bluuebunny/crossref_metadata_2025 huggingface dataset:
Electron cyclotron radiation measurements on the PLT tokamak
Authors: Tait G. D. , Stauffer F. J. , Boyd D. A.
Published: March 2003

A grating polychromator and Fourier transform spectrometer have been used to study the electron cyclotron radiation emitted by the PLT plasma. Results are presented which illustrate the power of these diagnostics in following the spatial and temporal changes in the plasma electron temperature. Specifically, data showing electron heating during neutral beam injection, fluctuations associated with sawteeth, m = 2 oscillations, and minor disruptions as well as data affected by radiation from runaway electrons are presented. A detailed comparison of temperature profiles obtained by Thomson scattering and electron cyclotron radiation measurements is made.
Theory of off-axis mode production by free-electron lasers
Authors: Cary John R. , Kwan Thomas J. T.
Published: March 2003

The two-dimensional dispersion relation for the cold-beam, free-electron laser is derived by applying a Lorentz transformation to the Raman decay instability of plasma. It is found that a low-density, relativistic, free-electron laser is actually a broad-band amplifier; it can amplify waves throughout a frequency range of 4g2. Of these waves, the forward, high-frequency wave has the largest temporal growth rate. However, the off-axis, lower-frequency waves have larger spatial growth rates. In fact, the backward waves are absolutely unstable. These low-frequency, absolute instabilities can be very detrimental, because they have very large nonlinear saturation levels, and, hence, they can deplete the energy of the electron beam.
Electron plasma wave breaking with ion flow
Authors: Speziale Thomas
Published: March 2003

The effects of ion flow on the nonlinear development of resonantly driven electron plasma oscillations in a nonuniform plasma are investigated. The Lagrangian oscillator equation is generalized to include ion flow. A solution of the oscillator equation is obtained and is examined in detail for a model profile. Plasma flow through the critical surface is found to substantially reduce the energy of electrons at wave breaking when the flow velocity exceeds the oscillating velocity of electrons in the driver field.
Round buoyant laminar and turbulent plumes
Authors: Yih Chia-Shun , Wu Feng
Published: March 2003

Two approximate solutions, which become exact for Prandtl numbers 1 and 2, are given for laminar round plumes for arbitrary Prandtl number σ. The first of these gives a very accurate solution for laminar found plumes in air, for which σ = 0.73, and the second provides a good solution for laminar round plumes in water, for which σ = 6.7. Two approximate solutions, which become exact for turbulent Prandtl numbers 1.1 and 2, respectively, are given for turbulent round plumes. The one which becomes exact at σ = 1.1 is used to give a highly accurate solution for σ = 1, which, for an eddy-viscosity coefficient λ equal to 0.0156, provides a remarkably good agreement with the experimental data of Beuther, Capp, and George, Jr.
Numerical solutions to water waves generated by shallow underwater explosions
Authors: Li Kon-Ming , Holt Maurice
Published: March 2003

Numerical solutions are given for surface waves generated by underwater explosions. The shallow water approximation is used for the governing equations. An axisymmetric initial impulse is applied to the surface of the water. The initial impulse distribution is taken from the results obtained by Falade and Holt. Due to the unavailability of the initial displacement distribution, the latter is assumed to be zero, but the method can work for the case when both initial impulse and displacement are presented. Glimm’s scheme is used to obtain the solution for the shallow water equations. The scheme was developed to solve one-dimensional gas dynamic problems. With slight modification, the scheme can be used for the shallow water equations. It is tested successfully on the dam break problems. The calculations confirm the existence of the upper critical depth effect, namely, that for near surface explosions, the maximum amplitude surface wave is that generated by an explosion just below the surface.
Anisotropic magnetohydrodynamic turbulence in a strong external magnetic field
Authors: Montgomery David , Turner Leaf
Published: March 2003

A strong external dc magnetic field introduces a basic anisotropy into incompressible magnetohydrodynamic turbulence. The modifications that this is likely to produce in the properties of the turbulence are explored for the high Reynolds number case. The conclusion is reached that the turbulent spectrum splits into two parts: an essentially two-dimensional spectrum with both the velocity field and magnetic fluctuations perpendicular to the dc magnetic field, and a generally weaker and more nearly isotropic spectrum of Alfvén waves. A minimal characterization of the spectral density tensors is given. Similarities to measurements from the Culham–Harwell Zeta pinch device and the University of California, Los Angeles Macrotor tokamak are remarked upon, as are certain implications for the Belcher and Davis measurements of magnetohydrodynamic turbulence in the solar wind.
Stationary localized envelope waves in plasmas
Authors: Han S. J.
Published: March 2003

The nonlinear propagation of an intense circularly polarized electromagnetic wave in a plasma due to a weak relativistic mass variation of plasma electrons has been studied. In the limit of a small strength parameter, the condition for the electromagnetic wave to form a stationary localized envelope wave in an overdense plasma has been obtained in terms of the strength parameter. Also, it is shown that the cylindrical envelope wave is unstable to an s state perturbation, whereas the envelope wave is stable to a p state perturbation. Furthermore, the growth rates are proportional to the strength parameter.
Multiple equilibria and poloidal rotation instabilities in tokamak plasmas
Authors: Ware A. A. , Wiley J. C.
Published: March 2003

In tokamak plasma with substantial impurity (nzZ2≫ni), convective inertia effects lead to strong nonuniformity of both nz and the electrostatic potential on a magnetic surface. These effects make the response of the total ion population to poloidal rotation (V̄ϑ) highly nonlinear, introducing the possibility of multiple equilibria. The equations are applied to the central sawtooth region of the plasma where the gradients nj′, Tj′ are small. Above a critical electron temperature (Tc1) the equilibrium with low V̄ϑ is lost, leading to an m = 0, n = 0 poloidal rotation instability. The properties of this mode match the sawtooth disruptions and Tc1 accurately predicts the central electron temperature. The cause of sawtooth disruptions in low impurity plasmas is discussed.
Onset of convection in a box of fluid-saturated porous material with a permeable top
Authors: Tewari P. K. , Torrance K. E.
Published: March 2003

The onset of natural convection is examined for a fluid-saturated porous material contained within a box. The top of the box is permeable. Critical Rayleigh numbers and the preferred convective mode shapes are determined as functions of the box geometry.
A relativistic cylindrical vortex
Authors: Suresh Ambady
Published: March 2003

The equations for the special relativistic flow of an incompressible fluid are solved to obtain a relativistic version of the classical vortex. While the solution goes over to the classical vortex in the far field, the velocity at the center is finite and equals the speed of light.
On the instability threshold of a helical magnetic field
Authors: Lashmore-Davies C. N. , Stenflo L.
Published: March 2003

The stability of a circularly polarized pump wave which is not necessarily a natural mode of the plasma has been considered, and it has been shown that the instability threshold can be much lower than for the usual case where the pump is a natural Alfvén wave.
Brownian motion in a flowing fluid revisited
Authors: Ramshaw John D.
Published: March 2003

It is shown how the phenomenon of osmosis may be treated using the phenomenological theory of Brownian motion in a flowing fluid. The theory is also generalized to include viscous stresses in the particle and mixture momentum equations.
Stability of a diffuse linear pinch with axial boundaries
Authors: Einaudi Giorgio , Van Hoven Gerard
Published: March 2003

A formulation of the stability behavior of a finite-length pinch is presented. A general initial perturbation is expressed as a uniformly convergent sum over a complete discrete k set. A variational calculation is then performed, based on the energy principle, in which the end-boundary conditions appear as constraints. The requisite Lagrange multipliers mutually couple the elemental periodic excitations. The resulting extended form of δW still admits a proper second-variation treatment so that the minimization and stability considerations of Newcomb remain applicable. Comparison theorems are discussed as is the relevance of this end-effect model to the stability of solar coronal loops.
Algebraic growth of disturbances in a laminar boundary layer
Authors: Hultgren Lennart S. , Gustavsson L. Håkan
Published: March 2003

The temporal evolution of small three-dimensional disturbances with a large streamwise scale in viscous, parallel, semi-bounded flows is studied. In the limit of the initial disturbance being independent of the streamwise coordinate, the vertical velocity component consists solely of a continuous spectrum part. Tollmien–Schlichting waves do not appear in this special case. The streamwise perturbation velocity is obtained by solving a forced initial value problem. While the vertical velocity remains constant for small times, the streamwise perturbation velocity exhibits a linear growth due to the forcing. Eventually, viscous dissipation becomes dominant and the disturbance decays. Asymptotic solutions valid for small and large times are presented. The relation of these results to the longitudinal streaky structure found in many shear flows is discussed.
Stability of interface and shock wave driven by initial pressure discontinuity
Authors: Kivity Y. , Hanin M.
Published: March 2003

The flow arising from an initial pressure discontinuity across a perturbed interface of two ideal gases is studied using analytical and numerical methods. In particular, the stability of the shock wave, the interface, and the rarefaction wave in the resulting flow are investigated. The equations of motion and the initial and boundary conditions are linearized for small perturbations, and a Fourier analysis is made in the lateral direction. The equations are then solved by the method of characteristics. The results show that the interface is unstable and its perturbations asymptotically acquire a constant rate of growth. The shock wave is stable and has rapidly damped oscillations, which appear to be unaffected by the instability of the interface.
Gasdynamics of very small Laval nozzles
Authors: Abraham Oommen , Binn Jack H. , DeBoer Barry G. , Stein Gilbert D.
Published: March 2003

An investigation of diverging supersonic nozzles with throat diameters in the range of 0.025 to 0.25 mm has been carried out using gasdynamic measurements for a variety of gases and mixtures with sulfur hexafluoride. Due to the small nozzle size, boundary layers, although thin, may constitute a major fraction of the flow or, indeed at low pressures, may be fully developed. Nevertheless these nozzles have been shown to be very efficient for production of clusters condensed from the expanding gas. They produce orders of magnitude increases in molecular beam intensities, relative to the conventional, ’’isentropic’’ free jet sources. The effects of gas properties and nozzle design on performance have been analyzed and compared to theoretical solutions of the governing equations of motion including cluster nucleation and growth.
Kink and displacement instabilities in imploding wire arrays
Authors: Felber F. S. , Rostoker N.
Published: March 2003

Cylindrical arrays of parallel wires can be imploded by the magnetic forces generated by currents through the wires to form hot, dense Z-pinch plasmas. Analytic growth rates of displacements and deformations of wires in imploding wire arrays are calculated. Arrays of six or more wires are reasonably stable against asymmetric displacements. The growth rate of the kink instability on a single wire of linear mass density μ, radius a, and carrying current I peaks at λmax = 0.7I/μ1/2ca at a kink wavelength of about 4a. The most unstable kink modes of n-wire arrays are the symmetric (l = 0) radial modes and antisymmetric (l = n/2) tangential modes. The effect of a center wire is to tend to destabilize radial kink modes and stabilize tangential modes. In the experimental parameter range of the largest current generators, the number of kink growth times before collision is insensitive to values of maximum current and current pulse width. In general, the kink instability will grow nonlinearly if the initial array radius is more than a few plasma wire radii. In the limit of long wavelengths, the kink instability is shown to be equivalent to the displacement instability.
Critical β of a D-shaped toroidal plasma with sharp boundary
Authors: Kito Masafumi
Published: March 2003

Under the cap-cyclide coordinate system, the marginal stability of a sharp boundary toroidal plasma whose cross section is D shaped is examined using the energy principle. The analytical results are valid for arbitrary β, arbitrary aspect ratio, and arbitrary elongation of the plasma. There exists a maximum elongation for a given aspect ratio. The critical beta βc is computed for several aspect ratios and elongations. For given aspect ratio, βc increases as long as the elongation increases.
Quasi-linear diffusion and radial transport in tokamaks
Authors: Hazeltine R. D. , Mahajan S. M. , Hitchcock D. A.
Published: March 2003

An important difference between the classical collision operator, C(f), and Kaufman’s quasi-linear diffusion operator in action space, D(f), is that only the former conserves particles, momentum, and energy at each spatial point. The nonlocal character of action-space diffusion allows all transport fluxes to be expressed directly in terms of appropriate moments of D. Thus, a general description of quasi-linear diffusion and convection across flux surfaces in any collisionless, axisymmetric toroidal system is obtained, in terms of scale factors relating the invariant surfaces to the flux surfaces. Several analogues to the neoclassical problem are apparent, including the collisionless version of the Ware–Galeev pinch effect, whose derivation in action space is especially straightforward. Toroidicity modifies not only particle orbits but also the spatial structure of the fluctuations, and both modifications affect the resulting transport in an important way. The use of appropriate action-angle variables automatically includes the orbital effects; crucial features of the toroidal eignmode structure are incorporated by use of the ballooning representation. This makes the fastest radial variation explicit, in terms of a single parameter describing the degree to which submodes localized on different rational surfaces overlap. The variation on slower length scales, and the overall spectral amplitude, are not determined. The radial particle flux corresponding to a Maxwellian distribution function is displayed and its dependence on properties of the spectrum is analyzed.
Electric sheath between a metal surface and a magnetized plasma
Authors: Daybelge U. , Bein B.
Published: March 2003

A collisionless electric sheath model between a metal surface and a magnetized plasma is given. The magnetic field is assumed to be uniform and has a small angle of incidence with respect to the surface. It is shown that the ambipolar wall potential is essentially independent of the angle of incidence. The finite Larmor radius and secondary electron effects on the wall potential are derived. The sheath thickness is shown to depend strongly on the surface absorption characteristics.
Simulation of slow cyclotron wave growth on a scattered relativistic electron beam
Authors: Shanahan W. R. , Faehl R. J.
Published: March 2003

Simulations demonstrating effective growth of slow cyclotron waves on a beam exhibiting a scattered distribution of particle velocities are described. No dramatic changes from the cold beam results for the dispersive properties are observed, but significant modifications of radial eigenmode structure appear.
Nonlinear shift of resonance velocity in the electron cyclotron wave-particle interactions
Authors: Ido K. , Sugai H.
Published: March 2003

Electron cyclotron waves (whistlers) of large amplitude give rise to nonlinear shift of cyclotron-resonance velocity. Several effects of the shift on the wave propagation are discussed.
Whistler wave self-modulation in a tokamak plasma
Authors: Antani S. N. , Kaup D. J.
Published: March 2003

Steady-state self-modulation of a whistler wave propagating at an arbitrary angle to the applied magnetic field, in a typical tokamak plasma, is investigated. The envelope is found to be modulationally stable for the parameter regime chosen.
Ion cyclotron loss cone electron diamagnetic instability
Authors: Guzdar P. N.
Published: March 2003

An unstable ion cyclotron loss cone mode propagating in the electron diamagnetic direction has been found. This mode may explain the observation on 2XIIB in the early and late phases of the discharge.
Limiting currents in shielded source configurations
Authors: Genoni T. C. , Miller R. B.
Published: March 2003

Limiting currents for laminar flow equilibria of relativistic electron beams in shielded source configurations are discussed. Results are presented for the constant applied magnetic field case, and for the case of constant beam radius.
Kinetic description of a plasma under constant current conditions
Authors: Crescentini A. Airoldi , Lazzaro E. , Orefice A.
Published: March 2003

A kinetic model based on the Fokker–Planck equation is exploited in order to analyze the quasi-stationary features corresponding to constant values of the current in a plasma discharge.
Finite ion Larmor radius stabilization of m = 1 modes of a high-β screw pinch
Authors: Cayton Thomas E. , Freidberg J. P.
Published: March 2003

In the near ϑ-pinch limit, a radially diffuse high-β screw pinch may be rendered completely stable through a combination of finite ion Larmor radius effects and wall effects.
Interaction of lower hybrid wave fields with drift-cyclotron loss-cone instability
Authors: Shaing Ker-Chung
Published: March 2003

The dispersion relation for the drift-cyclotron loss-cone mode in the presence of the lower hybrid wave is calculated using both electrostatic and finite β models. It is found that lower hybrid wave fields with frequency ω0 can stabilize the mode if ωlh<ω0<ω+, or ω0<ω−<ωlh, where ωlh = ωpi/(1+ω2pe/ω2ce)1/2, ω± = [±A+(A2+4ω2lh)1/2]/2, and A = ω2lhε/ωcik. If the plasma β is greater than a critical value βc, there is another stabilization region, namely, ω0≳δωlh, where δ is a numerical constant. Even though the stabilization effect is small in this region, the lower hybrid wave frequency for electron heating should be in this region in order to avoid enhancing the particle loss rate.
Effects of the fast wave on the drift-cyclotron loss-cone mode
Authors: Shaing Ker-Chung
Published: March 2003

Particle orbits in the presence of the fast wave fields are calculated. It is found that the resonant interaction of ions with the wave can be neglected at ω0 = 2ωci, provided that the wave electric field strength is less than a critical value Ec( = 4k∥T/e). The dominant effect on the dispersion relation of the drift-cyclotron loss-cone mode is thus found to be due to the nonresonant effects of the wave on electrons and ions. It is found that a fast wave with ω0 = 2ωci destabilizes the mode. For ω0<2ωci, fast waves can stabilize the mode for certain values of the plasma β, which is calculated numerically.
Motion of two superposed viscous fluids
Authors: Prosperetti Andrea
Published: March 2003

The initial-value problem associated with the small-amplitude waves on the interface between two superposed viscous fluids is studied in the stable and in the unstable case (Rayleigh–Taylor instability). The results are illustrated with examples obtained by numerical and analytic inversion of the Laplace-transformed solution for the wave amplitude. The diffusion of vorticity from the free surface into the fluids is also shown.
Stability of shear flow of stratified fluids with fine dust
Authors: Palaniswamy V. I. , Purushotham C. M.
Published: March 2003

The linear stability of plane parallel shear flows of a stably stratified incompressible fluid laden with uniformly distributed fine dust particles is studied. It is shown that the Miles criterion for stability, the Rayleigh–Synge criterion for instability, and Howard’s semicircle theorem can be extended under the assumptions that the mass concentration is very small and that the relaxation time of the dust particles is very much less than the time scale characterizing the basic flow. The effect of fine dust is found to increase the region of instability. In addition, a semi-ellipse criterion for instability has been given as an improvement over Howard’s semicircle criterion.
A bubble in an axially symmetric shear flow
Authors: Miksis Michael J.
Published: March 2003

The shape of a three-dimensional bubble in an axially symmetric shear flow of an inviscid incompressible fluid is calculated numerically. The shape depends upon a single dimensionless constant related to the Weber number. It is found that there is a maximum Weber number above which there is no steady solution.
Evolution of the centerline probability density function of temperature in a plane turbulent wake
Authors: Sreenivasan K. R.
Published: March 2003

Measurements are presented of the evolution of the probability density function of the temperature fluctuation along the centerline of the wake of a heated circular cylinder in the range 4⩽x/d⩽300.
Ponderomotive effects in collisionless plasma: A Lie transform approach
Authors: Cary John R. , Kaufman Allan N.
Published: March 2003

A new method for the kinetic analysis of ponderomotive effects in collisionless plasma is presented. This method involves the application of the Lie-transform perturbation technique to the Hamiltonian formulation of the Vlasov equation. Basically, a new system, in which the high frequency oscillations are absent, is found. In this system the distribution function evolves according to a ponderomotive Hamiltonian, which is the kinetic generalization of the ponderomotive potential. It is shown that the ponderomotive Hamiltonian can easily be determined from the well-known linear susceptibility. This formalism is used to calculate several new results. Among these results are the general formula for the quasi-static density perturbation produced by a hot magnetoplasma wave, a generalization of previous formulas for the laser-generated quasi-static magnetic field, and the general formula for the ponderomotive gyrofrequency shift produced by an electromagnetic wave propagating at an arbitrary angle.
Collisional drift waves in a plasma with electron temperature inhomogeneity
Authors: Drake J. F. , Hassam A. B.
Published: March 2003

A fluid theory of collisional electrostatic drift waves in a plasma slab with magnetic shear is presented. Both electron temperature and density gradients are included. The equations are solved analytically in all relevant regions of the parameter space defined by the magnetic shear strength and the perpendicular wavelength and explicit expressions for the growth rates are given. For shear strengths appropriate for present-day tokamak discharges the temperature gradient produces potential wells which localize the mode in the electron resistive region, well inside the ion sound turning points. Mode stability arises from a competition between the destabilizing influence of the time dependent thermal force and the stabilizing influence of electron energy dissipation. Convective energy loss is not important for shear parameters of present-day fusion devices.
Finite Larmor radius theory of resistive instabilities
Authors: Mondt J. P.
Published: March 2003

The hybrid-kinetic model, previously used to investigate stability properties of collisionless high-beta plasmas characterized by finite ion gyroradius, is generalized to include the effects of finite resistivity and gravitation (to simulate toroidal field curvature). Possible applications of the present formalism include investigations of finite ion Larmor radius effects on the stability of screw-pinch and tokamak equilibria against ideal and resistive interchange instabilities as well as tearing modes. A simple example of such an application is carried out for the case of local slow resistive interchange modes within the context of a near-theta-pinch ordering.
Analytic solution for a weakly rotating, collisionless z pinch
Authors: Maxon Stephen
Published: March 2003

The system of time independent Vlasov and Maxwell’s equation is solved for a cylindrically symmetric z pinch including weak rotation of both electrons and ions. The solution clearly shows the effect of rotation on the density profile and azimuthal magnetic field. Limitations on the rotation frequency and radius are found by insisting on self consistency of the approximation scheme.
Viscous plasma flow in a multiple-mirror configuration
Authors: Bravenec R. V. , Lichtenberg A. J. , Lieberman M. A. , Berk H. L.
Published: March 2003

The steady-state, axial plasma confinement by a multiple-mirror device is studied in the ’’viscous fluid regime,’’ λ/lm≪1 (but not negligible), where λ is the ion-ion mean-free-path and lm is the scale length of magnetic field variations. An approximate analytical solution is obtained by averaging over the rapid variations caused by the individual mirrors and compared to a numerical solution without averaging. A smooth transition is found, with increasing values of λ/lm, from sonic flow to a diffusive flow. Studies are made of the variation in density profiles and confinement times versus λ/lm, mirror ratio, relative mirror width, and number of mirror cells. The viscous fluid regime is found to have the same characteristics as the ideal multiple-mirror regime for λ/lm→1.
Analytic equilibria with quadrupole symmetry in the paraxial limit
Authors: Pearlstein L. D. , Kaiser T. B. , Newcomb William A.
Published: March 2003

Mirror equilibria for arbitrary mirror ratio and flux-tube eccentricity are obtained to leading order in the plasma pressure (beta expansion) in the paraxial limit (axial scale lengths long compared with radial scale lengths). The solutions are given in terms of quadratures over known functions. The theory is applied to a tandem-mirror configuration.
Anomalous toroidal field penetration in Tormac V
Authors: Feinberg B. , Vaucher B. G. , Shaw R. S. , Vella M. C.
Published: March 2003

Magnetic field penetration into a cool, collisional, magnetized plasma has been investigated in Tormac V. Magnetic probe and laser interferometer studies reveal anomalous penetration of the applied toroidal field into a plasma with an initial parallel bias toroidal field. The applied poloidal field, however, formed a well-defined magnetic front which was effective at sweeping up particles. Strong shear in the vacuum magnetic field does not inhibit the apparent decoupling of the applied toroidal field from the applied poloidal field.
Symmetric, relativistic charged particle beam equilibria
Authors: Kadish Abraham
Published: March 2003

The macroscopic equilibrium of relativistic charged particle beams is studied for configurations which are azimuthally symmetric and free of radial divergence. It is proved that in the limit of negligible internal energy all such equilibria are necessarily axially independent. Special radially dependent equilibria are derived.
Wall emission dominated discharge channel
Authors: Cohen Ira M.
Published: March 2003

The diffusion of ions and electron through a uniform neutral gas was treated with complete wall emission-absorption boundary conditions. Volumetric ionization and recombination processes were ignored. In the limit of the small ratio of Debye length to channel width (ε→0), the problem splits into three regions: anode sheath, cathode sheath, and quasi-neutral region. The solution is obtained in closed form in each of the three regions and matched in the overlap domains. The unusual feature of this problem is that the boundary conditions are coupled to the solution in a transcendental manner requiring iteration in order to achieve a consistent solution. The degree of surface coverage is an important parameter in determining emission and absorption rates. The results show that ion densities are elevated (above quasi-neutral levels) in the anode and cathode sheaths tending to enhance electron emission. The quasi-neutral density at each electrode is the geometric mean of the true charged particle densities at the boundary. Electrical current between the electrodes increases linearly, then saturates sharply with increasing voltage between the electrodes.
Lower hybrid density drift instability with magnetic curvature
Authors: Rahal L. J. , Gary S. Peter
Published: March 2003

The linear Vlasov theory of electrostatic drift instabilities is considered using the slab model and the local approximation. The effects of magnetic field curvature on the lower hybrid density drift instability are studied. Magnetic curvature does not significantly affect the growth rate at low beta.
Reply to comments by C. F. F. Karney
Authors: Villalón E.
Published: March 2003

Reply to the comment on parametric instability in an inhomogeneous plasma is made.(AIP)
Low-frequency longitudinal instability in collisionless single-ended Q machines
Authors: Kuhn S. , Phelps A. D. R. , Fang M. T. C.
Published: March 2003

The linear stability of low-frequency, long-wavelength longitudinal modes in a collisionless single-ended Q machine is investigated using self-consistent velocity distribution functions. The so-called ion-acoustic instability occurring at positive biases is shown to actually be of the Buneman type.
Parametric instabilities in an electron beam plasma system
Authors: Nakach R. , Cuperman S. , Gell Y. , Levush B.
Published: March 2003

The excitation of low-frequency parametric instabilities by a finite wavelength pump in a system consisting of a warm electron plasma traversed by a warm electron beam is investigated in a fluid dissipationless model. The dispersion relation for the three-dimensional problem in a magnetized plasma with arbitrary directions for the waves is derived, and the one-dimensional case is analyzed numerically. For the one-dimensional back-scattering decay process, it is found that when the plasma-electron Debye length (λDp) is larger than the beam-electron Debye length (λDb), two low-frequency electrostatic instability branches with different growth rates may exist simultaneously. When λDp≃λDb, the large growth rate instability found in the analysis depends strongly on the amplitude of the pump field. For the case λDp<λDb, only one low-frequency instability branch is generally excited.
Integral-equation formulation for drift eigenmodes in cylindrically symmetric systems
Authors: Linsker Ralph
Published: March 2003

A method for solving the integral eigenmode equation for drift waves in cylindrical (or slab) geometry is presented. A leading-order kinematic effect that has been noted in the past, but incorrectly ignored in recent integral-equation calculations, is incorporated. The present method also allows electrons to be treated with a physical mass ratio (unlike earlier work that is restricted to artificially small mi/me owing to resolution limitations). Results for the universal mode and for the ion-temperature-gradient driven mode are presented. The kinematic effect qualitatively changes the spectrum of the ion mode, and a new ’’second region of instability’’ for k⊥ ρi≳1 is found.
Temperature effects on harmonic generation in laser-irradiated plasmas
Authors: Andreev N. E. , Auer G. , Baumgärtel K. , Sauer K.
Published: March 2003

The generation of second and third harmonics at the oblique incidence of a p-polarized wave on an inhomogeneous plasma (resonance absorption) is studied. The relevant wave equations are solved numerically. First, the dependence of the emitted harmonics on the temperature, the density scale length, and the angle of incidence is investigated for a linear density profile. The strong oscillations of the harmonic emission in a certain temperature range are attributed to the position of the point where the condition for phase matching is fulfilled. In the second part a modified density profile with a caviton is considered, and it is shown that a large enhancement of harmonic emission is possible because of the formation of electrostatic resonant structures. This effect will become important under experimental nonstationary conditions when the density profile is deformed by the ponderomotive force.
Collisional shear Alfvén waves in sheared magnetic fields
Authors: Drake J. F. , Kleva Robert G.
Published: March 2003

The structure of the shear Alfvén waves is investigated in a collisional plasma with shear. The fourth-order equation obtained by combining Ampere’s law and the quasi-neutrality condition is solved by the method of matched asymptotic expansions for k⊥ ρs≫≪1 to obtain the dispersion relation. A hierarchy of damped, localized modes are found which can have either even or odd parity. The solutions basically have the structure of kinetic Alfvén modes trapped between the two Alfvén cutoffs on either side of the rational surface. The mode damping arises from Ohmic dissipation by electrons near the rational surface. The relation between these modes, microtearing modes, and the Alfvén continuum is discussed.
Destabilitization of low mode number Alfvén modes in a tokamak by energetic or alpha particles
Authors: Tsang K. T. , Sigmar D. J. , Whitson J. C.
Published: March 2003

With the inclusion of finite Larmor radius effects in the shear Alfvén eigenmode equation, the continuous Alfvén spectrum, which has been extensively discussed in ideal magnetohydrodnamics, is removed. Neutrally stable, discrete radial eignmodes appear in the absence of sources of free energy dand dissipation. Alpha (or energetic) particle toroidal drifts destabilize these modes, provided the particles are faster than the Alfvén speed. Although the electron Landau resonance contributes to damping, a stability study of the parametric variation of the energy and the density scale length of the energetic particles shows that modes with low radial mode numbers remain unstable in most cases. Since the alpha particles are concentrated in the center of the plasma, this drift-type instability suggests anomalous helium ash diffusion. Indeed, it is shown that stochasticity of alpha orbits due to the overlapping of radially neighboring Alfvén resonances is induced at low amplitudes, eiφ/Ti≳0.05, implying a diffusion coefficient Drα≳4.4×103 cm2/sec.
Interpretation of the fine structure of electrostatic waves excited in space
Authors: Pottelette R. , Hamelin M. , Illiano J. M. , Lembège B.
Published: March 2003

Preliminary results are presented from an active wave experiment performed with a double-dipole probe aboard the F4 rocket launched during the PORCUPINE campaign. They show that electrostatic cyclotron waves can be excited linearly around the half-harmonics of the electron gyrofrequency. The most striking fact is that, under certain plasma conditions, the amplitude of waves excited at these peculiar frequencies can be even stronger than those observed at the characteristic resonances of the magnetoplasma. The fine structure of the signals received is also observed and interpreted. Theoretical numerical calculations of the potential created by a dipole antenna in a Maxwellian plasma are presented; good agreement is obtained with the complicated pattern of the various experimental results.
Görtler instability
Authors: Ragab S. A. , Nayfeh A. H.
Published: March 2003

Görtler instability for boundary-layer flows over generally curved walls is considered. The full-linearized disturbance equations are obtained in an orthogonal curvilinear coordinate system. A perturbation procedure to account for second-order effects is used to determine the effects of the displacement thickness and the variation of the streamline curvature on the neutral stability of the Blasius flow. The streamwise pressure gradient in the mean flow is accounted for by solving the nonsimilar boundary-layer equations. Growth rates are obtained for the actual mean flow and compared with those for the Blasius flow and the Falkner–Skan flows. The results demonstrate the strong influence of the streamwise pressure gradient and the nonsimilarity of the basic flow on the stability characteristics.
Instabilities of a compressible stratified fluid in horizontal sheared motion
Authors: Sachdev P. L. , Narayanan A. Satya
Published: March 2003

The stability characteristics of a Helmholtz velocity profile in a stably stratified, compressible atmosphere in the presence of a lower boundary are studied. A jump in the Brunt–Väisälä frequency is introduced and the level at which this jump occurs is assumed to be different from the shear zone, to simulate sharp temperature discontinuities in the atmosphere. The results are compared with those of Pellacani, Tebaldi, and Tosi and Lindzen and Rosenthal. In the present configuration, new unstable modes with larger growth rates are found. The wavelengths of the most unstable gravity waves for the parameters pertaining to observed cases of clear air turbulence agree quite closely with the experimental values.
Stability of colliding ion beams
Authors: Foote E. A. , Kulsrud R. M.
Published: March 2003

Conditions are determined for the stability of two identical colliding ion beams in the presence of neutralizing electrons, but no background ions. Such a situation is envisioned for the Counterstreaming Ion Torus. The ion beams are taken to be Maxwellian in their frames of reference. The approximation of decoupled electrostatic and electromagnetic modes is made. The stability of the electrostatic modes depends on the relation between the ion-electron temperature ratio and the relative beam velocities. The stability of the electromagnetic mode depends on the relation between the ion plasma β and the relative beam velocities.
Experimental observation of stable arrangement of vortex rings
Authors: Takamoto Masaki , Izumi Kouji
Published: March 2003

A vortex ring version of the Kármán vortex street is observed through flow visualization. A remarkably stable configuration of discrete vortex shedding is recognized with a distinction from the two-dimensional case that the spacing between the alternating vortices is not equal.
Diffusion on two length scales
Authors: Cohen Ronald H. , Nevins William McCay , Rowlands George
Published: March 2003

One-dimensional diffusion is considered for a system in which the diffusion coefficient D has a rapid oscillation in the spatial variable as well as a slow variation. For long times, the distribution function evolves diffusively with an effective diffusion coefficient given by averaging 1/D.
Tilting instability of a cylindrical spheromak
Authors: Bondeson A. , Marklin G. , An Z. G. , Chen H. H. , Lee Y. C. , Liu C. S.
Published: March 2003

The stability of a low-beta spheromak with a perfectly conducting cylindrical boundary of length L and radius R is analyzed in terms of force-free fields with J = λB(λ = const). The axisymmetric equilibrium is found unstable to tilting when the elongation L/R is larger than about 1.67. Numerical solutions of the time-dependent ideal magnetohydrodynamic equations confirm this result.
A non-Gaussian model of turbulence (soccer-ball integrals)
Authors: Betchov Robert , Larsen P. S.
Published: March 2003

The statistics of the time evolution of a nonlinearly coupled system of first-order equations representing the Euler equations is studied. The probability distribution of functions is nearly Gaussian, while that of their time derivatives has exponential tails and moments of order 4, 6, and 8 that approach those of the exponential distributions.
A second-order theory for solitary waves in deep fluids
Authors: Grimshaw R.
Published: March 2003

Benjamin and Davis and Acrivos have established the existence of an algebraic solitary wave in deep fluids. This theory is here extended to second order in amplitude. The second-order correction to the wave amplitude, the second-order correction to the wave phase speed, and the first-order correction to the wavelength are all determined for solitary waves propagating in a stratified shear flow. Two special cases are discussed in detail.
Perturbation analysis of a simple model of magnetic island structures
Authors: Thyagaraja A.
Published: March 2003

Singular perturbation theory is used to construct a class of stationary solutions to the resistive plasma equilibrium equations in a plane slab geometry. These are nonlinearly saturated magnetic island structures which bifurcate from the basic Ohmic state when Δ′(k) is positive and small in some sense. The relationship between the nondimensional wavenumber k and the size of the islands is obtained by a self-consistent, matched asymptotic expansion. The assumed resisitivity profile is found to determine the relationship uniquely. It is found that either two bifurcating branches exist or none at all depending upon the profile chosen. The structure of the plasma current due to the islands is evaluated in terms of two functions which are independent of the resistivity profile. It is found that for sufficiently large Δ′(k) and suitable resistivity, a self-consistent, steady magnetic island state cannot be found. A possible connection between this phenomenon and disruptive instabilities observed in experimental plasmas is discussed very briefly. The proposed model complements the work done on magnetic islands by various groups using powerful numerical codes. In contrast to such codes, the current distributions due to a wide class of resistivity profiles have been calculated using the model. The solutions constructed shed some light on how nonlinear saturation in the island states can occur.
Some nonlinear optical phenomena
Authors: Hammouda Boualem , Osborn Richard K.
Published: March 2003

Some nonlinear optical phenomena are investigated, especially stimulated scattering, from the point of view of the kinetic theory of radiation (i.e., photon transport theory). Kinetic theory provides a perspective, different from Maxwell’s wave theory, from which an examination of these complex matters may proceed with some advantages: (i) considerable mathematical simplication in some instances, (ii) clear and natural separation of microscopic versus macroscopic nonlinearities, (iii) kinetic theory couples the radition field nonlinearly to a formally exact description of the matter field, and (iv) it is believed that the mathematical model provided by kinetic theory is perhaps better suited for numerical studies of the effect of diverse nonlinear optical phenomena upon laser-fusion implosion dynamics than Maxwell’s wave theory. Although the main emphasis is upon stimulated scattering, the incorporation of other nonlinearities into the kinetic model is discussed briefly.
Hamiltonian formulation of guiding center motion
Authors: Littlejohn Robert G.
Published: March 2003

A Hamiltonian theory of guiding center motion which uses rectangular coordinates in physical space and noncanonical coordinates in phase space is presented. The averaging methods preserve two important features of Hamiltonian systems, viz., conservation of energy (for time-independent fields) and Liouville’s theorem. These features are sacrificed by the traditional averaging methods. The methods also relieve much of the burden of higher order perturbation calculations, and the drift equations for fully electromagnetic fields are extended to one higher order than they have been known in the past. The first correction to the relativistic magnetic moment is also calculated. Many applications are anticipated, both to single particle motion and to kinetic theory.
Nonparallel effects on the stability of developing flow in a channel
Authors: Garg V. K. , Gupta S. C.
Published: March 2003

A spatial stability study of the nonparallel developing flow in a channel shows that in the near inlet region, the critical Reynolds number based on the growth rate of stream function at the channel center line is only 80% of that for the parallel flow theory, but the difference diminishes downstream.
Decay of scalar variance in terms of a modified Richardson law for pair dispersion
Authors: Nelkin Mark , Kerr Robert M.
Published: March 2003

A simple extension of recent work by Larcheveque and Lesieur leads to a one parameter analytic expression for the decay of scalar variance in an isotropic homogeneous turbulent flow. The essential qualitative features of the Warhaft–Lumley experiment are reproduced.
Shock wave propagation in a reentrant corner
Authors: Schmitt J. A.
Published: March 2003

An idealized model predicts the peak pressure and its duration at the vertex of a reentrant corner. The model only requires repeated use of the shock relations. Both regular and Mach reflections can be handled. Comparisons with experimental shock tube data are given.
Frequency mismatch and stochastic heating in the cyclotron frequency range
Authors: Hsu Jang-Yu
Published: March 2003

A large-amplitude rf electric field can heat particles at their gyrofrequency and its harmonics despite a significant mismatch between the wave frequency and the gyrofrequency through physical processes analogous to the trapping of particles in large-amplitude waves. For eE0k0/mΩ2 near unity, the fundamental and the second harmonic resonances may overlap and give rise to stochasticity. The implications for cyclotron heating are discussed.
Periodic boundary model for fast magnetosonic wave propagation in the Elmo Bumpy Torus
Authors: Owens T. L. , Mullen J. H. , Huddleston P. L.
Published: March 2003

Fast-wave propagation in a cylindrical magnetoplasma with periodic boundary conditions approximating those of the Elmo Bumpy Torus (EBT) is analyzed. Significant differences from straight cylinder models are found. For example, for the m = −1 poloidal mode and for model EBT-S (scale) parameters (i.e., n≲4×1012 cm−3, B = 7–14 kG, and plasma radius ≃15 cm), branches of the dispersion relation occur in bands of frequency separated by frequency intervals where no waves or only short wavelength modes occur, analogous to the stop band zones of free space periodic structures. Another difference is that the number of mode onsets which occur in a given frequency interval is larger than that found for straight cylinder problems. Other results indicate good wave-energy penetration for eigenmodes in both EBT-S and EBT-P (proof of principle). For EBT-P, with n = 3×1013, B = 22.5 kG, and plasma radius = 17 cm, the wave fields peak strongly in the midplane of the mirror sectors near the minor axis.
Tilt and shift mode stability in spheromaks with line tying
Authors: Finn John M. , Reiman Allan
Published: March 2003

Magnetohydrodynamic stability of force-free spheromak plasmas to n = 1 free boundary tilt and radial shift modes is studied. The exterior region of open field lines is treated either as a conducting plasma or as a vacuum. In the former case the effect of line tying of the open field lines is present and is found to improve stability greatly. The equilibria which have optimum stability properties to the tilt and shift modes have a length-to-diameter ratio of 0.6, and can be stable with conducting walls at a relatively large distance.