Volume 11, Issue 2, February 2004
 REVIEW ARTICLE


The physics basis for ignition using indirectdrive targets on the National Ignition Facility
View Description Hide DescriptionThe 1990 National Academy of Science final report of its review of the Inertial Confinement Fusion Program recommended completion of a series of target physics objectives on the 10beam Nova laser at the Lawrence Livermore National Laboratory as the highestpriority prerequisite for proceeding with construction of an ignitionscale laser facility, now called the National Ignition Facility (NIF). These objectives were chosen to demonstrate that there was sufficient understanding of the physics of ignition targets that the laser requirements for laboratory ignition could be accurately specified. This research on Nova, as well as additional research on the Omega laser at the University of Rochester, is the subject of this review. The objectives of the U.S. indirectdrive target physics program have been to experimentally demonstrate and predictively modelhohlraum characteristics, as well as capsule performance in targets that have been scaled in key physics variables from NIF targets. To address the hohlraum and hydrodynamic constraints on indirectdrive ignition, the target physics program was divided into the Hohlraum and Laser–Plasma Physics (HLP) program and the Hydrodynamically Equivalent Physics(HEP) program. The HLP program addresses laser–plasma coupling, xray generation and transport, and the development of energyefficient hohlraums that provide the appropriate spectral, temporal, and spatial xray drive. The HEP experiments address the issues of hydrodynamic instability and mix, as well as the effects of flux asymmetry on capsules that are scaled as closely as possible to ignition capsules (hydrodynamic equivalence). The HEP program also addresses other capsule physics issues associated with ignition, such as energy gain and energy loss to the fuel during implosion in the absence of alphaparticle deposition. The results from the Nova and Omega experiments approach the NIF requirements for most of the important ignition capsule parameters, including drive temperature, drive symmetry, and hydrodynamic instability. This paper starts with a review of the NIF target designs that have formed the motivation for the goals of the target physics program. Following that are theoretical and experimental results from Nova and Omega relevant to the requirements of those targets. Some elements of this work were covered in a 1995 review of indirectdrive [J. D. Lindl, “Development of the indirectdrive approach to inertial confinement fusion and the target physics basis for ignition and gain,” Phys. Plasmas 2, 3933 (1995)]. In order to present as complete a picture as possible of the research that has been carried out on indirect drive, key elements of that earlier review are also covered here, along with a review of work carried out since 1995.
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 LETTERS


Observation of collisionless inward propagation of electrons into helical vacuum magnetic surfaces via stochastic magnetic fields
View Description Hide DescriptionElectrons are injected into a stochastic magnetic region (SMR) of a stellarator vacuum configuration. Remarkably, when the SMR is present, some fieldfollowing electrons in the SMR move inwardly across the last closed flux surface. This inward propagation occurs in a collisionless process, but it is never observed for cases where the SMR is lost, nor is the electron density small in the SMR. These suggest the existence of crossfield transport that is associated with freestreaming of electrons along the stochastically wandering field lines in the SMR.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Kinetic theory of dusty plasmas. V. The hydrodynamic equations
View Description Hide DescriptionThe collisional hydrodynamicequations for electrons, ions, and dust particles in dusty plasmas are derived from the kinetic equations [V. N. Tsytovich and U. de Angelis, Phys. Plasmas 6, 1093 (1999)] which consistently take into account the elastic and inelastic (charging) collisions of plasma particles with dust and the effects of dust charge fluctuations. These equations are valid in the parameter regime where the collisions of plasma particles with dust dominate with respect to the binary plasma collisions. New expressions for the fluid collision frequencies, transport coefficients, viscosity, and ion drag are found and compared with previous results.

Generalized electron Bernstein modes in a plasma with a kappa velocity distribution
View Description Hide DescriptionPerpendicularly propagating electron Bernstein modes in a uniformly magnetized plasma having an isotropic kappa velocity distribution are investigated within the framework of a fully electromagneticplasmamodel but one which ignores particle relativistic effects. The dispersion relations for the Bernstein mode waves are found to be significantly dependent on the spectral index, κ, of the electron kappa distribution. In particular, waves with frequencies exceeding the upper hybrid frequency are seen to occupy a diminishing range of frequencies above the nearest cyclotron harmonic as κ is reduced. The Bernstein mode wave whose frequency lies closest to the upper hybrid frequency is found to couple to the cold plasma,electromagneticZ mode, as it does in a Maxwellianplasma. For waves whose frequencies lie below the upper hybrid frequency, diminishing κ gives rise to an increasingly weak dependence of frequency on wave number and a slower frequency fall off with this parameter, but the frequency occupies the entire intraharmonic band here. All Bernstein modes are observed to become significantly electromagnetic at very long wavelengths, or small wave numbers, having in general elliptical polarization whose elliptical eccentricity depends on κ and wave number. At smaller wavelengths the modes are found to be electrostatic to a very good approximation, irrespective of κ value. The significance of the results to the interpretation of banded emissions in planetary magnetospheres is briefly discussed.

Thermal instability of ionized dusty plasmas
View Description Hide DescriptionWe investigate the role of thermal instability, arising from radiative cooling of an optically thin, ionized, dusty plasma, by linear stability analysis. The corresponding isobaric stability condition for condensation mode is found to be modified significantly by the concentration of finite sized, relatively heavy, and negatively charged dust particles. It has been shown that the radiation condensation mode is severely affected by the presence of dust particles. A distinct departure from the classical behavior (Field 1965) is that the existence of unstable acoustic modes depends on the dustcharge fluctuation parameter and is not affected by the cooling through radiation.

Lowfrequency instabilities in a laboratory magnetized plasma column
View Description Hide DescriptionA detailed analysis of the phase velocity of unstable lowfrequency waves is performed in a laboratory magnetized plasma column. The measurement of the radial profiles of the density, electron temperature and plasma potential allows to determine the radial profile of the electric drift velocity and electron diamagnetic drift for increasing values of the magnetic field. In the case of a large diameter plasma column, only diamagneticdrift waves without Doppler shift occur. On the other hand, in the case of a restricted diameter plasma column, the radial electric field induces a rotation of the plasma column. At low magnetic field the recorded unstable waves are in that case flute modes propagating azimuthally at the drift velocity.

Excitation of electron Bernstein waves by a gyrating relativistic electron beam in a plasma slab
View Description Hide DescriptionA nonlocal theory of excitation of electron Bernstein waves in a magnetized plasma column by a gyrating relativistic electron beam has been developed. The beam response is obtained using the Vlasov equation. For a onedimensional parabolic density profile of the background plasma, the mode structure equation yields Hermite polynomial eigenfunctions. The growth of the Bernstein wave occurs via a fast cyclotron interaction. For a typical case when the electron cyclotron frequency is comparable to the electron plasma frequency and beam velocity the growth rate is maximum for The nonlocal effects reduce the growth rate.

Magneticcurvaturedriven interchange modes in dusty plasmas
View Description Hide DescriptionThe magneticcurvaturedriven interchange mode instability of a weakly inhomogeneous dusty plasma is rigorously investigated. It is shown that the electric drift convection of the equilibrium dust charge density is a stabilizing factor for long wavelength interchange modes. In a fully nonlinear regime, the finite amplitude interchange modes may selforganize in the form of a dipolar vortex. The present results should be useful in the understanding of the properties of the interchange mode turbulence in nonuniform magnetized plasmas containing charged dust particles.

Stability of drift waves in the presence of dust
View Description Hide DescriptionIn the presence of dust particles in the plasma, it is shown that the wellknown stability of the drift wave in a sheared slab geometry does not hold. Due to the presence of dust particles in tokamaks, the magnetic shear damping is reduced drastically. As a result, both the collisionless and collisional (dissipative) drift modes become unstable under the typical parameter regimes of a tokamak. Consequently, drift waves must still be considered as an underlying dynamic of anomalous transport in tokamak edges, where dust particles are found to be abundant.
 Nonlinear Phenomena, Turbulence, Transport

Landau damping
View Description Hide DescriptionThe damping of a longitudinal plasma wave of finite amplitude is considered. It is shown that the Landau result is the first term in a systematic expansion in a small parameter, and the corrections for finite wave amplitude are shown to be fifth order in the small parameter. The contributions to the damping from particles with different velocities near the phase velocity are explicitly calculated and this leads to a simple physical picture of the damping process.

Spectral energy transfer and generation of turbulent structures in toroidal plasma
View Description Hide DescriptionNonlinear energy cascades in turbulent spectra are studied in the H1 toroidalheliac [S. M. Hamberger et al., Fusion Technol. 17, 123 (1990)] using the spectral energy transfer estimation and the amplitude correlation technique. An inverse energy cascade of the spectral energy from the unstable range is shown to be responsible for the generation of the largescale coherent structures dominating turbulence spectra. Among such structures are zonal flows which are also found to be generated via the inverse cascade. The generation of zonal flows is correlated with the increased strength in the nonlinear energy transfer. The onset of the strongly sheared radial electric field across the low–high (L–H) transition dramatically changes the energy transfer in the spectra and the spectral power of the fluctuations.

Streamer formation and collapse in electron temperature gradient driven turbulence
View Description Hide DescriptionA simple model is useful to understand the formation and persistence of radially elongated structures (streamers) in electron temperature gradient (ETG) driven modes. The ETG model is very similar to the thermal Rossby wave model, a system of broad interest. The detailed correspondence of these two models is discussed. Streamer formation in this simple model is analyzed using the modulational stability method. In the inviscid limit of the model, an amplitude equation similar to the nonlinear Schrödinger equation (NLS) is derived. This equation has a second derivative cubic nonlinearity and is identified as a special case of a more general higher order NLS. Analytical solutions are found in the form of travelling waves and a localized thorn. Using the Lagrangian structure of the amplitude equation, it is shown that onedimensional collapse in the poloidal direction is possible in this system for certain parameter values, and for sufficiently localized inital flow. This identifies a parameter regime basin in which there is an attractor with the structure of a thin extended streamer. In the viscous limit, another amplitude equation, which is a certain special case of the generalized complex Ginzburg–Landau equation, is obtained. Fixed points of the corresponding dynamical system are identified and their stability is investigated.

Complete theory for Langmuir envelope solitons in dusty plasmas
View Description Hide DescriptionA complete theory for Langmuir envelope solitons in an unmagnetized dusty plasma is presented, taking into account interactions between finite amplitude Langmuir waves and fully nonlinear dust ionacoustic (DIA), dust acoustic (DA), and ion hole (IH) perturbations. For this purpose, a nonlinear Schrödinger equation is employed for the Langmuir wave envelope and expressions for plasma slow responses are derived, including a modified (by the Langmuir waveponderomotive force)Boltzmann electron distribution and appropriate ion and dust density distributions for fully nonlinear dispersive DIA, DA, and IH perturbations, which include departure from the quasineutrality condition. In the stationary frame, the governing equations can be cast in the form of a Hamiltonian which is used to check the accuracy of the numerical scheme predicting stationary localized solutions of our governing nonlinear equations. Numerical results reveal different classes of Langmuir envelope solitons (cavitons) whose features differ from those in an electronion plasma without dust. Ion and dust thermal effects for the DIA and DA waves, respectively, have been included. It is suggested that new beamplasma experiments in laboratory dust plasmas should be conducted to verify our theoretical predictions of cavitons.
 Magnetically Confined Plasmas, Heating, Confinement

Magnetic diagnostic responses for compact stellarators
View Description Hide DescriptionThe formulation of magnetic diagnostic response functions for a threedimensional stellarator plasma is described. Reciprocity relations are used to compute unique response functions for each type of magnetic diagnostic.Green’s function response tables (databases) are generated from which both external coil and internal plasma current contributions to diagnostic signals can be rapidly computed. Applications to compact stellarators are described.

Numerical study of tokamak equilibria with arbitrary flow
View Description Hide DescriptionThe effects of toroidal and poloidal flows on the equilibrium of tokamak plasmas are numerically investigated using the code FLOW. The code is used to determine the changes in the profiles induced by large toroidalflows on NSTXlike equilibria [with NSTX being the National Spherical Torus Experiment, M. Ono, S.M. Kaye, Y.K.M. Peng et al., Nucl. Fusion40, 557 (2000)] where flows exceeding the sound speed lead to a considerable outward shift of the plasma. The code is also used to study the effects of poloidal flow when the flowvelocity profile varies from subsonic to supersonic with respect to the poloidal sound speed. It is found that pressure and density profiles develop a pedestal structure characterized by radial discontinuities at the transonic surface where the poloidal velocity abruptly jumps from subsonic to supersonic values. These results confirm the conclusions of the analytic theory of R. Betti and J. P. Freidberg [Phys. Plasmas 7, 2439 (2000)], derived for a lowβ, large aspect ratio tokamak with a circular cross section.

Global eigenmodes of low frequency waves in fieldreversed configuration plasmas
View Description Hide DescriptionGlobal eigenmodes of low frequency waves in field reversed configuration (FRC) plasmas have been obtained using the magnetohydrodynamic(MHD) model and onedimensional equilibrium model. Dispersion relation and radial structure of the global wave fields are shown for the azimuthal mode number The results are compared with the results of a low frequency wave heating experiment. Possibilities of ion heating by the ion cyclotron damping, the transittime magnetic damping, and Landau damping are discussed.

Plasma flow and confinement in the vicinity of a rotating island in collisional tokamak plasmas
View Description Hide DescriptionThe theory for the electric field,plasma flows, and plasma confinement in the vicinity of a rotating magnetic island in tokamaks [Phys. Plasmas9, 3470 (2002)] is extended to the collisional plasmas, i.e., the plateauPfirsch–Schluter regime. The electric field that is parallel to the magnetic field B , is assumed to vanish. It is found that plasmas flow in the toroidal direction at the same rate as the island rotation frequency. Island rotation frequency is calculated using an islandinduced symmetrybreaking viscosity. The radial electric field in the vicinity of the island is also determined from the toroidal momentum balance equation that includes islandinducedtoroidalviscosity.

Edgedriven rotating magnetic field current drive of fieldreversed configurations
View Description Hide DescriptionFieldreversed configurations (FRCs) are created and sustained using a rotating magnetic field (RMF) in the Translation Confinement and Sustainment experiment. Normally this experiment is operated in a manner where the RMF only partially penetrates the plasma column. This method of operation may have significant advantages in producing less disturbances to the bulk of the FRC, but requires driving an overall radially inward flow to maintain everywhere (through the term in the generalized Ohm’s law). However, some RMF penetration is still required at the field null where For some experimental conditions it appears that the RMF does not even penetrate as far as the null, raising the question as to how can be maintained at zero despite a finite Numerical simulations with a resistivity profile that is sharply peaked near the plasma edge yield similar profiles, and provide insight into this physical process. An inner magnetic structure forms, which rotates at a much lower frequency than the RMF. A tearing and reconnection process produces a torque transfer from the outer RMF to the inner structure, allowing it to act as an RMF downshifted to a lower frequency, and thus provide current drive to the inner region of the FRC. This mode of RMF current drive is being called “edgedriven mode.”

Aspect ratio scaling of ideal nowall stability limits in high bootstrap fraction tokamak plasmas
View Description Hide DescriptionRecent experiments in the low aspect ratio National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] have achieved normalized beta values twice the conventional tokamak limit at low internal inductance and with significant bootstrap current. These experimental results have motivated a computational reexamination of the plasma aspect ratio dependence of ideal nowall magnetohydrodynamic stability limits. These calculations find that the profileoptimized nowall stability limit in high bootstrap fraction regimes is well described by a nearly aspect ratio invariant normalized beta parameter utilizing the total magnetic field energy density inside the plasma. However, the scaling of normalized beta with internal inductance is found to be strongly aspect ratio dependent at sufficiently low aspect ratio. These calculations and detailed stability analyses of experimental equilibria indicate that the nonrotating plasma nowall stability limit has been exceeded by as much as 30% in NSTX in a high bootstrap fraction regime.

Mode and plasma rotation in a resistive shell reversedfield pinch
View Description Hide DescriptionMode rotation studies in a resistive shell reversedfield pinch, EXTRAP T2R [P. R. Brunsell et al., Plasma Phys. Control. Fusion 43, 1 (2001)] are presented. The phase relations and nonlinear coupling of the resonant modes are characterized and compared with that expected from modeling based on the hypothesis that mode dynamics can be described by a quasi stationary force balance including electromagnetic and viscous forces. Both and resonant modes are studied. The modes have rotation velocities corresponding to the plasma flow velocity (20–60 km/s) in the core region. The rotation velocity decreases towards the end of the discharge, although the plasma flow velocity does not decrease. A rotating phase locked structure is observed with a velocity of about 60 km/s. The modes accelerate throughout the discharges and reach velocities as high as 150–250 km/s. The observed phase locking is consistent with theory for certain conditions, but there are several conditions when the dynamics are not described. This is not unexpected because the assumption of quasi stationarity for the mode spectra is not fulfilled for many conditions. Localized perturbations are formed in correlation with highly transient discrete dynamo events. These perturbations form at the location of the phase locked structure, but rotate with a different velocity as they spread out in the toroidal direction.