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

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Alfvén‐type wave motion induced by the Hall effect

Michael L. Goodman

Phys. Fluids B 1, 2305 (1989); http://dx.doi.org/10.1063/1.859047 (7 pages)

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The Hall effect is studied as a correction to ideal magnetohydrodynamics (MHD) in the context of how it affects the linear stability of the cylindrical pinch in the simple case of a static, homogeneous equilibrium state. The effects of compressibility and electron pressure are included. The presence of the electron pressure gives rise to an electric field tangent to the boundary of the plasma. This introduces an additional boundary condition in the case of a perfectly conducting plasma boundary. Imposing this boundary condition eliminates the wave solutions presented in this paper. With respect to large radial wavenumber, the accumulation point of the slow magnetoacoustic wave frequency spectrum is changed from its finite value in ideal MHD to infinity by the Hall effect. The Hall effect gives rise to linear waves that do not exist in ideal MHD. Specifically, the Hall effect induces azimuthally symmetric, compressible, Alfvén‐type wave propagation. The frequency spectrum of these waves is discrete and infinite and is a singular perturbation of the incompressible Alfvén wave spectrum in ideal MHD. These Alfvén‐type waves do not exist if the plasma is incompressible or if H≡K⋅B=0, where K is the wave vector of the perturbation and B is the equilibrium magnetic field.

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52.30.-q	Plasma dynamics and flow
52.35.-g	Waves, oscillations, and instabilities in plasmas and intense beams
52.55.Ez	Theta pinch

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Relaxation time of potential formation across the magnetic field in a collisionless plasma

Yoshihiro Okuno, Shinya Yagura, and Hiroharu Fujita

Phys. Fluids B 1, 2312 (1989); http://dx.doi.org/10.1063/1.859048 (4 pages)

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The relaxation time of potential formation across the magnetic field in a collisionless plasma is experimentally studied. The time variation of the local potential is directly measured with a high time resolution technique when a pulsed potential is applied between magnetized coaxial cylindrical double plasmas. It is found that the relaxation times of the potential and density decrease with the applied voltage and the density of the target plasma, and increase with the magnetic field strength and the density of the driver plasma. These results could be understood consistently by the diffusion of ions in the driver plasma to the target plasma.

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52.25.Fi	Transport properties
52.30.-q	Plasma dynamics and flow
52.70.Ds	Electric and magnetic measurements

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Electrostatic ion‐cyclotron waves in a plasma with negative ions

Bin Song, D. Suszcynsky, N. D’Angelo, and R. L. Merlino

Phys. Fluids B 1, 2316 (1989); http://dx.doi.org/10.1063/1.859049 (3 pages) | Cited 39 times

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Electrostatic ion‐cyclotron (EIC) waves have been investigated in plasmas containing K⁺ positive ions, electrons, and SF⁻₆ negative ions. Two EIC wave modes are generally present, the K⁺ and SF⁻₆ modes. Their frequencies increase with increasing ϵ, the percentage of negative ions, while the critical electron drift velocities for excitation of either mode decrease with increasing ϵ. The observations are discussed on the basis of available theories.

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52.35.Fp	Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.35.Qz	Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)

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Quasiperiodic behavior in beam‐driven strong Langmuir turbulence

P. A. Robinson and D. L. Newman

Phys. Fluids B 1, 2319 (1989); http://dx.doi.org/10.1063/1.859050 (11 pages) | Cited 33 times

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The evolution of unmagnetized beam‐driven strong Langmuir turbulence is studied in two dimensions by numerically integrating the Zakharov equations for systems pumped by monochromatic and broadband negative‐damping drivers with nonzero central wavenumber. Long‐time statistically steady states are reached for which the dependence of the evolution on the driver wavenumber, growth rate, and bandwidth is examined in detail. For monochromatic drivers, a quasiperiodic cycle is found to develop if the driver wavenumber is sufficiently large. In this cycle, energy from the driven mode undergoes a sequence of weak‐turbulence backscatter decays, which transfer energy to an approximately isotropic long‐wavelength condensate. During this phase, beam‐aligned chains of propagating beat waves develop and perpendicular density waves are also excited. Subsequently, nucleation of waves in density cavities causes a series of wave collapses (involving coherent wave–wave interactions) to occur, during which short‐wavelength damping reduces the system energy in discrete steps. Finally, the cycle restarts. The characteristic frequency of the quasiperiodic cycle and the average system energy are both approximately proportional to the growth rate. Broadening of the driver in wavenumber tends to degrade the system‐wide coherence of the cycle, but its main features appear to survive on the scale of the coherence length of the driver.

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52.35.Ra	Plasma turbulence
52.35.Mw	Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Qz	Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.65.-y	Plasma simulation

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Inertial ranges and resistive instabilities in two‐dimensional magnetohydrodynamic turbulence

H. Politano, A. Pouquet, and P. L. Sulem

Phys. Fluids B 1, 2330 (1989); http://dx.doi.org/10.1063/1.859051 (10 pages) | Cited 47 times

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Direct numerical simulations of decaying two‐dimensional magnetohydrodynamic flows at Reynolds numbers of several thousand are performed, using resolutions of 1024² collocation points. An inertial range extending to about one decade is observed, with spectral properties depending on the velocity–magnetic field correlation. At very small scales, resistive tearing destabilizes current sheets generated by the inertial dynamics and leads to the formation of small‐scale magnetic islands, which may then grow and reach the size of inertial scales.

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52.30.-q	Plasma dynamics and flow
52.30.Cv	Magnetohydrodynamics (including electron magnetohydrodynamics)
47.27.Gs	Isotropic turbulence; homogeneous turbulence
52.65.-y	Plasma simulation

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Nonlinear evolution of Alfvén waves in a finite beta plasma

B. K. Som, Brahmananda Dasgupta, V. L. Patel, and M. R. Gupta

Phys. Fluids B 1, 2340 (1989); http://dx.doi.org/10.1063/1.859052 (5 pages) | Cited 11 times

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A general form of the derivative nonlinear Schrödinger (DNLS) equation, describing the nonlinear evolution of Alfvén waves propagating parallel to the magnetic field, is derived by using two‐fluid equations with electron and ion pressure tensors obtained from Braginskii [in Reviews of Plasma Physics (Consultants Bureau, New York, 1965), Vol. 1, p. 218]. This equation is a mixed version of the nonlinear Schrödinger (NLS) equation and the DNLS, as it contains an additional cubic nonlinear term that is of the same order as the derivative of the nonlinear terms, a term containing the product of a quadratic term, and a first‐order derivative. It incorporates the effects of finite beta, which is an important characteristic of space and laboratory plasmas.

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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.Hr	Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.25.Gj	Fluctuation and chaos phenomena
52.35.Ra	Plasma turbulence

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Equilibrium of a plasma in the fluid‐ and Vlasov–Maxwell systems

Swadesh M. Mahajan and Wann‐Quan Li

Phys. Fluids B 1, 2345 (1989); http://dx.doi.org/10.1063/1.859053 (4 pages) | Cited 6 times

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It is shown that a recently constructed exact solution of the Vlasov equation describing a plasma with density and temperature gradients can be expressed in terms of the constants of motion. The distribution function is then used to illustrate the differences between a Vlasov and a one‐fluid description. In fluid theory, only the pressure profile is determined (unless one postulates an equation of state), while the Vlasov description leads to a separate determination of density (g) and temperature (ψ²) profiles; the equation of state, g=ψ³⁻²^/^β, comes out naturally in the latter case.

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52.25.Fi	Transport properties
52.55.Dy	General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.

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Stability of elongated cross‐section tokamaks to axisymmetric even poloidal mode number deformations

R. Weiner, S. C. Jardin, and N. Pomphrey

Phys. Fluids B 1, 2349 (1989); http://dx.doi.org/10.1063/1.859054 (4 pages) | Cited 1 time

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In a recent paper, Nakayama, Sato, and Matsuoka [Phys. Fluids 31, 630 (1988)] suggested that elliptical cross‐section tokamaks with aspect ratio R/a=3.2 and with elongation κ=2.6 are unstable to a splitting (m=2, n=0) instability for plasma β>5%, and that κ≥4.0 plasmas are unstable to a splitting for β≥1%. The magnetohydrodynamic evolution code tsc [J. Comput. Phys. 66, 481 (1986)] indicates, however, that such plasmas are robustly stable with respect to this splitting. In fact, a κ=3.7 plasma with β=23.0% shows no tendency to split. However, the addition of pinching coils at the waist will cause the plasma to split if the current in these coils exceeds a critical value I_c, which decreases with increasing beta.

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52.30.Cv	Magnetohydrodynamics (including electron magnetohydrodynamics)
52.65.-y	Plasma simulation

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Kinetic effects in Alfvén wave heating. Part I: Surface eigenmodes in a pure plasma

Wann‐Quan Li, David W. Ross, and Swadesh M. Mahajan

Phys. Fluids B 1, 2353 (1989); http://dx.doi.org/10.1063/1.859055 (11 pages) | Cited 9 times

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Kinetic effects of Alfvén wave spatial resonances near the plasma edge are investigated numerically and analytically in a linearized cylindrical tokamak model. In Part I, cold plasma surface Alfvén eigenmodes (SAE’s) in a pure plasma are examined. Numerical calculations of antenna‐driven waves exhibiting absorption resonances at certain discrete frequencies are reviewed first. From a simplified kinetic equation, an analytical dispersion relation is then obtained with the antenna current set equal to zero. The real and imaginary parts of its roots, which are the complex eigenfrequencies, agree with the central frequencies and widths, respectively, of the numerical antenna‐driven resonances. These results serve as an introduction to the companion paper, Part II [Phys. Fluids B 1, 2364 (1989)], in which it is shown that, in the presence of a minority species, certain SAE’s, instead of heating the plasma exterior, can dissipate substantial energy in the two‐ion hybrid layer near the plasma center.

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52.50.Gj	Plasma heating by particle beams
52.35.Hr	Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.25.Dg	Plasma kinetic equations
52.25.Os	Emission, absorption, and scattering of electromagnetic radiation

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Kinetic effects in Alfvén wave heating. Part II: Propagation and absorption with a single minority species

Wann‐Quan Li, David W. Ross, and Swadesh M. Mahajan

Phys. Fluids B 1, 2364 (1989); http://dx.doi.org/10.1063/1.859171 (8 pages) | Cited 8 times

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The effects of a heavy minority on Alfvén wave heating are examined in a linearized circular cylindrical tokamak model. It is shown that a suitable minority concentration and radially varying charge profile produces a two‐ion hybrid resonance in the plasma interior and an Alfvén wave resonance near the edge. The latter situation, which gives rise to cold plasma surface Alfvén eigenmodes (SAE’s), was described in Part I [Phys. Fluids B 1, 2353 (1989)] for a pure plasma. Here, numerical results, exhibiting substantial absorption in the hybrid layer as a result of the dissipation of these modes, are presented. It is shown that the poloidal mode number strongly affects the amount of the energy absorbed in the hybrid layer. Generally, electron heating due to electron Landau and collisional damping of SAE’s and two‐ion hybrid fields [ω>(ω_c2)_max, with ω_c2 being the fundamental minority gyrofrequency] dominates minority heating excepting for cases when k_∥, the parallel wavenumber, is large enough that no SAE occurs near the plasma edge. For the larger k_∥ system, there occurs a stronger coupling between the two‐ion hybrid and fundamental minority gyroresonance layers, resulting in comparable electron and minority heating. The majority heating is zero everywhere because ω<(ω_c1)_min, where ω_c1 is the fundamental majority gyrofrequency.

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52.50.Gj	Plasma heating by particle beams
52.35.Hr	Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.25.Vy	Impurities in plasmas
52.25.Dg	Plasma kinetic equations

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Current sheets and nonlinear growth of the m=1 kink‐tearing mode

F. L. Waelbroeck

Phys. Fluids B 1, 2372 (1989); http://dx.doi.org/10.1063/1.859172 (9 pages) | Cited 81 times

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A calculation is presented that accounts for rapid nonlinear growth of the m=1 kink‐tearing instability. The equilibrium analysis contained in the Rutherford theory [Phys. Fluids 16, 1903 (1973)] of nonlinear tearing‐mode growth is generalized to islands for which the constant‐ψ approximation is not valid. Applying the helicity‐conservation assumption introduced by Kadomtsev [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1977), Vol. I, p. 555], the presence of a current‐sheet singularity is shown that gives rise to a narrow tearing layer and rapid reconnection. This rapid reconnection, in turn, justifies the use of the helicity conservation assumption. The existence of a family of self‐similar m=1 equilibrium islands is demonstrated. The formalism introduced here is shown to apply both to the case of the m=1 kink‐tearing mode and to the case of forced reconnection. These two cases are compared and contrasted.

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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.)
52.35.Bj	Magnetohydrodynamic waves (e.g., Alfven waves)

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Linear stability of low mode number tearing modes in the banana collisionality regime

R. Fitzpatrick

Phys. Fluids B 1, 2381 (1989); http://dx.doi.org/10.1063/1.859173 (16 pages) | Cited 4 times

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The semicollisional layer equations governing the linear stability of small mode number tearing modes in a low beta, large aspect ratio, tokamak equilibrium are derived from an expansion of the gyrokinetic equation. In this analysis only the cases where the ion Larmor radius is either much less than, or much greater than, the layer width are considered. Both the electrons and the ions are assumed to lie in the banana collisionality regime. One interesting feature of the derived layer equations, in the limit of small ion Larmor radius, is a substantial reduction in the effective collisionality of the system due to neoclassical ion dynamics. Next, using a shooting code, a dispersion relation is obtained from the layer equations in the limits of small ion Larmor radius and a vanishingly small fraction of trapped particles. As expected, strong semicollisional stabilization of the mode is found, but, in addition, a somewhat weaker destabilizing effect is obtained in the transition region between the collisional and semicollisional regimes.

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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.Bj	Magnetohydrodynamic waves (e.g., Alfven waves)
52.55.Fa	Tokamaks, spherical tokamaks

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Some parametric instabilities which arise during ion‐Bernstein wave heating in fusion plasmas

A. Kumar and R. P. Sharma

Phys. Fluids B 1, 2397 (1989); http://dx.doi.org/10.1063/1.859174 (7 pages) | Cited 3 times

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In the present paper, the parametric decay instability of an ion‐Bernstein wave (ω_ci<ω₀≲2ω_ci) into a scattered ion‐Bernstein wave and a low‐frequency wave (either an ion‐acoustic wave or a kinetic‐Alfvén wave) has been examined. It has been demonstrated that this parametric process may be one of the possible sources of ion heating in tokamaks. In addition to this, the possibility of oscillating two‐stream instability (OTSI) of an ion‐Bernstein wave (ω_ci<ω₀≲2ω_ci) or a cold plasma ion‐Bernstein wave (ω₀≲ω_ci) has also been discussed. The explicit expressions for threshold and convective threshold of the decay processes are given. For OTSI, the expressions for maximum growth rate have also been given explicitly.

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52.35.Mw	Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.40.Db	Electromagnetic (nonlaser) radiation interactions with plasma
52.50.Gj	Plasma heating by particle beams
52.55.Fa	Tokamaks, spherical tokamaks

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Stability of the global Alfvén eigenmode in the presence of fusion alpha particles in an ignited tokamak plasma

G. Y. Fu and J. W. Van Dam

Phys. Fluids B 1, 2404 (1989); http://dx.doi.org/10.1063/1.859175 (10 pages) | Cited 30 times

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The stability of global Alfvén eigenmodes is investigated in the presence of super‐Alfvénic energetic particles, such as fusion‐product alpha particles in an ignited deuterium–tritium tokamak plasma. Alpha particles tend to destabilize these modes when ω_@B|α>ω_A, where ω_A is the shear‐Alfvén modal frequency and ω_∗α is the alpha particle diamagnetic drift frequency. This destabilization due to alpha particles is found to be significantly enhanced when the alpha particles are modeled with a slowing‐down distribution function rather than with a Maxwellian distribution. However, previously neglected electron damping due to the magnetic curvature drift is found to be comparable in magnitude to the destabilizing alpha particle term. Furthermore, the effects of toroidicity are also found to be stabilizing, since the intrinsic toroidicity induces poloidal mode coupling, which enhances the parallel electron damping from the sideband shear‐Alfvén Landau resonance. In particular, for typical ignition tokamak parameters, global Alfvén eigenmodes are found to be completely stabilized by either the electron damping that enters through the magnetic curvature drift or the damping introduced by finite toroidicity.

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52.55.Pi	Fusion products effects (e.g., alpha-particles, etc.), fast particle effects
52.35.Bj	Magnetohydrodynamic waves (e.g., Alfven waves)
52.55.Fa	Tokamaks, spherical tokamaks

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Line tying of interchange modes in a nearly collisionless mirror‐trapped plasma

Guy Vandegrift

Phys. Fluids B 1, 2414 (1989); http://dx.doi.org/10.1063/1.859176 (8 pages) | Cited 2 times

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If the confining potential of electrostatically trapped electrons fluctuates, then the number of trapped electrons also fluctuates. The linear relationship between potential fluctuations and the number of trapped electrons is investigated, considering two loss mechanisms for a nearly collisionless plasma: (1) small‐angle collisions (diffusion), and (2) large‐angle collisions. This nearly collisionless model predicts the line tying of interchange modes in a mirror‐trapped plasma is orders of magnitude larger than previously thought for a fusion plasma, yet still not strong enough to completely line tie an axisymmetric mirror. Also, a nonlinearity in the response can occur at low amplitude.

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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.Cv	Magnetohydrodynamics (including electron magnetohydrodynamics)

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Estimation of the electrical resistivity in field‐reversed configuration plasmas from detailed interferometric measurements

S. Okada, Y. Kiso, S. Goto, and T. Ishimura

Phys. Fluids B 1, 2422 (1989); http://dx.doi.org/10.1063/1.859177 (8 pages) | Cited 17 times

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Electrical resistivity at the magnetic axis η(R) and at the separatrix η(r_s) of a field‐reversed configuration (FRC) plasma produced by theta pinch machines are estimated from detailed interferometric measurements, assuming that the temperature is uniform within the separatrix. The ratio f₀[=η(R)/η(r_s)] increases with the beta value at the separatrix β_s, which is consistent with the fact that f₀ decreases when x_s (separatrix radius normalized by the inner radius of a theta pinch coil) increases [Phys. Fluids 28, 888 (1985)]. This tendency is a natural consequence of the transport properties of the FRC plasma when the particle confinement time is nearly equal to the decay time of the trapped reversed magnetic flux, as is normally the case. Theoretical expectations of the anomaly of η(r_s) over the classical resistivity η₀ increases and decreases slightly with β_s for the case of the lower hybrid drift and the low‐frequency drift instability, respectively. On the other hand, the observed η(r_s)/η₀ decreases substantially with β_s. [The value of η(r_s)/η₀ changes from about 15 to 5 as β_s changes from 0.45 to 0.6.]

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52.25.Fi	Transport properties
52.70.Kz	Optical (ultraviolet, visible, infrared) measurements
52.55.Ez	Theta pinch

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Nonviability of some nonlocal electron heat transport modeling

M. K. Prasad and D. S. Kershaw

Phys. Fluids B 1, 2430 (1989); http://dx.doi.org/10.1063/1.859178 (7 pages) | Cited 19 times

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Using exact analytical solutions, it is shown that two recent models of nonlocal electron heat transport are beset with mathematical anomalies leading to unphysical results. First, heat flow with a nonlocal heat flux does not smooth out steep temperature gradients in any finite time. Second, a computation of the thermoelectric field from a vanishing nonlocal current flux is an ill‐posed problem leading to instabilities that violate the very assumption on which the model is based. It is verified that these anomalies can lead to a negative entropy production rate, which implies local thermodynamic instability. In particular, it is proved that a temperature distribution that is initially positive can later become negative for certain nonuniform electron density distributions. These results provide a basic understanding of the various difficulties encountered in numerical implementations of these models.

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52.25.Fi	Transport properties
52.50.Jm	Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)

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Numerical simulations of induced spatial incoherence laser light self‐focusing

R. Rankin, C. E. Capjack, and C. R. James

Phys. Fluids B 1, 2437 (1989); http://dx.doi.org/10.1063/1.859179 (13 pages) | Cited 1 time

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The effect of induced spatial incoherence (ISI) on laser light self‐focusing is investigated using a two‐dimensional Eulerian hydrodynamic plasma simulation code. In homogeneous low‐density plasmas (one‐tenth of the critical density for radiation of wavelength λ_L=0.25 μm) it is found that ISI can effectively eliminate thermal and ponderomotive self‐focusing for a wide range of intensities. In plasma containing an initial linear gradient in density, strong self‐focusing occurs when the maximum intensity in the incident light I₀ (where I₀ represents the intensity that would be achieved for a perfectly coherent beam) is allowed to approach 10¹⁷ W cm⁻². At lower intensities, I₀∼10¹⁶ W cm⁻², thermal self‐focusing is eliminated and ponderomotive self‐focusing is significantly reduced. The dwell time of the filamented light varies from the laser light coherence time to a few tens of picoseconds.

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52.38.-r	Laser-plasma interactions
52.50.Jm	Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)
52.65.-y	Plasma simulation

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Self‐consistent resonance absorption with two‐layer profile steepening

E. Ahedo and J. R. Sanmartín

Phys. Fluids B 1, 2450 (1989); http://dx.doi.org/10.1063/1.859180 (12 pages) | Cited 1 time

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Resonance absorption of p‐polarized light, incident at angle θ on a flowing, stratified plasma, is analyzed; profile steepening within (i) a layer around the turning point, and (ii) a thinner, embedded sublayer at the critical surface is taken into account self‐consistently. The entire steepened region is taken as collisionless and isothermal. The structure of the main layer shows a variety of regimes, depending on how the flow crosses a sonic point. The structure of the sublayer is also determined; it is entirely subsonic (with no wave breaking) for a well‐defined, broad parameter range. Density changes across both layer and sublayer, and fractional absorption, are given in terms of [(wavelength)²×intensity/temperature], θ, and (temperature/m_ec²). The flow outside the double structure is also analyzed for particular conditions.

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52.38.-r	Laser-plasma interactions
52.50.Jm	Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)

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Modeling of a cylindrically expanding hydrogenlike fluorine x‐ray laser

D. C. Eder

Phys. Fluids B 1, 2462 (1989); http://dx.doi.org/10.1063/1.859181 (8 pages) | Cited 13 times

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Modeling results are presented for a hydrogenlike fluorine soft x‐ray amplifier experiment performed at Rutherford Appleton Laboratory [Plasma Phys. Controlled Fusion 30, 35 (1988)] in which a gain coefficient of 4.4 cm⁻¹ was observed. Simulations using various values of the flux limiter, f (used to inhibit heat transport), and the amount of resonance absorption, RA, are compared to the experimental results. The maximum calculated gain coefficient is 2 cm⁻¹ for f=0.1 and RA=1%. For this choice of hydrodynamic modeling parameters the dependence of gain on intensity is in qualitative agreement with the experimental data. It is shown that the experiment can be modeled adequately in one dimension by comparing to a two‐dimensional calculation. The use of escape probabilities in an expanding cylindrical medium is discussed. General modeling techniques useful in modeling cylindrically symmetric systems are presented.

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52.25.Os	Emission, absorption, and scattering of electromagnetic radiation
07.85.-m	X- and γ-ray instruments
52.50.Jm	Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.)

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Final focusing of intense ion beams with radially nonuniform current density z discharges

J. J. Watrous and P. F. Ottinger

Phys. Fluids B 1, 2470 (1989); http://dx.doi.org/10.1063/1.859198 (9 pages)

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The spot size and focal length of a one‐eighth betatron wavelength final focusing cell with a nonuniform current density distribution are predicted. The final focusing cell is modeled with an azimuthal magnetic field distribution that varies as r^N. A Lie transform method is used to determine the behavior of the ion beam as it passes through the focusing cell. The analysis indicates that a final focusing cell with a current density distribution that is strongly concentrated at the channel edge focuses the beam much less efficiently than a channel with a uniform current density distribution, and provides a scaling relation for the focused beam radius: r_foc ∝r_c (I_c/ I_f)^1/2N, where r_c is the unfocused beam radius, I_f is the discharge current in the focusing cell, and I_c is the discharge current in the transport channel.

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52.20.Dq	Particle orbits
52.40.Mj	Particle beam interactions in plasmas
52.65.-y	Plasma simulation
52.55.Ez	Theta pinch

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A model of strong beam–plasma turbulence

William Main and Gregory Benford

Phys. Fluids B 1, 2479 (1989); http://dx.doi.org/10.1063/1.859182 (9 pages) | Cited 12 times

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Strong beam–plasma interactions occur when beam density n_b approaches plasma density, n_b/n_p >0.01. Energy flow from resonant waves to short wavelengths is modeled with existing theory, using instability rates from linear and nonlinear (Zakharov) dispersion relations. Langmuir waves lose energy by wave convection, through observed electromagnetic emission, and to heating by induced return currents acting on anomalous resistivity. Inputs to the model equations are current, voltage, and other parameters of a 600 keV, 5 kA electron beam. The beam propagates in 10 mT helium preionized to 2×10¹² cm⁻³, emitting radiation of peak power 100 kW at an efficiency of 3×10⁻⁵. Turbulent electric fields reach 27 kV/cm [Phys. Fluids B 1, 2488 (1989)]. Comparison between experiment and model calculations shows satisfactory agreement.

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52.35.Ra	Plasma turbulence
52.40.Mj	Particle beam interactions in plasmas
52.25.Os	Emission, absorption, and scattering of electromagnetic radiation
52.70.Gw	Radio-frequency and microwave measurements

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Optical diagnosis of electric fields in a beam‐driven turbulent plasma

Amikam Dovrat and Gregory Benford

Phys. Fluids B 1, 2488 (1989); http://dx.doi.org/10.1063/1.859183 (7 pages) | Cited 13 times

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Optical diagnostics using laser fluorescence techniques are used to measure the rms electric field in a superstrongly turbulent, relativistic beam–plasma system. This yields the mapping of 〈E²〉 as a function of radial location r and time t. This 〈E²(r,t)〉 allows studies of growth and evolution of turbulent fields, their diffusion, and decay. Fluctuating electric fields occur when a 700 keV, 4 kA, 2 μsec electron beam propagates into a 20 cm diam, 1.5 m long drift tube filled with 10 mTorr of helium plasma. Stark effect shifts appear in suitable forbidden and allowed transitions, originating from the same upper energy level for the measurement: Hei 6632 Å and Hei 5015.7 Å. The spectral bandwidth includes the forbidden line and its satellites. Using the ratio of the intensity of the forbidden plus satellite lines, to the allowed line intensity, yields the rms field as the combined field of oscillation near the plasma frequency. Fields up to 28 kV/cm result. These results can be explained by an analytical model of production of strong electric fields by beam–plasma instability, including modulational transfer in k space, plasma heating, radiation, and wave convection. Comparison between experiment and the numerically integrated model shows good agreement.

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52.35.Ra	Plasma turbulence
52.40.Mj	Particle beam interactions in plasmas
52.27.Ny	Relativistic plasmas
52.70.Kz	Optical (ultraviolet, visible, infrared) measurements

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Analysis of free‐electron lasing stimulated by a counterpropagating plasma wave

K. Akimoto and Y. T. Yan

Phys. Fluids B 1, 2495 (1989); http://dx.doi.org/10.1063/1.859184 (7 pages) | Cited 1 time

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A relativistic fluid theory is constructed to analyze the inverse Compton scattering of an unmagnetized counterpropagating plasma wave by a cold relativistic electron beam. A Langmuir wave and electromagnetic plasma wave wigglers are considered, and the properties of the two types of wigglers are comparatively discussed. The growth rates are comparable to those of the ac free‐electron laser and the free‐electron lasers with magnetostatic wigglers in the Raman regime.

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52.59.Px	Hard X-ray sources
52.27.Ny	Relativistic plasmas
52.35.Fp	Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.35.Hr	Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)

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Gyrokinetics of transverse‐magnetic‐mode gyrotron, gyropeniotron, cyclotron autoresonance maser, and nonwiggler free‐electron laser amplifiers

Shi‐Chang Zhang

Phys. Fluids B 1, 2502 (1989); http://dx.doi.org/10.1063/1.859185 (5 pages) | Cited 15 times

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In this paper a comprehensive kinetic, gyrokinetics theory is presented to provide a unified description of transverse‐magnetic‐mode gyrotron, gyropeniotron, cyclotron autoresonance maser, and nonwiggler free‐electron laser amplifiers. By introducing gyrokinetic variables, a unified dispersion equation is derived in which the effect of the guiding‐center shift is taken into account. Similar to the transverse‐electric‐mode cases, it is found that at the zero point of the J_m−l ( math

) instability is still effective, where J_m−l is the Bessel function of order (m−l), m and l are, respectively, the azimuthal index of the mode and the index of the synchronous harmonic, and math

is the electron beam radius normalized by the cutoff wavenumber.

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84.40.Ik	Masers; gyrotrons (cyclotron-resonance masers)
41.60.Cr	Free-electron lasers
84.40.Fe	Microwave tubes (e.g., klystrons, magnetrons, traveling-wave, backward-wave tubes, etc.)

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1 Dec 1989

Volume 1, Issue 12, pp. 2305-2535

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