Showing papers in "Physics of Plasmas in 1995"

Development of the indirect‐drive approach to inertial confinement fusion and the target physics basis for ignition and gain

Abstract: Inertial confinement fusion (ICF) is an approach to fusion that relies on the inertia of the fuel mass to provide confinement. To achieve conditions under which inertial confinement is sufficient for efficient thermonuclear burn, a capsule (generally a spherical shell) containing thermonuclear fuel is compressed in an implosion process to conditions of high density and temperature. ICF capsules rely on either electron conduction (direct drive) or x rays (indirect drive) for energy transport to drive an implosion. In direct drive, the laser beams (or charged particle beams) are aimed directly at a target. The laser energy is transferred to electrons by means of inverse bremsstrahlung or a variety of plasma collective processes. In indirect drive, the driver energy (from laser beams or ion beams) is first absorbed in a high‐Z enclosure (a hohlraum), which surrounds the capsule. The material heated by the driver emits x rays, which drive the capsule implosion. For optimally designed targets, 70%–80% of the d...

Laboratory observation of the dust-acoustic wave mode

Abstract: A laboratory observation of the dust‐acoustic instability is reported. The results are compared with available theories.

Flow shear induced fluctuation suppression in finite aspect ratio shaped tokamak plasma

Abstract: The suppression of turbulence by the E×B flow shear and parallel flow shear is studied in an arbitrary shape finite aspect ratio tokamak plasma using the two point nonlinear analysis previously utilized in a high aspect ratio tokamak plasma [Phys. Plasmas 1, 2940 (1994)]. The result shows that only the E×B flow shear is responsible for the suppression of flute‐like fluctuations. This suppression occurs regardless of the plasma rotation direction and is, therefore, relevant for the very high (VH) mode plasma core as well as for the high (H) mode plasma edge. Experimentally observed in–out asymmetry of fluctuation reduction behavior can be addressed in the context of flux expansion and magnetic field pitch variation on a given flux surface. The adverse effect of neutral particles on confinement improvement is also discussed in the context of the charge exchange induced parallel momentum damping.

Helical temperature perturbations associated with tearing modes in tokamak plasmas

Abstract: An investigation is made into the electron temperature perturbations associated with tearing modes in tokamak plasmas. It is found that there is a critical magnetic island width below which the conventional picture where the temperature is flattened inside the separatrix is invalid. This effect comes about because of the stagnation of magnetic field lines in the vicinity of the rational surface and the finite parallel thermal conductivity of the plasma. Islands whose widths lie below the critical value are not destabilized by the perturbed bootstrap current, unlike conventional magnetic islands. This effect may provide an explanation for some puzzling experimental results regarding error field‐induced magnetic reconnection. The critical island width is found to be fairly substantial in conventional tokamak plasmas, provided that the long mean‐free path nature of parallel heat transport and the anomalous nature of perpendicular heat transport are taken into account in the calculation.

Ion-acoustic solitons in electron-positron-ion plasmas

Abstract: The ion‐acoustic solitons are investigated in three‐component plasmas, whose constituents are electrons, positrons, and singly charged ions. It is found that the presence of the positron component in such a multispecies plasma can result in reduction of the ion‐acoustic soliton amplitudes.

Field‐aligned coordinates for nonlinear simulations of tokamak turbulence

Abstract: Turbulence in tokamaks is characterized by long parallel wavelengths and short perpendicular wavelengths. A coordinate system for nonlinear fluid, gyrokinetic ‘‘Vlasov,’’ or particle simulations is presented that exploits the elongated nature of the turbulence by resolving the minimum necessary simulation volume: a long thin twisting flux tube. It is very similar to the ballooning representation, although periodicity constraints can be incorporated in a manner that allows E×B nonlinearities to be evaluated efficiently with fast Fourier transforms (FFT’s). If the parallel correlation length is very long, however, enforcing periodicity can introduce artificial correlations, so periodicity should not necessarily be enforced in the poloidal angle at θ=±π. This method is applied to high resolution three‐dimensional simulations of toroidal ion temperature gradient (ITG) driven turbulence, which predict fluctuation spectra and ion heat transport similar to experimental measurements.

Quantitative predictions of tokamak energy confinement from first‐principles simulations with kinetic effects

Abstract: A first‐principles model of anomalous thermal transport based on numerical simulations is presented, with stringent comparisons to experimental data from the Tokamak Fusion Test Reactor (TFTR) [Fusion Technol. 21, 1324 (1992)]. This model is based on nonlinear gyrofluid simulations, which predict the fluctuation and thermal transport characteristics of toroidal ion‐temperature‐gradient‐driven (ITG) turbulence, and on comprehensive linear gyrokinetic ballooning calculations, which provide very accurate growth rates, critical temperature gradients, and a quasilinear estimate of χe/χi. The model is derived solely from the simulation results. More than 70 TFTR low confinement (L‐mode) discharges have been simulated with quantitative success. Typically, the ion and electron temperature profiles are predicted within the error bars, and the global energy confinement time within ±10%. The measured temperatures at r/a≂0.8 are used as a boundary condition to predict the temperature profiles in the main confinement ...

Design and modeling of ignition targets for the National Ignition Facility

Abstract: Several targets are described that in simulations give yields of 1–30 MJ when indirectly driven by 0.9–2 MJ of 0.35 μm laser light. The article describes the targets, the modeling that was used to design them, and the modeling done to set specifications for the laser system in the proposed National Ignition Facility. Capsules with beryllium or polystyrene ablators are enclosed in gold hohlraums. All the designs utilize a cryogenic fuel layer; it is very difficult to achieve ignition at this scale with a noncryogenic capsule. It is necessary to use multiple bands of illumination in the hohlraum to achieve sufficiently uniform x‐ray irradiation, and to use a low‐Z gas fill in the hohlraum to reduce filling of the hohlraum with gold plasma. Critical issues are hohlraum design and optimization, Rayleigh–Taylor instability modeling, and laser–plasma interactions.

On the dynamics of turbulent transport near marginal stability

Abstract: A general methodology for describing the dynamics of transport near marginal stability is formulated. Marginal stability is a special case of the more general phenomenon of self‐organized criticality. Simple, one field models of the dynamics of tokamak plasma self‐organized criticality have been constructed, and include relevant features such as sheared mean flow and transport bifurcations. In such models, slow mode (i.e., large‐scale, low‐frequency transport events) correlation times determine the behavior of transport dynamics near marginal stability. To illustrate this, impulse response scaling exponents (z) and turbulent diffusivities (D) have been calculated for the minimal (Burgers’) and sheared flow models. For the minimal model, z=1 (indicating ballistic propagation) and D∼(S20)1/3, where S20 is the noise strength. With an identically structured noise spectrum and flow with shearing rate exceeding the ambient decorrelation rate for the largest‐scale transport events, diffusion is recovered with z=...

A dispersion function for plasmas containing superthermal particles

Abstract: It is now well known that space plasmas frequently contain particle components that exhibit high, or superthermal, energy tails with approximate power law distributions in velocity space. Such nonthermal distributions, with overabundances of fast particles, can be better fitted, for supra‐ and superthermal velocities, by generalized Lorentzian or kappa distributions, than by Maxwellians or one of their variants. Employing the kappa distribution, with real values of the spectral index κ, in place of the Maxwellian we introduce a new plasma dispersion function expected to be of significant importance in kinetic theoretical studies of waves in space plasmas. It is demonstrated that this function is proportional to Gauss’ hypergeometric function 2F1[1,2κ+2;κ+2;z] enabling the well‐established theory of the hypergeometric function to be used to manipulate dispersion relations. The reduction, for integer values of κ, to the less general so‐called modified plasma dispersion function [Phys. Fluids B 3, 1835 (1991...

Wavelet bicoherence: A new turbulence analysis tool

Abstract: A recently introduced tool for the analysis of turbulence, wavelet bicoherence [van Milligen, Hidalgo, and Sanchez, Phys. Rev. Lett. 16, 395 (1995)], is investigated. It is capable of detecting phase coupling—nonlinear interactions of the lowest (quadratic) order—with time resolution. To demonstrate its potential, it is applied to numerical models of chaos and turbulence and to real measurements. It detected the coupling interaction between two coupled van der Pol oscillators. When applied to a model of drift wave turbulence relevant to plasma physics, it detected a highly localized coherent structure. Analyzing reflectometry measurements made in fusion plasmas, it detected temporal intermittency and a strong increase in nonlinear phase coupling coinciding with the L/H (low‐to‐high confinement mode) transition.

Beyond paradigm: Turbulence, transport, and the origin of the radial electric field in low to high confinement mode transitions in the DIII-D tokamak

Abstract: The paradigm of shear suppression of turbulence as the mechanism for the low to high confinement mode (L to H) transition is examined by quantitative comparison of the predictions of the paradigm with experimental results from the DIII‐D tokamak [Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159]. The L to H transition trigger is V×B rotation, not the main ion pressure gradient. The radial electric field Er shear increases before the fluctuation suppression, consistent with increasing Er shear as the cause of the turbulence suppression. The spatial dependence of the turbulence reduction is consistent with shear suppression for negative Er shear. For positive Er shear, the turbulence suppression is consistent with the effect of Er curvature for modes for which an Er well is destabilizing. Finally, the transport barrier depends on the phase angle between the density and potential fluctuations inside the Er well, an effect not included in existing L to H...

Effect of toroidal plasma flow and flow shear on global magnetohydrodynamic MHD modes

Abstract: The effect of a subsonic toroidal flow on the linear magnetohydrodynamic stability of a tokamak plasma surrounded by an external resistive wall is studied. A complex non‐self‐adjoint eigenvalue problem for the stability of general kink and tearing modes is formulated, solved numerically, and applied to high β tokamaks. Results indicate that toroidal plasma flow, in conjunction with dissipation in the plasma, can open a window of stability for the position of the external wall. In this window, stable plasma beta values can significantly exceed those predicted by the Troyon scaling law with no wall. Computations utilizing experimental data indicate good agreement with observations.

Advances in the simulation of toroidal gyro Landau fluid model turbulence

Abstract: The gyro-Landau fluid (GLF) model equations for toroidal geometry have been recently applied to the study ion temperature gradient (ITG) mode turbulence using the 3D nonlinear ballooning mode representation (BMR). The present paper extends this work by treating some unresolved issues conceming ITG turbulence with adiabatic electrons. Although eddies are highly elongated in the radial direction long time radial correlation lengths are short and comparable to poloidal lengths. Although transport at vanishing shear is not particularly large, transport at reverse global shear, is significantly less. Electrostatic transport at moderate shear is not much effected by inclusion of local shear and average favorable curvature. Transport is suppressed when critical E{times}B rotational shear is comparable to the maximum linear growth rate with only a weak dependence on magnetic shear. Self consistent turbulent transport of toroidal momentum can result in a transport bifurcation at suffciently large r/(Rq). However the main thrust of the new formulation in the paper deals with advances in the development of finite beta GLF models with trapped electron and BMR numerical methods for treating the fast parallel field motion of the untrapped electrons.

Rotating nonlinear magnetic islands in a tokamak plasma

Abstract: The nonlinear dynamics of rotating low m (poloidal mode number) tearing modes in a tokamak with external resonant magnetic perturbations is examined. Nonlinear evolution equations for the island width and the toroidal rotation frequency are derived within the two‐fluid magnetohydrodynamic model, taking into account the plasma rotation and neoclassical parallel viscosity. The nonlinear stability of magnetic islands interacting with a static external magnetic perturbation is considered, and the critical magnetic field for the appearance of a locked mode is determined. It is shown that the coupling of the perpendicular and longitudinal plasma flow due to the neoclassical plasma viscosity enhances the amplitude of the critical magnetic field compared to the value obtained in a slab approximation. The perpendicular plasma viscosity causes a finite phase shift between the applied external field and the magnetic island, and further increases the value of the critical magnetic field required to induce a magnetic island.

Fast reconnection in high temperature plasmas

Abstract: Pressure forces acting on electrons are shown to dramatically alter magnetic field line reconnection in high temperature plasmas. The electron pressure introduces a new physical scale length ρs, the ion gyroradius based on the electron temperature, into the resistive magnetohydrodynamic (MHD) equations. The single dissipation layer of resistive MHD is split into two distinct layers by this effect: a very small inner current layer and a larger flow layer. Unlike resistive MHD, the current layer is microscopic in the outflow, as well as the inflow, direction. As a consequence, the current layer is not unstable to the formation of secondary magnetic islands at low values of resistivity and patchy reconnection does not occur. The absence of a strong current sheet in the outflow region enables the magnetic nozzle controlling the outflow to open up. The magnetic reconnection rate therefore remains large as the resistivity η and ρs become small.

Current and vorticity dynamics in three‐dimensional magnetohydrodynamic turbulence

Abstract: Spectral numerical simulations of homogeneous incompressible magnetohydrodynamic turbulence at Reynolds mumbers up to about 500, are performed using a uniform grid of 1803 collocation points. Strong vorticity and current sheets obtain both in the presence and in the absence of magnetic nulls. Contrary to vortex sheets in hydrodynamics, these structures do not destabilize into filaments, but are locally disrupted. They are the main loci of kinetic and magnetic dissipations.

Trapping and acceleration in nonlinear plasma waves

Abstract: The trapping and acceleration of a test electron in a nonlinear plasma wave is analyzed in one dimension using Hamiltonian dynamics. The plasma wave is described by a nonlinear, cold fluid model. The maximum energy gain and the minimum energy required for trapping of the test electron are determined. The separatrix is plotted for several values of plasma wave amplitude. In the large wave amplitude limit, the maximum energy of a trapped electron scales as 2γ2pE2z, where γp is the relativistic factor associated with plasma wave phase velocity and Ez is the electric field amplitude of the nonlinear plasma wave. This is in contrast to the well‐known results for a sinusoidal wave, in which the maximum energy scales as 4γ2pEz. As the nonlinear plasma wave approaches wavebreaking, the maximum energy is given by γmax→4γ3p−3γp, where γmax is the relativistic factor of the trapped electron.

Gyrokinetic particle simulation of neoclassical transport

Abstract: A time varying weighting (δf ) scheme for gyrokinetic particle simulation is applied to a steady‐state, multispecies simulation of neoclassical transport. Accurate collision operators conserving momentum and energy are developed and implemented. Simulation results using these operators are found to agree very well with neoclassical theory. For example, it is dynamically demonstrated that like‐particle collisions produce no particle flux and that the neoclassical fluxes are ambipolar for an ion–electron plasma. An important physics feature of the present scheme is the introduction of toroidal flow to the simulations. Simulation results are in agreement with the existing analytical neoclassical theory. The poloidal electric field associated with toroidal mass flow is found to enhance density gradient‐driven electron particle flux and the bootstrap current while reducing temperature gradient‐driven flux and current. Finally, neoclassical theory in steep gradient profile relevant to the edge regime is examine...

Nonlinear gyrokinetic Vlasov equation for toroidally rotating axisymmetric tokamaks

Abstract: The nonlinear gyrokinetic Vlasov equation is derived for an arbitrary magnetized plasma in a local reference frame moving with the nonuniform equilibrium fluid velocity u(r). The derivation of the guiding‐center and gyrocenter Hamilton equations, which appear as the characteristics of the gyrokinetic Vlasov equation, is based on the use of Lie‐transform perturbation techniques. Although a general form for u is initially used, attention is later focused on an incompressible toroidal equilibrium flow when considering axisymmetric tokamak geometry.

Hybrid magnetohydrodynamic‐gyrokinetic simulation of toroidal Alfvén modes

Abstract: Resonant energetic particles play a major role in determining the stability of toroidal Alfven eigenmodes (TAE’s) by yielding the well‐known driving mechanism for the instability and by producing an effective dissipation, which removes the singular character of local oscillations of the shear‐Alfven continuum and gives discrete kinetic Alfven waves (KAW’s). Toroidal coupling of two counterpropagating KAW’s generates the kinetic analog of the TAE, the KTAE (kinetic TAE). The nonperturbative character of this phenomenon and of the coupling between TAE and KAW’s, and the relevance of finite drift‐orbit effects limit the effectiveness of the analytical approach to asymptotic regimes, which are difficult to compare with realistic situations. A three‐dimensional hybrid fluid‐particle initial‐value code for the numerical simulation of the linear and nonlinear evolution of toroidal modes of the Alfven branch has been developed. It is shown that for typical parameters the KTAE is, indeed, more unstable than the TAE.

Computer simulation of a magnetohydrodynamic dynamo. II

Abstract: A computer simulation of a magnetohydrodynamic dynamo in a rapidly rotating spherical shell is performed. Extensive parameter runs are carried out changing electrical resistivity. When resistivity is sufficiently small, total magnetic energy can grow more than ten times larger than total kinetic energy of convection motion which is driven by an unlimited external energy source. When resistivity is relatively large and magnetic energy is comparable or smaller than kinetic energy, the convection motion maintains its well‐organized structure. However, when resistivity is small and magnetic energy becomes larger than kinetic energy, the well‐organized convection motion is highly irregular. The magnetic field is organized in two ways. One is the concentration of component parallel to the rotation axis and the other is the concentration of perpendicular component. The parallel component tends to be confined inside anticyclonic columnar convection cells, while the perpendicular component is confined outside convection cells.

Helicon wave excitation with helical antennas

Abstract: Components of the wave magnetic field in a helicon discharge have been measured with a single‐turn, coaxial magnetic probe. Left‐ and right‐handed helical antennas, as well as plane‐polarized antennas, were used; and the results were compared with the field patterns computed for a nonuniform plasma. The results show that the right‐hand circularly polarized mode is preferentially excited with all antennas, even those designed to excite the left‐hand mode. For right‐hand excitation, the radial amplitude profiles are in excellent agreement with computations.

Industrial applications of low-temperature plasma physics

Abstract: The application of plasma physics to the manufacturing and processing of materials may be the new frontier of our discipline. Already partially ionized discharges are used in industry, and the performance of plasmas has a large commercial and technological impact. However, the science of low‐temperature plasmas is not as well developed as that of high‐temperature, collisionless plasmas. In this paper several major areas of application are described and examples of forefront problems in each are given. The underlying thesis is that gas discharges have evolved beyond a black art, and that intellectually challenging problems with elegant solutions can be found.

Resistive drift‐wave turbulence

Abstract: Two‐dimensional resistive drift‐wave turbulence is studied by high‐resolution numerical simulations in the limit of small viscosity. Density and potential fluctuations are cross‐coupled by resistive dissipation, proportional to the adiabaticity parameter, C, which determines the character of the system: adiabatic (C≫1) or hydrodynamic (C≪1). Various cases are computed for 0.1≤C≤5. Energy spectra exhibit a maximum at some wave number k0(C) and an inertial range behavior for k≳k0. The transfer of energy and vorticity is directly computed and confirms the persistence of local cascade dynamics in all regimes: the familiar dual cascade for the E×B flow eddies, and the direct cascade to small scales for the density as it is advected by the eddies. Inertial range spectral power laws agree surprisingly well with simple scaling predictions. No prominent large‐scale long‐lived coherent structures are observed, an absence that is consistent with the statistical properties, which are found to be perfectly Gaussian for k≲k0, but exhibit the non‐Gaussian behavior, typical for small‐scale intermittency, in the inertial range.

The frequency and damping of ion acoustic waves in hydrocarbon (CH) and two‐ion‐species plasmas

Abstract: The kinetic theory of ion‐acoustic waves in multi‐ion‐species plasmas is discussed. Particular application is made to hydrocarbon (CH) plasmas, which are widely used in laser–plasma experiments. The mode frequencies and Landau damping of the two, dominant, ion‐acoustic modes in CH plasmas are calculated by numerical solution of the kinetic dispersion relation. In addition, some useful results are obtained analytically from expansions of the kinetic dispersion relation and from fluid models. However, these results disagree with the numerical results in domains of particular practical interest. When ion temperatures exceed two‐tenths of the electron temperature, the least damped mode is the one with the smaller phase velocity, and this mode is then found to dominate the ponderomotive response of the CH plasma.

Single‐mode and multimode Rayleigh–Taylor experiments on Nova

Abstract: Rayleigh–Taylor (RT) experiments have been conducted with planar CH(Br) foils accelerated by x‐ray ablation from a shaped, low adiabat drive. The surface perturbations investigated consisted of single‐mode, two‐mode, and eight‐mode sinusoids. The perturbation evolution begins during the shock transit phase, when perturbations show gradual growth due to Richtmyer–Meshkov‐like dynamics. After shock breakout, the compressed foils accelerate and perturbation growth continues due to the Rayleigh–Taylor instability. Detailed comparisons with simulations indicate that in the linear Rayleigh–Taylor regime, the single‐mode perturbations grow exponentially in time. In the nonlinear regime, the growth slows and the perturbation shape changes from sinusoidal to ‘‘bubble and spike’’ with the appearance of higher Fourier harmonics. In the multimode perturbations, the individual modes grow independently in the linear regime, but become coupled in the nonlinear regime. In addition to the higher harmonics of the individua...

Red sprites and blue jets: Thunderstorm‐excited optical emissions in the stratosphere, mesosphere, and ionosphere

Abstract: Recent low light level monochrome television observations obtained from the ground and from the space shuttle, and low light level color and monochrome television images obtained from aboard jet aircraft, have shown that intense lightning in mesoscale thunderstorm systems may excite at least two distinct types of optical emissions that together span the space between the tops of some thunderstorms and the ionosphere. The first of these emissions, dubbed ‘‘sprites,’’ are luminous red structures that typically span the altitude range 60–90 km, often with faint bluish tendrils dangling below. A second, rarer, type of luminous emission are ‘‘blue jets’’ that appear to spurt upward out of the anvil top in narrow cones to altitudes of 40–50 km at speeds of ∼100 km/s. In this paper the principal observational characteristics of sprites and jets are presented, and several proposed production mechanisms are reviewed.

An experimental counter‐example to the local transport paradigm

Abstract: The response of a tokamak discharge to a sharp drop in edge temperature differs significantly from that expected from typical local transport models in several important respects. Laser ablation of carbon induces large (ΔT/T≤70%), rapid (<200 μs) electron temperature drops in the outermost region of the plasma, r/a≥0.9. This cold pulse proceeds through the outer plasma (r/a≥0.75), rapidly compared with power balance or sawtooth predictions. However, the pulse shrinks markedly thereafter, disappearing near r/a∼0.5. Within r/a∼0.3, the temperature rises promptly. The results are inconsistent with conventional local transport models; a nonlocal phenomenology, in which transport coefficients increase in the edge and decrease in the core, is suggested. The turbulence levels measured with a heavy ion beam probe increase near the edge but are unchanged in the core.

Stabilization of ideal modes by resistive walls in tokamaks with plasma rotation and its effect on the beta limit

Abstract: It is shown that pressure‐driven, ideal external modes in tokamaks can be fully stabilized by resistive walls with plasma rotation. For wall stabilized plasmas, there are two types of potentially unstable external modes: (i) the ‘‘resistive wall modes’’ that penetrate, and are nearly locked to the wall, and (ii) modes that rotate with the plasma and for which the wall acts as a good conductor. For the quickly rotating modes, the stabilizing effect of the wall increases when the wall is brought closer to the plasma, while for the resistive wall modes, the stabilization improves with increasing wall distance. When the plasma rotates at some fraction of the sound speed, there is a window of stability to both the wall‐locked and the rotating mode. The stabilization depends principally on the toroidal coupling to sound waves and is affected by ion Landau damping. Two‐dimensional stability calculations are presented to evaluate the gains in beta limit resulting from this wall stabilization for different equilibria and rotation speeds. Results are shown for advanced tokamak configurations with bootstrap fractions of ≊100%.