Index of content:
Volume 3, Issue 6, June 1996

Interaction of crossed laser beams with plasmas
View Description Hide DescriptionThe parametric interaction of two crossed collimated laser beams with ion plasma modes has been studied. The underlying process is a density grating that is created by the two laser beams. The Bragg diffraction that is produced enhances forward stimulated Brillouin scattering(SBS) which results in a time dependent energy exchange between the two beams. A diversity of other SBS processes which depend on the symmetry of driving laser beams are also discussed.

Generation of the saturated electrostatic potential along a magnetic field line
View Description Hide DescriptionThe formation of plug potential is usually observed in a tandem mirror experiment without neutral beam injection in the plug region [Phys. Plasmas 2, 2321 (1995)]. The formation requires only the electron cyclotron resonance heating experimentally. In this Letter the plug potential is analytically shown to be created in a tandem mirror with passing ions, mirror trapped ions in the thermal barrier, passing electrons and φ‐trapped electrons in a plug potential but without high energy sloshing ions.

Physical mechanism of enhanced stability from negative shear in tokamaks: Implications for edge transport and the L‐H transition
View Description Hide DescriptionThe enhancement of stability to ballooning modes from negative shear in tokamaks is shown to be a simple consequence of the orientation of the convective cell with respect to the toroidally outward effective gravity, g↘. For modest positive shear, convective cells remain oriented along g↘ as they map along field lines. In contrast, for negative shear or very positive shear convective cells twist strongly away from g↘ and are less strongly driven. The twist of convection cells is controlled by the profile of the vertical magnetic field along the outer midplane, B _{ z }. Twist is a minimum in regions where B _{ z } is independent of the major radius. Transport should be highest in such locations. Resistive ballooning modes in the tokamak edge are strongly stabilized by modest values of negative shear. Tokamak discharges with finite values of β_{ p } develop regions of local negative shear on the outside midplane of the plasma torus. This local negative shear should self‐stabilize resistive ballooning modes at finite values of the poloidal beta. This effect may impact the transition to high confinement operation (H‐mode).

Theory of drift waves in the presence of parallel and perpendicular flow curvature. I. Slab model
View Description Hide DescriptionIt has recently [S. Sen and M. G. Rusbridge, Phys. Plasmas2, 2705 (1995)] been shown that, contrary to the usual belief, parallel flow curvature (V _{∥} ^{″}) can stabilize drift‐like microinstabilities. Here the earlier work is extended to include the effect of the perpendicular flow curvature (V _{⊥} ^{″}), which is known to have a stabilizing role on the drift‐like microinstabilities. The full analytic stability analysis shows that the ratio of the stabilizing influences of the perpendicular to the parallel flow curvature scales as L _{ s }/2L _{ n }, where L _{ s } and L _{ n } are the magnetic shear and the density variation scale length, respectively. Thus, at the plasma edge (since L _{ s }≫L _{ n }) the perpendicular flow may play a crucial role in stabilizing microinstabilities and turbulence in the improved regimes of confinement [like the high (H) modes]. However, in the core confinement improvement [like the very high (VH) mode] both the parallel and the perpendicular flow curvatures are important, since L _{ s }∼2L _{ n }. Furthermore, as the confinement improvement in the core is usually related to the toroidal velocity and since V _{∥} coming from the toroidalflow is much more than V _{⊥} (V _{⊥}∼εV _{∥}, here ε is the inverse aspect ratio), this implies that it is the parallel component of the toroidalflow and not the perpendicular component, as is usually thought, which is responsible for the core confinement improvement.

Kinetic theory of charged particles of variable shape
View Description Hide DescriptionRecently a new kind of computational technique for kinetic plasma simulation has been developed, making use of particles of variable shape (blobs). The aim of the present work is to derive a kinetic equation governing the evolution of the blobs and solve it in the case of small perturbations. Results are compared with those obtained for the real plasma and for a plasma of particles of fixed shape (the model usually employed in popular particle‐in‐cell simulations). The comparison is useful to find out whether the additional cost of dealing with more degrees of freedom is balanced by the superior accuracy provided by the new technique in describing the phase‐space distribution.

On the fast rotational equilibrium of a non‐neutral plasma column
View Description Hide DescriptionThe equation governing the stability of a single species non‐neutral plasma column to small amplitude electrostatic perturbations is shown to remain unchanged under a certain transformation. This transformation can be used to predict the stability of the fast rotational equilibrium using the results for the slow rotational equilibrium. For the fast rotational equilibrium the zero frequency modes, which can give rise to field error driven transport, are identified.

Exact solutions for steady‐state, planar, magnetic reconnection in an incompressible viscous plasma
View Description Hide DescriptionThe exact planar reconnection analysis of Craig and Henton [Astrophys. J. 450, 280 (1995)] is extended to include the finite viscosity of the fluid and the presence of nonplanar components in the magnetic and velocity fields. It is shown that fast reconnection can be achieved for sufficiently small values of the kinematicviscosity. In particular, the dissipation rate is sustained by the strong amplification of planar magnetic field components advected toward the neutral point. By contrast, nonplanar field components are advected without amplification and so dissipate energy at the slow Sweet–Parker rate.

Joule heating of a current layer due to plasma density inhomogeneities
View Description Hide DescriptionIn the present paper the magnetic fielddynamics in the frame of electron magnetohydrodynamics (EMHD) theory is considered in the case of a current passing through a plasma of inhomogeneous density. It is shown: (1) due to the Hall effect the Joule heating of a current layer increases up to (ωτ)_{ ei } times the Joule heating of ordinary homogeneous plasma. (2) The EMHD magnetic fielddynamics can be considered as an enhanced magnetic fielddiffusion in the frame of MHD theory, using ‘‘efficient’’ coefficients of plasmaconductivity and of magnetic fielddiffusion. The ‘‘efficient’’ coefficient of the magnetic fielddiffusioncT/10eH in the case of magnetic field‐plasma equilibrium is the same order of magnitude as the Bohm’s coefficient cT/16eH.

Construction of the weakly‐relativistic Fokker‐Planck kinetic equation in the Darwin approximation
View Description Hide DescriptionThe explicit form of the weakly‐relativistic Vlasov and the Fokker‐Planck collision operators for a multispecies plasma are evaluated by using a systematic expansion in β_=v_/c and retaining corrections up to the second order. Properties of these operators are investigated.

Electromagnetic instability and anomalous resistivity in a magnetic neutral sheet
View Description Hide DescriptionAn electromagnetic instability in a magnetic neutral sheet is investigated by means of a two‐and‐one‐half dimensional (21/2‐D) semi‐implicit particle simulation code. Electromagnetic waves are excited slowly in a field null region after saturation of the lower hybrid drift waves excited in an early time on both sides of the neutral sheet. This instability is found to be a new instability, independent of the lower hybrid drift instability. Examination of its characteristic properties indicates that the new instability is highly related to the meandering motions of ions in the neutral sheet. The growth of the instability gives rise to anomalous resistivity in the neutral sheet current.

Nonlinear magnetic chains associated with plasma flow
View Description Hide DescriptionNonlinear equations describing magnetic electron mode in a nonuniform, unmagnetized plasma, with a space‐dependent flow are derived. A set of two coupled equations, for the self‐generated magnetic field and electron temperature perturbation is obtained, and two kinds of solutions, in the form of a moving single and double chain of magnetic islands are found.

Plasma–neutral interaction in tokamak divertor for ‘‘gas box’’ neutral model
View Description Hide DescriptionPlasma flow through the gas cloud in a tokamakdivertor for ‘‘gas box’’ divertor geometry and Knudsen regime of neutral transport is investigated. It is shown that similar to the neutral models that have considered previously, (i) plasma parameters near the target is sensitive to the energy flux into the hydrogen recycling region and can change rapidly, resulting in bifurcation‐like behavior, which might be interpreted as a transition to detached regime, (ii) plasma flux onto the target starts to decrease at a very low plasma temperature near the target, while a strong pressure drop already occurs. At low plasma temperature near the target the recombination processes can significantly alter the plasma flux onto the target.

Analysis of noble gas recycling at a fusion plasma divertor
View Description Hide DescriptionNear‐surface recycling of neon and argon atoms and ions at a divertor has been studied using impurity transport and surfaceinteraction codes. A fixed background deuterium–tritium plasma model is used corresponding to the International Thermonuclear Experimental Reactor (ITER) [ITER EDA Agreement and Protocol 2, ITER EDA Documentation Series No. 5 (International Atomic Energy Agency, Vienna, 1994)] radiative plasma conditions (T _{ e }≤10 eV). The noble gas transport depends critically on the divertorsurface material. For low‐Z materials (Be and C) both neon and argon recycle many (e.g., ∼100) times before leaving the near‐surface region. This is also true for an argon on tungsten combination. For neon on tungsten, however, there is low recycling. These variations are due to differences in particle and energy reflection coefficients, mass, and ionization rates. In some cases a high flux of recycling atoms is ionized within the magnetic sheath and this can change local sheath parameters. Due to inhibited backflow, high recycling, and possibly high sputtering, noble gas seeding (for purposes of enhancing radiation) may be incompatible with Be or C surfaces, for fusion reactor conditions. On the other hand, neon use appears compatible with tungsten.

Finite‐β and alpha particle effects on kinetic Alfvén wave in a fusion tokamak plasma
View Description Hide DescriptionIn this paper, a model for the kinetic Alfvén wave (KAW) in the presence of fusion alphas is established. The finite‐β (relative to low β) and alpha particleeffects on KAW are investigated. In this model, ion sound, transit time magnetic pumping (TTMP), the response of alpha particles (alphas), and those effects considered by preceding authors are included. In cylindrical geometry, a set of three second‐order differential equations in r for the perturbed fields E _{ r }, E _{⊥}, and E _{∥} is numerically solved. A dispersion relation of the Alfvén wave in the fusiontokamakplasma is derived. The mode conversion and the energy deposition are qualitatively discussed on the basis of this relation. Both the analytical and numerical analyses indicate that (i) no matter whether m (poloidal mode number) is positive [N. Ding et al., Phys. Plasmas2, 1529 (1995)] or negative (mainly studied in the present paper), the alphas do not affect the compressional Alfvén wave, but they do affect the KAW evidently; (ii) for m<0, it is preferable to choose the frequency ω of the injected wave so that the inequality ω≳(P _{ m±1}/R _{ m±1})^{−1}ω_{*αm } holds for optimal power absorption. The energy deposition at the resonant position close to the interior of the fusiontokamakplasma in taking account of the effects of ion sound and TTMP is less than that without taking account of these effects. But for the same β value, at the position adjacent to the edge the contrary is the case. For a certain resonant position, as the β value increases, the energy deposition decreases.

Fast wave propagation studies in the DIII‐D tokamak
View Description Hide DescriptionFast Alfvén waves radiated from the phased arrayantenna in the DIII‐D tokamak [L. G. Davis et al. in Proceedings of the 12th IEEE Symposium on Fusion Engineering, Piscataway, 1987 (Institute of Electrical and Electronics Engineers, New York, 1987), p. 991] and used for heating and current drive are studied by employing a Ḃ‐loop array mounted on the vacuum vessel wall. The wave propagation direction controlled by the antenna phasing is clearly observed. A small divergence of the rays arising from the anisotropic nature of the fast wave is found. Comparison with a ray tracing code confirms that the ray position calculated by the code is precise up to at least one toroidal turn of the rays. Conservation of k _{ tR }, which is a basic assumption in computer codes, is tested. Although the upshift of toroidal wave number k _{ t } at small major radius R is confirmed, k _{ tR } is not well conserved. The so‐called ‘‘eigenmode’’ is observed and the cause is identified. A mass density interferometer is demonstrated by employing the extraordinary fast wave.

Model for relaxation in reversed‐field pinch plasmas
View Description Hide DescriptionIn this article, a model for anomalous ion heating, a dynamo current‐sustained edge toroidal field, and a sawtooth oscillation during the relaxation in the reversed‐field pinch (RFP) plasma is presented. The dynamo (α), the turbulent resistivity (β) and viscosity (χ), dependent on the magnetohydrodynamics(MHD)fluctuations, are incorporated into the model.Turbulentviscous dissipation of the fluctuation energy is proposed as the mechanism of the anomalous ion heating. This is a straightforward corollary of the turbulentviscosity heating of ions in that the temperature of the heavier ions is higher than that of the lighter ions and that the ion temperature increases with the MHDfluctuation level. Correspondingly, the turbulent resistivity heats electrons anomalously. It is shown that the dynamo current, generated by the back‐transfer of fluctuating magnetic field helicity to mean magnetic field, sustains the RFP magnetic configuration. In the edge the total current density is approximately equal to the dynamo current density, while at the core the dynamo current opposes the applied electric‐field‐driven current, flattening the current profile. Provided the α dynamo has a periodic behavior in time, the physical quantities of the RFP plasma have a sawtooth time dependence. The local poloidal current density in the edge increases during the sawtooth crash and peaks at the end of the crash, as do the ion and electron temperatures. In contrast, the toroidal current density at the core decreases during the crash and arrives at its minimum at the end of the crash. Qualitatively, the conclusions drawn from the present model are in good agreement with many of the experimental results [Scime et al., Phys. Rev. Lett. 68, 2165 (1992); Ji et al., ibid. 73, 668 (1994)] and the numerical simulations.

Plasma diagnostics in the Tokamak Fusion Test Reactor using emission of electron cyclotron radiation at arbitrary frequencies
View Description Hide DescriptionEmission of cyclotron radiation at arbitrary wave frequency for diagnostic purposes is discussed. It is shown that the radiation spectrum at arbitrary frequencies is more informative than the first few harmonics and it is suited for diagnosis of superthermal electrons without any ‘‘ad hoc’’ value of the wall reflection coefficient.Thermal radiation from the TokamakFusion Test Reactor (TFTR) [Fusion Technol. 21, 1324 (1992)] is investigated and it is shown that the bulk and the tail of the electron momentum distribution during strong neutral beam injection is a Maxwellian with a single temperature in all ranges of electron energies.

Magnetohydrodynamic kink stability of high pressure (εβ_{ pol }≫1) toroidal plasmas
View Description Hide DescriptionHigh pressuretoroidal equilibria with εβ_{ pol }≫1 are shown to be violently unstable to magnetohydrodynamic(MHD)kink modes. Here, ε is the inverse aspect ratio of a torus with a square conducting wall and β_{ pol } is the ratio of the plasma pressure to the poloidal magnetic fieldpressure. A broad spectrum of toroidal mode numbers is unstable at large εβ_{ pol }. These modes grow rapidly, with a very short exponential growth time of the order of the Alfvén time. The growth rate of the kink mode is independent of the magnitude of the resistivity of the plasma.

Mode coupling effects on resistive wall instabilities
View Description Hide DescriptionIt is shown that destabilization of resistive wall magnetohydrodynamic(MHD)modes in the presence of rotation is a mode coupling phenomenon. Based on this observation, certain unanticipated effects are readily explained. These include the fact that resistive wall modes with rotation can be unstable, even for parameters for which the MHD modes are stable with the wall at infinity, and the fact that this destabilization depends critically on the plasma parameters.

Gyrokinetic‐magnetohydrodynamic hybrid simulation of the transition from toroidal Alfvén eigenmodes to kinetic ballooning modes in tokamaks
View Description Hide DescriptionA gyrokinetic‐magnetohydrodynamic (MHD)hybrid simulation code has been developed in order to study high‐n (where n is the toroidal mode number) MHDinstabilities driven by energetic particles in finite‐β tokamaks. Here β is the ratio between plasma and magnetic pressures. Specifically, it is observed that as the core plasma β value increases, there is a corresponding transition from the toroidal Alfvén eigenmode (TAE) to the kinetic ballooning mode (KBM). The energetic particle mode (EPM) branches of both the toroidal Alfvén mode (TAM) and KBM are shown to be important in this transition. KBM are preferentially excited when the energetic particle velocity is small compared to the Alfvén velocity.