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Volume 2, Issue 10, October 1995

Laboratory observation of the dust‐acoustic wave mode
View Description Hide DescriptionA laboratory observation of the dust‐acoustic instability is reported. The results are compared with available theories.

Neoclassical rotation of tokamak plasmas in the plateau regime
View Description Hide DescriptionThe poloidal rotation of tokamak plasmas is studied in the plateau regime. It is shown that the relaxation rate is given by v _{ T }/(qR)ν̂^{1/3} O(1), while the inertia enhancement in this regime is 1+q ^{2}ν̂^{−1/3} O(1), resulting from the time‐dependent parallel viscosity, where q is the safety factor, ν̂=ε^{3/2}ν_{*} is the plateau collisionality parameter (ε^{3/2}<ν̂<1), ε is the inverse aspect ratio, and ν_{*} is the standard neoclassical collisionality parameter. An evolutionary equation for the radial electric field is derived.

Space charge effects in the Paul trap
View Description Hide DescriptionThe effects of finite space charge on the equilibrium characteristics of charges confined in a Paul trap are investigated. It is found that space charge introduces two effects that have opposing influences on the confining pseudopotential well. The effect of electrostatic repulsion between like charges is to make the potential well shallower, but the plasma collective response can lead to a deepening of the well. Illustrative numerical solutions of thermal equilibria as well as an approximate analytical equilibrium are discussed.

Effect of antenna orientation and plasma anisotropy on the directivity of fast wave antenna radiation
View Description Hide DescriptionAsymmetry in the transverse wave number spectrum of the radiated power of a screenless fast waveantenna at an ion cyclotron range of frequencies is calculated with a model that takes into account the nonsymmetry of the plasma surface impedance matrix for an inhomogeneous tokamak plasma in front of the antenna. The directivity of the wave number spectrum transverse to the ambient magnetic field caused by the asymmetry in the surface impedance is found to be strongly asymmetric with respect to the parallel wave number by the effect of the nonperpendicular angle between the antenna current strap and the magnetic field. The latter is shown to be responsible also for the asymmetry in the parallel wave number spectrum of an undirected antenna, and can lead to deviations of order ≤30% in the corresponding spectrum of a phased antenna array with directivity. The consequences of the observed effects to the antenna performance in the current drive applications as well as in excitation of poloidally asymmetric spectra are discussed.

Excitation mechanism of standing waves produced by electron beam plasma instability
View Description Hide DescriptionThe excitation mechanism of standing waves produced by the electron beamplasma instability is experimentally studied using a Double Plasma device. When an electron beam is injected into the target plasma, standing waves around the electron plasma frequency are excited. A test wave is propagated in an electron beam plasma system and is identified as the beam mode from the dispersion relation. The propagation direction of the beam mode is determined from the wave pattern utilizing a phase shifter. It is found that a reflected beam mode exists as well as a forward beam mode, and is generated by the reflection of the forward beam mode from a potential well produced by the injection of the electron beam. The observed standing waves are formed by superposing the beam modes propagating in opposite directions from each other.

Measurements of plasma loading in the presence of electrostatic waves
View Description Hide DescriptionAn experimental analysis of the plasma impedance with respect to the coupling of ES(electrostatic)waves is described in this paper. The waves are excited through a slow‐wave antenna and the experiment performed in a toroidal device [C. Riccardi et al., Plasma Phys. 36, 1791 (1994)]. The measured impedance is compared with a simple theoretical model for magnetized homogeneous plasma, in order to establish the presence of bulk or surface waves and of some nonlinear effects when power is raised.

Single‐particle motion in nonaxisymmetric static electric and magnetic fields
View Description Hide DescriptionThe technique of iteration of canonical transformations for a Hamiltonian system is applied to study the motion of a single particle of small Larmor radius in static, nonaxisymmetric electric and magnetic fields. For use in applications in kinetic theory, it is asked when is μ(r,v), where μ is the magnetic moment adiabatic invariant, single valued in r, with v held fixed? Even when μ(r,v) is a good adiabatic invariant, it may fail this additional condition, so that f[1/2v ^{2}+Φ(r), μ(r,v)] is not an acceptable particle distribution function, where Φ(r) is a single‐valued electrostatic potential. It is shown that in a toroidal domain the condition is satisfied only for axisymmetric fields, or for magnetic fields near a zero shear field with nested flux surfaces that fill a toroidal domain. The appropriate transformations to guiding center coordinates and Hamiltonians are given for these cases.

Observation of spontaneously excited chaos‐like ion plasma oscillations
View Description Hide DescriptionAn oscillation which behaves quite similarly to chaos under some conditions is observed to exist among ion plasma oscillations spontaneously excited in an ion beam–plasma system. There are two different states of the system, the ‘‘silent’’ and ‘‘chaotic’’ states, sensitively depending on the value of a direct current (DC) voltage V _{ B }, which determines the beam energy and is adopted as a control parameter here. In the chaotic state, a spontaneously excited ion plasma oscillation is observed to become chaotic. Here, the correlation dimension for the oscillation in the chaotic state is calculated to be 1.64±0.22. The result shows that an attractor for the oscillation has a low degree of freedom and a noninteger dimension.

Kinetic self‐organization: Creation of super ion acoustic double layer
View Description Hide DescriptionA ‘‘super’’ ion acoustic double layer is realized through a particle simulation. This double layer is an illustration of self‐organization in an open system, where a fresh, constant flux of electrons is continuously supplied from the upstream boundary and disordered (‘‘dirty’’) particles are discharged from the downstream boundary. The entropy production rate is found to be maximized in accordance with creation of normal (weak) and super (strong) double layers and to vanish as they disappear. The amplitude of the potential jump in such super double layers reaches an unexpectedly large magnitude, which is far above the electron thermal energy, and a superthermal electron beam is generated on the downstream side.

A new solution method for the gyrokinetic Fokker‐Planck equation
View Description Hide DescriptionA new non‐perturbative and non‐variational solution method is proposed for the gyrokineticequation, based on a suitable approximation for the linearized Fokker‐Planck collision operator. The approach, which allows, in principle, the accurate evaluation of arbitrary moments of the distribution function for a weakly collisional magnetoplasma with toroidal equilibria of arbitrary aspect‐ratio, is susceptible of numerous significant applications, both for transport calculations, i.e., in particular, leading to the evaluation of neoclassical fluxes, as well for the investigation of linear stability analyses of dissipative perturbations.

Coherent structures and turbulent cascades in two‐dimensional incompressible magnetohydrodynamic turbulence
View Description Hide DescriptionNumerical solutions of decaying two‐dimensional incompressible magnetohydrodynamicturbulence reach a long‐lived self‐similar state which is described in terms of a turbulent enstrophy cascade. The ratio of kinetic to magnetic enstrophy remains approximately constant, while the ratio of energies decreases steadily. Although the enstrophy is not an inviscid invariant, the rates of enstrophy production, dissipation, and conversion from magnetic to kinetic enstrophy are very evenly balanced, resulting in smooth power law decay. Energy spectra have a k ^{−3/2} dependence at early times, but steepen to k ^{−5/2}. Local alignment of the intermediate and small‐scale fields grows, but global correlation coefficients do not. The spatial kurtosis of current grows and is always greater than the vorticity kurtosis. Axisymmetric monopole patterns in the current (magnetic vortices) are dominant structures; they typically have a weaker concentric, nonmonotonic vorticity component. Fast reconnection or coalescence events occur on advective and Alfvén time scales between close vortices of like sign. Current sheets created during these coalescence events are local sites of enstrophy production, conversion, and dissipation. The number of vortices decreases until the fluid reaches a magnetic dipole as its nonlinear evolutionary end‐state.

On the dynamics of turbulent transport near marginal stability
View Description Hide DescriptionA 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 transportdynamics near marginal stability. To illustrate this, impulse response scaling exponents (z) and turbulent diffusivities (D) have been calculated for the minimal (Burgers’) and sheared flowmodels. For the minimal model,z=1 (indicating ballistic propagation) and D∼(S ^{2} _{0})^{1/3}, where S ^{2} _{0} 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=2 and D∼(S ^{2} _{0})^{3/5}. This indicates a qualitative change in the dynamics, as well as a reduction in losses. These results are consistent with recent findings from dimensionless scaling studies. Several tokamaktransport experiments are suggested.

Ergodic mixing for turbulent drift motion in an inhomogeneous magnetic field
View Description Hide DescriptionThe turbulent E×B drift of a test particle in an inhomogeneous magnetic field is not reducible to a simple diffusion, but rather leads to a biased diffusion producing an inhomogeneous density distribution (pinch effect). The statistical properties of the long‐time chaotic two‐dimensional drift motion of a charged particle in the magnetic fieldB(x,y) and the time‐dependent electrostatic potential φ(x,y,t) are studied by numerical symplectic integration. For a conditionally periodic potential with two or more incommensurate frequencies, an ergodic behavior is demonstrated in which the probability density of the particle position is proportional to the magnetic fieldB. The accuracy of this prediction is found to be independent of the number N _{ω} of the incommensurate frequencies for N _{ω}≥2. The relation of this result with the Kolmogorov‐Arnold‐Moser theory is discussed.

A topological approach to the problem of charged particle trajectories in a toroidal axisymmetric configuration
View Description Hide DescriptionThis paper proposes a new approach for solving the general problem of Charged Particle Orbits in an axisymmetric toroidal configuration. This method is based upon the guiding center theory and gives a general and ‘‘a priori’’ classification of the topological properties of the trajectories. For a typical tokamakplasma, fifteen topological classes of orbits and their boundaries in a Constant‐Of‐Motion‐space are found without any trajectory computation. The confinement of these energetic orbits into the plasma region is then discussed. The method remains useful for any arbitrary toroidal axisymmetric configuration, as X‐points, doublets, etc., being strictly independent of the equilibrium mathematical form. This new approach may be applied mainly to charged fusion products and runaway electrons produced during disruptions.

The influence of the spectral properties of electrostatic fluctuations on the ambipolar electric field and plasma rotation
View Description Hide DescriptionA general system of momentum balance equations that take into account neoclassical effects and the fluctuations of plasma quantities and electromagnetic field is established. This is used to study the influence of the properties of electrostaticfluctuations on the radial anomalous flows and ambipolar electric field. The case when the momentum drag is provided by collisions with neutrals is considered, which is relevant for the edge plasma. It is shown that a change of the spectrum accompanied by a transfer of 40% of the fluctuationenergy from the big wavelength region to the small wavelength region of the spectrum can lead to a change of up to 20% in the magnitude of the electric field. As a result the plasma rotation will change. The possibility to induce plasma spin‐up through the ambipolar electric field produced by monochromatic waves delivered from an external source is also considered.

Stabilization of ballooning modes with sheared toroidal rotation
View Description Hide DescriptionStabilization of magnetohydrodynamicballooning modes by sheared toroidal rotation is demonstrated using a shifted circle equilibrium model. A generalized ballooning mode representation is used to eliminate the fast Alfvén wave, and an initial value code solves the resulting equations. The s−α diagram (magnetic shear versus pressure gradient) of ballooning mode theory is extended to include rotational shear. In the ballooning representation, the modes shift periodically along the field line to the next point of unfavorable curvature. The shift frequency (dΩ/dq, where Ω is the angular toroidal velocity and q is the safety factor) is proportional to the rotation shear and inversely proportional to the magnetic shear. Stability improves with increasing shift frequency and direct stable access to the second stability regime occurs when this frequency is approximately one‐quarter to one‐half the Alfvén frequency, ω_{A}=V _{A}/qR.

Dynamics of spatiotemporally propagating transport barriers
View Description Hide DescriptionA simple dynamic model of spatiotemporally propagating transport barriers and transition fronts from low (L) to high (H) confinement regimes is presented. The model introduces spatial coupling (via transport) into the coupled evolution equations for flow shear and fluctuation intensity, thus coupling the supercritical L to H bifurcationinstability to turbulent transport. Hence, fast spatiotemporal front propagation and evolutionary behavior result. The theory yields expressions for the propagation velocity and termination point of an L–H transition front and transport barrier. When the evolution of the pressure gradient, ∇ P _{ i }, and the contribution of ∇ P _{ i } to sheared electric field,E _{ r } ^{′}, is included, the ambient pretransition pressure gradient acts as a local source term that drives the evolution of the poloidal velocity shear. The transition may then evolve either as a spatiotemporally propagating front or as a uniform (i.e., nonlocal) fluctuation reduction or quench. The precise route to transition adopted depends on the relative magnitudes of the front transit time, τ_{ T }, and the fluctuation reduction time, τ_{ f }, respectively. The relevance of spatiotemporally propagating L–H transition fronts to the very high confinement regime (VH mode) evolution in DIII‐D [R. I. Pinsker and the DIII‐D Team, Plasma Physics and Controlled Nuclear Fusion Research 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. 1, p. 683] and in the Joint European Torus (JET) [Plasma Physics and Controlled Nuclear Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 27] is discussed.

Alpha currents driven by ion cyclotron resonance heating in a tokamak fusion reactor
View Description Hide DescriptionGeneration of plasma current by magnetic trapping of passing alpha particles through ion cyclotron resonance heating (ICRH) is studied. It is found that the efficiency of the ICRH‐driven alpha current can be comparable to the known efficiency of the usual fast‐wave‐driven electron current (e‐FWCD). However, the radial dependence can be quite different from the known behavior of e‐FWCD. Since a substantial fraction of the fast wave energy can be absorbed by the fusion‐born alpha particles through ICRH, the fast wavecurrent drive in a deuterium‐tritium reactor plasma may be substantially modified by the synergistic alpha current effect. The present study suggests that, without a careful choice of the waveproperties, the synergism may yield a destructive fast‐wave‐driven radial current profile for plasma equilibrium. However, it also suggests that a proper choice can produce a more favorable result than the e‐FWCD can alone.

Wave propagation through cyclotron resonance in the presence of large Larmor radius particles
View Description Hide DescriptionAbsorption of waves propagating across an inhomogenous magnetic field is of crucial importance for cyclotron resonance heating. When the Larmor radius of the resonant particles is small compared to the wavelength then the propagation is described by differential equations, a comparatively simple method for obtaining which has recently been given by Cairns et al. [Phys. Fluids B 3, 2953 (1991)]. In a fusion plasma there may, however, be a significant population of ions whose Larmor radius is not small compared to the wavelength. In this case the system is described by integro‐differential equations, reflecting the fact that the plasma response at a given position is determined by the wave field over a region of width of the order of the Larmor radius. The simplified method referred to above is adapted to this case and used to obtain various forms of the equations. Methods of simplifying the equations while still retaining information from the non‐local response, are discussed and some illustrated numerical results presented.

Hybrid magnetohydrodynamic‐gyrokinetic simulation of toroidal Alfvén modes
View Description Hide DescriptionResonant energetic particles play a major role in determining the stability of toroidal Alfvén 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‐Alfvén continuum and gives discrete kinetic Alfvén 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 Alfvén branch has been developed. It is shown that for typical parameters the KTAE is, indeed, more unstable than the TAE.