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Volume 3, Issue 10, October 1996

Hydromagnetic waves in a plasma of isotropic thermal and anisotropic suprathermal components
View Description Hide DescriptionLow frequency plane waves supported by a medium containing a thermal plasma of isotropic pressure and a suprathermal collisionless plasma having anisotropicpressure are investigated. The usual Alfvén, slow and fast modes of isotropic pressuremagnetohydrodynamics persist. In addition, a suprathermal mode appears which displays a rich variety of behavior due to an additional degree of freedom compared to the analogous mode when both the plasma components are described by collision‐dominated magnetohydrodynamics. Since these modes are significant in a number of situations, they are extensively investigated by computing their phase speeds for wide‐ranging numerical parameters.

Intuitive and rigorous derivation of spontaneous emission and Landau damping of Langmuir waves through classical mechanics
View Description Hide DescriptionClassical mechanics provides the intuitive and unified description of spontaneous emission, Landau growth and damping of Langmuir waves, the cold beam–plasma instability, and van Kampen modes. This is done by studying the interaction between M weak modes of a plasma without resonant particles and N quasiresonant particles, which leads to an exactly solvable high‐dimensional Floquet problem. Growth corresponds to an eigenmode of the system, whereas damping requires statistical averaging. Both imply synchronization of near‐resonant particles with waves, and the corresponding force on individual particles is computed explicitly.

Leaky electromagnetic wave resonances of a plasma sphere
View Description Hide DescriptionIn the paper we consider theoretically electromagnetic modes in a homogeneous cold plasma sphere. We find, in addition to the surface transverse magnetic modes, known from the electrostatic analysis of the same structure, two new families of weakly leaky modes (one of them consisting of transverse electric modes). A classification of the modes is proposed. An approximate analytic expression for the wave damping rate of the surface modes due to energy leakage is given, making it possible to draw conclusions on the behavior of more complex three‐dimensional plasmas.

Velocity shear generated Alfvén waves in electron–positron plasmas
View Description Hide DescriptionLinear magnetohydrodynamic(MHD) modes in a cold, nonrelativistic electron–positron plasmashear flow are considered. The general set of differential equations, describing the evolution of perturbations in the framework of the nonmodal approach is derived. It is found, that under certain circumstances, the compressional and shear Alfvén perturbations may exhibit large transient growth fueled by the mean kinetic energy of the shear flow. The velocity shear also induces mode coupling, allowing the exchange of energy as well as the possibility of a strong mutual transformation of these modes into each other. The compressional Alfvén mode may extract the energy of the mean flow and transfer it to the shear Alfvén mode via this coupling. The relevance of these new physical effects to provide a better understanding of the laboratory e ^{+} e ^{−}plasmas is emphasized. It is speculated that the shear‐induced effects in the electron–positron plasmas could also help solve some astrophysical puzzles (e.g., the generation of pulsar radio emission). Since most astrophysical plasmas are relativistic, it is shown that the major results of the study remain valid for weakly sheared relativistic plasmas.

Particle‐in‐cell simulations of fast magnetic field penetration into plasmas due to the Hall electric field
View Description Hide DescriptionParticle‐in‐cell (PIC) simulations are used to study the penetration of magnetic field into plasmas in the electron‐magnetohydrodynamic (EMHD) regime. These simulations represent the first definitive verification of EMHD with a PIC code. When ions are immobile, the PIC results reproduce many aspects of fluid treatments of the problem. However, the PIC results show a speed of penetration that is between 10% and 50% slower than predicted by one‐dimensional fluid treatments. In addition, the PIC simulations show the formation of vortices in the electron flow behind the EMHD shock front. The size of these vortices is on the order of the collisionless electron skin depth and is closely coupled to the effects of electron inertia. An energy analysis shows that one‐half the energy entering the plasma is stored as magnetic field energy while the other half is shared between internal plasma energy (thermal motion and electron vortices) and electron kinetic energy loss from the volume to the boundaries. The amount of internal plasma energy saturates after an initial transient phase so that late in time the rate that magnetic energy increases in the plasma is the same as the rate at which kinetic energy flows out through the boundaries. When ions are mobile it is observed that axial magnetic field penetration is followed by localized thinning in the ion density. The density thinning is produced by the large electrostatic fields that exist inside the electron vortices which act to reduce the space‐charge imbalance necessary to support the vortices. This mechanism may play a role during the opening process of a plasma opening switch.

Generalized magnetohydrodynamic equations for partially ionized dusty magnetoplasmas: Derivation and applications
View Description Hide DescriptionA comprehensive investigation of electromagnetic wave and instability phenomena in partially ionized, magnetized dusty plasmas has been carried out. By employing the multi‐fluid balance equations along with the Maxwell equations, a compact set of coupled field equations for the cases in which the dust grains are either robust (v _{ d }=0) or dynamic is derived. These systems of partial differential equations are used to study wave phenomena and resistive tearing mode instabilities analytically as well as by means of numerical simulations. For robust dust grains, it is shown that coupled sound‐Alfvén waves can appear even in the absence of ion‐neutral collisions. The unstable tearing modes are coupled to convective drift modes, if the dust number density is inhomogeneous. In the induction equation two new source terms for self‐generation of magnetic fields can be identified. In parameter regimes that are characterized by dynamic dust grains, the low‐frequency phenomena develop on timescales that are governed by the dust particle inertia rather than the ion inertia, as it is the case in dust‐free plasmas. The results of this investigation should be useful in understanding the properties of low‐frequency electromagnetic wave phenomena and the formation of coherent structures in dusty magnetoplasmas whose main constituents are negatively charged dust grains, singly charged positive ions, and neutrals.

Lyapunov stability and thermal stability of partially relaxed fluids and plasmas
View Description Hide DescriptionThe relation between the Lyapunov stability of a Hamiltonian system and the thermal stability of a fluid whose temperature is controlled from outside is explored: The free energy as a functional of the correct variables (specific volume, local entropy, and some Clebsch potentials of the velocity) may serve as a Lyapunov functional, depending on the ‘‘Casimirs’’ as exchanged quantities. For a multi‐species plasma one obtains a sufficient condition for stability: γ(v ^{2}/c ^{2} _{ s })−1 <d ln T/d ln n<γ−1 for each species, where γ is the adiabatic index and c _{ s } the sound speed. Some features of partially relaxed (T=const) cylindrical plasmas are also discussed.

Stability of magnetic vortices with flow in anisotropic magnetohydrodynamics
View Description Hide DescriptionThe eigenvalue problem for linear stability of concentric radial profiles of current and vorticity in reduced forms of three‐dimensional magnetohydrodynamics is solved numerically. Arbitrary relative amplitudes of the velocity and magnetic fields are considered. Vorticity profiles are unstable if nonmonotonic, but are stabilized by a poloidal magnetic field when the on‐axis vertical current is at least as large as the on‐axis vertical vorticity. Nonmonotonic current profiles are less efficient at stabilization. When the neutral modes have vertical structure, an added poloidal magnetic field does not stabilize the mode unless the vertical field is also moderately strong. Current profiles in which the integrated current changes sign, although spectrally stable, are shown to be nonlinearly unstable via both numerical solution and Lyapunov techniques.

Plasma beta limits for magnetic annihilation models
View Description Hide DescriptionMagnetic annihilation occurs when two oppositely directed magnetic fields are brought together by a plasma flow. Several exact nonlinear solutions exist which typically depend on the ratios of plasma pressure to magnetic pressure (the plasma beta), inflow speed to global Alfvén speed (the Alfvén Mach number) and of the advective to diffusive terms of the induction equation (the Lundquist number). Ensuring that the plasma pressure is everywhere positive restricts the freedom of choice of these parameters, however. Restrictions on the plasma beta are derived for the cases of two‐ and three‐dimensional annihilation and two‐dimensional reconnective annihilation. At the inflow speeds typically required for fast reconnection in diffuse astrophysical plasmas the minimum plasma beta is several orders of magnitude larger than the observed values of unity or less. In other words, at the observed plasma beta the models are only valid for extremely small annihilation rates.

Velocity shear effect on Rayleigh–Taylor vortices in nonuniform magnetized plasmas
View Description Hide DescriptionIn this paper, the effect of velocity shear on Rayleigh–Taylor vortices has been demonstrated. An inhomogeneous plasma is considered with a density profile such that the diamagnetic drift velocity V _{ n }=(cT _{ e }/eB)dn _{0}/dx is a constant and includes the effect of an ambient poloidal shear flowV _{ eq }(x)=V _{⊥0} ^{′}(x−x _{0})y. The final equation describing the stationary Rayleigh–Taylor vortex is shown to have the structure of a nonlinear Poisson equation, where the nonlinearity arises essentially because of the velocity shear term. This equation has been solved numerically and it has been shown that qualitatively new two‐dimensional monopole vortexsolutions may be obtained in the appropriate parameter space. Therefore, a new important nonlinear effect related to equilibrium shear flow has been identified in the calculations of Rayleigh–Taylor vortices which results in monopole‐like solutions in plasmas.

Stationary large‐scale magnetic fields generated by turbulent motion in a spherical region
View Description Hide DescriptionStationary large‐scale magnetic fields generated by an electrically conducting fluid in a spherical region are examined analytically, using the concept of the turbulent dynamo based on helicity and cross‐helicity effects. Under this concept, the toroidal magnetic field is induced through the combination of a rotational motion and the turbulent cross‐helicity effect. This field generates the poloidal one through the turbulent residual‐helicity (alpha) effect. A new magnetic‐field generation mechanism in the vicinity of the poles is also described. These findings are discussed in the context of the dimension of the convection part of a stellar object.

Reflectivity profiles of phase conjugate waves produced via four‐wave mixing in laser plasmas
View Description Hide DescriptionTheoretical profiles of power reflectivity of a phase conjugate electromagnetic wave generated by nearly degenerate four‐wave mixing in a carbon plasma via parametric decay instability (PDI) are studied. The plasma is considered to be produced by irradiating a carbon slab target with an Nd:glass high‐power laser pulse at an intensity above the PDI threshold. The plasma refractive index corresponding to the PDI region is taken into account in the wave equations. Two electromagnetic pump waves counterpropagating in the plasma are Nd:glass laser light waves and a weak electromagnetic probe wave incident upon the plasma, which is very slightly frequency upshifted relative to the pump waves. The effects of the frequency and angular detuning between the pump and probe waves, pump wave intensity, and plasma parameters on the reflectivity profiles have been investigated. It is noted that the plasma refractive index significantly affects the reflectivity profiles of the phase conjugate wave.

Non‐uniform rotation and the resistive wall mode
View Description Hide DescriptionAdvanced Tokamak Concepts [C. Kessel, J. Manickam, G. Rewoldt, and W. M. Tang, Phys. Rev. Lett. 72, 1212 (1994)] have been designed assuming that the ‘‘Resistive Wall Mode’’ (RWM) is stable. It has recently been shown that the RWM can be stabilized by a combination of strong uniform plasma rotation and visco‐resistive dissipation. In this paper we examine the consequences of a sheared flow on the RWM, and contrast the results to the case of uniform flow. It is shown that, as for uniform flow, the rotation initially further destabilizes the resistive wall mode, but for higher rotation velocities the growth rate is reduced, and the presence of plasma dissipation may completely stabilize the mode. However, sheared rotation allows the possibility of the RWM coupling to and converting into a Kelvin‐Helmholtz mode. It is shown that the position of the wall with respect to the critical position for stabilization of the external kinkmode is of crucial importance.

Stationary turbulent spectra of toroidal η_{ i } mode
View Description Hide DescriptionToroidal ion temperature gradient(ITG) driven drift modeturbulence has been analyzed analyti‐ cally and numerically. By using weak nonlinearity arguments and random phase approxima‐ tion, dynamic and wave kinetic equations are derived. Three different nonlinearities, namely E×B, convective, and diamagnetic nonlinearities, play important roles in the turbulent spectral transfer. The power spectra of the weak ITG‐mode turbulence are obtained analytically for k≫1 and k<1 ranges in the wave number space. Forward energy cascading due to convective and diamagnetic nonlinearities will balance the inverse energy cascading due to E×B nonlinearity at k≊1/ρ_{ s } (k is the wave number, ρ_{ s }=c _{ s }/ω_{ ci }, where c _{ s } is the sound velocity and ω_{ ci } is the ion cyclotron frequency) and results in energy condensation at k≊1/ρ_{ s }.

Vlasov description of implosion heating
View Description Hide DescriptionAn analytical treatment of plasma heating by a fast compression of a solenoidal field is given. An annular cylindrical plasma with a radius of 1 m is considered for the initial state, since this optimizes the nonadiabatic heating. The theory predicts that a 0.13 μs compression with 3 MV circuit voltage can give as much as 200 keV mean ion kinetic energy. The plasma beta increases by a factor of 100 in the compression. With the voltage decreased to 1 MV and a 0.36 μs compression time, the calculated mean ion kinetic energy is 60 keV. The calculated number of ions per unit length that gives tolerable magnetic shielding is 4×10^{17} m^{−1}. Some practical concerns such as endplate construction, control of plasma beta, electric insulation, and transportation of the compressed plasma along a tube are briefly analyzed.

Kinetic modeling of scrape‐off layer plasmas
View Description Hide DescriptionElectron transport along open field lines in the diverted scrape‐off layer of a tokamak is studied numerically via a kinetic Fokker–Planck approach. The method allows calculation of the distribution function in a situation where large parallel temperature gradients are maintained by collisional relaxation and, at the same time, superthermal electrons stream freely from the midplane of the plasma to the target/sheath boundary. The method also allows calculation of the self‐consistent electrostatic field associated with parallel gradients in the distribution function, as well as the potential drop across the target/sheath boundary, where the latter is calculated to enforce appropriate boundary conditions at the target, although the sheath itself is not resolved. The kinetic results are compared to classical fluid results for the case of a simple (nonradiative) divertor. The kinetic solutions exhibit an enhanced superthermal electron population in the vicinity of the target, which results in a larger sheath energy transmission factor, a lower bulk electron temperature, and a smaller sheath potential drop. The sheath potential largely determines the energy with which ions impact the target, thereby affecting the rate of target erosion. Ionization rates and radiation rates from impurities in the vicinity of the target also depend strongly on the local electron temperature and can be sensitive to superthermal tails.

The effect of partial poloidal wall sections on the wall stabilization of external kink modes
View Description Hide DescriptionAn analysis of the effect on the wall stabilization of external kinkmodes due to toroidally continuous gaps in the resistive wall is performed. The effects both with and without toroidal rotation are studied. For a high‐β equilibrium, the mode structure is localized on the outboard side. Therefore, outboard gaps greatly increase the growth rate when there is no rotation. For resistive wall stabilization by toroidal rotation, the presence of gaps has the same effect as moving the wall farther away, i.e., destabilizing for the ideal plasma mode, and stabilizing for the resistive wall mode. The region of stability, in terms of wall position, is reduced in size and moved closer to the plasma. However, complete stabilization becomes possible at considerably reduced rotation frequencies. For a high‐β, reverse‐shear equilibrium both the resistive wall mode and the ideal plasma mode can be stabilized by close fitting discrete passive plates on the outboard side. The necessary toroidal rotation frequency to stabilize the resistive wall mode using these plates is reduced by a factor of three compared to that for a poloidally continuous and complete wall at the same plasma‐wall separation.

Toroidal η_{ i }‐mode global vortices in a rotating plasma
View Description Hide DescriptionModel equations describing dynamics of a toroidal η_{ i } mode in a rotating plasma are derived. The stationary solution of the model equations is investigated analytically and the condition for global vortex formation is found. The form of the solution is verified numerically and it is shown that the shape of global vortices is affected strongly by the shear of the plasma poloidal rotation. In weak shear, the stationary solution looks like a dipole vortex, while in strong shear, the main part of the plasma cross section is occupied by vortexflow.

Magnetic ripple and the modeling of lower‐hybrid current drive in tokamaks
View Description Hide DescriptionUsing ray tracing, a detailed investigation of the lower‐hybrid (LH) wave propagation in presence of toroidalmagnetic field ripple is presented. The local ray behavior is first depicted for a cylindrical equilibrium periodically modulated along the axial direction. Variations along ray trajectories in the component of the wave vector parallel to the equilibrium magnetic field are observed, with a maximum relative amplitude that is locally of the order of the ripple level. For the full rippled toroidal equilibrium, a similar local behavior is found when the ray trajectory crosses a high ripple region. Despite the modest amplitude of the local ray perturbation, its global influence on ray trajectories may be strong, as a consequence of the combined effects of toroidal and poloidal inhomogeneities. By coupling ray tracing with a one‐dimensional relativistic Fokker–Planck code, simulations of LH experiments have been performed for the TORE SUPRA tokamak [Equipe TORE SUPRA, in Proceedings of the 15th Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville (International Atomic Energy Agency, Vienna, 1995), Vol. 1, p. 105, Paper IAEA‐CN‐60/A1‐5]. It is shown that magnetic ripple may induce significant modifications in the LH power deposition profiles, mainly in the ‘‘few passes’’ regime when the wave makes some, but not many, passes inside the plasma before being absorbed. The effect of magnetic ripple leads then to a broadening of the power deposition profile and a shift towards the center of the plasma, and a better coupling with high energy electrons. This behavior may be explained by an increase in the overall ray stochasticity. Taking into account magnetic ripple in LH simulations, a better agreement is found between numerical predictions and experimental observations.

Poloidal shear flow effect on toroidal ion temperature gradient mode: A theory and simulation
View Description Hide DescriptionThe effect of poloidal shear flow on the global structure and stability of toroidal ion temperature gradient mode is studied theoretically and also numerically using a toroidal particle simulation code. Reasonable agreements are found between the theoretical and simulation results; both indicating that with increasing shear flow the toroidal ion temperature gradient mode is stabilized in the increase of poloidal asymmetry and in the reduction of radial mode width.