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

Select this Article		THE 1992 JAMES CLERK MAXWELL PRIZE IN PLASMA PHYSICS Phys. Fluids B 5, 1 (1993); http://dx.doi.org/10.1063/1.3480477 (1 page) Full Text: \| Download PDF
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A gyrokinetic calculation of transmission and reflection of the fast wave in the ion cyclotron range of frequencies

C. N. Lashmore‐Davies, V. Fuchs, and R. O. Dendy

Phys. Fluids B 5, 3 (1993); http://dx.doi.org/10.1063/1.860865 (6 pages)

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A full‐wave equation has been obtained from the gyrokinetic theory for the fast wave traversing a minority cyclotron resonance [Phys. Fluids B 4, 493 (1992)] with the aid of the fast wave approximation [Phys. Fluids 31, 1614 (1988)]. This theory describes the transmission, reflection, and absorption of the fast wave for arbitrary values of the parallel wave number. For oblique propagation the absorption is due to both ion cyclotron damping by minority ions and mode conversion to the ion Bernstein wave. The results for a ³He minority in a D plasma indicate that for perpendicular propagation and minority temperatures of a few keV the power lost by the fast wave is all mode converted whereas for minority temperatures ∼100 keV∼30% of the incident power is dissipated by the minority ions due to the gyrokinetic correction. The gyrokinetic correction also results in a significant reduction in the reflection coefficient for low field side incidence when k_zL_B≲1 and the minority and hybrid resonances overlap.

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52.50.Gj	Plasma heating by particle beams
52.25.Os	Emission, absorption, and scattering of electromagnetic radiation
52.40.Db	Electromagnetic (nonlaser) radiation interactions with plasma
52.35.Hr	Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)

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Stability of drift‐wave modons in the presence of temperature gradients

D. Jovanović and W. Horton

Phys. Fluids B 5, 9 (1993); http://dx.doi.org/10.1063/1.860872 (10 pages) | Cited 9 times

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In the homogeneous Hasegawa–Mima equation, the dipole vortex or modon solution is well known to be robustly stable from both analytic and numerical studies. In the inhomogeneous plasma where ∇T_e≠0 the corresponding vortex has an external structure extending into the high‐temperature region. Lyapunov stability method is used to determine the stability properties of these extended vortex structures. The overall growth rate of deformation caused by the presence of temperature inhomogeneity is shown to be bounded by (R/L_T)², where R is the radius of the core of the vortex and L_T is the scale length of the temperature gradient. The most important source of instability is identified as the excitation of monopolar and dipolar perturbations with short spatial scales ≲R, which are approximately independent of the presence of the density and temperature gradients.

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52.35.Qz	Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.35.Sb	Solitons; BGK modes

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Coherent structures in rotating non‐neutral plasma

Steven M. Lund, Jesus J. Ramos, and Ronald C. Davidson

Phys. Fluids B 5, 19 (1993); http://dx.doi.org/10.1063/1.860853 (23 pages) | Cited 7 times

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Nonaxisymmetric (∂/∂θ≠0) rotating equilibria are investigated theoretically for strongly magnetized, low‐density (ω_pe²/ω_ce²≪1) pure electron plasmas confined in cylindrical geometry. These two‐dimensional equilibria are also called rotating coherent structures, and are stationary (time independent) in a frame of reference rotating with angular velocity ω_r=const about the cylinder axis (r=0). Radial confinement of the pure electron plasma is provided by a uniform axial magnetic field B₀e_z, and a grounded, perfectly conducting, cylindrical wall is located at radius r=r_w. The analysis is based on a nonrelativistic, guiding‐center model in the cold‐fluid limit (the continuity and Poisson equations) that treats the electrons as a massless fluid (m_e→0) with E×B flow velocity V_e=−(c/B₀)∇ϕ×e_z. Within this model, general rotating equilibria with electron density n_e≡n_R(r,θ−ω_rt) and electrostatic potential ϕ≡ϕ_R(r,θ−ω_rt) have the property that the electron density is functionally related to the streamfunction ψ_R=−eϕ_R+ω_r(eB₀/2c)r² by n_R=n_R(ψ_R).

The streamfunction ψ_R satisfies the nonlinear equilibrium equation ∇²ψ_R=−4πe²n_R(ψ_R)+2ω_reB₀/c with ψ_R=ω_r(eB₀/2c)r_w²≡ψ_w=const on the cylindrical wall at r=r_w. Following a general discussion of rotating equilibria, an integral equation formulation of the nonlinear equilibrium equation is developed to investigate equilibria with ‘‘waterbag’’ (step‐function) density profiles. In this investigation, a numerical method is formulated that can be used to construct diverse classes of highly nonlinear waterbag equilibria. This method is employed to investigate two classes of nonaxisymmetric equilibria that are nonlinear extrapolations of well‐known small‐amplitude equilibria. These two classes of rotating equilibria bear strong similarities to coherent structures observed experimentally by Driscoll and Fine [Phys. Fluids B 2, 1359 (1990)].

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52.27.Jt	Nonneutral plasmas
52.35.Mw	Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Sb	Solitons; BGK modes
52.55.Dy	General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.

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The evolution of strongly modulated, low‐frequency, moderate‐amplitude wave packets in a dispersive plasma

Bernard J. Vasquez and Peter J. Cargill

Phys. Fluids B 5, 42 (1993); http://dx.doi.org/10.1063/1.860866 (13 pages) | Cited 2 times

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The evolution of strongly modulated wave packets in a dispersive plasma that propagate parallel to the magnetic field is studied. Modulation effects are shown to reduce significantly (≊30%) the rate of spreading from that due to dispersion alone. For fluidlike behavior, nonlinearity has its greatest impact on evolution when the linear sound speed and initial wave packet speeds are well matched, resulting in a strong coupling between the wave magnetic and sonic components. Ion kinetic processes reduce the impact of nonlinearity and cause the rate of spreading to approach that expected from dispersion alone as the ratio of ion and electron temperatures, T_i/T_e→4. For β≳1 and T_i/T_e∼1, the coupled waveforms correspond qualitatively to kinetic treatments of the derivative nonlinear Schrödinger (DNLS) equation.

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52.35.Hr	Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.35.Mw	Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

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Nonlinear electrical conductivity in hydrogen plasma

Michael Stobbe, Ronald Redmer, and Axel Könies

Phys. Fluids B 5, 55 (1993); http://dx.doi.org/10.1063/1.860867 (8 pages) | Cited 1 time

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Employing the Zubarev method for the derivation of a nonequilibrium statistical operator, Vlasov–Uehling–Uhlenbeck quantum kinetic equations are derived for the distribution functions of clusters with arbitrary mass number. Considering a partially ionized hydrogen plasma, the electronic distribution function is determined numerically for the homogeneous and stationary case. Restricting to elastic scattering processes between the electrons, ions and atoms, the analytical solution of Schenter and Liboff [Phys. Fluids 30, 1789 (1987)] is reproduced. Furthermore, the influence of inelastic collisions such as ionization is investigated. Using the electronic distribution function, the electrical conductivity is calculated for hydrogen plasma of a given composition at arbitrary field strengths. The nonlinear behavior obtained is dependent on the different expressions applied for the electron–atom and the electron–ion cross sections. The effect of inelastic collisions is, in general, a lowering of the conductivity because such processes lead to a limitation of the energy gain of electrons in an electric field.

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52.25.Fi

Transport properties

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A renormalization group analysis of two‐dimensional magnetohydrodynamic turbulence

Wenli Z. Liang and P. H. Diamond

Phys. Fluids B 5, 63 (1993); http://dx.doi.org/10.1063/1.860868 (11 pages) | Cited 11 times

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The renormalization group (RNG) method is used to study the physics of two‐dimensional (2‐D) magnetohydrodynamic (MHD) turbulence. It is shown that, for a turbulent magnetofluid in two dimensions, no RNG transformation fixed point exists on account of the coexistence of energy transfer to small scales and mean‐square magnetic flux transfer to large scales. The absence of a fixed point renders the RNG method incapable of describing the 2‐D MHD system. A similar conclusion is reached for 2‐D hydrodynamics, where enstrophy flows to small scales and energy to large scales. These analyses suggest that the applicability of the RNG method to turbulent systems is intrinsically limited, especially in the case of systems with dual‐direction transfer.

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52.30.-q	Plasma dynamics and flow
47.65.-d	Magnetohydrodynamics and electrohydrodynamics
11.10.Gh	Renormalization

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On nonlocal electron heat conduction

S. I. Krasheninnikov

Phys. Fluids B 5, 74 (1993); http://dx.doi.org/10.1063/1.860869 (3 pages) | Cited 24 times

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An improvement of the Albritton nonlocal electron heat transport model is proposed for high‐Z plasmas. The thermal decay of the temperature perturbation in a uniform plasma as calculated by this model is compared with that obtained by Fokker–Planck simulations. Complete agreement is found up to values kλ_e≂0.1, where k is the wave number of the perturbation and λ_e is the thermal electron mean‐free path.

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51.10.+y

Kinetic and transport theory of gases

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A fully nonlinear characteristic method for gyrokinetic simulation

S. E. Parker and W. W. Lee

Phys. Fluids B 5, 77 (1993); http://dx.doi.org/10.1063/1.860870 (10 pages) | Cited 163 times

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A new scheme that evolves the perturbed part of the distribution function along a set of characteristics that solves the fully nonlinear gyrokinetic equations is presented. This low‐noise nonlinear characteristic method for particle simulation is an extension of the partially linear weighting scheme, and may be considered an improvement over existing δf methods. Some of the features of this new method include the ability to keep all nonlinearities, particularly those associated with the velocity space, the use of conventional particle loading techniques, and also the retention of the conservation properties of the original gyrokinetic system in the numerically converged limit. The new method is used to study a one‐dimensional drift wave model that isolates the parallel velocity nonlinearity. A mode coupling calculation for the saturation amplitude is given, which is in good agreement with the simulation results. Finally, the method is extended to the electromagnetic gyrokinetic equations in general geometry.

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52.65.-y	Plasma simulation
51.10.+y	Kinetic and transport theory of gases

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Two‐stage turbulence suppression and E×B velocity shear measured at the L–H transition

R. Philipona, E. J. Doyle, N. C. Luhmann, W. A. Peebles, C. L. Rettig, R. J. Groebner, K. H. Burrell, P. Gohil, H. Matsumoto, and R. D. Stambaugh

Phys. Fluids B 5, 87 (1993); http://dx.doi.org/10.1063/1.860871 (5 pages) | Cited 25 times

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At the onset of the L–H transition in the DIII‐D tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p.159], a fast (≊100 μsec) suppression of microturbulence is observed as the edge transport barrier is formed. This fast edge suppression is followed by a much slower (tens of msec), but substantial (≥50%) reduction in the relative density fluctuation level. This second turbulence suppression phase, which is observed to correlate with growing E×B velocity shear, has been localized to the plasma interior, and may explain why the observed transport reduction in the H mode has been observed to extend deep into the plasma, well beyond the edge transport barrier.

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52.35.Qz	Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.55.Pi	Fusion products effects (e.g., alpha-particles, etc.), fast particle effects
52.70.Gw	Radio-frequency and microwave measurements

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Parametric excitation of high‐frequency electromagnetic waves by the lower‐frequency dipole pumping

K. V. Gamayunov, G. V. Khazanov, E. N. Krivorutsky, and A. A. Veryaev

Phys. Fluids B 5, 92 (1993); http://dx.doi.org/10.1063/1.860973 (12 pages) | Cited 2 times

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The possibility of parametric excitation of high‐frequency electromagnetic waves by lower‐frequency dipole pumping is studied. It is shown that the obtained general dispersive equation may be reduced to the Mathieu equation, provided the case of the flux instability is neglected. In the framework of the developed approach, the excitation of magnetohydrodynamic waves and whistler oscillations is examined.

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52.35.Qz	Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.25.Dg	Plasma kinetic equations
52.25.Fi	Transport properties

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Stochastic energy diffusion of electrons in a plasma by an electron cyclotron wave

Daniela Farina, Roberto Pozzoli, Aniello Mennella, and Dario Ronzio

Phys. Fluids B 5, 104 (1993); http://dx.doi.org/10.1063/1.860857 (8 pages) | Cited 8 times

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The investigation of the energy diffusion process of the electrons in a magnetized plasma due to an electron cyclotron wave in perpendicular propagation with respect to the magnetic field is performed. Starting from the description of the relativistic electron motion by means of an action‐angle Hamiltonian H(I,θ,t), the Fokker–Planck–Kolmogorov (FPK) approach to the diffusion is considered for a globally stochastic regime of the system. In this regime, the phase correlation process is analyzed, and the characteristic decay time is estimated analytically. The action diffusion coefficient D(I) is derived and compared with a local quasilinear expression. With explicit reference to the low‐density regime, where D increases with I, and is very close to the quasilinear coefficient, the solution of the diffusion equation is compared with the results obtained by direct numerical integration of the motion equations for a statistically significant ensemble of particles. A good agreement with the local quasilinear FPK diffusion is observed. In addition, when the amplitude of the perturbation is varied, oscillations of the average action values around the quasilinear results are found on the long time scale.

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02.40.-k	Geometry, differential geometry, and topology
05.45.-a	Nonlinear dynamics and chaos
52.50.Gj	Plasma heating by particle beams
52.35.Mw	Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

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Nonlinear diffusive interpenetration of a plasma and a magnetic field

Jacob Levin and Baruch Meerson

Phys. Fluids B 5, 112 (1993); http://dx.doi.org/10.1063/1.860858 (6 pages)

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Nonlinear diffusive interpenetration of a finite‐β plasma and a magnetic field is considered in the framework of the one‐fluid magnetohydrodynamics (MHD) in the slab geometry. If the characteristic interpenetration time is much longer than the magnetoacoustic time, the process proceeds under the force equilibrium. Then the problem can be reduced to a single second‐order nonlinear diffusion equation in the Lagrangian coordinates. Two examples of the interpenetration are considered. The first presents the diffusion of a plasma into a plasma in a perpendicular magnetic field. The problem proves to be self‐similar, and its solution is found. The second one concerns the diffusive expansion of an initially confined plasma slab across a perpendicular magnetic field. The problem is solved numerically and the results are compared with an asymptotic self‐similar solution, found earlier in the low‐β limit.

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

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Magnetic surfaces in a steady‐state tokamak

R. Kinney, T. Tajima, and H. Irie

Phys. Fluids B 5, 118 (1993); http://dx.doi.org/10.1063/1.860859 (7 pages) | Cited 3 times

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The effects of self‐consistently interacting internal currents are modeled in a tokamak plasma with given external toroidal and poloidal magnetic fields. The unperturbed external magnetic surfaces are described through the well‐known nonlinear ‘‘standard map.’’ When the magnetic field is allowed to carry an internal current, the self‐interaction of these currents disturbs the integrity of the magnetic surfaces. A computational study of the effects of the interacting internal current filaments measures the diffusion of field lines from the unperturbed surfaces, and finds the self‐interaction to be a significant effect that always serves to increase diffusion. Perfect surfaces are not maintained even when magnetic islands would not otherwise overlap. Diffusion from the current interaction dominates when current fluctuations reach a fraction of the applied field.

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52.55.Fa	Tokamaks, spherical tokamaks
52.65.-y	Plasma simulation
52.30.Cv	Magnetohydrodynamics (including electron magnetohydrodynamics)

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Modeling and simultaneous sawtooth measurements of the thermal and energetic electron diffusivities from the Texas Experimental Tokamak

Peter J. Catto, J. R. Myra, Roger D. Bengtson, and A. J. Wootton

Phys. Fluids B 5, 125 (1993); http://dx.doi.org/10.1063/1.860860 (13 pages) | Cited 5 times

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Convenient mathematical models appropriate for simultaneously measuring the thermal and energetic electron diffusivities by their responses to internal disruptions are presented and compared to simultaneous soft and hard x‐ray sawtooth data from the Texas Experimental Tokamak (TEXT) [Nucl. Technol./Fusion 1, 479 (1981)]. The eigenfunction expansion technique employed is first illustrated on a constant diffusivity, single sawtooth crash model that is unable to give a satisfactory fit to the TEXT soft x‐ray data at disparate radii for an initial condition of a flattened temperature profile out to the mixing radius. A more sophisticated single crash model having a parabolic radial dependence for the thermal diffusivity and a flattened profile initial condition substantially improves the fit to the TEXT soft x‐ray data. Simultaneous measurements of the sawtooth oscillations on the hard x‐ray signal caused by runaway electrons hitting the limiter are interpreted to obtain a measure of the diffusivity of the energetic electrons in TEXT following the same crash used to measure the thermal diffusivity. A single sawtooth crash model is no longer adequate because the diffusivity of the energetic electrons may be substantially less than the thermal value. Therefore the eigenfunction expansion technique is extended to a periodic sawtooth crash model. Measurements of diffusivities far smaller than those that can be measured by a single crash model are possible and more than one value of diffusivity can fit the simultaneous TEXT hard x‐ray data. The lower values of diffusivity could not have been obtained by a single crash model. Additional hard x‐ray measurements having differing sawtooth periods are needed to remove the ambiguity. As more extensive hard x‐ray data become available on TEXT, it may become possible to simultaneously and unambiguously measure the thermal and energetic electron diffusivities during the same crash.

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52.25.Fi	Transport properties
52.25.Gj	Fluctuation and chaos phenomena
52.70.La	X-ray and γ-ray measurements

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Saturation of stimulated Raman scattering by Langmuir and ion‐acoustic wave coupling

T. Kolber, W. Rozmus, and V. T. Tikhonchuk

Phys. Fluids B 5, 138 (1993); http://dx.doi.org/10.1063/1.860861 (13 pages) | Cited 54 times

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Studies of stimulated Raman scattering (SRS) based on the one‐dimensional Zakharov–Maxwell equations for homogeneous, finite plasmas are presented for a wide range of parameters relevant to current laser–plasma interaction experiments. It was found that the primary mechanism responsible for saturation of SRS is the parametric decay instability (PDI) of the resonantly driven Langmuir wave. The different spatiotemporal evolution of SRS (convective) and PDI (absolute) leads to new physics in SRS nonlinear evolution, including disruption of PDI cascade, localization of Langmuir fields, and burstlike behavior of SRS reflectivity. The asymptotic saturation levels are well approximated by a simple scaling law, which is proportional to the PDI threshold and depends on the SRS convective gain factor.

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52.38.-r	Laser-plasma interactions
52.35.Mw	Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Ra	Plasma turbulence

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A model for magnetic energy storage and Taylor’s relaxation in the solar corona. I: Helicity‐constrained minimum energy state in a half‐cylinder

J. J. Aly

Phys. Fluids B 5, 151 (1993); http://dx.doi.org/10.1063/1.860862 (13 pages) | Cited 5 times

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The problem of the existence of a minimum energy state is studied in the set H of all the magnetic fields B: (i) occupying the half‐cylinder D={r<R,z≳0}; (ii) having a normal component vanishing on the vertical part {r=R} of the boundary of D and taking given values Q(r) on its horizontal part {z=0}; (iii) having a relative helicity equal to a prescribed value H. It is first shown that the only field that may possibly be an energy minimizer in H is the unique (and therefore axisymmetric) constant‐α force‐free field B_α contained in that set. Thus it is proved that B_α minimizes the energy indeed if and only if 0≤‖H‖≤H_c≤∞, where H_c is an estimated critical value. For H_c≤‖H‖≤∞, on the contrary, it is possible to construct in H nonaxisymmetric fields with an energy smaller than that of B_α and no minimum energy state does exist. However, B_α still minimizes the energy for H_c ≤‖ H‖ ≤ H^ax_c (with possibly H^ax_c = ∞) if attention is restricted to the axisymmetric fields of H. These results are used to put a limit on the validity of a popular model of the heating of the solar corona, in which the field of a coronal structure is supposed to release sporadically, by Taylor’s relaxation, a part of the energy it continuously extracts from the kinetic energy of the photospheric motions. It is argued that, as a consequence of the results above, one of the basic assumptions of the model breaks down when the field becomes highly sheared. It is speculated that, in such a situation, a completely new regime should set up, in which helicity and energy are continuously ejected at large distances by the system.

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52.30.Cv	Magnetohydrodynamics (including electron magnetohydrodynamics)
96.60.P-	Corona

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Coherent corrections to the synchrotron radiation spectrum of a relativistic electron beam

D. I. Kaltchev and E. A. Perelstein

Phys. Fluids B 5, 164 (1993); http://dx.doi.org/10.1063/1.860849 (7 pages) | Cited 1 time

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The coherent corrections to the radiation spectrum of a relativistic electron beam, propagating along an external magnetic field are investigated. In the beam reference frame the cyclotron radiation from a hot magnetoplasma is calculated taking into account the electron correlations. The fluctuation‐dissipation theorem for the case of an equilibrium plasma is used to find the spectrum of current‐density fluctuations. At harmonics of the cyclotron frequency ≥2, the collective distortion of this spectrum decreases the radiation intensity compared to the spontaneous one. The coherent effects manifest themselves at wavelengths of the order of the Debye shielding length and become important when the electronic density in the laboratory frame is higher than 10¹³ cm⁻³ for typical experimental beam parameters.

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29.27.Bd	Beam dynamics; collective effects and instabilities
52.27.Ny	Relativistic plasmas
52.35.Hr	Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)

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Kinetic theory of a whistler‐pumped free electron laser

Anamika Sharma and V. K. Tripathi

Phys. Fluids B 5, 171 (1993); http://dx.doi.org/10.1063/1.860850 (5 pages) | Cited 6 times

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A kinetic formalism of mode coupling in a whistler‐pumped free electron laser (FEL) is developed. The analysis includes the effect of finite space charge field of the electron beam. Kinetic effects appear through the beam plasma susceptibility in the coupling coefficient. For a Gaussian distribution in beam axial momentum, the growth rate of FEL instability falls off rapidly with increasing momentum spread. The growth rate is also a sensitive function of pump frequency and plasma density. Feasibility of this device in the low‐current Compton regime is also examined.

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52.59.Px	Hard X-ray sources
52.40.Mj	Particle beam interactions in plasmas
52.35.Hr	Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)

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Intense ion‐beam‐transport experiments using a z‐discharge plasma channel

J. M. Neri, P. F. Ottinger, D. V. Rose, P. J. Goodrich, D. D. Hinshelwood, D. Mosher, S. J. Stephanakis, and F. C. Young

Phys. Fluids B 5, 176 (1993); http://dx.doi.org/10.1063/1.860851 (14 pages) | Cited 15 times

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A z‐discharge plasma channel is used to confine and transport an intense proton beam. A pinch‐reflex ion diode on the NRL Gamble II accelerator focuses a proton beam onto the entrance aperture of a 2.5 cm diam, 1.2 m long z‐discharge transport system. The beam ions are charge and current neutralized in the discharge plasma, and execute betatronlike orbits in the magnetic field of the discharge. Ion beam diagnostics include shadowbox imaging and prompt‐γ radiation measurements from LiF targets. Under appropriate conditions, 95% particle transport and 90% energy transport are observed, with the only energy loss attributed to classical stopping in the channel gas. The transverse phase‐space distribution of the beam measured by the shadowbox is consistent with full charge and current neutralization of the transported beam.

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52.40.Mj	Particle beam interactions in plasmas
52.65.-y	Plasma simulation
52.70.Nc	Particle measurements

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A self‐consistent nonlinear theory of current modulation in relativistic klystron amplifiers

Han S. Uhm

Phys. Fluids B 5, 190 (1993); http://dx.doi.org/10.1063/1.860852 (11 pages) | Cited 18 times

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A self‐consistent nonlinear theory of the energy and current modulation in a relativistic electron beam propagating through a klystron amplifier is developed. A closed integrodifferential equation for the beam current is obtained, assuming that the beam current is a function of time t and propagation distance z. Properties of the current and energy modulation are investigated from this integrodifferential equation for a broad range of system parameters. Magnitudes of the energy and current modulation are determined in terms of the gap voltage, the cavity frequency, geometric configuration, the beam intensity, and initial kinetic energy of the beam. The modulation amplitude increases, reaches peak, and decreases slowly, as the beam propagates through the amplifier. A simple expression of scaling law for maximum current modulation is obtained. This scaling law could be useful in the design and fabrication of a high‐performance klystron. Nonlinear mode evolution in current profile is also investigated by Fourier decomposing the current modulation obtained from the integrodifferential equation. The mode evolution in a long‐range propagation of an electron beam exhibits various interesting physical properties. For example, the maximum amplitude of the fundamental mode (l=1) occurs at the propagation distance, where all other modes vanish or have a very small amplitude. This property ensures a monochromatic frequency.

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84.40.Fe

Microwave tubes (e.g., klystrons, magnetrons, traveling-wave, backward-wave tubes, etc.)

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Electron beam acceleration by nonlinear Landau damping of electromagnetic waves in a plasma

R. Sugaya

Phys. Fluids B 5, 201 (1993); http://dx.doi.org/10.1063/1.860972 (8 pages) | Cited 8 times

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Acceleration and heating of an electron beam caused by nonlinear Landau damping of intense electromagnetic waves in a plasma are investigated theoretically based on a velocity‐space diffusion equation. The beat wave, which does not satisfy the dispersion relation, is excited by the nonlinear interaction of two electromagnetic waves and interacts nonlinearly with the electron beam. As the frequency of the beat wave approaches the electron plasma frequency, the rates of acceleration and heating of the electron beam and the beat wave energy density become maximum values, being equal to those by stimulated Raman scattering. The beat wave is an electrostatic mode that can have a phase velocity near the light velocity and is able to accelerate the electron beam to a relativistic energy.

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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.Mj	Particle beam interactions in plasmas
52.35.Qz	Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.50.Gj	Plasma heating by particle beams

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Ion emission from anode foils during multistage acceleration of intense ion beams

S. A. Slutz

Phys. Fluids B 5, 209 (1993); http://dx.doi.org/10.1063/1.860854 (7 pages) | Cited 2 times

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Steady‐state calculations are presented that show that the ion current density extracted off an anode foil in a multistage ion diode is a monotonically decreasing function of the injected current density J, going to zero as J goes to a limiting value J₁. However, J₁ can be quite large, going to infinity as the diode voltage approaches the limiting voltage V₁ from below. Thus, it may not always be practical to inject a beam of current density exceeding J₁. The results presented in this paper can be used to determine the fraction of (typically unwanted) ions extracted from the anode foil when J≤J₁.

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41.75.Ak	Positive-ion beams
52.27.Jt	Nonneutral plasmas
41.75.-i	Charged-particle beams

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Reaction and diffusion in dense nonideal plasmas

D. Kremp, M. Schlanges, M. Bonitz, and T. Bornath

Phys. Fluids B 5, 216 (1993); http://dx.doi.org/10.1063/1.860855 (14 pages) | Cited 7 times

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The nonequilibrium properties of strongly coupled plasmas are investigated taking into account reaction and diffusion processes. The starting point is quantum kinetic equations for systems with chemical reactions involving many‐body effects like screening, self‐energy, and medium‐dependent scattering. The influence of these effects on the kinetics of reaction and diffusion processes is discussed. Generalized expressions for the coefficients of impact ionization and diffusion are derived exhibiting a strong density dependence due to the many‐body effects. Solving the reaction‐diffusion equation (RDE) for a dense hydrogen plasma, nonlinear phenomena such as bistability, running ionization fronts, and droplet formation are obtained.

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52.25.Fi	Transport properties
05.20.Dd	Kinetic theory
82.33.Xj	Plasma reactions (including flowing afterglow and electric discharges)
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking

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Semilocal kinetic analysis of the toroidal ion temperature gradient mode

A. Hirose

Phys. Fluids B 5, 230 (1993); http://dx.doi.org/10.1063/1.860856 (3 pages) | Cited 7 times

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The semilocal kinetic analysis based on appropriate norms of differential operators is able to recover the growth rates of the toroidal ion temperature gradient mode found from the rigorous integral equation formulation.

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