Phys. Fluids B (1984-1993) - Physics of Plasmas

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Particle simulation of non‐neutral plasma behavior

H. Ramachandran, G. J. Morales, and V. K. Decyk

Phys. Fluids B 5, 2733 (1993); http://dx.doi.org/10.1063/1.860712 (3 pages) | Cited 2 times

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It is demonstrated that particle‐simulation techniques can explore a broad range of dynamical behavior exhibited by non‐neutral plasmas. New features isolated by this approach include collective relaxation through generation of core and halo populations; self‐organization without radial transport as the plasma is cooled; spontaneous generation of solitonlike structures upon axial reflection from the external confining potential.

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52.27.Jt	Nonneutral plasmas
52.65.-y	Plasma simulation
52.35.Sb	Solitons; BGK modes

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Mode coupling effects on alpha‐particle‐driven long wavelength Alfvén wave instability

F. Y. Gang and J.‐N. Leboeuf

Phys. Fluids B 5, 2736 (1993); http://dx.doi.org/10.1063/1.860713 (3 pages) | Cited 2 times

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It is demonstrated both analytically and numerically that mode couplings play an important role in the nonlinear evolution of alpha‐particle‐driven long wavelength Alfvén wave instabilities. The mode coupling process is characterized by a beat between two linearly unstable Alfvén waves having opposite frequencies, which generates a linearly stable, static (zero frequency) mode. The backreaction of the static mode tends to stabilize the Alfvén instabilities by eliminating the phase shift between the alpha pressure and the Alfvén fluctuations.

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52.35.Mw	Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.25.Gj	Fluctuation and chaos phenomena

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Trapped ion absorption of non‐Maxwellian plasmas in ion cyclotron radio‐frequency heating

Yan Ping Chen and Shih Tung Tsai

Phys. Fluids B 5, 2739 (1993); http://dx.doi.org/10.1063/1.860714 (5 pages)

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The nonlocal power absorption of trapped ions in ion cyclotron radio‐frequency heating is calculated for several non‐Maxwellian distribution functions by keeping the full particle orbit and wave coupling. For slowing down distribution the finite Larmor radius effect enhances the power absorption in higher harmonic heating with n≥2. In bi‐Maxwellian plasma the absorption of trapped ions increases with the power of the ratio of the thermal perpendicular energy to the thermal parallel energy in the infinite aspect ratio limit and is slower in the small inverse aspect ratio case.

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52.50.Gj

Plasma heating by particle beams

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Cyclotron resonance in an inhomogeneous magnetic field

Jay M. Albert

Phys. Fluids B 5, 2744 (1993); http://dx.doi.org/10.1063/1.860715 (7 pages) | Cited 12 times

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Relativistic test particles interacting with a small monochromatic electromagnetic wave are studied in the presence of an inhomogeneous background magnetic field. A resonance‐averaged Hamiltonian is derived which retains the effects of passage through resonance. Two distinct regimes are found. In the strongly inhomogeneous case, the resonant phase angle at successive resonances is random, and multiple resonant interactions lead to a random walk in phase space. In the other, adiabatic limit, the phase angle is determined by the phase portrait of the Hamiltonian and leads to a systematic change in the appropriate canonical action (and therefore in the energy and pitch angle), so that the cumulative effect increases directly with the number of resonances.

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94.30.Hn

Energetic trapped particles

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Properties of transit‐time interactions in magnetized plasmas: Analytic and numerical results

A. Melatos and P. A. Robinson

Phys. Fluids B 5, 2751 (1993); http://dx.doi.org/10.1063/1.860716 (13 pages) | Cited 17 times

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The recently developed perturbation theory of transit‐time interactions between particles and coherent wave packets in magnetized plasmas is applied to particular field structures. Limits of validity are determined by comparison with test‐particle simulations, showing that the theory is accurate everywhere except near certain well‐determined resonances, for wave fields exceeding a characteristic threshold, and for particles below a particular velocity. The properties of transit‐time interactions in magnetized plasmas are investigated in detail to determine their dependence on the fields and parameters of the particle motion. Resonant particle scattering is found to occur at low particle velocities when the frequency of the coherent wave packet is an integer multiple of the gyrofrequency. Two different types of resonant transit‐time dissipation are also observed: one arises from transient cyclotron acceleration in the localized wave packet, the other from beating between the gyration of the particles and the oscillation of the wave packet field. Both effects involve an interplay between the field geometry and resonant oscillations.

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52.38.Bv	Rayleigh scattering; stimulated Brillouin and Raman scattering
52.40.Mj	Particle beam interactions in plasmas
52.25.Tx	Emission, absorption, and scattering of particles

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The electrostatic wake of a superthermal test electron in a magnetized plasma

A. A. Ware and J. C. Wiley

Phys. Fluids B 5, 2764 (1993); http://dx.doi.org/10.1063/1.860717 (5 pages) | Cited 4 times

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The electrostatic potential is determined for a test electron with v_∥ ≫ v_Te in a uniform magnetized plasma (ω_ce ≫ ω_pe). In the frame of the test electron, part of the spatially oscillatory potential has spherical symmetry over the hemisphere to the rear of the electron and is zero ahead of the electron. A second part of different character, which makes the potential continuous at the plane containing the electron, is oscillatory in the radial direction but decreases almost monotonically in the axial direction.

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52.25.-b

Plasma properties

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A Fokker–Planck operator for the emission and absorption of electron plasma waves in a magnetized plasma

Alan A. Ware

Phys. Fluids B 5, 2769 (1993); http://dx.doi.org/10.1063/1.860665 (9 pages) | Cited 8 times

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For slab geometry the perturbation of the electrostatic wake of a superthermal test electron in a magnetized plasma (ω_ce ≫ ω_pe) due to moderate magnetic shear is determined. Allowing for the spherical symmetry of the surfaces of constant phase to the rear of the test electron, the ‘‘resonant’’ field electrons causing the damping of the wave in a magnetic surface at a distance x from the test electron are those with parallel velocity v^′_∥ = v_∥cosβ/cos(β + γ). Here β is the angle between the emitted ray and B(0), γ is the angle between B(0) and B(x) and v_∥ is the velocity of the test electron. As a result the damping in the WKB approximation for the wave emission is a function of both the angle of emission and γ. A Fokker–Planck equation is derived for the rate of change of the electron distribution function (f) due to the emission and absorption of the waves under these conditions; f is assumed approximately Maxwellian for v_∥ ≲ v_T but with an arbitrary tail for v_∥ ≳ v_T.

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52.35.-g

Waves, oscillations, and instabilities in plasmas and intense beams

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Ion Bernstein wave propagation and absorption in general magnetic field configuration

Alessandro Cardinali

Phys. Fluids B 5, 2778 (1993); http://dx.doi.org/10.1063/1.860666 (8 pages) | Cited 7 times

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A linear analysis of ion Bernstein wave (IBW) propagation and absorption is considered in a general tokamak plasma magnetic equilibrium. The effects of elongation, triangularity, and Shafranov shift on radio‐frequency (rf) absorption are discussed with respect to the simple case of circular and concentric magnetic surfaces. The ray‐tracing equations are analytically and numerically solved in the flux surface coordinate system, and the power deposited in the plasma is calculated along the trajectory for the International Thermonuclear Experimental Reactor (ITER) [Nucl. Fusion 31, 1135 (1991)] plasma parameters.

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52.50.Gj

Plasma heating by particle beams

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Long‐time diffusion in plasma turbulence with broad uniform spectrum

O. Ishiharaa, H. Ha, and S. Watanabe

Phys. Fluids B 5, 2786 (1993); http://dx.doi.org/10.1063/1.860667 (7 pages) | Cited 3 times

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The long‐time behavior of charged particles in plasma turbulence with uniform broad wave spectrum is studied numerically. The diffusivity of the particle velocity distribution is characterized by the quasilinear nature for extended time, while a transient diffusion precedes with the enhanced nonquasilinear diffusion rate when resonance overlapping is relatively weak. The observed long‐time quasilinear diffusion coefficient eventually decreases due to the finiteness of the resonance region. The transient‐type diffusion is revealed only by the higher‐order numerical calculation.

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52.35.Ra	Plasma turbulence
51.10.+y	Kinetic and transport theory of gases

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Simulation study of a magnetohydrodynamic dynamo: Convection in a rotating spherical shell

A. Kageyama, K. Watanabe, and T. Sato

Phys. Fluids B 5, 2793 (1993); http://dx.doi.org/10.1063/1.860668 (13 pages) | Cited 15 times

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Numerical simulations on the thermal convection of a neutral fluid (without a magnetic field) in a rotating spherical shell have been carried out. The results indicate that sufficiently rapid rotation results in strong differential rotation, with a pronounced equatorial acceleration. The formation dynamics of convection columns aligned to the rotation axis is studied extensively. A new generation mechanism of differential rotation is then proposed which concludes that the fluid motion generates an equatorial acceleration by selectively exciting the cyclonic columns in the spherical shell.

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52.65.-y	Plasma simulation
52.30.-q	Plasma dynamics and flow
47.27.T-	Turbulent transport processes
47.65.-d	Magnetohydrodynamics and electrohydrodynamics

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Effects of anisotropic η_i and collisions on the mixed slab and toroidal ITG mode

H. Song and A. K. Sen

Phys. Fluids B 5, 2806 (1993); http://dx.doi.org/10.1063/1.860669 (10 pages) | Cited 8 times

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The effects of collisions and anisotropy in the ion temperature gradient on the ion‐temperature‐gradient‐driven (ITG) mode are investigated with dissipative trapped electrons and fully kinetic ions, in the presence of both transit and magnetic drift resonances. For the slab and toroidal modes, electron collisions stabilize the ion branch but destabilize the electron branch. For the mixed slab and toroidal mode, a coupling effect is found that causes a split of the stability region in the η_i∥‐η_i⊥ plane. A second stability region at large η_i⊥ with electron collisions may provide a possible stabilization scheme for ITG instabilities.

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52.20.Fs	Electron collisions
52.35.-g	Waves, oscillations, and instabilities in plasmas and intense beams
52.55.Fa	Tokamaks, spherical tokamaks

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Kinetic simulation of a plasma collision experiment

Olivier Larroche

Phys. Fluids B 5, 2816 (1993); http://dx.doi.org/10.1063/1.860670 (25 pages) | Cited 20 times

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The ionic Fokker–Planck code which was written for describing plasma shock wave fronts [M. Casanova et al. Phys. Rev. Lett. 67, 2143 (1991)] is applied to model the collision of two plasmas in plane geometry. Improvements brought to the code for that purpose are described. The initial phase of the experiment during which the plasmas interpenetrate is accounted for by a simple fluid model, which yields qualitative insight into the phenomena at play as well as an initial condition to start the kinetic simulation. The kinetic results obtained in the stagnation and thermalization phases are discussed with respect to a specific laser‐produced plasma collision experiment, as well as to existing fluid and kinetic (‘‘particle‐in‐cell’’) simulations.

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52.25.Fi	Transport properties
52.65.-y	Plasma simulation
52.38.-r	Laser-plasma interactions
52.35.Tc	Shock waves and discontinuities

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Fast magnetic field penetration into a cylindrical plasma of a nonuniform density

K. Gomberoff and A. Fruchtman

Phys. Fluids B 5, 2841 (1993); http://dx.doi.org/10.1063/1.860671 (12 pages) | Cited 19 times

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The penetration of a magnetic field into a cylindrical plasma of a density that varies both radially and axially is studied. The magnetic field penetrates rapidly due to the Hall field, along constant nr² lines (n is the dimensionless plasma density and r is the dimensionless radial coordinate). For a plasma that conducts between two cylindrical electrodes, it is shown that there is magnetic field penetration for both positive and negative polarity cases as long as there is penetration along the electrodes. The magnetic field evolution is found, analytically and numerically, for different time behaviors of the magnetic field at the boundaries. Ion velocities are also calculated.

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52.35.-g	Waves, oscillations, and instabilities in plasmas and intense beams
52.50.-b	Plasma production and heating
52.75.Kq	Plasma switches (e.g., spark gaps)
41.75.Ak	Positive-ion beams

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Propagations and collisions of drift wave vortices in a cylindrical plasma

K. Yabuki, K. Ueno, and M. Kono

Phys. Fluids B 5, 2853 (1993); http://dx.doi.org/10.1063/1.860672 (5 pages) | Cited 2 times

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Drift wave vortices in a cylindrical plasma is studied based on the modulated point vortex model for the Hasegawa–Mima equation. Various types of interactions are revealed such as exchange scattering, trapping, and detrapping, which sometimes bring about a long‐distance radial excursion, resulting in an enhancement of transport.

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52.35.Mw	Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Kt	Drift waves

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The coalescence instability and the development of current sheets in two‐dimensional magnetohydrodynamics

D. W. Longcope and H. R. Strauss

Phys. Fluids B 5, 2858 (1993); http://dx.doi.org/10.1063/1.860673 (12 pages) | Cited 12 times

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A class of two‐dimensional force‐free equilibria are shown to be subject to an ideal linear instability. This instability is similar to the coalescence instability for chains of magnetic islands. Semianalytic methods are used to find second magnetic equilibrium which is accessible from the first and has lower magnetic energy. This equilibrium has a discontinuous magnetic field and current sheets at these discontinuities. Numerical simulations indicate that the nonlinear evolution of the instability allows the plasma to relax to this discontinuous equilibrium.

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52.30.Cv	Magnetohydrodynamics (including electron magnetohydrodynamics)
52.35.Py	Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
96.60.P-	Corona

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Loss of equilibrium and reconnection in tearing of two‐dimensional equilibria

John M. Finn and Parvez N. Guzdar

Phys. Fluids B 5, 2870 (1993); http://dx.doi.org/10.1063/1.860674 (7 pages) | Cited 3 times

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Two‐dimensional tearinglike behavior is studied in reduced resistive magnetohydrodynamics (MHD) with flux conserving boundary conditions on a rectangular box. The tearinglike perturbations do not destroy the symmetries of the initial state, either discrete or continuous. In such cases, in which the perturbation does not break a symmetry of the equilibrium, linear instability is typically not directly observed. However, there can be a loss of equilibrium associated with the existence of a tearing unstable state. These ideas are illustrated with three examples: a very elongated tokamak, a tokamak with pinching coils to elongate its flux surfaces, and a model for the magnetotail or for solar arcades. The loss of equilibrium is demonstrated by means of a nonlinear energy functional. The importance of the fact that the dynamics shows a loss of equilibrium is that a large amount of free energy can be released, in the form of reconnection, and that there is a possibility of hysteresis.

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52.30.Cv	Magnetohydrodynamics (including electron magnetohydrodynamics)
52.55.Fa	Tokamaks, spherical tokamaks

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The small amplitude magnetohydrodynamic Riemann problem

C. C. Wu and C. F. Kennel

Phys. Fluids B 5, 2877 (1993); http://dx.doi.org/10.1063/1.860675 (10 pages) | Cited 2 times

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The small amplitude magnetohydrodynamic Riemann problem is studied using the Cohen–Kulsrud–Burgers equations. Unlike the coplanar Riemann problem, the evolution of noncoplanar Riemann problems is not self‐similar and its flow structures could change in time. But its large‐time behavior is very simple and a time‐dependent 2→3 intermediate shock is always involved for the noncoplanar field rotations. The time‐dependent 2→3 intermediate shock has a well‐defined structure and exists for any degree of field rotation.

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52.30.-q	Plasma dynamics and flow
52.35.Tc	Shock waves and discontinuities
52.35.Bj	Magnetohydrodynamic waves (e.g., Alfven waves)

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Boundary effects on the nonlinear interactions of surface waves

S. V. Vladimirov and M. Y. Yu

Phys. Fluids B 5, 2887 (1993); http://dx.doi.org/10.1063/1.860676 (5 pages) | Cited 12 times

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A traditional cold‐plasma boundary model is revised to allow for proper description of nonlinear effects in surface wave propagation. It is shown that induced nonlinear surface currents can exist at the boundary. As an example, the third‐order ponderomotive phenomena are considered, and the effect of the boundary condition on these nonlinear interactions is examined.

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52.35.Tc	Shock waves and discontinuities
52.35.Mw	Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.40.Hf	Plasma-material interactions; boundary layer effects
73.20.Mf	Collective excitations (including excitons, polarons, plasmons and other charge-density excitations)

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Non‐Markovian diffusion in plasma turbulence

H. Xia, O. Ishihara, and A. Hirose

Phys. Fluids B 5, 2892 (1993); http://dx.doi.org/10.1063/1.860677 (13 pages) | Cited 11 times

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Motion of charged particles in electrostatic plasma turbulence is studied analytically and numerically. Analytical study is based on a stochastic differential equation, the generalized Langevin equation, which is derived by the projection operator method with the assumption that the random fluctuation field is a Gaussian and wide sense stationary process. The equation describes the particle velocity as a stochastic process driven by field fluctuations, and is applied to evaluate the velocity diffusion coefficient. The non‐Markovian velocity diffusivity is characterized by the retarded turbulent collision term which contributes to the memory effect of the wave–particle interaction. Test‐particle numerical experiments are carried out by following trajectories of charged particles in Langmuir turbulence. The observed diffusion coefficient in a relatively strong turbulence deviates from predicted values of the quasilinear and the extended resonance broadening theories. The present non‐Markovian formulation explains well such a departure of the diffusion rate.

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52.35.Ra	Plasma turbulence
52.35.Fp	Electrostatic waves and oscillations (e.g., ion-acoustic waves)

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Viscoresistive stabilization of the Z pinch

F. L. Cochran and A. E. Robson

Phys. Fluids B 5, 2905 (1993); http://dx.doi.org/10.1063/1.860678 (4 pages) | Cited 3 times

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A two‐dimensional magnetohydrodynamic code that includes resistivity and viscosity has been used to study the growth of m=0 perturbations of a Z pinch in which the current increases with time. Stability for all wave numbers was found when the product SR was less than about 1000, where S is the Lundquist number and R is the Alfvén–Reynolds number. Since SR depends only on the line density N, the stability criterion translates as N<2×10¹⁶ ions cm⁻¹ (deuterium). This is two to three orders of magnitude smaller than the line density of fiber pinch experiments that have shown anomalous stability, and it is concluded that viscoresistive effects are inadequate to account for these observations.

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52.55.Ez	Theta pinch
52.30.Cv	Magnetohydrodynamics (including electron magnetohydrodynamics)
52.35.Py	Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.65.-y	Plasma simulation

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A kinetic model of fast wave propagation in the vicinity of the minority ion cyclotron resonance in a toroidal magnetic field

Peter J. Catto, C. N. Lashmore‐Davies, and T. J. Martin

Phys. Fluids B 5, 2909 (1993); http://dx.doi.org/10.1063/1.860679 (13 pages) | Cited 2 times

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Nearly all kinetic treatments of fast wave minority heating of inhomogeneous plasma in the cyclotron range of frequencies assume the magnetic field varies in the direction perpendicular to the magnetic field. However, the toroidal magnetic field of a tokamak varies along a field line due to the rotational transform and causes a small number of trapped particles to turn in the region of cyclotron resonance. In order to include the effects of rotational transform and, hence, trapped particles in the kinetic plasma response, a simplified, concentric circle flux surface model of a tokamak is employed. The most important result of this work is the derivation of response functions for Maxwellian and bi‐Maxwellian minority ions which generalize and extend previous replacement Z function forms obtained from a slab approximation of a tokamak (which also retains the variation of the strength of the magnetic field along a field line). The plasma response functions obtained include both passing and trapped ions, off‐axis heating, and are valid for arbitrary minority ion concentrations. The response function for a bi‐Maxwellian in the case of strong anisotropy substantially modifies the Maxwellian result. Anisotropy and the effects of toroidal geometry are illustrated graphically and tend to enter at higher toroidal mode numbers. For minority concentrations of the order or less than a critical value, the plasma response functions are used to obtain the standard transmission coefficient previously obtained for straight magnetic‐field models. The expression for the transmission coefficient is shown to be valid for more general unperturbed distribution functions of pitch angle and speed on each flux surface provided k_∥ρ≪1, where k_∥ is the parallel wave number and ρ the minority gyroradius.

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52.50.Gj	Plasma heating by particle beams
52.55.Fa	Tokamaks, spherical tokamaks
52.25.Dg	Plasma kinetic equations
52.35.Qz	Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)

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Analysis of the effects of elongation and triangularity on the propagation of lower‐hybrid waves

A. Cardinali, P. Micozzi, E. Barbato, and F. Romanelli

Phys. Fluids B 5, 2922 (1993); http://dx.doi.org/10.1063/1.860680 (11 pages) | Cited 5 times

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Lower‐hybrid (LH) wave propagation is studied for a general magnetic‐field configuration. The ray‐tracing equations in the geometric optics approximation are analytically and numerically solved in flux surface coordinates by using asymptotic techniques. In particular, the effects of elongation, triangularity, and the Shafranov shift on wave penetration are pointed out. Numerical applications devoted to the study of current drive generation for the International Thermonuclear Experimental Reactor (ITER) [Nucl. Fusion 31, 1135 (1991)] plasma parameters will also be presented.

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52.50.Gj

Plasma heating by particle beams

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Effect of rigid toroidal rotation on the stability of a high‐beta tokamak to external kink modes

S. N. Bhattacharyya

Phys. Fluids B 5, 2933 (1993); http://dx.doi.org/10.1063/1.860966 (5 pages) | Cited 2 times

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The effect of rigid toroidal rotation on the stability of a tokamak to external kink modes is examined. For simplicity a surface current model is assumed. For a high‐β tokamak it is shown that to leading order the equations governing stability in the presence of rotation are identical to those for a static plasma with β replaced by β+S, where β is the plasma beta and S is a parameter which provides a measure of the rotation rate. For a circular cross‐section tokamak the critical beta for stability to external kink modes in the presence of rigid toroidal rotation is given, to leading order in the inverse aspect ratio ϵ, by β=0.21ϵ−S. For an elliptical cross‐section tokamak the largest critical beta is obtained for a vertical elongation of 2.2 and is given, to leading order in ϵ, by β=0.37ϵ−S. The lower limit on the kink safety factor q∗ or the Mercier q increases with increase in S. Quantitative estimates of this increase can be obtained from the stability boundaries for the static problem.

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52.35.Py	Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.30.-q	Plasma dynamics and flow
52.55.-s	Magnetic confinement and equilibrium

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Compact toroid formation, compression, and acceleration

J. H. Degnan, R. E. Peterkin, G. P. Baca, J. D. Beason, D. E. Bell, M. E. Dearborn, D. Dietz, M. R. Douglas, S. E. Englert, T. J. Englert, K. E. Hackett, J. H. Holmes, T. W. Hussey, G. F. Kiuttu, F. M. Lehr, et al.

Phys. Fluids B 5, 2938 (1993); http://dx.doi.org/10.1063/1.860681 (21 pages) | Cited 18 times

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Research on forming, compressing, and accelerating milligram‐range compact toroids using a meter diameter, two‐stage, puffed gas, magnetic field embedded coaxial plasma gun is described. The compact toroids that are studied are similar to spheromaks, but they are threaded by an inner conductor. This research effort, named marauder (Magnetically Accelerated Ring to Achieve Ultra‐high Directed Energy and Radiation), is not a magnetic confinement fusion program like most spheromak efforts. Rather, the ultimate goal of the present program is to compress toroids to high mass density and magnetic field intensity, and to accelerate the toroids to high speed. There are a variety of applications for compressed, accelerated toroids including fast opening switches, x‐radiation production, radio frequency (rf) compression, as well as charge‐neutral ion beam and inertial confinement fusion studies. Experiments performed to date to form and accelerate toroids have been diagnosed with magnetic probe arrays, laser interferometry, time and space resolved optical spectroscopy, and fast photography. Parts of the experiment have been designed by, and experimental results are interpreted with, the help of two‐dimensional (2‐D), time‐dependent magnetohydrodynamic (MHD) numerical simulations. When not driven by a second discharge, the toroids relax to a Woltjer–Taylor equilibrium state that compares favorably to the results of 2‐D equilibrium calculations and to 2‐D time‐dependent MHD simulations. Current, voltage, and magnetic probe data from toroids that are driven by an acceleration discharge are compared to 2‐D MHD and to circuit solver/slug model predictions. Results suggest that compact toroids are formed in 7–15 μsec, and can be accelerated intact with material species the same as injected gas species and entrained mass ≥1/2 the injected mass.

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52.55.Jd	Magnetic mirrors, gas dynamic traps
52.30.Cv	Magnetohydrodynamics (including electron magnetohydrodynamics)
52.65.-y	Plasma simulation
41.20.Gz	Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems

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Shear flow effects on the nonlinear evolution of thermal instabilities

J.‐N. Leboeuf, L. A. Charlton, and B. A. Carreras

Phys. Fluids B 5, 2959 (1993); http://dx.doi.org/10.1063/1.860682 (8 pages) | Cited 13 times

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In the weak radiation drive regime, the coupling between the thermal instability driven by impurity radiation and the self‐consistent flow profile modification leads to a simple dynamical system that can be approximated by the Volterra–Lotka equations. In this system the shear flow acts as a predator and the temperature fluctuations act as prey. The solutions are oscillatory, and their behavior resembles that of edge‐localized modes (ELM’s). The solutions of the simplified model are compared with the three‐dimensional and two‐dimensional nonlinear numerical results for this instability.

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