Index of content:
Volume 2, Issue 11, November 1995

Development of the indirect‐drive approach to inertial confinement fusion and the target physics basis for ignition and gain
View Description Hide DescriptionInertial 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 driver energy can be converted to x rays. The optimal hohlraum geometry depends on the driver. Because of relaxed requirements on laser beam uniformity, and reduced sensitivity to hydrodynamic instabilities, the U.S. ICF Program has concentrated most of its effort since 1976 on the x‐ray or indirect‐drive approach to ICF. As a result of years of experiments and modeling, we are building an increasingly strong case for achieving ignition by indirect drive on the proposed National Ignition Facility (NIF).
The ignition target requirements for hohlraum energetics, radiation symmetry, hydrodynamic instabilities and mix, laser plasma interaction, pulse shaping, and ignition requirements are all consistent with experiments. The NIF laser design, at 1.8 MJ and 500 TW, has the margin to cover uncertainties in the baseline ignition targets. In addition, data from the NIF will provide a solid database for ion‐beam‐driven hohlraums being considered for future energy applications. In this paper we analyze the requirements for indirect drive ICF and review the theoretical and experimental basis for these requirements. Although significant parts of the discussion apply to both direct and indirect drive, the principal focus is on indirect drive.

On the dispersion relation of longitudinal waves in equilibrium plasmas
View Description Hide DescriptionThe dispersion relation of subluminal longitudinal waves in thermal non‐degenerated isotropic equilibrium plasmas is investigated. The dispersion relation is derived from the relativistically correct form of the kinetic plasmaequations and the appropriate Maxwell–Boltzmann–Jüttnerplasma equilibriumdistribution function. A simple analytic expression for the real part of the dispersion relation is obtained, which holds for all values of the plasma temperature and the index of refraction and improves earlier infinite series approximations. The new form of the dispersion function allows the derivation in implicit form of the wavenumber, real part and imaginary part (for weak damping) of all possible subluminal longitudinal plasma modes. The relativistically correct analysis leads to markedly different result than previous non‐relativistic work. The results are illustrated for a one‐component electron plasma and a two‐component electron‐ion plasma. In both cases it is found that Langmuir waves and sound waves are asymptotic solutions of the same longitudinal plasma mode and that they only occur for wavelengths above the electron thermal Debye length. While superluminal Langmuir waves have no Landau damping, subluminal Langmuir waves undergo weak Landau damping. The derived damping rate of subluminal Langmuir waves differs by orders of magnitude from the decrement derived by Landau and corrected by Jackson on the basis of non‐relativistic equations.

How fluctuations continue through an X point
View Description Hide DescriptionThe structure of waves around a magnetic X point is analyzed. A paradox is noted, in which theory implies that waves cannot propagate along the field past an X point, but experiment shows that they do anyway. The paradox may arise from the theoretical ‘‘eikonal in the perpendicular direction’’ ansatz, in which waves follow field lines to lowest order. This paper demonstrates that waves can encounter a boundary layer in which this ansatz is violated. Such waves can propagate around the X‐point region, thus avoiding the large wave number increase from magnetic shear, allowing them to correlate through such a region. This result has some unexpected implications concerning mode structure in the edge and scrape‐off layer of a diverted tokamak, and possibly for the core as well.

Analysis of transient and asymptotic behavior in relativistic Landau damping
View Description Hide DescriptionRelativistic electrostaticoscillations in a collisionless nonmagnetized plasma are considered. An integral form of the Vlasov–Poisson problem is solved numerically and both the transient and the asymptotic behavior of the electric field are calculated in a very accurate way. The existence of a critical value for the wave number, under which no Landau damping occurs, has been verified, and the asymptotic behavior of the oscillations in the one‐dimensional kinetic model has been evaluated. Some errors have been found in previously published analytical expressions. A new expression is proposed and verified numerically. An analytical expression of the asymptotic behavior for full three‐dimensional kinetic model is deduced and numerically tested.

Application of the kinetic transport theory to a unified treatment of longitudinal perturbations in neutral and charged gases
View Description Hide DescriptionA uniform treatment of longitudinal waves or wave‐like perturbations in neutral gases and plasmas is presented, using the method of kinetic transporttheory in conjunction with a ten‐moment collision model. The perturbations are considered to be generated by an oscillating boundary, and their spatial evolution for given frequency is investigated. Special emphasis is placed on the damping of the perturbations, as apparent from their spatial decay. The close intrinsic relation between longitudinal perturbations in plasmas and neutral gases is revealed by systematic variation of the collision to wave frequency ratio and of the charge number. The strong damping of neutral sound found in the small collision frequency limit is seen to be a continuous extension of Landau damping, either of ion‐acoustic or Langmuir waves, when starting at the full charge number and reducing the latter to zero. Application of the present theory to experimental neutral sound data leads to almost quantitative agreement, from the near‐collisionless to the collision‐dominated limit.

High harmonic fast waves in high beta plasmas
View Description Hide DescriptionHigh harmonic fast magnetosonic waves in high beta plasmas are investigated. In the high beta regime, a combination of reduced group velocity and a high beta enhancement of magnetic pumping lead to such large values of electron absorption that one can expect strong (≊100%) single pass absorption. In particular, by controlling the wave spectrum, the prospect of localized electron heating and current drive appears to be feasible in high beta low‐aspect‐ratio tokamak regimes. Inclusion of finite‐Larmor‐radius terms reveals an accessibility limit in the high ion beta regime (β_{ i }≊50% for a deuterium plasma) due to mode conversion into an ion‐Bernstein‐wave‐like mode. No similar beta limit is expected for electrons. With increasing ion beta, the ion damping can increase significantly, particularly near the mode‐conversion accessibility limit. The presence of an energetic ion component expected during intense neutral beam injection and α heating does not appear to modify the accessibility condition nor cause excessive wave absorption by the energetic ions.

Pulsed currents carried by whistlers. V. Detailed new results of magnetic antenna excitation
View Description Hide DescriptionA low frequency, oblique whistler wave packet is excited from a single current pulse applied to a magnetic loop antenna. The magnetic field is mapped in three dimensions. The dominant angle of radiation is determined by the antenna dimensions, not by the resonance cone. Topological properties of the inductive and space charge electric fields and space charge density confirm an earlier physical model. Transverse currents are dominated by Hall currents, while no net current flows in the parallel direction. Electron‐ion collisions damp both the energy and the helicity of the wave packet. Landau damping is negligible. The radiation resistance of the loop is a few tenths of an Ohm for the observed frequency range. The loop injects zero net helicity. Rather, oppositely traveling wave packets carry equal amounts of opposite signed helicity.

Axial propagation of helicon waves
View Description Hide DescriptionTraveling‐ and standing‐wave characteristics of the wave fields have been measured in a helicon discharge using a five‐turn, balanced magnetic probe movable along the discharge axis z. Helical and plane‐polarized antennas were used, and the magnitude and direction of the static magnetic field were varied, yielding three primary results. (1) As the density varies along z, the local wavelength agrees with the local dispersion relation. (2) Beats in the z variation of the wave intensity do not indicate standing waves, but instead are caused by the simultaneous excitation of two radial eigenmodes. Quantitative agreement with theory is obtained. (3) The damping rate of the helicon wave is consistent with theoretical predictions based on collisions alone.

Fast nonlinear magnetic reconnection
View Description Hide DescriptionThe nonlinear evolution of magnetic reconnection in collisionless and weakly collisional regimes is analyzed on the basis of a two‐dimensional incompressible fluidmodel. The initial equilibria are unstable to tearing modes. In the limit where the stability parameter Δ′ is relatively large, the mode structure is characterized by global convective cells. It is found that the system exhibits a quasiexplosive time behavior in the early nonlinear stage, where the fluid displacement is larger than the inertial skin depth but smaller than the typical size of the convective cells. The reconnection time is an order of magnitude shorter than the Sweet–Parker time for values of the inertial skin depth, of the ion Larmor radius, and of the magnetic Reynolds number typical of the core of magnetic fusion experiments. The reconnection process is accompanied by the formation of a current density sublayer narrower than the skin depth. In the strict dissipationless limit, this sublayer shrinks indefinitely in time. Physical mechanisms limiting this tendency to a singular current density profile are also discussed.

Spreading particle trajectories near a perfectly reflecting surface in a tilted magnetic field
View Description Hide DescriptionA description is given for electron trajectories near a specularly reflecting surface in a magnetic field that intersects the surface at a shallow angle. A simple analytical theory of electron motion is presented. It is shown that an electron experiences a large number of reflections from the wall and makes a long path along the surface, before eventually returning to the plasma. The importance of this phenomenon for the sheath structure and electron cross‐field transport is briefly discussed.

Large amplitude ion‐acoustic waves in a plasma with an electron beam
View Description Hide DescriptionThe nonlinear wave structures of large amplitude ion‐acoustic waves are studied in a plasma with an electron beam, by the pseudopotential method. The region of the existence of large amplitude ion‐acoustic waves is examined, showing that the condition of the existence sensitively depends on the parameters such as the electron beamtemperature, the ion temperature, the electrostatic potential, and the concentration of the electron beam density. It turns out that the region of the existence spreads as the beam temperature increases but the effect of the electron beam velocity is relatively small. New findings of large amplitude ion‐acoustic waves in a plasma with an electron beam are predicted.

Analytical criteria for nonlinear instability of thermal structures
View Description Hide DescriptionAnalytical criteria for supercritical and asymptotic stability and for subcritical and superexponential instability are obtained for slab‐like, spherical, and cylindrical thermal structures. It is assumed that both, the thermal conductivity κ(T) and the gain/loss function Q(T), can be written as continuous functions of the temperature and they have continuous derivatives. Conditions on κ and Q under which the symmetry of the structure determines the kind of instability (or stability) are obtained. Additionally, it is found that the response of the structure not only depends on the amplitude of the disturbance, but also on whether the disturbance increases or decreases the initial steady temperature. In particular, the threshold value for the amplitude of the disturbances beyond which a linearly stable configuration destabilizes, and explicit conditions for catastrophic heating or cooling are obtained. Applications to structures constituted by atomic and molecular gas are outlined.

Electrostatic shock wave in dusty plasmas
View Description Hide DescriptionThe present investigation reports the existence of a one‐dimensional (1‐D) shock wave profile for a weakly nonlinear modified acoustic‐like/dust‐acoustic waves. Here, unlike in the conventional plasma systems, the dissipative effect to balance the nonlinear steepening arises self‐consistently due to dust charge fluctuationdynamics in response to the collective plasma oscillations. The possibility of other localized coherent structures like dissipative/dispersive solitons in higher‐order solutions has been highlighted. Its implications in laboratory and space plasmas are discussed.

Self‐sustained plasma turbulence due to current diffusion
View Description Hide DescriptionPlasma turbulence and anomalous transport by the electrostatic current diffusive interchange mode are studied by the nonlinear simulation based on the magnetohydrodynamicmodel. The turbulence is found to have a typical characteristic of subcritical turbulence. The saturation level, as a function of the pressure gradient ∇p, is confirmed to scale like ‖∇p‖^{3/2}. This nature holds independent of the ratio ‖∇p‖/‖∇p _{ c }‖ where ‖∇p _{ c }‖, is a critical pressure gradient against linear instability. The turbulence‐driventransport is also evaluated. The simulation result confirms the theoretical prediction, which is based on the self‐sustained turbulence, with respect to the nonlinear growth and damping. Both the normal cascade and inverse cascade are essential in establishing the stationary turbulent state.

Nonlinear instability and chaos in plasma wave–wave interactions. II. Numerical methods and results
View Description Hide DescriptionIn Part I of this work [Phys. Plasmas2, 1926 (1995)], the behavior of linearly stable, integrable systems of waves in a simple plasmamodel was described using a Hamiltonian formulation. Explosive instability arose from nonlinear coupling between positive and negative energy modes, with well‐defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. The time evolution is modeled with an explicit symplectic integrator derived using Lie algebraic methods. For amplitudes large enough to support two‐wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region in phase space. Diffusive growth then leads to explosive instability, effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, slow growth via Arnold diffusion might still lead to instability; however, this was not observed in numerical experiments. The diffusion rate is probably underestimated in this simple model.

Ampère and Hall nonlinearities in the magnetic dynamo in the Arnol’d–Beltrami–Childress (ABC) flow
View Description Hide DescriptionThe effect of different nonlinearities (Ampère force and Hall effect) on the saturation of a magnetic field generated by flows of conducting fluid is studied by means of numerical simulations. A three‐fluid (i.e., ions, electrons, and neutral particles) model is considered. The velocity field of the neutral particles is a prescribed, deterministic, incompressible three‐dimensional field in the form of the Arnol’d–Beltrami–Childress (ABC) flow. The dynamics of the charged components of fluid is determined by two‐fluid magnetohydrodynamics when ion–neutral particle collisions are taken into account. Four typical regimes of the nonlinear evolution of the magnetic field, corresponding to different types of nonlinearities (Ampère force or Hall effect) and different types of collisions (ion–ion collisions or ion–neutral particle collisions) are found. The transitions between these regimes, the structure of the saturated magnetic field, and the evolution of the magnetic field in these regimes are studied. Scaling estimates of the level of the saturated magnetic field and conditions obtained for the different regimes of the magnetic field evolution are in agreement with the results of the numerical simulations.

Return current instability in laser heated plasmas
View Description Hide DescriptionThe localized heating of an underdense plasma by a focused laser beam has been studied with a kinetic Fokker–Planck code. Simulations show an inhibition of the electron heat flux in the region where temperature gradients are maximized. A time analysis of electron distribution function demonstrates that the heat flux inhibition does not interfere with the excitation of the return current ion acoustic instability. The conditions for onset of the instability and its possible effect on plasma transport are also discussed.

Shear‐flow generation by drift/Rossby waves
View Description Hide DescriptionThe generation of shear flow driven by a large amplitude drift wave, represented by the Hasegawa–Mima–Charney (HMC) equation, has been investigated. It is shown that, besides a finite amplitude threshold for the shear flow instability to occur, there is also a necessary condition on the aspect ratio of the large amplitude drift wave, due to conservation of the average potential vorticity, that needs to be satisfied. A comprehensive comparison of the shear‐flow instability criterion for the HMC equation and the incompressible, invisicid, hydrodynamic equation has been undertaken.

Characteristic speeds in high β isotropic/anisotropic plasmas
View Description Hide DescriptionGiven the importance of linear mode properties (e.g., characteristic speeds) in identification/classification of discontinuities, a detailed comparison between the mode properties in fluid theory and kinetic theory in high β plasmas is carried out. It is found that conventional fluid theories of linear modes in both isotropic and anisotropic plasmas do not yield the correct mode properties, even in the long‐wavelength limit. In particular, fluid phase velocities are very sensitive to the model and parameters (polytropic indices) employed. Because of this, fluid theory loses its predictive power. In linear kinetic theory, modes cannot be ordered according to their phase velocities. For instance, at small and moderate propagation angles, the slow/sound (S/SO) mode can have the fastest phase velocity. In such cases, a (quasiparallel) fast shock would be associated with the S/SO mode rather than the usual fast/magnetosonic (F/MS) mode. This has important implications for fast shocks. Since it is the F/MS rather than S/SO mode that connects to the whistler branch, low Mach number quasiparallel shocks associated with S/SO would not be expected to have a phase standing whistler wave train upstream, and their thickness is determined by dissipation rather than dispersion. The consequences of the kinetic modeproperties are demonstrated via hybrid simulations (fluid electron, kinetic ions) using the quasiparallel shock as an example.

Wave‐induced chaotic radial transport of energetic electrons in a laboratory terrella experiment
View Description Hide DescriptionThis paper reports the observation of wave‐induced chaotic radial transport of energetic electrons in a laboratory terrella, the Collisionless Terrella Experiment (CTX) [H. P. Warren and M. E. Mauel, Phys. Rev. Lett. 74, 1351 (1995)]. Electron cyclotron resonance heating is used to create a localized population of energetic electrons which excite the hot electroninterchange instability. The electrostaticfluctuations driven by this instability have time‐evolving spectra which resonate with the precessional drift motion of the hot electrons. We have established that the amplitude, frequency, and azimuthal mode number of the observed instabilities meet the conditions for the onset of chaotic particle motion. Electrontransport is observed with a gridded particle detector. Increases in the flux of energetic particles to the detector are well correlated with the presence of fluctuations which meet the conditions for global chaos. Greatly diminished transport is observed when the fluctuations lead to thin, radially localized bands of chaos. The flux of energetic electrons to the detector is strongly modulated. By examining time‐dependent Hamiltonian phase space flows, the modulation is shown to be the result of phase space correlations. A transport simulation based on the Hamiltonian motion of energetic electrons reproduces the frequency and modulation depth of the observed electron flux and allows for comparison between the Hamiltonian and quasilinear descriptions of transport.