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Aug 1988

Volume 31, Issue 8, pp. 2065-2377

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Turbulence spectrum of a passive temperature field: Results of a numerical simulation

J. Chasnov, V. M. Canuto, and R. S. Rogallo

Phys. Fluids 31, 2065 (1988); http://dx.doi.org/10.1063/1.867013 (3 pages) | Cited 14 times

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The spectrum of a passive temperature field, G(k), has been determined by a numerical simulation using three kinds of isotropic turbulent velocity fields. For a time independent and Gaussian velocity field, the resulting G(k) has the form G(k)=G0ϵθϵ2/3 χ−3k−17/3, with G0=0.33±0.02 Ko, confirming the prediction of Batchelor, Howells, and Townsend [J. Fluid Mech. 5, 134 (1959)]. For a velocity field developed through the Navier–Stokes equations and then frozen in time, G(k) has the same form as above, but with G0 =0.39±0.03 Ko. Finally, for a velocity field developed concurrently with the temperature field, G(k) collapses onto the spectrum obtained using a frozen, developed velocity field only for high enough values of the conductivity χ. For lower values of χ, the power law behavior of G(k) is less clear.
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47.27.T- Turbulent transport processes
47.27.Gs Isotropic turbulence; homogeneous turbulence

Magnetic tearing of plasma discharges due to nonuniform resistivity

A. B. Hassam

Phys. Fluids 31, 2068 (1988); http://dx.doi.org/10.1063/1.866658 (3 pages)

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The rearrangement of current in a plasma discharge in response to resistivity nonuniformities within a magnetic surface is studied. It is shown that macroscopic magnetic islands develop about those surfaces where the nonuniformity is aligned with the magnetic field. If the nonuniformity and the field are not aligned anywhere, there is no current rearrangement; instead, relatively large plasma flows are set up. Such resistivity inhomogeneities can obtain in solar coronal loops and, in some circumstances, in tokamak discharges.
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52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.55.Fa Tokamaks, spherical tokamaks
96.60.P- Corona

Flows over rectangular weirs

Frédéric Dias, Joseph B. Keller, and Jean‐Marc Vanden‐Broeck

Phys. Fluids 31, 2071 (1988); http://dx.doi.org/10.1063/1.866659 (6 pages) | Cited 15 times

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Flows over rectangular weirs and the corresponding discharge coefficient Cp are calculated for weirs of various lengths and heights. The fluid is assumed to be incompressible, inviscid, and in irrotational motion in two dimensions with gravity acting. The nonlinear free‐surface conditions are treated exactly. The resulting values of Cp are in good qualitative agreement, and in fair quantitative agreement, with experimentally determined values. Flows over thin weirs and over one triangular weir are also calculated, and a method for any polygonal weir is given.
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47.15.km Potential flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.32.Ef Rotating and swirling flows

Validation of the Sharp–Wheeler bubble merger model from experimental and computational data

J. Glimm and X. L. Li

Phys. Fluids 31, 2077 (1988); http://dx.doi.org/10.1063/1.866660 (9 pages) | Cited 44 times

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A statistical model to describe the late time chaotic behavior of a Rayleigh–Taylor unstable interface was introduced by Sharp and Wheeler [Physica D 12, 3 (1984); (private communication)]. Here the focus is on effective computations using this model and the comparison of the model with experiment. The numerical solution of the model shows that the height of the mixing layer, in which the bubbles of the light fluid penetrate the heavy fluid, is in a constant acceleration. This result agrees with the experiments of Read [Physica D 12, 45 (1984)].
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47.52.+j Chaos in fluid dynamics
47.27.W- Boundary-free shear flow turbulence
47.10.-g General theory in fluid dynamics
47.40.Nm Shock wave interactions and shock effects

Solutal convection during directional solidification of a binary alloy: Influence of side walls

R. Z. Guérin, B. Billia, P. Haldenwang, and B. Roux

Phys. Fluids 31, 2086 (1988); http://dx.doi.org/10.1063/1.866661 (7 pages) | Cited 10 times

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In this study the effect of rigid side walls on the onset of solutal convection in the melt is investigated for upward solidification of a binary alloy. The physics is described by the Navier–Stokes equations in the Boussinesq approximation and by the balance of solute, which is coupled with the appropriate boundary conditions. By using a Tau–Chebyshev spectral method the numerical resolution of the perturbed system has been carried out for two alloys: lead–tin, which is the reference in the literature, and lead–thallium, which is currently under study. For both cases the lateral confinement has a stabilizing effect for all the aspect ratios that have been considered.
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47.20.-k Flow instabilities
81.10.Fq Growth from melts; zone melting and refining
47.60.-i Flow phenomena in quasi-one-dimensional systems
02.70.-c Computational techniques; simulations

Optimal excitation of perturbations in viscous shear flow

Brian F. Farrell

Phys. Fluids 31, 2093 (1988); http://dx.doi.org/10.1063/1.866609 (10 pages) | Cited 95 times

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Evidence, both theoretical and experimental, is accumulating to support a mechanism for transition to turbulence in shear flow based on the 3‐D secondary instability of finite 2‐D departures from plane parallelism. It is of central importance for using this mechanism to understand how the finite amplitude 2‐D disturbances arise. To be sure, it is possible that in many experiments the disturbance is produced by the intervention of a mechanism that directly injects the requisite disturbance energy without calling on the store of kinetic energy inherent in the shear flow. It is shown here that it is also possible to tap the mean shear energy using properly configured perturbations that develop into the required primary disturbance on time scales comparable to those associated with the secondary instabilities even though the shear flow is stable or supports, at most, weak exponential instability.
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47.27.Cn Transition to turbulence
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.15.-x Laminar flows

Pulse interactions in an unstable dissipative‐dispersive nonlinear system

Takuji Kawahara and Sadayoshi Toh

Phys. Fluids 31, 2103 (1988); http://dx.doi.org/10.1063/1.866610 (9 pages) | Cited 53 times

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An attempt is made to understand several features of the wave evolutions in an unstable dissipative‐dispersive nonlinear system in terms of the interactions of localized solitonlike pulses. It is found that the wave evolutions can be qualitatively well described by weak interactions of pulses, each of which is the steady solution to the original evolution equation. The oscillatory structure of a tail of the pulse for weakly dispersive cases is responsible for the existence of bound states of pulses, which explains the numerical result that the interpulse distances in the initial value problem take certain fixed values or values in the definite regions. In cases of monotone tails for strongly dispersive cases, the effects of pulse interactions become repulsive, which explains the result that the pulses asymptotically tend to be arranged periodically, adjusting to the periodic boundary conditions in the numerical simulation.
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41.20.Jb Electromagnetic wave propagation; radiowave propagation
47.10.-g General theory in fluid dynamics
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

A kinetic analysis of unsteady evaporation and condensation with an Oseen‐like approximation

Takeo Soga

Phys. Fluids 31, 2112 (1988); http://dx.doi.org/10.1063/1.866611 (10 pages)

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A linearized kinetic model equation with an Oseen‐like approximation was applied to study the moderately strong unsteady evaporation and condensation problems. Asymptotic solutions were obtained for the weak (linearized) evaporation and condensation problems, disjoining the fluid dynamic equation with the Oseen approximation from the Knudsen layer equation. The asymptotic solution yielded correct features of the flow due to evaporation or condensation. The kinetic model equation was further applied to study the moderately strong evaporation and condensation problems. The results showed good agreement with the previous results derived from the nonlinear treatments and confirmed that the conventional slip flow theory is applicable for studying the moderately strong evaporation and condensation problems.
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47.45.Gx Slip flows and accommodation
51.10.+y Kinetic and transport theory of gases
44.30.+v Heat flow in porous media

Magnetohydrodynamic clump instability

D. J. Tetreault

Phys. Fluids 31, 2122 (1988); http://dx.doi.org/10.1063/1.866612 (13 pages) | Cited 6 times

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The theory of magnetohydrodynamic (MHD) clump instability in current driven plasma is presented. MHD clump fluctuations are current carrying bundles of correlated magnetic field lines. The instability occurs when turbulent mixing of the mean current density at island overlap produces clumps at a rate faster than their decay as a result of magnetic field line stochasticity. The renormalized dynamical equation describing MHD clump instability is derived from one‐fluid MHD equations and conserves the dynamical invariants of the exact equations. The renormalized equation is a nonlinear, turbulent version of the Newcomb equation of linear MHD stability theory and can be cast into the form of a nonlinear MHD energy principle. MHD clump instability is a dynamical route to the Taylor state.
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52.30.-q Plasma dynamics and flow
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Ra Plasma turbulence

Long‐term stability of a one‐dimensional current‐driven double layer

Naoko Hori and Takashi Yamamoto

Phys. Fluids 31, 2135 (1988); http://dx.doi.org/10.1063/1.866613 (9 pages) | Cited 1 time

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Long‐term (>an electron transit time over the system) stability of a one‐dimensional current‐driven double layer is studied by numerical experiments using particles. In these experiments, the potential difference across the system is self‐consistently determined by the space charge distributions inside the system. Each boundary of the system supplies a nondrifting half‐Maxwellian plasma. The current density is increased by increasing the number density of the source plasma at the injection (right) boundary. A double layer can be developed by injection of a sufficiently high current density. For a fixed level of current injection, plasmas carrying no current with various densities (n 0) are loaded on the left side of the system. Whether or not the generated double layer can maintain its potential drop for a long period depends on the density (n 0) relative to the initial density (n@B|0) near the injection boundary: (1) the double layer is found to grow when n 0=n∗0; (2) the steady double layer is seen for a long period when n 0≳n@B|0; (3) the double layer is found to decay when n 0 is even higher than n∗0. A new concept of the current polarizability Pc=J/n♯ is introduced for understanding these results, where J is the current density flowing through the double layer and n♯ is the plasma density at the injection front, i.e., the low‐potential edge of the double layer. Here Pc represents the potential of negatively polarizing a plasma. The different long‐term features of the double layers in results 1–3 above can be explained by analyzing physical processes to control the current polarizability Pc.
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52.65.-y Plasma simulation
52.38.Bv Rayleigh scattering; stimulated Brillouin and Raman scattering
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)

The plasma as a phase conjugate reflector

I. Nebenzahl, Amiram Ron, David Tzach, and Norman Rostoker

Phys. Fluids 31, 2144 (1988); http://dx.doi.org/10.1063/1.866614 (8 pages) | Cited 13 times

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Plasma is a nonlinear medium and two waves propagating in it interact electromagnetically with each other. If the plasma is pumped by two strong counterstreaming waves of equal frequency, and a third wave enters, the nonlinear interaction generates a fourth wave, phase conjugate to the third wave. This interaction becomes very significant if the frequency and wave vector differences between the third wave and one of the pump waves resonate with the frequency and wave vector of the ion acoustic mode of the plasma. This resonance can be predicted from a fluidlike description of the plasma, but it is shown that the Vlasov description can provide more details of behavior near the resonance. Possible applications of the emergent technology range from improved focusing of radiation in hyperthermia therapy of cancer to the formation of a microwave laser between a phase conjugate plasma reflector and a mirror, for improved radar imaging. Another application is cordless, self‐guiding, power transmission.
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42.65.Jx Beam trapping, self-focusing and defocusing; self-phase modulation
63.10.+a General theory
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma

Convective generation of a vortex street in plasma shear flow

Takashi Yamamoto and M. Andrew Yamashita

Phys. Fluids 31, 2152 (1988); http://dx.doi.org/10.1063/1.866615 (13 pages)

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By numerical calculation, it is shown that vortices are sequentially generated on the background charged layer forming parallel shear flows in a two‐dimensional low beta incompressible plasma when the charged layer is locally disturbed by a small amount of additional charge. Numerical experiments are performed in a rectangular domain with 0<x<Lx and −Ly/2<y<Ly/2 and the background charged layers are distributed to form the plasma flow U in the x direction with a velocity shear of ∂U/∂y≠0. The boundaries at x=0 and Lx are to supply plasmas identical to the background plasma initially loaded inside the domain. The plasma particles reaching the boundaries are freely allowed to leave the experimental domain. A vortex (named the mother vortex) first develops the local charge disturbance initially given, and subsequently new vortices (named the daughter vortices) are generated on the charged layer. This can be thought of as a result of propagation of the initial disturbance: A relative plasma flow as seen from the mother vortex can carry downstream the disturbances originating from the vortex, which can trigger growth of the daughter vortex. The numerical experiments in our nonperiodic system show that the intervals between the vortices are relatively close to the wavelength of the most unstable mode predicted by the linear analysis for periodic vortices. It is also shown that the temporal growth rate γ of the vortex in its early growing period is comparable to the corresponding linear growth rate of the unstable periodic vortices with the same wavelength.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Ra Plasma turbulence
52.65.-y Plasma simulation

Plasma transport by relaxation of localized perturbations

Murshed Hossain, Pung Nien Hu, Michael Kress, Albert A. Blank, and Harold Grad

Phys. Fluids 31, 2165 (1988); http://dx.doi.org/10.1063/1.866616 (6 pages) | Cited 5 times

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Localized perturbations in temperature and density are introduced on a background (approximate) steady‐state plasma. A simulation of the evolving plasma was carried out on a transport time scale. In all these simulations, the mass diffusion rate λξ is significantly less than that, λ1, based on resistivity alone. Braginskii transport has mainly been used and it has been found that λξ∼0.1λ1. Cases were also tested in which thermal conductivity is much larger than resistivity and it was found in the most extreme cases λξ=0.5λ1. The results are explained in terms of the linearized diffusion eigenvalues and their (approximate) eigenmodes. The eigenvalues reflect the coupled effect of plasma diffusion and heat flow. Since this coupling is intrinsic to the magnetohydrodynamic system of equations itself, the coupling should generally be taken into consideration. In particular, it is concluded that theories neglecting coupling may inevitably interpret transport as ‘‘anomalous.’’ These results are an initial step toward understanding the unresolved confinement issues for tokamaks including pellet induced increased particle confinement.
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52.25.Fi Transport properties
02.70.-c Computational techniques; simulations
52.65.-y Plasma simulation
52.55.Fa Tokamaks, spherical tokamaks

The evolution of cross helicity in driven/dissipative two‐dimensional magnetohydrodynamics

S. Ghosh, W. H. Matthaeus, and D. Montgomery

Phys. Fluids 31, 2171 (1988); http://dx.doi.org/10.1063/1.866617 (14 pages) | Cited 17 times

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A numerical study of the evolution of cross helicity in driven/dissipative magnetohydrodynamics (MHD) is presented. The magnetofluid is incompressible and a two‐dimensional (2‐D) periodic geometry is considered. Cross helicity, a measure of the correlation between fluctuations in the magnetic field and the velocity field, is injected by use of correlated Gaussian forcing over a finite bandwidth in wavenumber. Numerical experiments include the driving of initially uncorrelated spectra with highly correlated forcing and the driving of correlated spectra with anticorrelated forcing. A recurring and persistent feature of the simulations is the appearance of oppositely signed cross helicity at small scales relative to large scales. A simple argument based on the Elsässer variables and used previously in the context of decaying turbulence explains many of the observed features. The effect of a uniform external magnetic field is considered and the relation to purely decaying 2‐D MHD turbulence is discussed.
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52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.35.Ra Plasma turbulence
52.25.Gj Fluctuation and chaos phenomena
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

Electromagnetic radiation from strong Langmuir turbulence

K. Akimoto, H. L. Rowland, and K. Papadopoulos

Phys. Fluids 31, 2185 (1988); http://dx.doi.org/10.1063/1.866618 (5 pages) | Cited 28 times

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A series of computer simulations is reported showing the generation of electromagnetic radiation by strong Langmuir turbulence. The simulations were carried out with a fully electromagnetic 2 1/2 ‐dimensional fluid code. The radiation process takes place in two stages that reflect the evolution of the electrostatic turbulence. During the first stage while the electrostatic turbulence is evolving from an initial linear wave packet into a planar soliton, the radiation is primarily at ωe. During the second stage when transverse instabilities lead to the collapse and dissipation of the solitons, 2ωe and ωe radiation are comparable, and 3ωe is also present. The radiation power at ω=2ωe is in good agreement with theoretical predictions for electromagnetic emissions by collapsing solitons.
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52.25.Os Emission, absorption, and scattering of electromagnetic radiation
52.35.Ra Plasma turbulence
52.35.Sb Solitons; BGK modes
52.65.-y Plasma simulation

Dynamics of localized ion‐acoustic waves in a magnetized plasma

S. Qian, W. Lotko, and M. K. Hudson

Phys. Fluids 31, 2190 (1988); http://dx.doi.org/10.1063/1.866619 (11 pages) | Cited 11 times

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The evolution of negative potential pulses in a magnetized plasma is studied. A three‐dimensional (3‐D) nonlinear ion‐acoustic wave equation, including nonstationary effects of reflected electrons, has been derived from the Poisson–Vlasov equations with uniform magnetic field. In the low temperature limit, the equation is the Zakharov–Kuznetsov equation. Computer simulations of 1‐D and 2‐D versions of the equation have been performed. The studies show that a negative potential pulse can be enhanced by drifting electrons. The growing pulse develops asymmetrically with an oscillatory precursor and a local potential jump resembling the early phase of weak double layer formation. Two‐dimensional pulses also show different scale lengths along the magnetic field and in the transverse dimension. Comparisons are made with results from particle simulations and spacecraft observations.
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52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

Electron cyclotron absorption at downshifted frequencies in the presence of a current‐carrying superthermal tail

M. Bornatici and U. Ruffina

Phys. Fluids 31, 2201 (1988); http://dx.doi.org/10.1063/1.866620 (5 pages) | Cited 2 times

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The absorption of the extraordinary mode at frequencies downshifted with respect to either the fundamental or the second harmonic electron cyclotron resonance and such that the relevant resonance lies outside the plasma is evaluated for a Maxwellian distribution with a current‐carrying superthermal tail. The contribution from the current‐carrying electrons to the absorption is obtained by Lorentz‐transforming the dielectric tensor from the comoving to the laboratory frame. The dielectric tensor accounts for the fully relativistic cyclotron resonance condition and the corresponding Hermitian part includes the relevant thermal effects. The spatial dependence of the drift momentum, the density, and the temperature of both the bulk and the superthermals is accounted for in the evaluation of the absorption profile. The relevance of the relativistic effects is discussed with respect to both the profile of the absorption and the overall absorption.
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52.50.Gj Plasma heating by particle beams
52.40.-w Plasma interactions (nonlaser)

Lower hybrid wave propagation and absorption in inhomogeneous plasmas

S. Roy Choudhury

Phys. Fluids 31, 2206 (1988); http://dx.doi.org/10.1063/1.866621 (8 pages) | Cited 1 time

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The high‐frequency dielectric tensor for a cold, multispecies, current‐carrying plasma is derived in straight‐tokamak geometry, including both toroidal and poloidal magnetic fields in the equilibrium. Propagation and resonant absorption of lower hybrid waves in an inhomogeneous plasma column are investigated. The earlier treatment of Grossman and Weitzner [Phys. Fluids 27, 1699 (1984)] of the resonant‐layer solutions, power absorption and energy partition, and accessibility of the lower hybrid wave is generalized to include the effects of mode propagation parallel to the magnetic field and of an equilibrium plasma current. In particular, the density gradient coupled to the finite poloidal mode number and parallel wavenumber allows the lower hybrid wave to reach the hybrid layer, unlike the case of an infinite homogeneous plasma. Finally, the eigenvalue problem is solved for a homogeneous plasma column carrying zero current, and surrounded by a vacuum region delimited by a perfectly conducting shell. The spectrum of both axisymmetric and nonaxisymmetric lower hybrid oscillations is obtained for parameters characterizing the tokamak at Saha Institute for Nuclear Physics [in Proceedings of the IVth National Conference on Plasma Science and Technology (Institute for Plasma Research, Bhat, India, 1987), Paper M‐25].
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52.50.Gj Plasma heating by particle beams
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma

Mechanical injection of magnetic helicity

D. C. Barnes

Phys. Fluids 31, 2214 (1988); http://dx.doi.org/10.1063/1.866622 (7 pages) | Cited 4 times

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A novel technique for the injection of magnetic helicity into a closed volume is described. In this new approach, mechanical energy is converted directly into the production of magnetic helicity. Several geometries illustrate the flexibility of the approach. The application of mechanical injection of magnetic helicity to a magnetically insulated impact fusion system is briefly described. In this application, a β≫1 spheromak plasma is produced by impact of electrically conducting shells. Magnetic helicity is injected by the relative motion of these shells and subsequent plasma relaxation produces the spheromak magnetic field.
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52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.
52.55.Jd Magnetic mirrors, gas dynamic traps
52.50.Lp Plasma production and heating by shock waves and compression
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)

Runaway electron distributions and their stability with respect to the anomalous Doppler resonance

V. Fuchs, M. Shoucri, J. Teichmann, and A. Bers

Phys. Fluids 31, 2221 (1988); http://dx.doi.org/10.1063/1.866623 (7 pages) | Cited 3 times

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The stability of nonrelativistic runaway electron distributions with respect to the anomalous Doppler resonance is examined in a range of parameters of interest to tokamaks, i.e., for Y≡ωpe/Ωce≤2 and for Ohmic electric fields ϵ≡E/Ec≤0.1. Distribution functions are calculated numerically within a region up to 35ve (thermal velocities) using a finite‐element 2‐D Fokker–Planck code. Alternatively, an analytic approximation for the runaway distribution function is used, valid beyond the critical velocity vc≂ve(Ec/E)1/2. Stability thresholds in (ω,k∥) space are then determined. For example, for Y=1 and ϵ=0.1, and providing that the runaway tail extends at least to 30ve, unstable waves exist having ω≤0.6Ωce and k∥≤0.03Ωce/ve.
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52.25.Fi Transport properties
52.55.Fa Tokamaks, spherical tokamaks

Nonlinear cascade processes in magnetized plasmas with temperature anisotropy

M. Liljeström and J. Weiland

Phys. Fluids 31, 2228 (1988); http://dx.doi.org/10.1063/1.866624 (5 pages) | Cited 1 time

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A simplified nonlinear gyrokinetic formalism has been developed for general distribution functions and general magnetic perturbations. It has been found that the nonlinear coupling strength for low frequency electromagnetic modes in plasmas with anisotropic temperature is larger than for the isotropic case for small Larmor radius. A nonlinear cascade where the pump mode is the mode with intermediate parallel phase velocity has been found.
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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.Ra Plasma turbulence

Nonlinear wave propagation in collisionless finite‐beta inhomogeneous plasmas

K. Katou and J. Weiland

Phys. Fluids 31, 2233 (1988); http://dx.doi.org/10.1063/1.866625 (5 pages) | Cited 1 time

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Four coupled nonlinear evolution equations for the electrostatic potential, the density fluctuation, and the two vector potentials are derived from the two‐fluid and Maxwell’s equations that describe low‐frequency collisionless finite‐beta inhomogeneous plasmas. Under the assumption of weak turbulence, the above equations reduce to the nonlinear Schrödinger equation. The technique adopted here is considered as an extension of the formal Karpman–Krushkal [Sov. Phys. JETP 28, 277 (1969)] method to a system of nonlinear partial differential equations. The general exact traveling wave solution to the nonlinear Schrödinger equation is obtained with the help of the Hamilton–Jacobi theory. This general solution may be regarded as describing a final nonlinear stage of the modulational instability. It is also shown that a solitary wave solution to the nonlinear Schrödinger equation, which corresponds to the limiting case of the general solution, is given by means of the simple iterative method.
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52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.35.-g Waves, oscillations, and instabilities in plasmas and intense beams

Nonlinear wave interactions and evolution of a ring‐beam distribution of energetic electrons

S. Kainer, J. D. Gaffey, C. P. Price, X. W. Hu, and G. C. Zhou

Phys. Fluids 31, 2238 (1988); http://dx.doi.org/10.1063/1.867003 (11 pages) | Cited 3 times

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A ring‐beam distribution function of moderately relativistic electrons is unstable to electromagnetic and electrostatic waves. The results obtained in numerical simulations show that electromagnetic radiation corresponding to the normal modes of the background plasma is observed to grow even in the presence of a strong electrostatic instability and becomes very strong when the growth of the electrostatic Langmuir waves is minimized, and that the instability process is best described as a beam cyclotron resonance. Another strong radiation generated by the ring beam is the Z mode which is coupled to the electrostatic Langmuir wave. Under certain circumstances, these mechanisms may be significant in astrophysical situations.
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52.25.Fi Transport properties
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.27.Ny Relativistic plasmas
52.65.-y Plasma simulation

Neoclassical quasilinear transport theory of fluctuations in toroidal plasmas

K. C. Shaing

Phys. Fluids 31, 2249 (1988); http://dx.doi.org/10.1063/1.866626 (17 pages) | Cited 97 times

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A transport theory of fluctuations with frequencies less than the gyrofrequency in toroidal plasmas is developed to calculate particle and heat fluxes, bootstrap current, Ware pinch flux, and modification to plasma conductivity. It is found that the particle and heat fluxes are proportional to ∑m,n,ωm2(eΦmnω/Te)2, the bootstrap current and Ware pinch flux are proportional to ∑m,n,ωm[(m−nq)/‖m−nq‖] (eΦmnω/Te)2, and the modification
to plasma conductivity is proportional to ∑m,n,ω‖m−nq‖(eΦmnω /Te)2, where m (n) is the poloidal (toridal) mode number for the (m,n) mode with frequency ω, Φmnω is its mode amplitude, e is the electric charge, Te is the electron temperature, and q is the safety factor. Alternatively, in terms of the poloidal wave vector kθ and the parallel wave vector k∥, the particle and heat fluxes are proportional to 〈k2θ〉〈(eΦ/Te)2〉, the bootstrap current and Ware pinch flux are proportional to 〈kθk∥/‖k∥‖〉〈(eΦ/ Te)2〉, and the modification to plasma conductivity is proportional to 〈‖k∥‖〉〈(eΦ/Te)2〉, where 〈Φ2〉 is the averaged fluctuation level. Thus the sensitivities of various transport fluxes to plasma fluctuations are different: the most sensitive ones are particle and heat fluxes, the less sensitive ones are bootstrap current and Ware pinch flux, and the least sensitive one is the modification to plasma conductivity. The effects of fluctuations on bootstrap current and Ware pinch flux and on modification to plasma conductivity are smaller than those on particle and heat fluxes by factors of 〈kθk∥/‖k∥‖〉/〈k2
θ〉 and 〈k∥‖〉/〈k2θ〉, respectively. It is demonstrated explicitly that the matrix consisting of these transport coefficients satisfies Onsager symmetry. Furthermore, it is shown that the electron and ion transport are coupled through plasma flows. The theory is employed to discuss some qualitative transport properties observed in toroidal plasma experiments.
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52.25.Fi Transport properties
52.25.Gj Fluctuation and chaos phenomena
52.55.Fa Tokamaks, spherical tokamaks
52.55.Jd Magnetic mirrors, gas dynamic traps

Electrical circuit modeling of reversed field pinches

J. C. Sprott

Phys. Fluids 31, 2266 (1988); http://dx.doi.org/10.1063/1.866627 (10 pages) | Cited 35 times

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Equations are proposed to describe the radial variation of the magnetic field and current density in a circular, cylindrical reversed field pinch (RFP). These equations are used to derive the electrical circuit parameters (inductance, resistance, and coupling coefficient) for a RFP discharge. The circuit parameters are used to evaluate the flux and energy consumption for various start‐up modes and for steady‐state operation using oscillating field current drive. The results are applied to the MST device [Bull. Am. Phys. Soc. 32, 1830 (1987)].
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52.55.Ez Theta pinch
52.50.Gj Plasma heating by particle beams
52.70.Ds Electric and magnetic measurements
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