bluuebunny/crossref_metadata_2025 huggingface dataset:
Stability of an astrophysical plasma near the onset of electron runaway
Authors: Kaastra J. S.
Published: March 2009

The time-dependent behaviour of a homogeneous plasma in a weak electric field near the onset of runaway of electrons is studied for astrophysical applications. The relativistic Boltzmann equation is used to calculate the particle distribution function. It is shown that the plasma is stable against electric field fluctuations in the onset region for runaway, provided that the global behaviour of the System is determined by the magnetic field structure.
Nonlinear equilibrium and stability analysis of rippled, partially neutralized, magnetically focused electron beams
Authors: Cuperman S. , Petran F.
Published: March 2009

After giving a higher-order solution of the equation describing the nonlinear equilibrium of rippled electron beams, in the second part of the paper we derived mathematical expressions for the growth rates of electrostatic perturbations for the resonant coupling of (i) fast and slow and (ii) fast—fast or slow—slow waves. Actually, viewed from a physical point of view, only type (i) of wave coupling may lead to the kind of instability considered in the paper.
Dissipative instabilities of magnetic neutral layers with velocity shear
Authors: Dobrowolny M. , Veltri P. , Mangeney A.
Published: March 2009

We consider, in the framework of dissipative MHD, the general problem of instability of magnetic neutral sheets in the presence of velocity shear. Both resistivity and viscosity are included in the treatment. We show that velocity shear and/or viscosity introduce different orderings with respect to resistive tearing modes and that the classical tearing modes represent a singular case. Possible orderings for growth rates are discussed and a specific example containing the effect of velocity shear is treated in detail.
Linear and nonlinear modified electron-acoustic waves
Authors: Yu M. Y. , Shukla P. K.
Published: March 2009

It is shown that a modified electron-acoustic wave exists in a plasma with distinct hot and cold electron components. The frequency of this wave depends strongly on the cold electron number density. Solitons associated with the modified electron-acoustic waves are also discussed.
Deflagrations and discontinuities in laser-produced plasmas
Authors: Pert G. J.
Published: March 2009

The structure of deflagrations in one-dimensional flow is examined in detail. It is shown that the rule that deflagrations be weak or Chapman-Jouget must be obeyed unless a non-hydrodynamic discontinuity occurs. Such flows are shown to be unique and stable, once the downstream expansion is specified. It is shown that non-hydrodynamic discontinuities, if strong, are accompanied by a compression leading to a weak termination. The application to plasmas produced by laser irradiation of a solid is investigated and the flow structure in the presence of flux limitation evaluated.
Electron whistler mode instability in an inhomogeneous thermal plasma in the presence of an inhomogeneous beam of suprathermal electrons
Authors: Shah H.A. , Jain V.K.
Published: March 2009

The excitation of the whistler mode waves propagating obliquely to the constant and uniform magnetic field in a warm and inhomogeneous plasma in the presence of an inhomogeneous beam of suprathermal electrons is studied. The full dispersion relation including electromagnetic effects is derived. In the electrostatic limit the expression for the growth rate is given. It is found that the inhomogeneities in both beam and plasma number densities affect the growth rates of the instabilities.
The thermal self-focusing of a wave beam in an underdense plasma. Part 4. Quadratic nonlinear effects
Authors: Giles M. J.
Published: March 2009

In the fourth part of this paper devoted to the problem of the thermal self-focusing of an electromagnetic wave in an underdense plasma, we examine the spatial nonlinear development of the instability, assuming that a stationary state of the type described earlier has been established. Our treatment considers the interaction of the pump wave with the Stokes side-band waves and the density perturbation corresponding to the most unstable linear mode. We show that the system of equations describing their interaction possesses three invariants. These invariants are used to reduce the problem to a single differential equation for the axial behaviour of the amplitude of the density perturbation. The form of the invariants differs according as the inclination of the beam to the magnetic field is above or below the critical value defined earlier. Above the critical orientation, the amplitude of the density perturbation can be expressed algebraically in terms of the amplitudes of the pump and side-band waves. We show that this case is integrable in terms of the Jacobean elliptic function dn and we use the results to find the saturation level. Below the critical orientation, the response of the plasma becomes non-local, above a certain threshold power. The algebraic relation is then replaced by a differential equation which results in a significantly more complicated differential equation for the amplitude of the density perturbation. A particular solution of this equation is found for a special choice of initial conditions and from this the saturation level is found. The results of these calculations are applied to the problem of ionospheric modification by microwave transmissions from the proposed solar power satellite systems.
A linear model for the tearing mode of a tokamak plasma with flow and a resistive wall boundary condition
Authors: Jensen Torkil H. , Chu Ming S.
Published: March 2009

The tearing mode of a tokamak plasma without flow may be stabilized by the presence of a conducting wall surrounding the plasma. When the wall has a finite resistivity, its presence does not affect stability, only growth rates. If, however the plasma has a flow relative to the resistive wall, both stability and growth rates may be affected. For the cylindrical, circular cross-section tokamak the problem is formulated as a complex eigenvalue problem, with a complex eigenvalue Δ', which in the limit of vanishing flow becomes identical to the usual ‘delta prime’. The real part of Δ' describes as usual the power absorbed at the singular surface while the imaginary part describes absorption of momentum. It is found that for a plasma with shearless flow, a resistive wall has a stabilizing effect which even for relatively small flow velocities approaches that of a wall of infinite conductivity. Shear flow is found inherently destabilizing, but important only for very large flow velocities.
Scattering of waves by Langmuir solitons
Authors: Mendonça J. T.
Published: March 2009

Scattering of electromagnetic and electrostatic waves by one-dimensional Langmuir solitons in a uniform and isotropic plasma is studied analytically using a perturbation method. Mode conversion via scattering by solitons is also considered. The results are also relevant for the case of ion-acoustic solitons.
Plasma boundary motion and the ion-acoustic wave
Authors: Braithwaite N. St. J. , Wickens L. M.
Published: March 2009

Ion-acoustic waves can be launched into plasmas by applying an oscillating voltage wave form to an electrode. The precise mechanism by which these waves are launched from such an electrode is not fully understood. The work described here examines the modelling of sheath edge motion in connexion with acoustic wave launching in both planar and spherical geometries. A novel demonstration of the applicability of the kinetic Bohm criterion is given by using the method of characteristics. A characteristics analysis is also used to show that an expanding, but decelerating, non-planar sheath can give rise to quasi-neutral compression-like features in a plasma. It is also shown that in planar geometry neither this kind of expansion, nor an oscillatory sheath motion, generates compression-like features.
Guided modes between upper-hybrid and plasma resonance
Authors: Morales G. J. , Maggs J. E.
Published: March 2009

The structure of driven electrostatic oscillations is determined for a cold plasma with a zero-order density gradient along the magnetic field. A set of well-behaved structures, bounded at plasma resonance, exists for discrete values of the perpendicular wavenumber. A Green's function suitable for sources located in the overdense region of the plasma is constructed. The driven medium responds as a loss free guide.
Long-time states of inverse cascades in the presence of a maximum length scale
Authors: Hossain Murshed , Matthaeus William H. , Montgomery David
Published: March 2009

It is shown numerically, both for the two-dimensional Navier-Stokes (guidingcentre plasma) equations and for two-dimensional magnetohydrodynamics, that the long-time asymptotic state in a forced inverse-cascade situation is one in which the spectrum is completely dominated by its own fundamental. The growth continues until the fundamental is dissipatively limited by its own dissipation rate.
Bifurcation of a free boundary equilibrium
Authors: Turnbull A.
Published: March 2009

The problem of bifurcation of a free boundary equilibrium is reconsidered in a simple model. We find which combinations of specified parameters result in a non-unique solution and find the resulting bifurcation point. By including reversed current solutions, the model sheds some light on the equilibrium βp limit obtained in previous analytic and numerical models.
On the nonlinear development of the Langmuir modulational instability
Authors: Dendy R. O. , Haar D. Ter
Published: March 2009

Using the Zakharov equations in their Fourier-transformed form, we consider the development of the modulational instability (MI) both for the monochromatic and the finite-width cases. In the static approximation and considering a monochromatic Langmuir wave which is coupled only to a single pair of Stokes and anti-Stokes Langmuir perturbations, we show that the resultant set of equations is integrable and we discuss the analytical solution of these equations. We show how a finite-width driver will lead to a threshold for the MI. We compare our results with those obtained by other authors.
Transport of neutrals in the outermost region of a tokamak plasmas
Authors: Chhabra R. S.
Published: March 2009

The transport of neutrals in the outermost region of a tokamak plasma has been studied using kinetic theory. Analytical expressions for the density profiles of hydrogen and impurity neutrals are obtained. It is shown that the inclusion of recombination increases the density of hydrogen neutrals in the blanket region by orders of magnitude. It is also found that the major contribution to the impurity neutral density, for impurities which have a resonant mutual charge exchange with hydrogen, comes from mutual charge exchange for moderately dense plasmas whereas for dense plasmas this comes from recombination.
Plasma models and rescaling methods
Authors: Lotte Philippe , Feix M. R.
Published: March 2009

The plasma models used in analytical or numerical studies exhibit, mainly for practical reasons, symmetry reducing the dimensions of the space. It is not obligatory that the restrictions on the dynamics and the chosen form of the electrostatic interactions should correspond to the same symmetry and this introduces the concept of a d (dynamic), d' (electrostatic) model with d' ≥ d. We show that the crucial parameter is d' – d. For d' – d = 0, the model exhibits both at low and at high temperature the same characteristic plasma frequency. At high temperature we recover the Vlasov limit and the plasma acts as a high-pass filter. For d' – d = 1, the two frequencies (purely collective at high temperature and ‘crystal’ frequency at very low temperature) are different, while in its high temperature (Vlasov) limit the plasma acts as a low-pass filter. Finally if d' – d ≥ 2 there is no longer a Vlasov limit for all values of temperature and density. These properties are obtained through a systematic use of the homothety transformations and a search for the corresponding invariants.
Transformation and amplification of waves in a non-uniform plasma involving monoenergetic electron beam
Authors: Shamrai K. P.
Published: March 2009

Stationary wave interactions are considered in a non-uniform plasma involving a cold electron beam propagating along the plasma density gradient. The character of the interactions is shown to depend on the beam-to-plasma energydensity ratio. The coupling of the beam space-charge waves and slow Langmuir waves gives rise to anomalous mode conversion and to the excitation of intensive fields near the resonance point. The regime of amplification is proved to be universal but is found to be sensitive to the boundary conditions.
On the ignition of a self-sustained fusion reaction in a dense DT plasma
Authors: Liberman M. A. , Velikovich A. L.
Published: March 2009

Ignition of a self-sustained fusion reaction in a strong magnetic field is studied. The critical ignition dimensions and the threshold ignition energy are calculated as functions of the fuel density and the magnitude of the transverse magnetic field. A new method for producing ultra-high magnetic fields is proposed which provides at once heating of the fuel by induction currents and localization of the micro-explosion by the magnetic field. Simple analytic estimates show that a certain combination of inertial, magnetic and wall methods of plasma confinement may decrease the ignition energy below 100 kJ.
Analysis of ideal MHD equilibrium and axisymmetric stability for finite aspect ratio tokamaks with elliptic cross-section and flat current profile
Authors: Grauer R. , Rebhan E.
Published: March 2009

To calculate the equilibrium and stability of finite aspect ratio tokamaks, even for circular and elliptical plasma cross-sections, intricate numerical methods must usually be employed, which require a fast and large computer. So far, these calculations have been carried out analytically only for infinite aspect ratio. In fact certain analytical equilibrium solutions at finite aspect ratio are known, but these do not include such important cases as elliptical cross-sections. In this paper, finite aspect ratio equilibrium solutions are derived for circular, prolate and oblate elliptical cross-sections and for a flat current profile. In addition, the problem of axisymmetric stability is studied for prolate elliptical cross-sections, the approach being almost entirely analytical.
Laser-induced profile modifications in magnetized plasmas
Authors: Rao N. N. , Shukla P. K. , Yu M. Y.
Published: March 2009

An analysis of profile modifications in laser-plasma interactions in the presence of an externally applied constant d.c. magnetic field is presented. By considering the case of circular polarization for the incident laser light, the flow velocities and the shelf densities in the incident as well as the evanescent regions are calculated. For left-handed circular polarization, the flow velocity in the incident region is enhanced by the magnetic field, whereas the opposite occurs for right-handed circular polarization. On the other hand, the shelf density in the evanescent region is always supercritical for the former case, and for the latter case it can be either subcriticai or supercritical, depending on the strengths of the incident laser intensity as well as the external magnetic field.
Stability of a magnetized positive column between coaxial cylinders
Authors: Dogra Virendra K. , Uberoi Mahinder S.
Published: March 2009

Theoretical analysis for the stability of a diffusion dominated positive column between coaxial cylinders in the presence of an axial magnetic field is carried out under the assumptions of quasi-neutrality of charges and no sheath at the walls. Self-consistent infinitesimal perturbations of plasma density and electric potential, which satisfy the linearized governing equations to the same degree of approximation are used to derive the dispersion relation. The perturbations associated with aximuthal modes m ≤ 0 are stable for any gap size and plasma parameters. The stability of non-axisymmetric perturbations is studied for different gaps. It is found that the presence of inner cylinders increases the stability of a magnetized positive column and m = 2 defines the region of stability when the ratio of the radii of the inner and outer cylinders is less than 0·5. In the case of narrow gaps, higher and higher modes are excited. The minimum non-dimensional axial electric field at which the magnetized positive column between coaxial cylinders becomes unstable for different gaps is also determined.
Electron-acoustic and ion-ion hybrid resonance-drift instability in inhomogeneous multi-ion-species magnetoplasmas
Authors: Dash Shefali S. , Sharma A. S. , Buti B.
Published: March 2009

Electron-acoustic (EA) and ion-ion-hybrid resonance (IIHR) waves, in a multi-ion-species magnetoplasma with density gradients perpendicular to the magnetic field and the direction of wave propagation are found to be drift unstable provided the inhomogeneities exceed a certain threshold. The possibility of mode conversion between the EA and the IIHR waves is examined.
Linear and nonlinear propagation of electron-acoustic wave in a multi-species plasma
Authors: Guha S. , Dwivedi C. B.
Published: March 2009

The propagation of an electron-acoustic wave in a plasma consisting of two types of ion and two temperature electrons has been investigated in the linear and nonlinear regimes. The presence of the second species of ion modifies the characteristics of the wave. The analysis has been done for both the finite amplitude and the small amplitude case of the electron-acoustic solitary wave. The ion temperature ratio and the electron density ratio rather than the relative ion density are the effective parameters which govern the amplitude of the electron-acoustic soliton.
An asymptotic analysis of the radiation pattern of ion cyclotron resonance heating antennas
Authors: Koch R. , Bhatnagar V. P. , Weynants R. R.
Published: March 2009

Using the stationary phase method, a simple asymptotic analysis of a two-dimensional model of the coupling of the cold-plasma magnetosonic wave excited by an ion-cyclotron resonance heating (ICRH) antenna is presented. Such an analysis allows quick evaluation of the basic characteristics of the ICRH antenna radiation pattern and shows how the power spectrum radiated by the antenna and plasma dispersion properties combine to produce the power flux distribution observed in the far-field region. The results of the present simplified analysis are found to be in reasonably good agreement with more sophisticated coupling codes. This development thus serves as a simple analytic tool for quick investigation of the most fundamental features of coupling for antenna design studies. With a view to spectrum shaping for improved heating and tokamak RF current drive, the case of a phased antenna array is also analysed.
Theory of Raman sidescatter from a magnetized plasma
Authors: Barr H. C. , Boyd T. J. M. , Rankin R.
Published: March 2009

The effects of a d.c. magnetic field on stimulated Raman sidescatter from laser-produced plasmas is studied. For exact sidescatter along the magnetic field, the Raman instability separates into two distinct decays in which the scattered light is either a right (RHCP) or left (LHCP) circularly polarized electromagnetic wave. Growth rates of the instabilities can be enhanced in the former case but are diminished in the latter. The magnetic field induced effects are greatest near the quarter critical density where frequency shifts can be especially significant, being equal to ± ¼Ωc for decay into RHCP and LHCP waves, respectively.
Spontaneous generation of magnetic field in an imploding plasma
Authors: Auluck S. K. H.
Published: March 2009

Spontaneous generation of an axial magnetic field is predicted when the usually neglected centripetal acceleration term is properly taken into account in the two-fluid equations of motion for a cylindrically symmetric imploding plasma. An order-of-magnitude calculation is presented to illustrate spontaneous generation of a reversed-field configuration in a plasma imploded by a metallic liner.
A numerical investigation of current-driven instabilities near the ion-ion hybrid frequency
Authors: Grayson Diane J. , Hellberg M. A.
Published: March 2009

A dispersion relation for electrostatic waves in a current-carrying, resistive, magnetized, two-ion plasma has been solved numerically for a range of parameter values. The behaviour of the resistive ion-ion hybrid instability is described and in addition a two-stream ion-ion hybrid instability is identified.
Axisymmetric control of large tokamak devices
Authors: Jensen T. H. , McClain F. W.
Published: March 2009

The problem of controlling the position and cross-sectional shape of plasmas is addressed for circumstances relevant to large tokamaks. A principle for, as well as a practical method of analysis of, this control problem is presented. The relevant elements of the tokamak system included in the analysis are the plasma, a resistive wall (vacuum chamber wall) surrounding the plasma, toroidally wound coils which also surround the plasma, as well as their associated external circuitry and a number of monitors of properties of the magnetic field in the vicinity of the plasma; the signals obtained from these monitors are used for control of power supplies which are part of the external circuits.
A parametric survey of the first critical Mach number for a fast MHD shock
Authors: Edmiston J. P. , Kennel C. F.
Published: March 2009

The first critical fast Mach number is rigorously defined to be the one at which the downstream flow speed in the shock frame equals the ordinary downstream sound speed. Above the first critical Mach number, resistivity alone is unable to provide all the dissipation needed for the required Rankine-Hugoniot shock jump. A survey of the dependence of the first critical Mach number upon upstream plasma parameters is needed to guide studies of the structure of collisionless shocks in space. We vary the upstream plasma beta, the upstream shock normal angle, and the ratio of specific heats for the plasma. The first critical Mach number depends sensitively upon upstream plasma parameters, and is between 1 and 2 for typical solar wind parameters, rather than the often quoted value of 2·7, which is valid for perpendicular shocks propagating into a cold plasma. We introduce the suggestion that the flux of superthermal and energetic ions upstream at quasi-parallel shocks might increase suddenly at the first critical Mach number. Our parametric survey indicates that this hypothesis might be most conveniently tested using interplanetary shocks.
Continued fraction expansions for the plasma dispersion function
Authors: McCabe J. H.
Published: March 2009

Two continued fraction expansions for the plasma dispersion function are given. The first is a very simple expansion for which error estimates can be obtained and which provides better approximations as the modulus of the argument increases. The second, while not so simple, provides whole range approximations.
Effects of positive potential in the catastrophe theory study of the point model for bumpy tori
Authors: Punjabi Alkesh , Vahala George
Published: March 2009

With positive ambipolar potential, ion non-resonant neoclassical transport leads to increased particle confinement times. In certain regimes of filling pressure, microwave powers (ECRH and ICRH) and positive potential, new folds can now emerge from previously degenerate equilibrium surfaces allowing for distinct C, T, and M modes of operation. A comparison in the equilibrium fold structure is also made between (i) equal particle and energy confinement times, and (ii) particle confinement times enhanced over the energy confinement time. The nonlinear time evolution of these point model equations is considered and confirms the delay convention occurrences at the fold edges. It is clearly seen that the time-asymptotic equilibrium state is very sensitive, not only to the values of the control parameters (neutral density, ambipolar electrostatic potential, electron and ion cyclotron power densities) but also to the initial conditions on the plasma density, and electron and ion temperatures.
Nonlinear bound on unstable electrostatic fluctuation energy for non-relativistic non-neutral electron flow in a planar diode with applied magnetic field
Authors: Davidson Ronald C.
Published: March 2009

Global conservation constraints satisfied by the Vlasov-Maxwell equations are used to obtain a nonlinear bound on the unstable electrostatic fluctuation energy that can develop for non-relativistic non-neutral electron flow in a planar diode with an axial applied magnetic field. It is shown that the Heimholte free energy is a minimum for the thermal equilibrium reference state. The nonlinear bound on unstable fluctuation energy that can develop for general initial conditions is calculated for the case of flute perturbations with no axial dependence. To determine the lowest upper bound on fluctuation energy consistent with conservation constraints, the density, temperature and drift velocity of the reference state are chosen to minimize the nonlinear bound. The analysis assumes that the net flux of particles, momentum, and energy, vanish identically at the cathode and at the anode.
On the exponential flattening of current sheets near neutral X-points in two-dimensional ideal MHD flow
Authors: Sulem P. L. , Frisch U. , Pouquet A. , Meneguzzi M.
Published: March 2009

It is shown that the flattening of current sheets which has been observed near neutral X-points in numerical simulations of ideal MHD flow in two dimensions can be obtained from an asymptotic expansion of the dynamical equations. This asymptotic expansion suggests that exponential self-similar flattening proceeds forever and that there is no finite time singularity for ideal two-dimensional MHD flows. The equation for the spatial structure of the self-similar solution is reduced, via a hodograph transformation, to a nonlinear wave equation involving interactions with distant parts of the fluid and therefore non-universal features.
Resistive decay of Alfvén waves in a non-uniform plasma
Authors: Mok Y. , Einaudi G.
Published: March 2009

The effect of resistive dissipation on the propagation of an MHD disturbance in a non-uniform plasma is examined. The present analysis, based on a boundarylayer technique, shows the existence of resistive normal modes with complex eigenfrequencies. The real part of the eigenfrequency is associated with an oscillatory behaviour and defines the location in space of the layer where resistivity is important. The dissipation mechanism is responsible for the damping of the wave, in contrast with previous works in which the ideal MHD theory was used.
The Fermi golden rule for ideal magnetohydrodynamics
Authors: Lifshitz Alexander E.
Published: March 2009

The process of excitation of the Alfvén wave is studied by means of the qualitative method of quantum mechanics.
Propagation of hydromagnetic waves in a cold plasma mixed with hot ions
Authors: Hamabata Hiromitsu , Namikawa Tomikazu
Published: March 2009

The propagation of small-amplitude hydromagnetic waves in a cold plasma mixed with hot ions is investigated using the first-order CGL equations for ions. It is assumed that in an equilibrium state the ions consist of two components, cold ions and hot ions with bi-Maxwellians. Propagation properties of hydro-magnetic waves are analysed by use of phase speed and refractive index surfaces, polarization and the amplitude ratio between perturbed density and magnetic field. It is shown that the existence of cold ions affects the properties of hydro-magnetic waves through finite frequency corrections only when the temperature anisotropy exists; and that the critical angle, at which the polarization sense changes from right-handed to left-handed as well as from left-handed to right-handed, can exist for intermediate and slow waves.
Hydromagnetic waves for a collisionless plasma in strong magnetic fields
Authors: Duhau S. , De La Torre A.
Published: March 2009

A hydrodynamic system of equations, valid in the limit in which the Larmor radius and the electron to ion mass ratio are both zero, and including the thermo-dynamic variables and the energy equation of the electrons, is used to investigate the propagation of small-amplitude waves in a collisionless heat-conducting plasma. The result is compared with that derived from the Chew, Goldberger & Low equations. It is found that for zero heat flux, the inclusion of the electron pressure does not change the number and characteristic of the modes but modifies the mirror stability criterion. In the general case, the phase speed is symmetric with respect to two axes: one parallel to the heat flux vector and the other normal to it. The heat flux generates a new mode and couples strongly the slow and fast magnetosonic modes whose wavenumber vectors have projections in the positive flux vector direction, giving rise to a new overstability whose existence does not depend on the ion anisotropy.
Nonlinear theory of large-mode-number ballooning modes in fully toroidal geometry
Authors: Mondt J. P. , Weiland J.
Published: March 2009

A nonlinear model equation describing ballooning modes for β of the order of the inverse aspect ratio and including magnetic shear is derived. For the special case of circular concentric flux surfaces, we obtain an approximate dispersion relation, including finite Larmor radius effects, and show the possibility of explosive instability in the nonlinear regime. The results are shown to remain valid in the presence of a low-density hot-ion constituent.
Gyrokinetics of resonant particles in a collisionless plasma
Authors: Karnilovich S. P. , Malek G. F. , Milantiev V. P.
Published: March 2009

A consistent drift-kinetic theory is developed for the interaction of resonant particles in a relativistic magnetized plasma with HF (high-frequency) wave packets for arbitrary ratio of the gyroradius to the wavelength. Gyrokinetic equations for the plasma particles are obtained for Čerenkov and cyclotron resonances as well as for those at the harmonics of the gyrofrequency, the half-integer cyclotron resonances and those with the beats of two wave packets. The periodic parts of the distribution function for the relativistic non-uniform and non-stationary plasma are calculated.
Ion cyclotron electromagnetic wave structure in Elmo bumpy torus
Authors: Cotsaftis M. , Gladd N. T. , Krall N. A.
Published: March 2009

The problem of ion cyclotron wave structure in EBT has been analyzed using the smallness of the inverse aspect ratio ε = a/R0 and of the inverse cavity number ε' = 1/N. The procedure is to expand in these two parameters, reducing the complete toroidal problem to a system of equations to be solved in sequence. To second order in ε and ε', this system contains two ordinary differential equations of second order and one partial differential equation with periodic coefficients in a magnetically adapted system of co-ordinates. The smallness of the mean bumpiness parameter εB reduces the problem to a single second-order differential equation which, for a parabolic density profile, is a Whittaker equation. The EM wave structure corresponds to a simple mode with only a few wavelengths across the plasma radius, permitting multi-harmonic ion cyclotron heating with interesting efficiency, as observed in experiments.
Whistler-mode polarization in a hot anisotropic plasma
Authors: Sazhin S. S.
Published: March 2009

Polarization of whistler-mode waves in a hot anisotropic plasma is considered in the two limiting cases of quasi-longitudinal and quasi-electrostatic propagation. It is pointed out that electron thermal motion never influences the phase of the propagating waves; the polarization of whistler-mode waves propagating along the magnetic field is totally independent of electron thermal motion. The deformation of polarization (in both electric and magnetic fields), of obliquely propagating whistler-mode waves could be, in principle, observed in magnetospheric conditions and thus could be used to estimate electron temperature and anisotropy. This deformation seems to be especially pronounced for the electric field polarization of quasi-electrostatic waves.
Resistive Alfvén normal modes in a non-uniform plasma
Authors: Einaudi G. , Mok Y.
Published: March 2009

Resistive normal-mode solutions of the MHD equations are found numerically in a smooth, non-uniform, magnetic field. The (α, S) boundary within which normal-mode solutions exist is explicitly computed, where α is the normalized wavenumber and Sthe Lundquist number. As an extension of our previous analytic results (Mok & Einaudi 1985), the damping rate of these modes is computed to a higher accuracy, and is found to have an a + bS−1/3 dependence, where a and b are independent of S.
Resistive convection in a cylindrical plasma. Part 2
Authors: Gomberoff L.
Published: March 2009

It is shown that the combined effect of resistivity and thermal conductivity leads to convection in a cylindrical current-carrying plasma, under the action of a shearless magnetic field. In contrast to the case of part 1, these modes occur for large wavenumbers and Bθ≫ Bz The conditions, however, are the same as before. From this fact it is then conjectured that convection takes place for any wavenumber, determined only by the actual value of B0/Bz.
Resonant interaction of electron cyclotron waves with a plasma containing arbitrarily drifting suprathermal electrons
Authors: Orefice A.
Published: March 2009

A relativistic treatment of the plasma dispersion functions and of the dielectric tensor for electron cyclotron electromagnetic waves is given for non-thermal plasmas where the electron distribution function can be represented as a combination of Maxwellians with arbitrary drifts along the magnetic field.
General two-dimensional magnetohydrodynamic equilibria with mass flow
Authors: Agim Y. Z. , Tataronis J. A.
Published: March 2009

A set of reduced ideal MHD equations is derived to investigate equilibria of plasmas with mass flow in general two-dimensional geometry. These equations provide a means of investigating the effects of flow on self-consistent equilibria in a number of new two-dimensional configurations, such as helically symmetric configurations with helical axis, which are relevant to stellarators, as well as axisymmetric configurations. It is found that, as in the axisymmetric case, general two-dimensional flow equilibria are governed by a second-order quasilinear partial differential equation for a magnetic flux function, which is coupled to a Bernoulli-type equation for the density. The equation for the magnetic flux function becomes hyperbolic at certain critical flow speeds which follow from its characteristic equation. When the equation is hyperbolic, shock phenomena may exist. As a particular example, unidirectional flow along the lines of symmetry is considered. In this case, the equation mentioned above is always elliptic. An exact solution for the case of helically symmetric unidirectional flow is found and studied to determine flow effects on the magnetic topology.
Heating kinetic theory of a particle-beam generated plasma
Authors: Peyraud N.
Published: March 2009

The equilibrium electron distribution in a general high-energy particle-beam generated plasma is analysed in detail by a Laplace transformation method in the neighbourhood of the first excitation threshold of the target gas, where all collisional processes, elastic and inelastic, must be taken into account concurrently with a continuous source term. Two continuity conditions for the distribution (and.its derivative) calculated below and above the first threshold, enable us to obtain an analytic representation of the macroscopic quantities such as electron temperature and density. A numerical application is made for the case of a high-energy electron beam ionizing atomic argon and the results are compared with those of the Plasma Group of Orsay.
Gas-ionizing shocks in a magnetic field
Authors: Cowley M. D.
Published: March 2009

Ionizing shocks for plane flows with the magnetic field lying in the flow plane are considered. The gas is assumed to be electrically conducting downstream, but non-conducting upstream. Shocks whose downstream state has a normal velocity component less than the slow magneto-acoustic-wave speed and whose upstream state is supersonic are found to be non-evolutionary in the face of plane magneto-acoustic disturbances, unless the upstream electric field in a frame of reference where the gas is at rest is arbitrary. Velocity conditions are also determined for shock stability with the electric field not arbitrary.

Shock structures are found for the case of large ohmic diffusion, the initial temperature rise and ionization of the gas being caused by a thin transition having the properties of an ordinary gasdynamic shock. For the case where shocks are evolutionary when the upstream electric field is arbitrary, the shock structure requirements only restrict the electric field by limiting the range of possible values. When shocks are evolutionary with the electric field not arbitrary, they can only have a structure for a particular value of the electric field. Limits to the current carried by ionizing shocks and the effects of precursor ionization are discussed qualitatively.
Non-linear constant-profile plane waves in a cold plasma under an applied magnetic field
Authors: Alloucherie Yves J.
Published: March 2009

Periodic plane waves propagating in a homogeneous cold Vlasov plasma under the influence of an external magnetic fieldB0have been studied in this paper. Non-linear coupled differential equations for the two transverse components of the local magnetic field have been obtained for any angle α betweenB0and the wave vector. Starting from the previously obtained exact solution for α = 90° and the zeroth-order solution for α = 0, two perturbation methods are used to obtain first-order solutions for α = 0 and intermediate angles. A numerical example has been worked out in detail for a specific value of the field energy density; although it is not possible to match the two sets of results rigorously, they seem to converge smoothly to the same limit.
Resonantly unstable off-angle hydromagnetic waves
Authors: Kennel C. F. , Wong H. V.
Published: March 2009

We consider semi-quantitatively the cyclotron resonance instability of ion cyclotron and magnetosonic waves propagating at an angle to the magnetic field in an infinite uniform plasma. The velocity distributions of electrons and ions consist of a dense cold component and a diffuse high-energy tail. If the high-energy protons are sufficiently intense and their pitch angle distributions sufficiently anisotropic, instability occurs for those waves propagating parallel to the magnetic field. If the spectrum of resonant protons is sufficiently hard, a reasonably large cone of propagating angles about the magnetic field can be unstable. Observed fluxes of trapped protons in the magnetosphere should destabilise the ion cyclotron wave at a lower intensity threshold than for at least one class of electrostatic waves.
Stationary waves at a plasma—magnetic field interface
Authors: Savage M. D.
Published: March 2009

This paper considers the steady two-dimensional ‘magnetic bottle’ in which a moving, compressible and electrically conducting plasma is confined by a horizontally aligned magnetic field. It is assumed that dissipation by viscosity and resistivity is negligible and that the plasma-magnetic field interface is free from instabilities of all kinds.
On the steady Krook kinetic equation: Part 2
Authors: Anderson Donald G. M.
Published: March 2009

Numerically exact solutions of the problems of heat transfer between concentric circular cylinders and spheres have been obtained.
An experimental investigation into the behaviour of a spherical plasma resonance probe in a magnetic field
Authors: Davies P. G.
Published: March 2009

The rectified electron current to a non-magnetic and to a magnetic spherical plasma probe has been investigated as a function of the frequency of the applied alternating potential, the discharge current in the plasma source and the magnitude of the magnetic field produced by a Helmholtz coil pair. The frequency at the main peak in the rectified current was found to be always greater than the gyro- frequency and to lie within a range of frequency predicted by Crawford from an analysis of a simplified model. The results of this laboratory work have been applied to a rocket-borne experiment on resonance rectification previously carried out by R.S.R.S.
On the propagation of cylindrical waves in a magnetized self-gravitating collisionless plasma
Authors: Mattei Giulio
Published: March 2009

Solutions are obtained for cylindrical waves of the equations governing a magnetized self-gravitating collisionless plasma. Subject to certain conditions, we find two types of instability: (i) the hose instability which is related to the anisotropic pressure; and (ii) gravitational instability.
Nyquist diagrams for low-frequency oscillations in a non-uniform magnetoplasma
Authors: Bertotti Bruno , Nocentini Aldo
Published: March 2009

A modification of the Penrose criterion is applied to the local dispersion relation for low-frequency, electrostatic instabilities in a low-density, slightly inhomogeneous magnetoplasma. The Nyquist diagrams obtained can be classified according to their behaviour near the origin; this is sufficient in some cases to conclude that the equilibrium is unstable. With this method, in the limit of negligible ion Larmor radius, we find that the Langmuir waves propagating in a direction orthogonal to the external magnetic field are driven unstable by a temperature gradient.
Transition from ambipolar to free diffusion in a decaying plasma
Authors: Maldonado C. D.
Published: March 2009

The problem of transition from ambipolar to free diffusion due to charged particle density gradients in a decaying plasma of spherical symmetry is investigated in this paper. This investigation is carried out within the framework of the approximate procedure set forth by Allis & Rose (1954). A further simplification is introduced by using only the time-dependent ‘imperfect’ ambipolar diffusion coefficients for the electrons and ions evaluated at the centre of the plasma for carrying out calculations. The results for the time dependence of these ‘imperfect’ ambipolar diffusion coefficients and spatial distributions for the charge density, electric field, and potential which are obtained by this procedure are valid for all values of time in the neighbourhood of the centre of the plasma and for all other positions of space only during the time while the plasma is diffusing in an almost ‘perfect’ ambipolar manner.
Structure of the Bernstein modes for large values of the plasma parameter
Authors: Fredricks R. W.
Published: March 2009

The electrostatic modes for which k is perpendicular to the impressed field B0 (the ‘Bernstein modes’) have been examined, and dispersion curves (w vs. k) have been calculated numerically for hybrid frequencies in the vicinity of the thirtieth to fortieth harmonic of the gyrofrequency. Although the calculations were performed for the lower hybrid case (ion branch), they also apply to the upper hybrid cases in which the plasma parameter The structure of the dispersion curves for these large values of plasma parameter differs from that for smaller values investigated by others, in that broad bands in wave-number space have very small group speeds in narrow frequency bands close to many of the gyrofrequency harmonics. All of the Bernstein modes examined have group speeds less than 37 % of the ion thermal speed, and can be classified as very slow waves. Furthermore, the spectrum of propagating Bernstein modes is broadened as becomes large, with an effective total transmission region from the gyrofrequency up to several harmonics of gyrofrequency above the hybrid frequency.
Relativistic formulation for non-linear waves in a non-uniform plasma
Authors: Butler D. S. , Gribben R. J.
Published: March 2009

The mathematical formulation for the problem of non-linear oscillations in a self-consistent, non-uniform, collisionless plasma is considered. The fully nonlinear treatment illuminates the effect of the wave on the background distribution of the plasma through which it is passing. It is assumed that, although the overall non-uniformity may be large, significant changes occur only over time or length scales which are large compared with the plasma period or Debye length respectively. Exclusion of secular terms from the solution leads to a Liouvile type equation, which must be satisfied by the background distribution, and to propagation laws for the waves.

The theory is restricted to almost one-dimensional electrostatic waves and a general presentation is given from a relativistically-invariant point of view. Then the equations are derived in terms of physical variables for the special case in which: (i) the distribution functions and electrostatic potential depend on one space co-ordinate (that of propagation of the wave) and the former on the corresponding particle velocity component only, (ii) the wave is slowly-varying only with respect to this co-ordinate and time, and (iii) the magnetic field is zero. Finally, the non-relativistic limit of this case is considered in more detail. The boundary conditions satisfied by the distribution functions are discussed and this leads to the conclusion that in some circumstances thin sheets of probability fluid are formed in phase space and the background distribution cannot be strictly defined. This motivates a reformulation and subsequent re-solution of the problem (for this non-relativistic special case) in terms of weak functions, corresponding to the physical assumption of the presence of a small-scale mixing mechanism, which is excited by and smears the sheeted distribution but is otherwise dormant.

The results of the investigation are given as a system of differentio-integral equations which must be solved if necessary conditions for the absence of nonsecular solutions (of the Vlasov and Maxwell equations) are to be satisfied. No solution of this system is attempted here.
New boundary conditions in the transition régime
Authors: Cercignani Carlo , Tironi Gino
Published: March 2009

Starting from the Boltzmann equation, new boundary conditions are derived to be matched with the Navier—Stokes equations, that are supposed to hold in the main body of a gas. The idea upon which this method is based goes back to Maxwell and Langmuir. Since the distribution function is supposed to be completely determined by the Navier—Stokes equations, this new set of boundary conditions extends in some sense the validity of the macroscopic equations to the transition and free molecular régimes. In fact, it is shown that the free molecular and slip flow régimes are correctly described by this method; the latter is also supposed to give a reasonable approximation for the complete range of Knudsen numbers. The new procedure is applied to different problems such as plane Couette flow, plane and cylindrical Poiseuile flow, heat transfer between parallel plates and concentric cylinders. Results are obtained and compared with the exact numerical solutions for the above-mentioned problems.
Kinetic theory of the diochotron instability
Authors: Nocentini A. , Berk H. L. , Sudan R. N.
Published: March 2009

The diochotron instability of a thin, tenuous, cylindrical layer of charged particles, whose gyro-radius is of the order of the mean radius of the cylindrical layer, is investigated using the Vlasov equation. Two distribution functions are considered which give practically the same density in the physical space, but are quite different in the velocity space: in the first the velocity spread is practically zero; in the second the particles oscillate around the mean radius of the cylindrical layer. It is shown that the first distribution exhibits the usual diochotron instability, while the second one does not. It is also shown that, however small the velocity spread, the thickness of the cylindrical layer cannot go to zero. Its minimum value is roughly determined by equating the plasma frequency to the cyclotron frequency.