (high) transition; in addition, the observed levels of E×B shear significantly exceed the value theoretically required to stabilize turbulence. Furthermore, this same hypothesis is the best explanation to date for the further confinement improvement seen in the plasma core when the plasma goes from the H mode to the VH (very high) mode. Consequently, the most fundamental question for H-mode studies now is: How is the electric field Er formed? The radial force balance equation relates Er to the main ion pressure gradient ∇Pi, poloidal rotation vθi, and toroidal rotation vφi. In the plasma edge, observations show ∇Pi and vθi are the important terms at the L–H transition, with ∇Pi being the dominant, negative term throughout most of the H mode. In the plasma core, Er is primarily related to vφi. There is a clear temporal and spatial correlation between the change in E×B shear and the region of local confinement improvement when the plasma goes from the H mode to the VH mode. Direct manipulation of the vφi and E×B shear using the drag produced by a nonaxisymmetric magnetic perturbation has produced clear changes in local transport, consistent with the E×B shear stabilization hypothesis. The implications of these results for theories of the L–H and H–VH transitions will be discussed.

Notes: Generation of the edge radial electric field and corresponding plasma rotation is studied for toroidal confinement systems with a separatrix configuration of magnetic surfaces. It is shown that classical acceleration of plasma by ion orbital losses can explain the electric field and the plasma rotation observed near walls when plasma flow to the neutralizing wall is included.

Notes: Using active feedback, the turbulent fluctuation levels have been reduced by as much as a factor of 2 in the edge of the Texas Experimental Tokamak (TEXT) [K. W. Gentle, Nucl. Fusion Technol. 1, 479 (1981)]. A probe system was used to drive a suppressor wave in the TEXT limiter shadow. A decrease in the local turbulence-induced particle flux has been seen, but a global change in the particle transport at the present time has not been observed. By changing the phase shift and gain of the feedback network, the amplitude of the turbulence was increased by a factor of 10.

Notes: In a series of three idealized magnetohydrodynamic (MHD) calculations in cylindrical geometry, we show that an azimuthal magnetic field can produce well-collimated jets by the pinch effect. In a laser-produced plasma, the magnetic field is generated by crossed density and temperature gradients (∇n×∇T), and may be responsible for the "imprint problem.'' In an astrophysical plasma, differential rotation associated with an accretion disk can generate the magnetic field, which may then be responsible for jet formation on stellar and galactic scales.

Notes: Ultrahigh intensity lasers can potentially be used in conjunction with conventional fusion lasers to ignite inertial confinement fusion (ICF) capsules with a total energy of a few tens of kilojoules of laser light, and can possibly lead to high gain with as little as 100 kJ. A scheme is proposed with three phases. First, a capsule is imploded as in the conventional approach to inertial fusion to assemble a high-density fuel configuration. Second, a hole is bored through the capsule corona composed of ablated material, as the critical density is pushed close to the high-density core of the capsule by the ponderomotive force associated with high-intensity laser light. Finally, the fuel is ignited by suprathermal electrons, produced in the high-intensity laser–plasma interactions, which then propagate from critical density to this high-density core. This new scheme also drastically reduces the difficulty of the implosion, and thereby allows lower quality fabrication and less stringent beam quality and symmetry requirements from the implosion driver. The difficulty of the fusion scheme is transferred to the technological difficulty of producing the ultrahigh-intensity laser and of transporting this energy to the fuel.

Notes: The gyrokinetic and gyrofluid models show the most promise for large scale simulations of tokamak microturbulence. This paper discusses detailed comparisons of these two complementary approaches. Past comparisons with linear theory have been fairly good, therefore the emphasis here is on nonlinear comparisons. Simulations include simple two-dimensional slab test cases, turbulent three-dimensional slab cases, and toroidal cases, each modeling the nonlinear evolution of the ion temperature gradient instability. There is good agreement in both turbulent and coherent nonlinear slab comparisons in terms of the ion heat flux, both in magnitude and scaling with magnetic shear. However, the nonlinear saturation level for ||Φ|| in the slab comparisons shows differences of approximately 40%. Preliminary toroidal comparisons show agreement within 50%, in terms of ion heat flux and saturation level.

Notes: A novel remote suppressor consisting of an injected ion beam has been used for the stabilization of plasma instabilities. A collisionless curvature-driven trapped-particle instability, an E×B flute mode and an ion temperature gradient (ITG) instability have been successfully suppressed down to noise levels using this scheme. Furthermore, the first experimental demonstration of a multimode feedback stabilization with a single sensor–suppressor pair has been achieved. Two modes (an E×B flute and an ITG mode) were simultaneously stabilized with a simple state-feedback-type method where more "state'' information was generated from a single-sensor Langmuir probe by appropriate signal processing. The above experiments may be considered as paradigms for controlling several important tokamak instabilities. First, feedback suppression of edge fluctuations in a tokamak with a suitable form of insulated segmented poloidal limiter sections used as Langmuir-probe-like suppressors is proposed. Other feedback control schemes are proposed for the suppression of electrostatic core fluctuations via appropriately phased ion density input from a modulated neutral beam. Most importantly, a scheme to control major disruptions in tokamaks via feedback suppression of kink (and possibly) tearing modes is discussed. This may be accomplished by using a modulated neutral beam suppressor in a feedback loop, which will supply a momentum input of appropriate phase and amplitude. Simple theoretical models predict modest levels of beam energy, current, and power.

Notes: Experimental work which uses Penning and Paul traps to confine non-neutral ion plasmas is discussed. Penning traps use a static uniform magnetic field and a static electric field to confine ions. The Paul trap uses the ponderomotive force from inhomogeneous radio-frequency fields to confine ions to a region of minimum field strength. In many atomic physics experiments, these traps are designed to produce a harmonic restoring force for small numbers of stored ions (〈104). Under these conditions and at low temperatures, both traps produce plasmas with simple shapes whose mode properties can be calculated exactly. Laser cooling has been used to reduce the temperature of trapped ions to less than 10 mK with ion spacings less than 20 μm. At such temperatures and interion spacings, the Coulomb potential energy between nearest neighbor ions is greater than the ion thermal energy and the ions exhibit spatial correlations characteristic of a liquid or crystal. Laser beams also apply a torque which, by changing the plasma angular momentum, changes the plasma density. Atomic clocks are an important application of ion trap plasmas. Better control of the plasma dynamics will reduce fluctuations in the relativistic time dilation, yielding better clocks.

Notes: Stability at high beta (the ratio of plasma pressure to magnetic field pressure) is an important requirement for a compact, economically attractive fusion reactor. It is also important in present large tokamak experiments, where the best performance is now often limited by instabilities rather than by energy transport. The past decade has seen major advances in our understanding of the stability of high beta tokamak plasmas, as well as in the achievement of high values of beta. Ideal magnetohydrodynamic (MHD) theory has been remarkably successful in predicting the stability limits, and the scaling of maximum stable beta with the normalized plasma current predicted by Troyon and others has been confirmed in many experiments, yielding a limit βmax≈3.5 (%-m-T/MA) I/aB (where I is the plasma current, a is the minor radius, and B is the toroidal field). The instabilities which are predicted to limit beta have been observed experimentally, in good agreement with theoretical predictions, including long-wavelength kink modes and short-wavelength ballooning instabilities. Advances in understanding of tokamak stability have opened several paths to higher values of beta. The use of strong discharge shaping, approaching the limits of axisymmetric stability, has allowed beta values as high as 12% to be reached in agreement with Troyon scaling. Recent experimental results and ideal MHD modeling have shown that the beta limit depends on the form of the pressure and current density profiles, and modification of the current density to create a centrally peaked profile has allowed beta values up to 6I/aB to be achieved experimentally.Recent experiments have also begun to explore both local and global access to the predicted second stable regime for ballooning modes, with the potential for very high values of β/(I/aB). Preliminary experimental investigations of wall stabilization and radio-frequency (RF) current profile control hold the promise of further improvements in beta through passive and active control of instabilities. The developing understanding of high beta stability and the application of this understanding to present experiments and future fusion devices hold the potential for production of stable, steady state plasmas at high beta with good confinement.

Notes: The onset of chaotic ion dynamics in electrostatic waves is investigated in a linear magnetized plasma. The existence of a threshold for heating in agreement with the predictions of single particle Hamiltonian theories and the fast time scale for velocity space diffusion are observed in the experiment. Measurements of test-particle dynamics indicate an exponential separation of initially close ion trajectories for amplitudes above the heating threshold. Ion orbits in the different wave–particle interaction regimes are inferred using an optical tagging diagnostic method, which provides the two point correlation function in phase space.

Notes: Recent high-fusion-triple-product and current drive experiments in the JAERI Tokamak-60 Upgrade (JT-60U) [Plasma Devices Oper. 1, 43 (1990)] are reported. The fusion triple product of 1.1×1021 m−3 s keV has been achieved in a more improved confinement mode (high-βp H-mode) in which the confinement is improved in the edge region as well as the core region. The most remarkable feature in the improved confinement mode is the multistage formation of transport barriers. The transport barrier was formed in the plasma interior first. After that, the transport barrier was formed in the edge region. For steady-state operation and current profile control, lower hybrid current drive (LHCD) and neutral beam current drive (NBCD) experiments with bootstrap current contribution are also in progress. Full current drive of 3.6 MA has been achieved at a density of 1.1×1019 m−3 with a current drive efficiency of ne⋅Rp⋅ICD/PLH=2.5×1019 m−2 A W−1 with a 5.7 MW LH wave injection. Current profile control with various LH wave spectra and with NBCD were also demonstrated.

Notes: In the Tokamak Fusion Test Reactor (TFTR) [International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Wurzburg, Paper No. A-2-2 (International Atomic Energy Agency, Vienna, 1993)] there have been at least three types of anomalous loss of alpha-like deuterium–deuterium (D–D) fusion products: (1) a magnetohydrodynamic (MHD)-induced loss of D–D fusion products correlated with Mirnov and fishbone-type oscillations and sawtooth crashes, (2) a slow "delayed'' loss of partially thermalized D–D fusion products occurring without large MHD activity, and (3) ion cyclotron resonance heating (ICRH)-induced loss of D–D fusion products ions observed during direct electron heating experiments, and possibly also during 3He minority heating. In this paper each of these will be reviewed, concentrating on those due to MHD activity, which are the largest of these anomalous losses. The experimental results are compared with numerical models of various fusion product transport mechanisms.