bluuebunny/crossref_metadata_2025 huggingface dataset:
Weakly nonlinear dispersive waves: group velocity
Authors: Shivamoggi Bhimsen K.
Published: March 2009

For slowly varying wave trains in a linear system, it is known that a quantity proportional to the square of the amplitude propagates with the group velocity. It is shown here, by considering a specific problem of longitudinal waves in a hot electron-plasma and using an asymptotic analysis, that this result continues to be valid even when weak nonlinearities are introduced into the system provided they produce slowly varying wave trains. The method of analysis fails, however, for weakly nonlinear ion-acoustic waves.
Heating of electrons and ions by inverse bremsstrahlung absorption: a self-similar tate of the plasma
Authors: Balescu R.
Published: March 2009

It is shown that, under the influence of a monochromatic HF electric field (laser beam), both the electrons and the ions in a high-Z plasma reach a homogeneous and isotropic self-similar state (SSS) in which the distribution functions are of the factorized form: where W±(t) is a scaling velocity, the square of which is proportional to the effective temperature. Whereas the SSS for the electrons was known from previous work, with

it is shown here that the corresponding ion SSS exists and is characterized by a simple Maxwellian, øi ø exp (−v2). The discussion of the thermal velocities W±(t), which are obtained in analytical form, provides a transparent physical insight into the heating mechanism of the plasma by inverse bremsstrahlung absorption.
Large-scale disruptions in a current-carrying magnetofluid
Authors: Dahlburg Jill P. , Montgomery David , Doolen Gary D. , Matthaeus William H.
Published: March 2009

A pseudo-spectral three-dimensional Strauss-equations code is used to describe internal disruptions in a strongly magnetized, electrically-conducting fluid, with and without an externally applied, axial electric field. Rigid conducting walls form a square (x, y) boundary, and periodic boundary conditions are assumed in the axial (z) direction. Typical resolution is 64 × 64 × 32 and the maximum Lundquist number is approximately 400. The dynamics are dominated by a helical current filament which wraps itself around the axis of the cylinder; parts of this filament can sometimes become strongly negative. The ratio of turbulent kinetic energy to total poloidal magnetic energy rises from very small values to values of the order of a few hundredths, and executes ‘bounces’ as a function of time in the absence of the external electric field. In the presence of the external electric field, the first bounce is by far the largest, then the plasma settles into a non-uniform quasi-steady state characterized by a poloidal fluid velocity flow. At the large scales, this flow has the shape of a pair of counter-rotating bean-shaped vortices. The subsequent development of this fluid flow depends strongly upon whether or not a viscous term is added to the equation of motion. Inclusion of viscosity tends to damp the flow and leads to pronounced subsequent bounces suggestive of sawtooth oscillations, though the first bounce remains substantially the largest. By means of a three-mode (Lorenz-like) truncation of the Strauss equations, the evolution of the largest spatial scales alone may be examined. Some time-dependent solutions of the low-order truncation system suggest qualitative agreement with fully resolved solutions of the Strauss equations, while other solutions exhibit interesting dynamical-systems behaviour which is thus far unparalleled in the fully-resolved simulation results.
More on the expansion of a collisionless plasma into the wake of a body
Authors: Wright K. H. , Parks D. E. , Katz I. , Stone N. H. , Samir U.
Published: March 2009

Recent laboratory measurements of plasma expansion in a plasma wake experiment are compared with analytical expressions which approximate the plasma expansion model of Crow, Auer & Allen. Good quantitative agreement was found between the data and theory for the velocity and position of the ion expansion front. These results provide an important insight into the behaviour of the expansion early in its development.
Resonant electron diffusion as a saturation process of the synchrotron maser instability
Authors: Lee M. C. , Kuo S. P.
Published: March 2009

The theory of resonant electron diffusion as an effective saturation process of the auroral kilometric radiation has been formulated. The auroral kilometric radiation is assumed to be amplified by the synchrotron maser instability that is driven by an electron distribution of the loss-cone type. The calculated intensity of the saturated radiation is found to have a significantly lower value in comparison with that caused by the quasi-linear diffusion process as an alternative saturation process. This indicates that resonant electron diffusion dominates over quasi-linear diffusion in saturating the synchrotron maser instability.
Equilibrium and stability of collisionless systems in the paraxial limit
Authors: Newcomb William A.
Published: March 2009

The boundary term in the energy integral (105) is superfluous and should be dropped. If we use the Jacobian relation (86) to transform the dummy variables of integration from ψ, θ, to x, y (recalling that B = Bmax = const. at the ends), we see that this term reduces to the integral of a fixed function of x and y over a fixed region of the (x, y) plane. In other words, it reduces to a pure constant.
A mechanism for Taylor relaxation in Z-pinches. Part 1. Dynamo mechanism
Authors: Auluck S. K. H.
Published: March 2009

The dynamo mechanism in an RFP is explained on the basis of new terms in the MHD equations which are proportional to the electron mass and are traditionally neglected. A new azimuthal dynamo current is obtained which is shown to be positive definite. Sustained, spontaneous self-reversal of the toroidal field naturally follows from this. The (F, Θ) curve calculated from this theory under certain assumptions agrees well with experimental data. The theory predicts the presence of large-Larmor-radius particles in the RFP. It also predicts a spontaneous axial magnetic field in linear Z-pinches. Preliminary experiments on low-energy Z-pinches corroborate this prediction.
Magnetic field-line reconnection with jets
Authors: Soward A. M. , Priest E. R.
Published: March 2009

Some recent numerical simulations of driven magnetic field-line reconnection by Biskamp show no evidence of the Petschek mechanism when the reconnection rate or magnetic Reynolds number are large. Instead, an electric current sheet forms on the symmetry axis, across which a magnetic field is annihilated. The sheet terminates at a Y-point. Fluid driven into the current sheet escapes as jets along the separatrices emanating from the Y-point. This paper shows how many of the features such as the jets can be explained by a simple analytical model. Since the numerical simulations are necessarily on a bounded domain, the importance of the external boundary conditions in setting up a steady-state solution is stressed by illustrative examples.
Low-frequency waves in a high-beta collisionless plasma: polarization, compressibility and helicity
Authors: Gary S. Peter
Published: March 2009

This paper considers the linear theory of waves near and below the ion cyclotron frequency in an isothermal electron-ion Vlasov plasma which is isotropic, homogeneous and magnetized. Numerical solutions of the full dispersion equation for the magnetosonic/whistler and Alfvén/ion cyclotron modes at βi = 1·0 are presented, and the polarizations, compressibilities, helicities, ion Alfvén ratios and ion cross-helicities are exhibited and compared. At sufficiently large βi and θ, the angle of propagation with respect to the magnetic field, the real part of the polarization of the Alfvén/ion cyclotron wave changes sign, so that, for such parameters, this mode is no longer left-hand polarized. The Alfvén/ion cyclotron mode becomes more compressive as the wavenumber ulereases, whereas the magnetosonic/whistler becomes more compressive with increasing θ, At oblique propagation, the helicity of both modes approaches zero in the long-wavelength limit; in contrast, the ion cross-helicity is of order unity for the Alfvén/ion cyclotron wave and decreases as θ increases for the magnetosonic/whistler mode.
Theory of beat-wave current drive
Authors: Mendonça J. T. , Galvão R. M. O.
Published: March 2009

The beat-wave scheme for current drive is studied in the frame of plasma weakturbulence theory. The value of the driven current is limited by a quasi-linear diffusion mechanism. The one-dimensional problem, corresponding to the resonant excitation of electron plasma oscillations by two beating electromagnetic beams is discussed in detail. The results may be relevant to the continuous operation of tokamak discharges.
Nonlinear oblique modulation of ion-acoustic waves in a two warm ion plasma
Authors: Chhabra R. S. , Sharma S. R.
Published: March 2009

Using the KBM perturbation technique, the stability of oblique modulation on ion-acoustic waves in a plasma with two species of warm ions is studied. The effect of the temperatures of two ion species on the modulational instability is discussed in detail. The nonlinear frequency shift and the change in zeroth-order density are also calculated for different values of ion temperatures. Predictions of the theory are in fairly good agreement with the experimental observation of modulational instability.
Criteria governing ion-acoustic waves in two-ion plasmas
Authors: Gledhill I. M. A. , Hellberg M. A.
Published: March 2009

It has previously been observed that ion-acoustic waves exhibit two types of behaviour as the proportion of light ions in a mixed plasma is varied. Either the principal mode of the heavy ion plasma changes continuously into that of the light ion plasma, or it becomes too heavily damped to be observable while a second wave appears and develops into the principal light ion mode. A similar phenomenon is observed as the wavenumber or the ratio of electron temperature to ion temperature is changed. Criteria determining which behaviour occurs are derived by considering the form of the dielectric response function. The results may also be used to predict which of the higher-order modes of the plasma is involved in the process, and whether degeneracies exist in the dispersion relation.
Nonlinear Landau damping of purely perpendicular Bernstein modes
Authors: Riyopoulos Spilios
Published: March 2009

The linear dispersion relation for Bernstein modes, obtained by the integration of Vlasov's equation along the unperturbed cyclotron orbits, predicts that the modes propagating perpendicularly to the magnetic field are undamped. However, when the frequency is close to a multiple of the cyclotron frequency, most of the particles become trapped for small wave amplitude and the unperturbed orbit approximation breaks down. The trapped particle trajectories are calculated analytically here using a resonant Hamiltonian approximation. Integration, consistent with the wave, along the orbits yields the nonlinear damping rate in a manner similar to that used by O'Neil for the damping of unmagnetized electrostatic modes. The results can be extended for the general case of almost perpendicular, short-wavelength electrostatic modes near cyclotron harmonics.
Thermal relaxation of light dilute particles in a heat bath: a model problem
Authors: Garrett A. J. M.
Published: March 2009

The relaxation of a very dilute test particle species undergoing elastic collisions with a distinct, thermally distributed second particle species is considered. The Boltzmann equation is set up for the component of the test particle distribution function isotropic in velocity space; external forces and spatial dependence are ignored. For small test particle: heat-bath particle mass ratio, collisions are adequately described by a differential operator that is second-or der with respect to collision speed, which depends on the functional form of the collision frequency in terms of speed. The evolution equation is transformed to the form of the time-dependent Schrödinger equation, and the equivalent Schrödinger potential evaluated in terms of the collision frequency-speed relation. The relaxation problem may be solved by specifying the Green's propagator, describing the relaxation of an initial monoenergetic distribution. The case of constant Schrödinger potential is studied: the corresponding form of the collision frequency is found by an inversion process, and the evolution equation studied in Schrödinger form. The transformed speed variable has a finite range as particle speeds vary from 0 to ∞, and it is necessary to specify that particles are not lost at the finite values corresponding to small and large speeds. The Green's propagator is continued beyond this physical range, rather as in the ‘method of images’ of electrostatics. The particle conservation requirements induce a Laplace transform problem for the initial value of the Green's propagator, which is reduced to a polynomial recurrence relation and solved by finding the generating function. The Green's propagator is itself propagated forward from its initial value by a ‘primitive’ propagator which is the solution of the problem for initial delta function not only in the physical range, but anywhere in the space of the transformed variable. This primitive propagator is readily found, and the propagation quadrature performed to yield the true propagator in terms of parabolic cylinder functions. A check is made with a special case, for which relaxation to thermal form is explicitly demonstrated. Differences and similarities between this analysis and those corresponding to more general collision frequencies and potentials are considered.
Magnetohydrodynamic standing oscillations in a spherical dipole field
Authors: Murata H.
Published: March 2009

The coupled toroidal and poloidal modes forming a standing oscillation along the line of force and propagating azimuthally in a spherical dipole magnetic field are investigated under the magnetohydrodynamic (MHD) approximation with infinite conductivity, including the pressure effect but neglecting compressibility. We obtain a linearized coupled differential equation. When the azimuthal wavenumber becomes zero in the coupled equation, the axisymmetric toroidal wave equation is obtained with no pressure effect. For a large azimuthal wavenumber, on the other hand, a differential equation of the poloidal wave associated with a compressional magnetic component, which is different from the equation hitherto obtained under the zero pressure term, is derived from the coupled equation. It is found that the fluid pressure perturbation acts on the poloidal wave like the spring for the stretched string model and then contributes to the enhancement of the eigenvalues of the standing oscillations, especially for the first few. In this case, the magnetic pressure perturbation is in antiphase to that of the fluid pressure.
Energy variations at the onset of the tearing instability
Authors: Torricelli-Ciamponi G.
Published: March 2009

The resistive instability of a simple one-dimensional current sheet model has been investigated both in the long and in the short wavelength approximation. For the linear phase of the instability it is possible to derive, by means of an expansion technique, an analytical expression for the growth rate and for the perturbation itself. The variations of each kind of energy (magnetic, kinetic and dissipated energies, Poynting vector, work against pressure gradients and magnetic forces) are then exactly computed. Different behaviour of the System is obtained for different wavelengths. In particular, the driving energy for the instability is found to come from different regions: for high wavenumber α there is a decrease of the magnetic energy in the inner resistive region where the reconnection occurs, whereas for low-α modes the magnetic energy decreases in the outer ideal region. Moreover, the amount of Joule dissipation is found to increase with decreasing α so that the low-α regime is the most efficient.
Nonlinear bound on unstable fluctuation level in low-density non-neutral plasma
Authors: Davidson Ronald C. , Tsang Kang T.
Published: March 2009

A cold-fluid model is used to describe the nonlinear evolutions of low-density non-neutral plasma immersed in a strong axial magnetic field. It is assumed that there is no axial dependence, and that the electron fluid moves with the usual E × B drift velocity. Use is made of global (spatially averaged) conservation constraints satisfied by the continuity and Poisson equations to obtain a nonlinear bound on the unstable fluctuation level for a general initial density profile.
Stimulated Brillouin scattering of whistler waves in low-density collisionless plasmas
Authors: Guha S. , Basu C.
Published: March 2009

We present a theoretical investigation of stimulated Brillouin scattering (SBS) of whistler waves in low-density collisionless plasmas in the presence of negative ions and incorporating the effect of the ponderomotive force on electrons. It is found that the growth rate of the excited ion quasi-mode decreases with increasing concentration of negative ions. The effect of negative ions on the SBS of the whistler waves during the ionospheric modification is discussed.
New electromagnetic hot plasma waves around electron cyclotron harmonics
Authors: Matsuda Kyoko
Published: March 2009

Several branches of strongly damped electromagnetic hot plasma modes have been found around the first two harmonics of the electron cyclotron frequency. They are right circularly polarized in parallel propagation, and their frequency mismatches and damping rates are linearly proportional to their parallel wavenumber, and almost independent of the plasma density when the density is sufficiently high. Details of the modes are presented.
Drift instabilities of a relativistic plasma. Part 1. Kinetic description of drift effects in a relativistic plasma
Authors: Mikhailovskii A. B. , Onishchenko O. G.
Published: March 2009

The role of relativistic effects in the problem of drift instabilities in an inhomogeneous magnetized plasma is analysed. The kinetic approach is developed, taking into account a non-zero plasma pressure and the electromagnetic character of the perturbations. The general dispersion relation for the perturbations in an inhomogeneous relativistic plasma is obtained. As in the case of a non-relativistic plasma, the dispersion relation is written in terms of the modified dielectric permittivity tensor. This tensor is calculated by taking into account the non-Maxwellian character of the equilibrium momentum distributions of the particles. The relation between the modified dielectric permittivity tensor and the ordinary tensor of dielectric permittivity of a homogeneous plasma is elucidated.
Spectrum cascade processes and nonlinear stability in interchange mode turbulence
Authors: Majumdar D.
Published: March 2009

An improved equation is derived for the interchange mode in the limit k‖ = 0. The possibilities are discussed of explosive instabilities and spectrum cascade processes by mode coupling in interchange mode turbulence in two limits.
Particle and energy transport due to magnetic field-line reconnection in a tokamak
Authors: Iizuka Satoru , Minamitani Yasujiroh , Tanaca Hiroshi
Published: March 2009

Plasma behaviour during magnetic field-line reconnection which is driven by a rapid toroidal current reversal in a tokamak is investigated by calculating plasma flow speed from the magnetohydromatic equations with variables measured in the experiment. A strong plasma acceleration appears in the outside region of the X-type separatrix formed in the poloidal magnetic field lines. The induced electric field inside the plasma is evaluated directly from Ohm's law by using the fact that the toroidal current density vanishes during the current reversal. Then, plasma resistivity is estimated in the cross-section and the resulting value of energy flow is compared with that given by Poynting's theorem. It is found that the input energy is dissipated effectively through anomalous resistivity in the reconnection region.
The interaction of long-wavelength compressive waves with a cosmic ray shock
Authors: Zank G. P. , Mckenzie J. F.
Published: March 2009

This paper investigates the stability of a cosmic ray shock to long-wavelength perturbations. The problem is formulated in terms of finding the transmission coefficient for compressive waves across a cosmic ray shock by solving the generalized, two-fluid Rankine-Hugoniot relations. For strong shocks, the transmission coefficient confirms that compressive waves can undergo considerable amplification on passage through such shocks. The resonances of the transmission coefficient provides us with the dispersion equation governing the stability of the shock to long-wavelength ripple-like distortions. By using the principle of the argument method, it is established that cosmic ray shocks are stable.
A new collisional relaxation model for small deviations from equilibrium
Authors: Stubbe Peter
Published: March 2009

A new collisional relaxation model, applicable to small deviations from equilibrium, is established. In distinction from previous models, the new model involves three different collision frequencies for momentum transfer, energy transfer and randomization, extends the relaxation function to include the full pressure tensor rather than only its trace, and describes relaxation to individual rather than composite Maxwellian distributions. The new model is deduced in §2, and the final result is represented by equations (28) to (31). Simplified versions of the model are given in §3, and all relevant collision frequencies are quantitatively specified there. In §4, the model is applied to the kinetic theory of waves in a magnetized two-component plasma. As a particular example, magnetosonic waves are discussed for the sake of demonstrating a wave damping mechanism due to incomplete collisional activation of translatorial degrees of freedom.
Fundamental plasma emission involving ion sound waves
Authors: Cairns Iver H.
Published: March 2009

The theory for fundamental plasma emission by the three-wave processes L ± S→T (where L, S and T denote Langmuir, ion sound and transverse waves, respectively) is developed. Kinematic constraints on the characteristics and growth lengths of waves participating in the wave processes are identified. In addition the rates, path-integrated wave temperatures, and limits on the brightness temperature of the radiation are derived.
Spectral characteristics of hydromagnetic waves in the magnetosphere
Authors: Kuo S. P. , Lee M. C. , Wolfe A.
Published: March 2009

This work is intended to explain why the resonant response of the magnetosphere prefers to have discrete frequencies. Using a cylindrical model for the outer magnetosphere with a plasma density profile proportional to 1/r, we show that the eigenequation characterizing the eigenmodes of the hydromagnetic waves in this model has two turning points along the radial axis. The locations of the turning points depend upon the values of the eigenperiod and the associated east-west wavenumber of the eigenmode. The energy spectrum of the excited cavity modes is seen to have sharp peaks at discrete frequencies when the surface perturbations have a uniform spectrum in the frequency range of interest. We, therefore, have also shown that only the discrete set of the magnetospheric cavity eigenmodes can efficiently couple the perturbations excited on the boundary of the magnetosphere to the field-line resonant mode excited inside the inner turning point of the cavity eigenmode. The most likely values of east-west wavenumbers and wave period range are determined.
A physical model of parallel whistler-mode propagation in a weakly relativistic plasma
Authors: Sazhin S. S.
Published: March 2009

The process of parallel whistler-mode propagation in a weakly relativistic plasma is interpreted in terms of the periodic energy exchange between wave field and perturbed electron currents. The physical meaning of the thermal and relativistic corrections to the value of the refractive index of these waves in a cold plasma is considered in detail.
Nonlinear regular structures of drift magneto-acoustic waves
Authors: Aburdzhaniya G. D. , Lakhin V. P. , Mikhailovskii A. B.
Published: March 2009

Nonlinear regular structures in a magnetized plasma connected with drift magneto-acoustic waves (DMA) are investigated theoretically. Three-dimensional nonlinear equations of weakly dispersive DMA waves are obtained. These equations contain both the scalar nonlinearity and the vector one, and generalize the two-dimensional Kadomtsev–Petviashvili (KP) equation. The existence is shown of regular stationary structures due to the scalar nonlinearity: one-dimensional solitons, two-dimensional rational solitons, chains of solitons and so-called ‘crosses’. The stability of one-dimensional DMA solitons is investigated. It is shown that soliton stability depends on the sign of the wave dispersion as in the case of systems described by the KP-type equation.
Envelope solitons of surface waves in a plasma column
Authors: Grozev D. , Shivarova A. , Boardman A. D.
Published: March 2009

The problem of envelope solitons of surface waves is considered on the basis of results for the nonlinear dispersion relation of the waves in a plasma column. The soliton solutions are derived as particular cases of the general solutions obtained by a universal procedure and expressed in terms of Jacobi elliptic functions. Since the two types of interactions, namely the (ω + ω) – ω and the (ω – ω) + ω interactions (where ω is the frequency of the carrier wave) included in the nonlinear dispersion relation act in opposite ways, existence both of bright and dark solitons is shown to be possible. The effect of the ponderomotive force that in our case is expressed through the contribution of the (ω – ω) + ω interaction leads to the formation of dark solitons. The effect of the losses is also considered.
Observation of three-half harmonic radiation from plasmas irradiated by a 0·26 μm wavelength laser
Authors: Labaune C. , Fabre E. , Bonnaud G.
Published: March 2009

Time-integrated measurements have been made of three-half harmonic light energy emitted from 0·26 μm laser-produced plasmas. The main results are the experimental dependence of 3/2ω0 conversion efficiency and threshold on electron density-profile shape. Various density profiles are achieved by irradiating different kinds of target; their shapes are estimated with the help of two-dimensional hydrodynamic simulations.
Temporal evolution of reactive and resistive nonlinear instabilities
Authors: Melrose D. B.
Published: March 2009

A kinetic theory for nonlinear processes involving Langmuir waves, developed in an earlier paper, is extended through consideration of three aspects of the temporal evolution, (i) Following Falk & Tsytovich (1975). the dynamic equation for the rate of change of one amplitude at t is expressed as an integral over T of the product of two amplitudes at t – T and a kernel functionf(T); two generalizations of Falk & Tsytovich's form (f(T) ∝ T) that satisfy the requirement f(∞) = 0 are identified, (ii) It is shown that the low-frequency or beat disturbance may be described in terms of fluctuations in the electron number density, and that its time evolution involves an operator that is essentially the inverse of f(t). (iii) The transition from oscillatory evolution in the reactive or ‘coherent-wave’ version of the three-wave instability to the secular evolution of the resistive or ‘random-phase’ version is discussed qualitatively.
Effects of ballooning instability on tokamak confinement
Authors: Fu Guoyong , Van Dam J. W.
Published: March 2009

Using the ballooning-mode transport model proposed by Connor, Taylor & Turner (1984), we derive the thermal conductivity induced by ideal ballooning instability and compare it to experimental observations from auxiliary-heated tokamaks. We show how this model can be improved by means of a finite-beta equilibrium and also apply it to obtain a confinement scaling law for high-beta, purely Ohmically heated tokamaks. Finally, we employ this transport mode to find that tokamaks with supplemental stabilization, for example due to gyroradius, energetic particle or shaping effects, can self-consistently access the second stability regime at rather high heating power.
Electron thermal transport in laser-target plasmas on the basis of Grad's 13-moment transport equations
Authors: Boyd T. J. M. , Lonsdale R. D. , Sanderson J. J.
Published: March 2009

Grad's 13-moment theory is used to model thermal transport in laser-produced plasmas where conditions are such that one may not assume that the plasma is collision-dominated. The equations are presented for a multi-fluid model in slab geometry and are solved numerically for various cases. Comparisons are made with classical theory and with simulations of collisionless plasmas. Results show that, although there are differences between 13-moment and classical predictions, the two theories agree on the general behaviour of the plasma. In particular, 13-moment theory fails to explain the heat-flux inhibition implied by some experimental observations. The theory has also been applied to model thermal transport in plasmas with a population of suprathermal electrons.
Electron cyclotron masing and the force due to net stimulated bremsstrahlung in an electron cyclotron maser using a dilute non-relativistic electron beam
Authors: Kim S. H.
Published: March 2009

The amplification of an electromagnetic wave by net stimulated bremsstrahlung (the emission by stimulated bremsstrahlung minus the absorption by inverse bremsstrahlung) injected into a non-relativistic dilute electron beam travelling in a uniform magnetic field is considered. The d.c. ponderomotive force by net stimulated emission is calculated by using quantum kinetics. From the calculated ponderomotive force, the amplification of the intensity of the electromagnetic wave by the net stimulated bremsstrahlung is derived as a function of the relevant parameters of the electromagnetic wave and the electron beam. It is found that masing is possible when the perpendicular temperature of the electron beam is greater than its parallel temperature. It is shown that the efficiency of a practical gyrotron cannot be explained by the phase-bunching concept, and that simulated bremsstrahlung has nothing to do with any phase bunching.
The generalized Balescu-Lenard collision Operator
Authors: Mynick Harry E.
Published: March 2009

The generalization of the Balescu-Lenard collision operator to its fully electromagnetic counterpart in Kaufman's action-angle formalism is derived and its properties investigated. The general form may be specialized to any particular geometry where the unperturbed particle motion is integrable, and thus includes cylindrical plasmas, inhomogeneous slabs with non-uniform magnetic fields, tokamaks and the particularly simple geometry of the standard operator as special cases. The general form points to the commonality between axisymmetric, turbulent and ripple transport, and implies properties (e.g. intrinsic ambipolarity) that should be shared by them, under appropriate conditions. Along with a turbulent ‘anomalous diffusion coefficient’ calculated for tokamaks in previous work, an ‘anomalous pinch’ term of closely related structure and scaling is also implied by the generalized operator.
Turbulent magnetohydrodynamic density fluctuations
Authors: Shebalin John V. , Montgomery David
Published: March 2009

A spectral-method numerical code is used to compute mass-density fluctuation spectra in turbulent magnetofluids. The computations are used to test and extend a recent analytical theory of density variations in slightly compressible magnetofluids given by Montgomery, Brown and Matthaeus, and used by them to infer inertial-range density-fluctuation spectra for the nearby interstellar medium and solar wind. A local equation of state is assumed, relating density to pressure. Constant, scalar resistivities and viscosities are used. In the limit of low Mach numbers and high mechanical-to-magnetic pressure ratios, the fit of the computations to the analytical theory is seen to be close.
Driven, steady-state RFP computations
Authors: Dahlburg J. P. , Montgomery D. , Doolen G. D. , Turner L.
Published: March 2009

A previously described pseudospectral three-dimensional MHD code is used to compute the dynamical behaviour of a channel of magnetofluid carrying an axial current and magnetic flux. This situation contains the essential MHD behaviour of the reversed-field-pinch (RFP). An externally imposed electric field is applied to an initially current-free magnetofluid, and drives currents that rise and eventually fluctuate about values corresponding to pinch ratios Θ ≈ 1·3, 2·2 and 4·5. A period of violent turbulence leads to an approximately force-free core, surrounded by an active MHD boundary layer that is not force-free. A steady state is reached that can apparently be sustained indefinitely (≥several hundred Alfvén transit times). The turbulence level and time variability in the steady state increase with increasing Θ. The average toroidal magnetic field at the wall reverses for the Θ ≈ 2·2 and 4·5 runs, but not for the Θ ≈ 1·3 one. Negative toroidal current filaments are observed. The Lundquist numbers are of the order of a few hundred.
Diffusion processes in the field of a monochromatic wave propagating in an inhomogeneous magnetoplasma
Authors: Shklyar D. R. , Solov'ev V. V.
Published: March 2009

Particle diffusion in phase space due to the crossing of multiple cyclotron resonances in an inhomogeneous magnetic field is investigated. The influence of the inhomogeneity is most significant for small wave amplitudes, when stochastic heating is absent in a homogeneous plasma. The diffusion depends on the relationship between the wave amplitude, the inhomogeneity parameter and the angle of wave propagation. The dependence of the diffusion coefficients upon the mentioned parameters is investigated by means of computer simulations for the case of constant inhomogeneity and for two models of variable inhomogeneity: a monotonic change typical of magnetospheric conditions, and a sinusoidal change typical of tokamaks.
Weakly nonlinear theory of fast steady-state magnetic reconnection
Authors: Jardine M. , Priest E. R.
Published: March 2009

A family of models for fast steady-state reconnection has recently been presented by Priest and Forbes, of which the Petschek-like and Sonnerup-like solutions are special cases. This essentially linear treatment involves expanding about a uniform flow and field in powers of the external Alfvén Mach number Me, and hence is valid for small values of that parameter. To lowest order, the discrete slow-mode compressions attached to the diffusion region are straight, while downstream of them the plasma flows at simply the external Alfvén speed vAe and the field lines are straight. Here we present an extension of these solutions to the next order, which not only reveals that the wave itself is curved (as are the downstream magnetic field lines), but also that the downstream solution is sensitive to changes in the upstream boundary conditions. In the downstream solution there is a free parameter, which may be specified as a downstream boundary condition. Thus the boundary conditions at both the inflow and the outflow boundaries are crucial in determining the nature of the reconnection.
Unmagnetized diffusion for azimuthally symmetric wave and particle distributions
Authors: Dusenbery P. B. , Lyons L. R.
Published: March 2009

The general equations describing the quasi-linear diffusion of charged particles from resonant interactions with a spectrum of electrostatic waves are given, assuming the wave and particle distributions to be azimuthally symmetric. These equations apply when a magnetic field organizes the wave and particle distributions in space, but when the local interaction between the waves and particles can be evaluated assuming that no magnetic field is present. Such diffusion is, in general, two-dimensional and is similar to magnetized diffusion. The connection between the two types of diffusion is presented. In order to apply the general quasi-linear diffusion coefficients in pitch angle and speed, a specific particle-distribution model is assumed. An expression for the unmagnetized dielectric function is derived and evaluated for the assumed particle distribution model. It is found that slow-mode ion-sound waves are unstable for the range of plasma parameters considered. A qualitative interpretation of unmagnetized diffusion is presented. The diffusion coefficients are then evaluated for resonant ion interactions with ion-sound waves. The results illustrate how resonant ion diffusion rates vary with pitch angle and speed, and how the diffusion rates depend upon the distribution of wave energy in k–space. The results of this study have relevance for ion beam heating in the plasma-sheet boundary layer and upstream of the earth's bow shock.
Statistical mechanics of a spin-polarized plasma
Authors: Zhang W. Y. , Balescu R.
Published: March 2009

The statistical mechanics of a spin-polarized plasma is investigated in detail. A rigorous quantum-mechanical description is constructed in terms of a generalized matrix Wigner function. In order to ensure the manifest gauge invariance of the theory, the non-canonical variables q (position) and π (mechanical momentum) are used for the particles. The evolution equation for the phase-space Wigner function, as well as the BBGKY hierarchy for the reduced distribution functions, are derived. A general expression is found for the quantum-mechanical realization of the Lie bracket of any pair of dynamical functions. In the quasi-classical limit, the equations of evolution and the Lie bracket reduce to a simple form. Our approach is compared with the previous semi-phenomenological theory of Cowley, Kulsrud and Valeo.
Nonlinear Alfvén waves in a finite-beta plasma
Authors: Mjølhus Einar , Wyller John
Published: March 2009

The DNLS equation for parallel nonlinear and weakly dispersive MHD waves is extended to finite beta values as well as to three spatial dimensions, by means of the reductive perturbation method. Kinetic effects are included by means of the hybrid fluid and kinetic guiding-centre model of Grad (1961). The resulting equation contains a nonlinear and non-local term representing the effect of resonant particles.
Caustics and virtual cathodes in electron beams
Authors: Coutsias Evangelos A.
Published: March 2009

A simplified model is discussed that captures the basic physics of the phenomenon of oscillatory virtual cathodes in electron beams. A monoenergetic non-relativistic one-dimensional electron beam is injected through a conducting grid into a semi-infinite drift space. Attraction from image charges (and, possibly, an adverse externally applied electric field) cause particle reflection and the formation of a caustic where the charge density has an integrable singularity. The steady-state solution of the Vlasov equation describing the flow is known from numerical simulation to be unstable, but analytical demonstration of this instability has proved intractable. Here we derive an integral-delay equation describing the time-dependent evolution of the electron beam under the assumption that the caustic accelerates much more slowly than the electrons in its neighbourhood and thus at most two streams are present at each point. Under this assumption we show that the charge singularity is ~|x-xc|-½ the presence of an external field, exactly what it would be for non-interacting particles, but in the absence of applied field it is weaker, ~|x-xc|-⅓ Our methods can be used to estimate the charge singularity, and thus the collisionless ‘shock conditions’ for virtual cathodes in any geometry. The importance of delay effects for the onset of beam oscillations is demonstrated in an exactly solvable version of the model in which the interaction between the two streams is ignored. This solution, although unphysical, can provide a means for testing the performance of numerical schemes, which have difficulties in problems of this type due to the charge singularity.
Stochastic magnetic field generation in MHD resistive instabilities: validity limits of linear stability analysis
Authors: Pettini Marco , Torricelli-Ciamponi Guidetta
Published: March 2009

This paper aims at determining the validity limits of a linear analysis for a resistive instability. To this purpose, the effects of mode-coupling on the magnetic field structure are investigated in the reconnecting layer. Given an equilibrium magnetic field and a perturbation field, the conditions are found under which the equations for the magnetic field lines of force can be expressed in Hamiltonian form. These conditions can be fulfilled by a resistive instability. Consequently, in a simple equilibrium magnetic field the resistive eigenmodes have been analytically derived. This result is used to give an explicit expression of the Hamiltonian for field-line equations when two resistive eigenmodes are taken into account. The analytical form of the resulting Hamiltonian coincides with the so-called paradigm Hamiltonian (1·5 degrees of freedom) for which the Escande–Doveil renormalization procedure leads to an explicit expression for the global stochasticity threshold. Thus it can be shown that any pair of modes – in a suitable range of parameters – yields spatial stochasticity of magnetic field lines when the perturbation amplitude is still very low. Hence a limit of validity of the linear theory can be found. The linear phase of the resistive instability turns out to be relevant only to describe the onset of the instability itself.
Enhancement of collisional drift waves in a plasma cylinder
Authors: Praburam G. , Jain V. K.
Published: March 2009

The nonlinear coupling between collisional drift waves and a lower-hybrid pump is studied in a cylindrical geometry. A dispersion relation for the collisional drift wave is derived incorporating both ponderomotive and Ohmic-heating effects. It is found that Ohmic heating of electrons enhances the frequency as well as the growth rate of the drift waves. Effects due to the ponderomotive force are insignificant.
On tokamak equilibrium
Authors: Hazeltine R. D. , Montgomery M. H.
Published: March 2009

Large-aspect-ratio tokamak equilibrium is studied, including effects, such as ellipticity of the flux surfaces, of second order in the inverse aspect ratio. To facilitate the interpretation of experimental data, the analysis uses simple coordinates that are readily evaluated, rather than co-ordinates based on the exact flux surfaces. An explicit formula for the safety factor, including second-order terms, is presented, along with a brief discussion of rotational effects. The analysis assumes near-circularity of the outermost closed surface and low plasma pressure.
The unstable modes of a two-component electron plasma
Authors: McQuillan P. , McClements K. G.
Published: March 2009

In this paper we investigate the linear generation of electrostatic waves in a homogeneous, collisionless, unmagnetized plasma with two Maxwellian electron components, one drifting with respect to the other. The ions are assumed to be infinitely massive. It is shown that such a system may be unstable to a beam mode rather than the well-known Langmuir mode, if the drifting electron component is sufficiently dense and has a sufficiently low temperature. This ‘electron-beam instability’ is driven by the free energy in the particle distribution, and the associated phase velocity is greater than the electron thermal speed. The dispersion characteristics of the electron-beam instability and the Langmuir instability at the critical drift velocity for wave growth are determined for a wide range of parameters. The results of our investigation are applied to electron beams producing hard X-ray emission in solar flares, and it is argued that such beams may be unstable to the generation of electrostatic waves at frequencies below the electron plasma frequency.
Global energetics of fast magnetic reconnection
Authors: Jardine M. , Priest E. R.
Published: March 2009

We examine the global energetics of a recent weakly nonlinear theory of fast steady-state reconnection in an incompressible plasma (Jardine & Priest 1988). This is itself an extension to second order of the Priest & Forbes (1986) family of models, of which Petschek-like and Sonnerup-like solutions are special cases. While to first order we find that the energy conversion is insensitive to the type of solution (such as slow compression or flux pile-up), to second order not only does the total energy converted vary but so also does the ratio of the thermal to kinetic energies produced. For a slow compression with a strongly converging flow, the amount of energy converted is greatest and is dominated by the thermal contribution, while for a flux pile-up with a strongly diverging flow, the amount of energy converted is smallest and is dominated by the kinetic contribution. We also find that the total energy flowing out of the downstream region can be increased either by increasing the external magnetic Mach number Me or the external plasma beta βe Increasing Me also enhances the variations between different types of solutions.
Leakage of MHD surface waves in structured media
Authors: Čadež V. M. , Okretič V. K.
Published: March 2009

Surface-wave propagation along a double step is investigated within ideal compressible MHD. The occurrence of surface-wave leakage is emphasized and the relevant conditions are discussed. A numerical example is presented to illustrate the process.
Drift-kinetic stability analysis of z–pinches
Authors: Åkerstedt Hans O.
Published: March 2009

From the Vlasov-fluid model, a set of approximate stability equations describing the stability of a cylindrically symmetric z–pinch is derived. The equations are derived in the limit of small gyroradius and include kinetic effects such as finite Larmor radius, particle drifts and resonant particles. In the limit of zero Larmor radius and short wavelengths, we apply the equations to the internal m = 0 and m = 1 modes. If the drift term mωD + kVD is neglected in the resonant denominators, we find stability criteria that are more optimistic than the corresponding stability criteria for perpendicular MHD. The neglect of the drift term is, however, not justified for the m = 1 mode, where mωD needs to be retained in order to preserve the property that this approximate model should have the same point of marginal stability as the exact Vlasov-fluid model. Retaining the drift terms, growth rates have been calculated for the m = 1 mode, for a constant-current-density equilibrium and for the Bennett equilibrium. For the Bennett profile, we obtain, when compared with perpendicular MHD, a substantial reduction in growth rate γ/γMHD ≈ 0·2.
A cosmic-ray-driven plasma instability
Authors: Zank G. P.
Published: March 2009

The stability of the MHD equations describing the mutual interaction of cosmic rays, thermal plasma, magnetic field and Alfvén waves used in cosmic-ray-shock acceleration theory (e.g. McKenzie & Völk 1982) is analysed for linear compressive instabilities. It is found that the inclusion of wave effects implies that the forward propagating sub-Alfvénic mode is unstable on wavelength scales greater than 1 parsec. The role of the instability in astrophysical models is considered.
Lower-hybrid wave generation in an electron beam of finite transverse dimension
Authors: Crew G. B.
Published: March 2009

The generation of lower-hybrid waves in an inhomogeneous electron beam is examined. Wave amplitudes are invariably limited by the convective nature of the instability. The self-consistent shear of the magnetic-field geometry due to the beam current is limited to the role of dividing the general problem into separate cases according to the relative orientation of the wave vector and direction of inhomogeneity. Moreover, the limiting case of small shear is smoothly connected to the case where shear is altogether negligible. Estimates of the amplification of lower-hybrid waves propagating across the electron beam are made for the various cases.