Index of content:
Volume 3, Issue 11, November 1996

Current–voltage response of anodic plasma contactors with external ionization
View Description Hide DescriptionA spherical, steady‐state model that considers the combined influence of plasma emission and external ionization of neutral gas on the operation of electron‐collecting contactors is presented. Ionization by both Maxwellian and streaming electrons is investigated. A core (or quasineutral cloud) and a no‐core mode are considered and the transition conditions from one to another are derived. The collected current is determined in terms of the main plasma and contactor parameters. The current‐voltage response reproduces the ignited regime observed in experiments. The transition to the ignited regime and the transition to the core mode are not equivalent. It is shown that ionization by the electron beam is the main driver of ignition. The Langmuir law for the double layer causes a self‐regulation of the core that affects the collection of current and leads to a multiplicity of solutions. Different neutral gas profiles are analyzed. It is uncertain whether ignition is reached when the neutral gas is provided by the contactor exclusively. The appearance of nonmonotonic potential profiles for low plasma emissions is noted.

Effective charge in heavy ion stopping in classical collisionless plasmas
View Description Hide DescriptionThe Brandt–Kitagawa (B–K) model for the effective charge is revisited in order to account for the effect of trapped electrons on the energy loss of a slow ion moving in a classical and collisionless plasma. The electrons trapped in the potential created in the plasma by the projectile are treated as classically bound, and it is shown that their main effect is to reduce the effective charge state of the projectile. This effect is expected to be important when the strength of the perturbation is non‐negligible.

Lattice waves in dust plasma crystals
View Description Hide DescriptionTechniques previously known from solid state physics are used to look at linear and weak non‐linear wave propagation in dust lattices. These expansion techniques include only electrostatic interactions between neighbor particles in addition to assuming small vibrations in the dust lattice. As a simple model for the dust lattice, a one‐dimensional Bravais lattice is considered. For this particular lattice, expressions for the linear phase velocity are compared to a quasi‐particle simulation. The word quasi here means that only the dust particles are represented as diffuse objects, while the plasma is treated as a fluid. The simulation is also used to study the breakdown of the analytical theory and to investigate non‐linear dust lattice waves. A very good agreement is found between the analytical expressions and the particle simulations, for cases where the average dust separation a is of the order of or larger than the plasma Debye length λ_{ D }. This is a condition which very often applies to dust crystal in laboratory experiments. Application of this wavetheory is therefore discussed with respect to recent laboratory experiments where dust lattice waves are excited.

On the conical refraction of hydromagnetic waves in plasma with anisotropic thermal pressure: General consideration
View Description Hide DescriptionA phenomenon analogous to the conical refraction well known in crystalo‐optics and crystaloacoustics is considered for the magnetohydrodynamical waves in a collisionless plasma with anisotropic thermal pressure. Imposing the most general condition for the existence of the phenomenon, the angle of the conical refraction is calculated, which appeared to be dependent on the ratio of the Alfvén velocity and sound speedmeasured in the perpendicular direction with respect to the external magnetic field. Feasible ways to experimentally demonstrate the phenomenon are discussed and a novelty brought about by the general consideration is outlined.

Dynamics of relativistic electron‐positron plasma cloud moving across a magnetic field
View Description Hide DescriptionResults from a three‐dimensional electromagnetic and relativistic particle simulation of a relativistic electron‐positron plasma cloud (Lorentz factor γ=5/3) moving perpendicular to an ambient magnetic field with background plasmas are presented. It is shown that, in addition to the charge sheaths created at both sides of the cloud, secondary charge structures are created in the central region of the cloud and many cloud particles expand along the magnetic field. The Alfvén waves with large amplitude (δB/B _{0}≊0.03) and linear polarization are excited dominantly with wave number k _{ zc }/Ω_{ c }<1, while the electromagnetic waves are weakly excited because of the relativistic effect of the cloud particles.

The influence of magnetic fluctuations on collisional drift‐wave turbulence
View Description Hide DescriptionA two‐dimensional isothermal collisional drift‐wave turbulencemodel including magnetic fluctuations is studied numerically. The model has as limits the electrostatic collisional drift‐wave and two‐dimensional magnetohydrodynamic systems. The electromagnetic and electrostatic regimes for thermal gradient‐driven (drift‐wave) turbulence are decided by the parameter β̂=(4πnT/B ^{2})(L ^{2} _{ s }/L ^{2} _{ n }), where L _{ s } and L _{ n } are the parallel and background profile scale lengths, respectively. Significant electromagnetic effects were found only for β̂∼10 for most parameters, and were most pronounced in the strongly adiabatic regime for drift waves. The principal effect of the magnetic fluctuations is magnetic induction in the parallel force balance for electrons, which is linear. This diminishes the adiabaticity of the system by reducing the immediacy of the dissipative coupling between the density and electrostatic potential fluctuations. The transport was still found to be dominantly electrostatic even for β̂=10, although its level decreased with β̂ due to reduced coherency in the coupling between E×B velocity and density fluctuations.

Reflection of ion acoustic solitons in a plasma having negative ions
View Description Hide DescriptionReflection of compressive and rarefactive ion acoustic solitons propagating in an inhomogeneous plasma in the presence of negative ions is investigated. Modified Korteweg–de Vries equations for incident and reflected solitons are derived and solved. The amplitude of incident and reflected solitons increases with negative to positive ion density ratio. With increasing density ratio, reflection of rarefactive solitons is reinforced whereas that of compressive solitons weakened. The rarefactive solitons are found to undergo stronger reflection than the compressive ones.

Large Mach number ion acoustic rarefactive solitary waves for a two electron temperature warm ion plasma
View Description Hide DescriptionAn exact analytical form of Sagdeev pseudopotential has been derived for a two electron temperature warm ion plasma, from which ion acoustic rarefactive solitary wavesolutions could be investigated for a wide range of different plasma parameters, viz., ion temperature (σ), cold to hot electrontemperature ratio (β), and initial cold electron concentration (μ). Explicitly large Mach numbers have been obtained for increasing hot to cold electron temperature ratios, and an analytical condition for the upper bound of the Mach number has been derived for such a rarefactive solitary wave. It is found that the width of these waves obey Korteweg–de Vries soliton‐type behavior only for small amplitudes (i.e., eφ/T _{eff}<1) while for large amplitudes, the width of the rarefactive solitary waves increases with increasing amplitude.

Three‐dimensional collisional drift‐wave turbulence: Role of magnetic shear
View Description Hide DescriptionThree‐dimensional (3‐D) nonlinear simulations of collisional drift‐wave turbulence are presented. Results for the Hasegawa–Wakatani equations (without magnetic shear) in 3‐D are compared to former two‐dimensional (2‐D) simulations. In contrast to the 2‐D system the 3‐D situation is completely dominated by a nonlinear drive mechanism. The final state of the system is sensitive to the configuration of the computational grid since the sheared flow develops at the longest scales of the system. When magnetic shear is included, the system is linearly stable but the turbulence is self‐sustained by basically the same nonlinear mechanism. Magnetic shear limits the size of the dominant eddies, so the system evolves to a stationary turbulent state independent of the computational box. Finally, it is shown that the level of turbulence in the system with magnetic shear depends sensitively on the size of the effective Larmor radius ρ_{ s } compared with the characteristic transverse scale length of the eddies.

The role of nonlinear beating currents on parametric instabilities in magnetoplasmas
View Description Hide DescriptionA general coupled mode equation for the low‐frequency decay modes of parametric instabilities in magnetoplasmas is derived. The relative importance of the nonlinear contributions from the ponderomotive force, nonlinear beating current, and anisotropic effect to the parametric coupling is then manifested by the coupling terms of the equation. It is first shown in the unmagnetized case, that the contribution of the nonlinear beating current is negligibly small because of the small coefficient (i.e., weight) of this current contribution, instead of the beating current itself. It then follows that the weight of the beating current contribution increases significantly in the magnetized case, and consequently, this contribution to the parametric coupling is found to be important, as exemplified by two specific examples.

Regimes of the magnetized Rayleigh–Taylor instability
View Description Hide DescriptionHybrid simulations with kinetic ions and massless fluid electrons are used to investigate the linear and nonlinear behavior of the magnetized Rayleigh–Taylor instability in slab geometry with the plasma subject to a constant gravity. Three regimes are found, which are determined by the magnitude of the complex frequency ω=ω_{ r }+iγ. For ω≪Ω_{ i }(Ω_{ i }= ion gyrofrequency), one finds the typical behavior of the usual fluid regime, namely the development of ‘‘mushroom‐head’’ spikes and bubbles in the density and a strongly convoluted boundary between the plasma and magnetic field, where the initial gradient is not relaxed much. A second regime, where ω∼0.1Ω_{ i }, is characterized by the importance of the Hall term. Linearly, the developing flute modes are more finger‐like and tilted along the interface; nonlinearly, clump‐like structures form, leading to a significant broadening of the interface. The third regime is characterized by unmagnetized ion behavior, with ω∼Ω_{ i }. Density clumps, rather than flutes, form in the linear stage, while nonlinearly, longer‐wavelength modes that resemble those in fluid regime dominate. Finite Larmor radius stabilization of short‐wavelength modes is observed in each regime.

Charged‐neutral collision models in the presence of drifts
View Description Hide DescriptionA charged‐neutral collision model is presented for application to the kinetic theory of weakly ionized plasmas with immobile neutrals. The model is a modification of the well‐known Bhatnagar‐Gross‐Krook model, which has been the main model used in space plasmas so far. In comparison, the new model produces self‐consistently correct zero order drifts, and properly behaved zero order evolutions, while otherwise leaving identically unchanged all the kinetic dispersion equations of space plasmainstabilities derived by the old model. Also, the present model allows to use directly the zero order κ‐distributions recently introduced by Summers and Thorne [Phys. Fluids B 3, 1835 (1991)] for space plasmas, as input parameters, to which the actual distribution relaxes in time, as well as their generalized plasma dispersion function Z _{κ} ^{*}(z) for the solution of dispersion equations. The new model is compared throughout to a previous model by Mikhailovskii and Pogutse [Sov. Phys. Tech. Phys. 11, 153 (1966)], which also produces the correct zero order drifts, but predicts autonomously the zero order distribution.

Magnetic reconnection and the topology of interacting twisted flux tubes
View Description Hide DescriptionThe self‐consistent evolution of a pair of initially straight and either parallel or antiparallel magnetic flux tubes with prescribed boundary twist is studied using fully compressible three‐dimensional (3‐D) resistivemagnetohydrodynamics(MHD). 3‐D visualization techniques specially designed for divergence free vector fields are employed to investigate topological changes in the field lines and current lines associated with 3‐D reconnection in the system. Four cases are studied, corresponding to either parallel or antiparallel initial magnetic fields and to the same or opposite sign of footpoint twist. It is found that in the case with antiparallel field and opposite twist, so that the currents are parallel, the evolution proceeds in two phases. In the first phase, a series of topological changes involving magnetic nulls (where B=0) create an X‐type closed field line. In the second phase, the X‐type line serves as the separator for reconnection, allowing field lines from the two tubes to merge and form loops. The magnetic field lines exhibit spatial chaos and chaotic scattering. The observed reconnection involves the X‐type closed field line with evident current sheets. Later in time, the X‐type line changes to an O‐type closed field line, surrounded by a ring of toroidal flux surfaces.Reconnection continues until there emerges a final steady state having two reconnected loops and a toroidal ring of flux surfaces in between. The torus of magnetic surfaces has zero current in steady state because it is not connected by field lines to the twist imposed at the boundary. It is discussed how it is possible that such a region of zero current density can exist. The other three cases involve breaking of the ideal MHD flux constraint and changes in topology, but without localized current sheets, i.e., without reconnection. Implications for coronal loop interaction are discussed.

Technique for the experimental estimation of nonlinear energy transfer in fully developed turbulence
View Description Hide DescriptionA new procedure for calculating the nonlinear energy transfer and linear growth/damping rate of fully developed turbulence is derived. It avoids the unphysically large damping rates typically obtained using the predecessor method of Ritz [Ch. P. Ritz, E. J. Powers, and R. D. Bengtson, Phys. Fluids B 1, 153 (1989)]. It enforces stationarity of the turbulence to reduce the effects of noise and fluctuations not described by the basic governing equation, and includes the fourth‐order moment to avoid the closure approximation. The new procedure has been implemented and tested on simulated, fully developed two‐dimensional (2‐D) turbulence data from a 2‐D trapped‐particle fluid code, and has been shown to give excellent reconstructions of the input growth rate and nonlinear coupling coefficients with good noise rejection. However, in the experimentally important case where only a one‐dimensional (1‐D) averaged representation of the underlying 2‐D turbulence is available, this technique does not, in general, give acceptable results. A new 1‐D algorithm has thus been developed for analysis of 1‐D measurements of intrinsically 2‐D turbulence. This new 1‐D algorithm includes the nonresonant wave numbers in calculating the bispectra, and generally gives useful results when the width of the radial wave number spectrum is comparable to or less than that of the poloidal spectrum.

Asymmetry and thermal effects due to parallel motion of electrons in collisionless magnetic reconnection
View Description Hide DescriptionFast collisionless reconnection of magnetic flux loops by the macro‐particle simulation code shows significant asymmetry of the plasma flow under an ambient toroidalmagnetic field. The parallel motion of electrons induced by the reconnectionelectric field is found to produce large density and toroidalmagnetic field inhomogeneities of a quadrupole shape, δn/n _{0}∼0.3, unlike the m=1 mode. The divergence of the plasma flow is locally not identical to zero with each species, ∇ ⋅ V ^{(s)}≠0 (s=e,i), due to the electron spatial movement along the magnetic field. This internal structure results in a thick current layer and enhances the reconnection process. A plasmoid that impedes magnetic reconnection is created when the parallel mass diffusivity of electrons arising from their thermal motion is suppressed (the fluid limit). The reconnection rate becomes a smoothly increasing function of the ion mass and an inverse of the toroidalmagnetic field, the latter of which being due to the compressional effect. The rate is drastically reduced when the ion Larmor radius far exceeds the ion skin depth.

Bounce averaged trapped electron fluid equations for plasma turbulence
View Description Hide DescriptionA novel set of nonlinear fluid equations for mirror‐trapped electrons is developed which differs from conventional fluid equations in two main respects: (1) the trapped‐fluid moments average over only two of three velocity space dimensions, retaining the full pitch angle dependence of the trapped electron dynamics, and (2) closure approximations include the effects of collisionless wave‐particle resonances with the toroidal precession drift. Collisional pitch angle scattering is also included. By speeding up calculations by at least √m _{ i }/m _{ e }, these bounce averaged fluid equations make possible realistic nonlinear simulations of turbulent particle transport and electron heat transport in tokamaks and other magnetically confined plasmas.

Acceleration of electrons in the vicinity of a lower hybrid waveguide array
View Description Hide DescriptionThe interaction of tokamak plasma edge electrons with the electric near field generated by a lower hybrid slow waveantenna is studied. Antenna field spectra of interest for current drive and/or plasma heating have lobes at high‐n _{∥} values (n _{∥}≳30) intense enough for resonant acceleration of the relatively cold (∼25 eV) edge electrons. For waveguide electric fields, typically around 3 kV/cm, the higher‐order modes overlap in the phase‐space [B. V. Chirikov, Phys. Rep. 52, 263 (1979)], so that electron global stochasticity is induced. For Tokamak de Varennes (TdeV) [Décoste et al., Phys. Plasmas 1, 1497 (1994)] conditions and for 90° waveguide phasing, the stochastic limit in the current drive direction is about 2 keV, determined by the last overlapping mode. The progress of electrons through accessible phase space is very efficient: the TdeV 32 waveguide array can accelerate the electrons to the possible limit. An area‐preserving map is derived to study the electron dynamics. Surface‐of‐section plots fully confirm the resonant wave‐particle nature of the interaction.

Analysis of alpha particle‐driven toroidal Alfvén eigenmodes in Tokamak Fusion Test Reactor deuterium–tritium experiments
View Description Hide DescriptionThe toroidal Alfvén eigenmodes (TAE) are calculated to be stable in the presently obtained deuterium–tritium plasmas in the TokamakFusion Test Reactor (TFTR) [Plasma Phys. Controlled Nucl. Fusion Res. 26, 11 (1984)]. However, the core localized TAE mode can exist and is less stable than the global TAE modes. The beam ion Landau damping and the radiative damping are the two main stabilizing mechanisms in the present calculation. In future deuterium–tritium experiments, the alpha‐driven TAE modes are predicted to occur with a weakly reversed shear profile.

Toroidal gyrofluid equations for simulations of tokamak turbulence
View Description Hide DescriptionA set of nonlinear gyrofluid equations for simulations of tokamakturbulence are derived by taking moments of the nonlinear toroidal gyrokineticequation. The moment hierarchy is closed with approximations that model the kinetic effects of parallel Landau damping, toroidal drift resonances, and finite Larmor radius effects. These equations generalize the work of Dorland and Hammett [Phys. Fluids B 5, 812 (1993)] to toroidal geometry by including essential toroidal effects. The closures for phase mixing from toroidal ∇ B and curvature drifts take the basic form presented in Waltz et al. [Phys. Fluids B 4, 3138 (1992)], but here a more rigorous procedure is used, including an extension to higher moments, which provides significantly improved accuracy. In addition, trapped ion effects and collisions are incorporated. This reduced set of nonlinear equations accurately models most of the physics considered important for ion dynamics in core tokamakturbulence, and is simple enough to be used in high resolution direct numerical simulations.

Radially localized measurements of superthermal electrons using oblique electron cyclotron emission
View Description Hide DescriptionIt is shown that radial localization of optically thin electron cyclotron emission from superthermal electrons can be imposed by observation of emission upshifted from the thermal cyclotron resonance in the horizontal midplane of a tokamak. A new and unique diagnostic has been proposed and operated to make radially localized measurements of superthermal electrons during lower hybrid current drive on the Princeton Beta Experiment‐Modified (PBX‐M) tokamak [Bernabei, et al., Phys. Fluids B 5, 2562 (1993)]. The superthermal electron density profile as well as moments of the electron energy distribution as a function of radius are measured during lower hybrid current drive. The time evolution of these measurements after the lower hybrid power is turned off are given and the observed behavior reflects the collisional isotropization of the energy distribution and radial diffusion of the spatial profile.