bluuebunny/crossref_metadata_2025 huggingface dataset:
Relativistic self-focusing of laser beams in time-harmonic plane waves: arbitrary intensity
Authors: Asthana Meenu , Sodha M. S. , Maheshwari K. P.
Published: March 2009

This paper presents a paraxial theory of relativistic self-focusing of a Gaussian laser beam in plasma for a time-harmonic plane wave at arbitrary beam intensity. Since the relativistic mechanism is instantaneous, the theory is also applicable to self-focusing of laser pulses. The analysis leads to two values for the critical beam power for self-focusing, Pcr1 and Pcr2. When P < Pcr1 < Pcr2, the beam diverges. When Pcr1 <P  Pcr2 it first diverges, then converges, and so on.
Magneto-acoustic surface waves on current sheets
Authors: Cramer N. F.
Published: March 2009

The theory of linear magneto-acoustic surface waves is investigated for current sheets across which the magnetic field has an arbitrary change of direction: in the first place discontinuously, and in the second place via a narrow transition region in which the magnetic field rotates with constant amplitude, so that the gas pressure remains constant. It is found that the effect of non-zero pressure is to eliminate the surface wave for certain angles of propagation and to allow the existence of an additional, slower, surface wave for other angles of propagation. The resonance damping of the surface waves when the current sheet is of small non-zero width is considered, and it is found that Alfvénresonance damping always occurs, as well as (for high β and certain angles of propagation) compressive- or cusp-resonance damping.
Modulations of slow sausage surface waves travelling along a magnetized slab
Authors: Zhelyazko I. , Murawski K. , Goossens M. , Nenovaki P. , Roberts B.
Published: March 2009

In this paper we consider a set of nonlinear MHD equations that admits in a linear approximation a solution in the form of a slow sausage surface wave travelling along an isolated magnetic slab. For a wave of small but finite amplitude, we investigate how a slowly varying amplitude is modulated by nonlinear self-interactions. A stretching transformation shows that, at the lowest order of an asymptotic expansion, the original set of equations with appropriate boundary conditions (free interfaces) can be reduced to the cubic nonlinear Schrödinger equation, which determines the amplitude modulation. We study analytically and numerically the evolution of impulsively generated waves, showing a transition of the initial states into a train of solitons and periodic waves. The possibility of the existence of solitary waves in the solar atmosphere is also briefly discussed.
Three-dimensional steady-state magnetic reconnection
Authors: Jardine M.
Published: March 2009

A family of three-dimensional models of reconnection is presented in which the different members of the family are characterized by the vorticity with which plasma flows towards the reconnection site. The nature of this inflow also determines the size and speed of the outflow jet that carries reconnected field lines away from the reconnection site, and the shape of the MHD shocks that bound it. Flows with positive vorticity are of a flux pile-up type, for which the outflow jet is fastest and narrowest. Among those with negative vorticity is the three-dimensional analogue of Petschek reconnection. Not all combinations of vorticity and reconnection rate are possible; for those solutions with negative vorticity, there is a maximum reconnection rate. As the magnetic Reynolds number Rme or the current density is increased, this maximum is reduced and the possible types of solution become more polarized towards the two extremes of flux pile-up and slow compression regimes. Given a distribution of vorticities and inflow speeds, these models give the corresponding distribution of possible steady-state reconnection rates. As an illustrative example, we take Gaussian distributions of both to show that the resulting distribution is dominated by the flux pile-up regime.
Large-amplitude relativistic nonlinear Langmuir waves in a two-fluid plasma
Authors: Nejoh Yasunori
Published: March 2009

Large-amplitude relativistic nonlinear Langmuir waves are analysed using the pseudo-potential method. The existence conditions for nonlinear Langmuir waves are confirmed by considering relativistic high-speed electrons in a two- fluid plasma. The significant feature of this investigation is that the propagation of nonlinear Langmuir waves depends on the ratio of the electron streaming velocity to the velocity of light, the normalized potential and the ratio of ion mass to electron mass. The constant energy depends on the ratio of electron velocity to that of light. In the non-relativistic limit large-amplitude relativistic Langmuir waves do not exist. This investigation predicts new findings of large-amplitude nonlinear Langmuir waves in space plasma phenomena in which relativistic electrons are important.
Transport coefficients for a two-temperature equal-mass plasma in a uniform magnetic field
Authors: Abdul-Rassak S. Y. , Laing E. W.
Published: March 2009

Transport coefficients for electric current and heat flux have been calculated for a two-temperature equal-mass plasma for several values of the temperature ratio R in the range 1 < R ≤ 100. Transport coefficients have been obtained using the linearized Fokker—Planck equations.
Thermal effects on the dynamics of a two-gas gas-puff Ζ–θ pinch
Authors: Nasim M. H. , Salahuddin M. , Mirza Arshad M.
Published: March 2009

The imploding plasma column of a gas-puff Ζ-pinch has been used to compress the target-gas-embedded axial magnetic field in the presence of plasma pressure. The dynamics of a two-gas gas-puff Ζ-θ pinch is studied with different forms of applied current profiles. We find that the inclusion of a kinetic pressure term introduces the usual β–term, which delays and reduces the maximum compression. On the other hand, for fixed β, compression at an earlier time can be achieved for a large density ratio of the test to the driver gas at the interface position. For the pressure-free case, our earlier results are completely recovered.
Modulated electromagnetic waves in relativistic plasmas: field and kinetic equations
Authors: Ekiel-Jeżewska Maria L. , Flå Tor , Kaufman Allan N.
Published: March 2009

Modulated electromagnetic plane waves in relativistic collisionless, unmagnetized plasmas are investigated through expansion in a small parameter, corresponding to weak dispersion and weak nonlinearity. The oscillation-centre transformation is applied to construct a Hamiltonian action principle for the slow oscillation-centre variables. A description in terms of the relativistic Vlasov equation for oscillation-centre distribution functions is introduced. A system of coupled field and kinetic eequations is obtained order by order.The final result is a generalized vector nonlineat schrödinger equation, with resonant particle effects included through the coupling to the perturbed Vlasov equations.
Quasi-particles in magnetized plasmas: second-order approximation
Authors: Sosenko† Petro P.
Published: March 2009

A second-order approximation is formulated and studied within the context of the quasi-particle description of magnetized plasmas. The general case of relativistic particles in non-uniform but stationary magnetic fields, and in additional force fields that are strongly non-uniform but slowly evolving in time compared with particle gyrations with the cyclotron frequency, is considered. In order to reveal the physical significance of the second-order approximation, the mean (reduced) particle velocity is calculated up to second order, when polarization particle drift as well as the renormalization of the lower-order result become equally significant. A general expression for the velocity of particle polarization drift is obtained in terms of quasi-particle properties, and with account taken of finite-Larmor-radius effects and non-uniformity of magnetic fields. A guiding-centre transformation is found that makes it possible to achieve equal mean velocities of particle, guiding centre and quasi-particle up to second order. Then polarization drifts enter the particle, guiding-centre and quasi-particle equations of motion.
Contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic warm plasma. Part 2. Non-isothermal case
Authors: El-Labany S. K. , Shaaban S. M.
Published: March 2009

The contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic plasma consisting of a warm ion fluid and hot non- isothermal electrons is studied using reductive perturbation theory. At the lowest order of the perturbation theory a modified Korteweg–de Vries equation is obtained. At the next order a linear inhomogeneous equation is obtained. The stationary solution of the coupled equations is obtained using the renormalization method introduced by Kodama and Taniuti for reductive perturbation theory.
Mode conversion of laser radiation in the presense of a magnetic wiggler
Authors: Parashar Jetendra , Pandey H. D. , Singh R. K.
Published: March 2009

Laser radiation propagating through a non-uniform plasma along the direction of the density gradient suffers total reflection at the critical layer. However, when a wiggler magnetic field exists near the critical layer, the laser drives a Langmuir wave. For suitable values of Bw and kw, the power transfer from the laser to the Langmuir wave could be as high as 60%. The Langmuir wave deposits its energy on the electrons via Landau damping. This may be an efficient mechanism of laser absorption when large self-generated magnetic fields exist in the plasma.
Multiple scattering of electromagnetic waves by a collection of plasma drift turbulent vortices
Authors: Resendes David
Published: March 2009

An application of the self-consistent multiple-scattering theory of electromagnetic waves to drift turbulent vortices is presented. Using the known single-vortex solution, the integral equation describing the scattering from a finite density of drift turbulent vortices is obtained. Rather than solving this equation and then averaging, the averaging operation is taken first to obtain statistical moment equations, from which the coherent and incoherent scattering follow. These results are expressed in a Fourier basis, and the cross-section is evaluated. Limiting forms of the theory and straightforward generalizations are discussed.
Liouvillian theory of magnetic fluctuations
Authors: Eijnden E. Vanden , Balescu R.
Published: March 2009

The study of the diffusion of magnetic field lines is based on a stochastic model with a Hamiltonian structure. A Liouville equation can then be associated with Hamilton's equations representing the magnetic line. This allows a statistical description of all observable quantities. In particular, the mean-square displacements (MSD) of a field line and the mean-square relative distance (MSRD) of two lines are considered. Equations for these quantities are obtained by applying the direct-interaction approximation (DIA) to the stochastic Liouville equation. The running diffusion coefficient is derived from the MSD equation. The status of the temporal and spatial Markovian approximations in the DIA is discussed. The MSRD's evolution establishes the existence of a clumping effect between two lines, which eventually leads to gyrotropization of the system. A clump life length is defined. In both cases the equations of motion are shown to be identical to the equations obtained within the Langevin treatment of magnetic fluctuations. This shows the equivalence between the DIA and the Corrsin approximation performed in the Langevin approach.
Weakly relativistic effect on the modulation of nonlinear ion-acoustic waves in a warm plasma
Authors: El-Labany S. K.
Published: March 2009

The derivative expansion perturbation method is applied to investigate the modulation of nonlinear ion-acoustic waves in a weakly relativistic warm plasma. At the second order of perturbation theory, a nonlinear Schrödingertype equation for the complex amplitude of the perturbed ion density is obtained. The coefficients in this equation show that the condition of modulational stability is modified by the relativistic effect as well as by the finite ion temperature. The association between the small-wavenumber limit of the nonlinear Schrödinger-type equation and the oscillatory solution of the Korteweg-de Vries equation obtained by reductive perturbation theory is considered. Different limits are considered in order to compare with previous work.
Kinetic theory of very high-frequency and high-pressure continuous atomic discharges
Authors: Peyraud-Cuenca N. , Faucher P.
Published: March 2009

We derive the analytical solution of the Boltzmann equation for the stationary electron distribution function that is reached in a plasma generated on the application of a uniform very high-frequency electric field in an atomic gas. The theory includes all excitation transitions: ionization and electronic transitions. The analytic solution is also extended to continuous discharges with low electric field or high pressure in the gas. Then the electron rate coefficient for excitation of the first state (which is the most significant) is calculated analytically. We apply the results to the modelling of very high-frequency argon discharges and to high-pressure continuous discharges in argon and in sodium. The results are compared with numerical results of Ferreira and co-workers for argon and of LaVerne for sodium: in both cases we find good agreement between numerical and analytical approaches.
Thermal instability of a compressible finite-Larmor-radius Hall plasma in a porous medium
Authors: Sharma R. C. , Sunil
Published: March 2009

The thermal instability of a compressible plasma in a porous medium is considered in the presence of a uniform vertical magnetic field to include the Hall-current and finite-Larmor-radius effects. The system is found to be stable for (cp/g) β < 1, where cp, β and g are the specific heat at constant-pressure, the uniform adverse temperature gradient and the acceleration due to gravity respectively. The uniform vertical magnetic field, Hall-current and finite. Laimor-radius effects introduce oscillatory modes in the system for (cp/g) β ≤ 1, which were non-existent in their absence. The Hall current and finite Larmor radius (FLR) individually have destabilizing and stabilizing effects respectively on the system. In their simultaneous presence there is competition between the destabilizing role of the Hall current and the stabilizing role of the FLR, and each succeeds in stabilizing a certain wavenumber range. In the absence of a magnetic field (and hence the absence of an FLR and Hall current), the destabilizing effect of medium permeability is seen, but in the presence of a magnetic field (and hence the presence of an FLR and Hall current), the medium permeability may have a stabilizing or a destabilizing effect on the thermal instability of the plasma. The effect of compressibility is found to postpone the onset of thermal instability in plasma.
Two-dimensional shear Alfvén-wave turbulence in a plasma with arbitrary β
Authors: Brodin G.
Published: March 2009

Two-dimensional shear Alfvén-wave turbulence is investigated for a plasma with arbitrary β value. A set of three equations, which reduces to the derivative nonlinear Schrödinger equation in the limit of parallel propagation, is derived. The genuinely two-dimensional case is governed by two coupled equations. For a non-parallel one-dimensional space dependence, the nonlinearity is shown to vanish to all orders.
Comments on the paper ‘Specular reflection as a probe for diagnostics of laser-produced plasmas’
Authors: Gupta G. P. , Sinha B. K.
Published: March 2009

In a recent paper, Desai et al. (1994) have reported the observed characteristics of the specularly reflected laser light from a copper plasma created by laser irradiation of a planar copper target. They have measured specular reflection, and attributed the observed diffusivity of specularly reflected radiation to the curved and rippled surface at the radiation turning point in the plasma. The aim of this comment is to reanalyse the possible causes for the diffusion of specular reflection relevant to their experimental conditions.
A new Hamiltonian formulation for fluids and plasmas. Part 3. Multifluid electrodynamics
Authors: Larsson Jonas
Published: March 2009

The Hamiltonian structure underlying ideal multifluid electrodynamics is formulated in a way that simplifies Hamiltonian perturbation calculations. We consider linear and lowest-order nonlinear theory, and the results in Part 1 of this series of papers are generalized in a satisfactory way. Thus the Hermitian structure of linearized dynamics is derived, and we obtain the coupling coefficients for resonant three-wave interaction in symmetric form, giving the Manley–Rowe relations.
Electrostatic parametric resonances in a plasma revisited
Authors: McKenzie J. F. , Hagfors T.
Published: March 2009

We generalize Silin's dispersion equation for electrostatic parametric resonances in an unmagnetized plasma to include interactions hitherto overlooked. Of particular interest to ionospheric physicists in this generalization is the interaction between an ion acoustic wave (shifted up in frequency by that of the pump) and an unshifted Langmuir wave. This yields growth rates equal to that of its counterpart in the Silin version, namely the ‘classical’ interaction between a Langmuir wave (shifted down by the pump frequency) and an unshifted ion acoustic wave. The more general (truncated) dispersion equation also displays resonances between ion acoustic sidebands, but this requires pump frequencies of the order of, or less than, the ion plasma frequency and therefore may be of little practical interest in the ionosphere. The system is analysed using Fourier techniques, which lead to two dispersion equations governing the Fourier transforms of the ion and electron perturbation densities. It is shown that, as far as the structure of the coupled recursion relations for the ion and electron Fourier components is concerned, there is an equivalence between the fluid and kinetic treatments. In the case of weak pump fields we calculate the growth rates associated with the various instabilities from a truncated three-wave interaction dispersion relation. Where it is appropriate, these growth rates are compared both with those from the Sum dispersion equation and the counterparts from the Zakharov model. We also discuss the case of very strong pump fields where the ‘natural’ interacting mode frequencies are not those associated with the usual Langmuir—ion acoustic modes of the unpumped plasma, but rather the oscillator frequencies corresponding to the coupled oscillator paradigm that is applicable to the system. Here again we find instabilities of a nature analogous to those arising in the weak pump case.
Effect of ion temperature and inhomogeneity on modulational instability of ion acoustic waves
Authors: Durrani Ijaz-Ur Rahman
Published: March 2009

The propagation of ion acoustic waves in an inhomogeneous plasma is studied in the presence of finite ion temperature. The standard nonlinear Schrödinger equation is obtained, and the regions of instability are plotted. It is claimed that these extraneous factors tend to lower the value of the critical wavenumber.
Quasimode decay of a lower-hybrid wave in a two-electron-temperature plasma
Authors: Sudarshan A. , Sharma S. K.
Published: March 2009

We study the quasimode decay of a lower-hybrid wave and a damped ion cyclotron wave in a plasma having two kinds of electrons. This decay channel is also investigated for a cylindrical plasma. The behaviour of the threshold and growth rate with variations in Tn/Tc and non/noc are studied, and a comparison is made with previous results. Our results show that the growth rate and the threshold for the onset of parametric decay are influenced by the presence of the second electron species.
Symmetries in hydrodynamic turbulence and MHD dynamo theory
Authors: Knorr George
Published: March 2009

The three-dimensional equations of ideal hydrodynamics and ideal MHD are expanded in eigenfunctions of the curl, and the resulting basic interactions of these nonlinear systems are analysed. As the equations are invariant under time and amplitude reversal, a criterion defining the arrow of time is introduced. A new parameter, the center of energy, serves to characterize a basic interaction. In the 3D Euler equations we find four different interactions and their mirror images, two of which can transport energy to smaller wavenumbers. This can lead to the appearance of structures in turbulent flow, and throws doubt on a derivation of Kolmogorov's law based on a cascading of energy to higher wavenumbers.In energy the corresponding two-dimensional equations, which are isomorphic to the guiding centre model in plasma physics, only one interaction exists, with a strong inverse cascade, which can lead to accumulation of energy in the spatially largest accessible modes. In MHD theory it is possible to separate magnetic from kinetic interactions. The former give again four basic interactions, two being regular and two being inverse cascades. One of these is quite strong, and can lead to the MHD dynamo effect. Kinetic energy can be transferred into magnetic energy. The dynamo effect is is accompanied by alignment of velocity and magnetic fields. We show that stationary velocity fields may lead to exponentially growing magnetic fields and we give an explicit criterion for this instability.
Stochasticity in the Josephson map
Authors: Nomura Y. , Ichikawa Y. H. , Filipov A. T.
Published: March 2009

The Josephson map describes the nonlinear dynamics of systems characterized by the standard map with a uniform external bias superposed. The intricate structures of the phase-space portrait of the Josephson map are examined here on the basis of the associated tangent map. A numerical investigation of stochastic diffusion in the Josephson map is compared with the renormalized diffusion coefficient calculated using the characteristic function. The global stochasticity of the Josephson map occurs at far smaller values of the stochastic parameter than is the case of the standard map.
The importance of trapping in strong plasman turbulence
Authors: Rolland P.
Published: March 2009

Sturrock's theory of stochastic acceleration and Dupree's theory of strong plasma turbulence are here derived in a very simple way, showing that trapping cannot correctly be taken into account by this kind of theory. A comparison of Sturrock and Dupree's diffusion coefficients D shows that they differ significantly only in the domain where these theories fail, and where the highest values of D are reached. The need for a theory taking trapped orbits into account appears clearly. Such an attempt is the object of a sequel.
Lagrangian density for collisional plasma
Authors: Peng Y. K. M.
Published: March 2009

For the purpose of deriving appropriate Lagrangians for equations in plasma physics that include effects of energy loss, the paper examines the inverse problem of the calculus of variations for systems of first and second order quasi- linear partial differential equations. This results in convenient forms of the sufficient conditions, under which the given differential equations are Euler Lagrange equations of a Lagrangian. These conditions are then applied, to determine the necessary transformation that converts equations, apparently not already in it, into Euler—Lagrange form. The appropriate Lagrangian for a warm collisional plasma is obtained. As an additional example, the Lagrangian is derived for a resistive transmission line.
The thickness of a resistive sheath in a magnetic separatrix
Authors: Kilkenny J. D.
Published: March 2009

The formation of an electrostatic double sheath at a magnetic separatrix is described, with particular reference to the polytron. Results are discussed for a collisionless plasma, and for a simple MHD model where the sheath thickness is determined by collisional effects. Expressions are given for the sheath thickness in the polytron. Of more general interest is the result that the formation of a sheath makes the resistance of the plasma to current flow across the separatrix proportional to ωτ, not ω2τ2 as expected for a homogenous magnetic field.
Nonlinear Landau damping of a broad-band spectrum of electron plasma waves in a bounded plasma
Authors: Matthieussent G.
Published: March 2009

The nonlinear Landau damping of a broad-band spectrum of electron plasma waves propagating in a plasma column is considered.

Finite geometrical effects inherent to the boundary value problem are taken into account. It is shown that nonlinear Landau damping of such a spectrum can be easily observed on a plasma column with a density of the order of 2 × 108 particles cm−3 and an electron temperature of about 3eV.
Analytical study of crossed atom-laser beam plasma diagnostics
Authors: Nygaard Kaare J.
Published: March 2009

A new method using crossed laser and atom beams within a plasma is capable of determining the electron density with a spatial resolution of 1 mm and a time resolution of 2–5 nsec. The measurement is done in the forward direction of the atom beam and is to a first approximation independent of electric and magnetic fields inside and outside the plasma region. A calculation is carried out for a neutral cesium beam probing a fully ionized hydrogen plasma. It is pointed out that a laser beam can also be combined with available ion beam diagnostics.
Dynamics and conservation laws in electrostatic plasma turbulence
Authors: Elsässer Klaus , Schamel Hans
Published: March 2009

We show how the Hamiltonian description of an ideal fluid can be used for a two fluid plasma. Translation to wave variables leads to a simple rule to obtain coupled-mode equations if the energy is known as a function of wave variables. In this context we discuss the intimate connexion between a particular dynamical model, specified by the interaction Hamiltonian, and the associated invariants of motion. By this method we derive an improved version of Zakharov's equations for Langmuir and ion sound waves with the correct invariants of motion. As a result of these corrections we find a stationary power law k−2 for the plasmon energy.
Inelastic collision integral approximation of the Boltzmann equation
Authors: Ségur Pierre , Lerouvillois-Gaillard Joëlle
Published: March 2009

A study is made of the inelastic collision integral of the Boltzmann equation using scattering probability formalism. The collision operators are expanded in a power series in the square root of the ratio of masses.

Furthermore, a spherical harmonic expansion is made of all the operators so obtained. These developments are valid whatever the shape of the distribution function of the particles.
Anomalous transport due to long-lived fluctuations in plasma Part 1. A general formalism for two-time fluctuations
Authors: Krommes John A. , Oberman Carl
Published: March 2009

A general formalism for describing two-time fluctuations in magnetized plasma is presented. Two-time expectations of one-body operators (phase functions) are written in terms of the phase space density autocorrelation function

where δN is the fluctuation in the singular Klimontovich microdensity. It is shown that is the first member of a set of two-time quantities

which collectively obeys the linearized BBGKY cumulant hierarchy in the (Xi, t) variables, with initial conditions successively smaller in the plasma parameter . We study in detail the case of fluctuations in thermal equilibrium, although the general formalism holds also for the non-equilibrium case. To lowest order in εP, Γ obeys the linearized Vlasov equation. From this are recovered all of Rostoker's results for fluctuations excited by Cherenkov emission and absorbed by Landau damping, as well as a constructive proof of the test particle superposition principle. To first order, Γ obeys (in the Markovian approximation) the linearized Balescu-Guernsey-Lenard equation. For frequencies and wavenumbers in the hydrodynamic regime, the velocity moments of Γ obey linearized fluid equations with classical transport coefficients (i.e. essentially those computed by Braginskii in the 3-D case). It has been found that the classical theory is in disagreement with certain computer and laboratory experiments performed in strong magnetic fields. This defect is attributed to the absence in the classical theory of contributions to the collision operator, hence transport coefficients, of fluctuations long-lived on the Vlasov scale. Analogous difficulties arise in the theory of hydrodynamics in neutral fluids. To improve the plasma theory, a renormalization of the two-time hierarchy is proposed which sums selected terms from all orders in εP and thus treats the hydrodynamic fluctuations self-consistently. The resulting theory retains appropriate fluid conservation laws, thereby avoiding erroneous results encountered in certain diffusing orbit theories, when the fluid viscosity is indiscriminantly replaced by the test particle diffusion coefficient. In order to explain the results of the computer simulations, the theory is applied in part 2 to the problem of anomalous hydrodynamic contributions to the transport coefficients.
The electromotive force generated by driven plasma motions
Authors: Gimblett C. G. , Allan D. W.
Published: March 2009

We investigate the electromotive force produced by plasma motions which are excited by an assigned body force. Two specific enquiries are made: (i) Can the Hall term create helicity in a plasma which is isotropically forced? (ii) What is the general form of the turbulent electromotive force when magnetic shear is present in the system? It proves possible to answer (ii) for weak shear in the two cases of weak and strong magnetic field.
Study of longitudinal electron oscillations in a plasma with a cut-off Maxwellian velocity distribution
Authors: Trotignon J. G. , Feix M. R.
Published: March 2009

Using a Van Kampen treatment, we study the longitudinal electron oscillations for a plasma with a cut-off Maxwellian velocity distribution. Having defined and computed excitation coefficients in the real w, k plane, we represent this ‘wave density’ through the greyness of this plane. This representation should be useful as a help to the experimenter. Moreover we show the appearance of a slightly damped pole with a phase velocity slightly smaller than the cut-off velocity Vc if this velocity is in the interval 2 to 4VT and a modification of the Landau mode which propagates for higher and higher frequencies when Vc decreases.
Finite geometry effect on the interaction of a hot beam with a plasma
Authors: Shoucri M. M. , Gagne R. R. J.
Published: March 2009

The effect of finite geometry on the interaction of a hot low-density beam with a uniform plasma filling a circular waveguide is studied. An expression is derived for the growth rate of the instabilities developing at the harmonic of the beam gyrofrequency, taking the finite beam gyroradius into account. The calculations are done in the quasistatic approximation.
Stationary nonlinear interaction between high- and low-frequency waves and the generation of density cavities in a plasma
Authors: Baumgärtel K. , Sauer K.
Published: March 2009

The nonlinear interaction of a high-frequency wave (transverse or longitudinal) and an ion-acoustic wave in a homogeneous plasma is investigated. The waves are assumed to be simultaneously excited by two localized external sinusoidal disturbances with frequencies ω0 and ωS in the plasma. From the coupled wave equations a system of ordinary differential equations for the spatial change of the amplitudes of the interacting waves (including the primary frequencies ω0, ωS and the mixed frequencies ω0±ωS) and a zero-frequency density disturbance is derived. The spatial development of the high-frequency amplitudes is characterized by localized regions of high intensities, coupled with local depressions of the plasma density. The influence of the initial amplitudes and the frequencies ω0, ωS on the maximum of the primary high-frequency amplitude and the ‘cavity’ depth is shown. The numerical results are compared with conclusions from a simplified model of three resonantly interacting normal modes.
Higher harmonics of electron plasma waves
Authors: Märk E. , Sato N.
Published: March 2009

A model based on nonlinear mixing of dispersive waves is used to predict higher harmonic waves generated by weakly nonlinear electron plasma waves. The total harmonic wave is given by superposition of modes which lie at different points (with the same frequency) in the dispersion diagram. The model well explains the experimental results concerning the harmonic waves produced by externally excited electron plasma waves propagating along a collisionless plasma column.
Self-modulation of a nonlinear ion wave packet
Authors: Watanabe S.
Published: March 2009

The modulational instability of the ion wave is observed experimentally. Two kinds of wave packets are launched in the plasma by means of a grid. One is a broad-band wave packet excited by a positive step voltage. The other is a quasi-monochromatic wave packet modulated by a pulse. For the step voltage response, we observe a large oscillation in the wave front which evolves to Korteveg–de Vries solitons and a small amplitude wave packet in the tail. The wave packet becomes modulationally unstable and divides into smaller wave packets. Whenever the wave packet is modulated, the spread of the packet is suppressed and is much smaller than is expected from linear dispersion. For the quasi-monochromatic wave packet, we also observe the modulational instability if the carrier frequency is high. The frequency of the carrier is shifted by the instability. The result of the quasi-monochromatic wave packet is qualitatively explained by the modified nonlinear Schrödinger equation taking account of the wave-particle interaction at the group velocity.
Obliquely propagating whistler mode waves in cold plasmas permeated by dilute low-β anisotropic plasmas
Authors: Hashimoto K. , Kimura I.
Published: March 2009

We analyse the growth rate of obliquely propagating whistler mode waves in a cold plasma that also contains some hot electrons in a bi-Maxwellian distribution. Approximate analytic expressions for the growth rate are derived explicitly. They are represented by elementary functions only, consisting of a Landau damping term and a cyclotron instability term. They are found to be valid for a wide range of wave normal angles. Landau damping in the oblique propagation does not always become larger even if the wave normal angles increase. The necessary conditions for the minimal parallel growth are Ω > 0.5Ωe and T≥> 2T∥ in the bi-Maxwellian hot plasma. This method is applied to calculations of the net growth along the ray paths of obliquely propagating non-ducted whistler mode waves in a model magnetosphere.
Heating and ionization in MHD switch-on shocks in partially ionized plasmas
Authors: Bighel L. , Collins A. R. , Cramer N. F.
Published: March 2009

The structure of MHD switch-on shocks propagating along a magnetic field into an upstream partially ionized plasma is studied experimentally and theoretically. Detailed measurements of density, temperature and magnetic field are presented, and compared with a model based on the fluid equations for electrons, ions and neutral atoms. The main feature of the model is that dissipation of shock energy occurs primarily through ion collisions with neutrals. According to the model, at low upstreain ionization levels, ions and neutrals are preferentially heated above the electrons. At high ionization levels, the electrons are more strongly heated. This is found to be in agreement with the shock structures obtained for 4 switch-on shocks, differing in the level of upstream ionization.
On the non-uniqueness of ideal MHD equilibria, with implications for tokamak calculations
Authors: Field J. J. , Papaloizou J. C. B.
Published: March 2009

Non-linear ideal MHD equilibria in axisymmetric systems are examined, both in diffuse and free boundary cases. Attention is restricted to the situation in present low-β tokamak experiments, in which there are no current reversals. Both general qualitative results on the uniqueness and bifurcation of solutions are provided and exact solutions of several problems in a circular cylinder are given, exhibiting bifurcation phenomena. In particular sufficient conditions for bifurcation behaviour are conjectured, for both diffuse and free boundary equilibria.
Effect of growth-rate modulation on the nonlinear mode coupling between stable and unstable plasma waves
Authors: Anderson D. , Bondeson A. , Falk L.
Published: March 2009

An investigation is made of the effect of an external growth-rate modulation on the saturation of a linearly unstable plasma wave by means of nonlinear Landau damping. Different ways of exciting the saturated system by suitable choices of modulation frequency are discussed and the characteristics of the resulting instabilities, like thresholds, growth-rates, maximum amplitudes and final saturation levels are determined.
A note on the modulational instability of long Alfvén waves parallel to the magnetic field
Authors: Mjølhus Einar
Published: March 2009

An amplitude dependent criterion for modulational stability of long Alfvén waves parallel to the magnetic field is interpreted in terms of a recently obtained inverse scattering solution to the modified nonlinear Schrödinger equation. It is found that the solitons formed are of two types. In the strongly unstable case, normal solitons are formed. In the transition region of weakly unstable and stable cases, the anomalous type, which in a limiting case becomes the algebraic soliton, dominates. In the strongly stable case, no solitons are formed.
Dynamic feedback for multi-mode plasma instabilities
Authors: Sen Amiya K.
Published: March 2009

Constant feedback, which has been used exclusively, fails to stabilize more than one mode of a plasma instabiliity. It is shown that a suitable dynamic or frequency-dependent feedback can stabilize all modes. Methods are developed in which such a feedback strucutre can be chosen in terms of its poles and zeros in relation to those of the plasma transfer function in the complex frequency plane. The synthesis procedure for such a feedback sturcure, in the form of an integrated electronic circuit is also discussed. As an example, a dynamic feedback for multi-mode stabilization of a collisional drift wave instability is developed in detail.
A strictly Markovian expansion for plasma turbulence theory
Authors: Jones Frank C.
Published: March 2009

The collision operator that appears in the equation of motion for a particle distribution function that has been averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. In this note we derive an expansion of the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest nontrivial order. The validity of this expansion is seen to be the same as that of the standard quasi-linear expansion.
Confinement times in quasi-trapping orbits
Authors: Scheetz D. C. , Flynn R. W.
Published: March 2009

Baker proposed a method of injecting charged particles into a static magnetic field such that particles on these ‘trapping orbits’ never return to the vicinity of the injector and remain permanently trapped. Their infinite confinement time requires that their energy, Eo, be specified with infinite precision. When the energy differs from this by a small amount, E, the particle escapes after a finite confinement time, of the order of In (Eo/E) cyclotron periods.
Linearized expressions for perturbed quantities for propagation at arbitrary angle to the static magnetic field in plasmas with non-uniform density and thermal anisotropy
Authors: Koch R.
Published: March 2009

This paper is concerned with the derivation of linear wave equations for nonuniform magnetized Vlasov plasmas. By the operator method it is shown that a close connection exists between the case of perpendicular propagation and the general one. Combining this with previous results, expressions for the perturbed density and velocity are derived for the case of propagation at any angle to the uniform static magnetic field in a two-temperature Maxwellian plasma. These results apply for arbitrary inhomogeneities of equilibrium density and temperatures in directions perpendicular to the static magnetic field.
On the stability of self-consistent large-amplitude waves in a cold plasma. Part 2. Longitudinal waves in the absence of large-scale magnetic field
Authors: Lee M. A. , Lerche I.
Published: March 2009

We demonstrate that self-consistent large-amplitude longitudinal waves in a cold plasma are unstable to at least transverse perturbations, with an instability growth rate which is roughly of the order of the plasma frequency of the system. The instability statements derived here are conservative, since modes not discussed may be more unstable.
On the stability of self-consistent large-amplitude waves in a cold plasma. Part 3. Transverse circularly polarized waves in the presence of a large-scale magnetic field
Authors: Lee M. A. , Lerche I.
Published: March 2009

We demonstrate that a self-consistent large-amplitude circularly polarized wave, propagating in a cold plasma in the presence of a large-scale magnetic field, is unstable if the constant bulk streaming speed of the plasma is zero in the frame in which the wave depends oniy on time. The growth rate is of the order of the plasma frequency or the gyrofrequency at short perturbation wavelengths, and is proportional to the perturbation wave vector at long wavelengths. For nonzero but small streaming the instability rate increases for one streaming direction and decreases for the other. We conclude that instability is the rule rather than the exception for large-amplitude waves in a cold plasma.
A technique for calculating finite Larmor radius corrections
Authors: Robertson Colette
Published: March 2009

Finite Larmor radius corrections may be significant in plasma stability theory, and the geometry of the cylindrical pinch is appropriate for theoretical development. The study presented here is limited to calculation of the perturbation of the energy of a particle by a normal mode disturbance. This is found to be complicated when terms proportional to the square of the Larmor radius are retained. It is concluded that stability theory becomes identical with drift wave theory in complex geometry.
Cold plasma dispersion surfaces
Authors: Oakes M. E. , Michie R. B. , Tsui K. H. , Copeland J. E.
Published: March 2009

Three-dimensional plots of dispersion in a cold anisotropic plasma are presented. The ω(κ, θ) surfaces provide a clear picture of the behaviour of cold plasma waves as the direction of propagation is varied. The group velocity (dω/dκ) has a simple geometrical interpretation on the surfaces.
Generation of ultra-itense heavy ion beams for inertial confinement fusion
Authors: Winterberg F.
Published: March 2009

A pulse-power-driven, heavy-ion beam, ignition and inertial confinement system for thermonuclear microexplosions is proposed. The proposed method depends on already developed and tested techniques and has the potential of a high repetition rate, one of the requirements for a thermonuclear microexplosion reactor. In the proposed method, a space charge neutralized ion beam of modest intensity is projected into a long drift tube where it is radially confined by an applied axial magnetic field and axially compressed by a programmed variation of the diode voltage with time. Because the beam consists of a space charge neutralized flow of heavy ions, it behaves like a high atomic number plasma and, as such, rapidly looses internal energy by radiation during its axial compression. The axial compression proceeds isothermally until the beam becomes optically opaque where it reaches its maximum density. The axial beam compression greatly amplifies the final beam power over its initial value at the beam producing diode. In typical cases the initial beam power is ≃ 1010W, and in a drift tube ≃ 100 meters long can be amplified ≃ 104fold up to ≃ 1014W; but much larger beam powers are also possible. The accelerating voltage is typically in the range of several 106V and the diode current several 103A. Because the collision mean free path in the beam is smaller than the beam length, some unavoidable deviation from the programmed diode voltage will not lead to a dispersion of the beam. For typical cases the beam has, at its maximum compression, an atomic number density of ≃ 1018cm−3and a radius of ≃ 1 cm. After being compressed to its final maximum density the beam can, from there on, be easily focused on to the thermonuclear target. The use of singly ionized heavy ions in combination with an accelerating voltage of several 106V has the further advantage that the ion velocities are of the order of several 108cm sec−1, ideally matching the required optimal implosion velocity for the microexplosion target and thus implying a high beam energy conversion efficiency for ignition and confinement. For a final beam power of ≃ 1014W the diode cross-section is ≃ 102cm2. With a diode cross-section ≃ 103times larger, that is ≃ 10 m2, final beam powers up to ≃ 1017W will be possible, opening the prospect for igniting the DD and perhaps the HB11thermonuclear reactions.
Equation of state for a partially degeneerate plasma
Authors: Johnstion J. W. , Cumming J. , Laing E. W.
Published: March 2009

The methods of thermodynamic quantum field theory are used to obtain the equation of state and other thermodynamic properties of a plasma. Electrons may be partially degenerate, while ions are treated classically and restricted to charge number Z = 1 or 2. Results are obtained for densities in the range 1026–1034 m−3and for temperatures of 105–108 K.
Wave–wave interactions in rotating gases
Authors: Stenflo L.
Published: March 2009

The resonant nonlinear interaction between three waves in a non-uniform rotating plasma is considered. The coupling coefficients are calculated for the case where the axis of rotation is parallel to an external magnetic field. Owing to similarities between this plasma and a gas of gravitating particles, it is likely that these coefficients can also be useful in the theory of galactic density waves.
Effect of perturbation theory on the spectrum of ideal magnetohydrodynamic and guiding centre plasmas
Authors: Ambrosiano John , Vahala George
Published: March 2009

For a high β screw pinch it is shown explicitly how the perturbation theory distorts the spectrum of ideal magnetohydrodynamics and guiding centre plasmas. In particular it is seen why the Cauchy integrals (present in the nonperturbative linearized guiding centre plasma model, and which are necessary for the isotropic pressure guiding centre plasma eigenvalue problem to differ from that for magnetohydrodynamics) are absent in the perturbation theory. This result holds also for axially and helically symmetric systems. The distortions in the m = 1 growth rates are also presented.