bluuebunny/crossref_metadata_2025 huggingface dataset:
Renormalized Compton scattering and nonlinear damping of collisionless drift waves
Authors: Krommes John A.
Published: March 2003

A kinetic theory for the nonlinear damping of collisionless drift waves in a shear-free magnetic field is presented. The general formalism is a renormalized version of induced scattering on the ions and reduces correctly to weak turbulence theory. The approximation studied explicitly reduces to Compton scattering, systematizes and corrects the earlier calculations of Dupree and Tetreault [Phys. Fluids 21, 425 (1978)], and extends that theory to finite ion gyroradius. Certain conclusions differ significantly from those of Dupree and Tetreault. In particular, at long wavelengths the nonlinear ion growth rate is large and positive, proportional to k2⊥D both at zero and at finite gyroradius. (Here, k⊥ is the perpendicular wavenumber and D is the test particle diffusion coefficient.) Nevertheless, the rate of change of total mean kinetic energy due to the nonlinear interaction is small and proportional to q2∥, where q∥ is a typical parallel wavenumber.
Critical lengths for high density mirror machines
Authors: Gerver M. J.
Published: March 2003

Critical lengths are found for the stability of mirror-confined plasmas to the convective loss-cone mode (driven absolutely unstable by wave reflection from the mirror throats), using the straight-line ion orbit approximation. Electromagnetic effects are included. For fusion reactor parameters, the critical length in ion Larmor radii is roughly 10β−1/2 (where β is the ratio of plasma pressure to magnetic pressure). Taking the drift cone instability into account, no mirror fusion plasma can be linearly stable unless there is some warm plasma (about 1%) in the loss cone.
Pulsating flow over a step
Authors: Mullin T. , Greated C. A. , Grant I.
Published: March 2003

An experimental study has been made of air flow over a rearward facing step where the free-stream velocity has been perturbed by a sinusoidal fluctuation of 1 Hz. Velocities have been measured using a laser Doppler anemometer employing a gated photon correlation signal detection system. This allows mean velocities and fluctuating components to be measured at different phase positions in the cycle. It is shown that the stability of the separated flow region behind the step is strongly perturbed by the free-stream oscillations and that the position of reattachment of the turbulent boundary layer is dependent on the phase of the free-stream velocity. Shedding of the vortex occurs when the retardation of the free-stream velocity is a maximum.
Transonic nozzle flows of dispersive compressible fluids
Authors: Morioka Shigeki , Yoshinaga Takao
Published: March 2003

The transonic equation is derived for several dispersive compressible fluids. A similar transformation by Tomotika–Tamada is still applicable and provides nozzle flow solutions. When the coefficient of the dispersion term is positive, the choked flow with a shock wave in the divergent section in ordinary gasdynamics is replaced by the flow with a wavetrain and an appreciable change in the flow rate. There is a critical state of maximum mass flow as in ordinary gasdynamics. For negative coefficients of the dispersion term, the features of the low supersonic flow resemble that of the high subsonic flow for positive coefficients. The detailed calculation shows that the weak dispersion and the two-dimensional structure play an important role in the nozzle flow near the critical state.
Measurements of dissipation rate and some other characteristics of turbulent plane and circular jets
Authors: Antonia R. A. , Satyaprakash B. R. , Hussain A. K. M. F.
Published: March 2003

The mean rate of dissipation ε is measured along the axes of a plane jet and three circular jets, covering good ranges of the jet Reynolds number Ujd/ν and the downstream distance x. The data confirm the universal relations, derived from requirements of self-preservation, between ε and x, for both the circular jet and the plane jet. For either type of jet, the turbulence Reynolds number Rλ and the local Reynolds number Rc (based on local velocity and length scales) are found to be related as Rλ∼2.3Rc1/2.
Linear stability of high-m drift-tearing modes
Authors: D’Ippolito D. A. , Lee Y. C. , Drake J. F.
Published: March 2003

A new model for the electron parallel conductivity in a plasma of moderate collisionality is formulated using the Williamson collision operator. With this model, the linear stability of high-m drift-tearing modes (driven unstable by ∇Te) is studied as a function of the electron-ion collision frequency νc with no restriction placed on the ratio νc/ω. It is shown that the growth rate of this instability can be substantial for realistic tokamak parameters. The implication for understanding the observed magnetic turbulence and anomalous electron heat transport in tokamaks is discussed.
Accurate approximation of the dispersion differential equation of ideal magnetohydrodynamics: The diffuse linear pinch
Authors: Barnes D. C. , Cayton Thomas E.
Published: March 2003

The ideal magnetohydrodynamic stability of the diffuse linear pinch is studied in the special case when the poloidal magnetic field component is small compared with the axial field component. A two-term approximation for growth rates is derived by straightforward asymptotic expansion in terms of a small parameter that is proportional to (Bϑ/rBz). Evaluation of the second term in the expansion requires only a trivial amount of additional computation after the leading-order eigenvalue and eigenfunction are determined. For small, but finite, values of the expansion parameter the second term is found to be non-negligible compared with the leading term. The approximate solution is compared with exact solutions and the range of validity of the approximation is investigated. Implications of these results to a wide class of problems involving weakly unstable near ϑ-pinch configurations are discussed.
Equilibrium and stability of high-β toroidal multipoles
Authors: D’Ippolito D. A. , Adler E. A. , Lee Y. C.
Published: March 2003

The equilibrium and stability of finite-β toroidal plasmas confined by multipole fields (with no toroidal component) is studied within the framework of ideal magnetohydrodynamics. Equilibria are obtained by the numerical solution of the Grad–Shafranov equation, including the effect of rigid current-carrying rings within the plasma. Stability to pressure-driven modes (interchange and ballooning) is examined for these equilibria using standard methods. The spatial variation of the critical pressure gradient and the nature of the marginally stable eigenfunctions are discussed. Results are presented for three configurations (quadrupole, octopole, and dodecapole) with parameters similar to those for the Surmac experiment.
Theory of second harmonic electron cyclotron resonance heating of tokamak plasma
Authors: Hui Bertram , Chu K. R. , Ott Edward , Antonsen Thomas
Published: March 2003

A theoretical and numerical study of tokamak plasma heating by the second harmonic of the electron cyclotron resonance is presented. It is found that the extraordinary mode is very efficiently absorbed. In contrast to previous calculations, it is also found that the ordinary mode is well absorbed at oblique incidence to the toroidal magnetic field. This finding indicates the feasibility of heating devices of higher densities than would otherwise be possible.
Energy loss of a Korteweg–de Vries solitary wave in a slowly varying medium
Authors: Ko K. , Kuehl H. H.
Published: March 2003

An irreversible transfer of energy is shown to occur between the main body and the trailing structure of a Korteweg–de Vries solitary wave in a slowly varying medium.
Whistler-Alfvén turbulence
Authors: Nambu Mitsuhiro
Published: March 2003

The interaction of whistler wave turbulence with Alfvén wave turbulence is studied within the framework of the linear response theory of a turbulent plasma. The theory demonstrates that the turbulent energy flows in from the microscopic region and into the macroscopic dissipation region.
Nonlinear saturation of the drift cyclotron loss-cone instability
Authors: Myer R. C. , Simon Albert
Published: March 2003

The nonlinear behavior of the drift cyclotron loss-cone instability close to a stability boundary is considered. The time-asymptotic small-amplitude saturation of a single mode is determined by a variation of the Bogoliubov method. A collisionless plasma model is used with no mirror losses or particle sources. Flute-like local perturbations are considered. The stability boundary in density, density-gradient space is determined for several different ion loss-cone distributions. The modified equilibrium ion distribution function, the electric field, and the amplitude of the fluctuating electrostatic potential are then obtained as a function of the fractional increase in density gradient above the critical value. The nonlinear frequency shift remains indeterminate. In all cases, stable saturation occurs and is due to a slight filling-in of the loss cone. Comparison with numerical simulation results show good agreement when the high thermal level of neighboring modes is artificially suppressed.
Convective amplification of drift waves and thermal fluctuation levels in a stable plasma
Authors: Waltz R. E. , Pfeiffer W. , Dominguez R. R.
Published: March 2003

The possibility that convective amplification of drift waves gives rise to significant thermal fluctuation levels in a stable tokamak plasma is investigated. A test particle formulation yields a differential dispersion equation, which is amenable to numerical solution. It is found that, for realistic tokamak parameters, the calculated thermal fluctuation levels are far below those measured experimentally. Convective amplifications are localized and relatively small. The largest calculated fluctuation levels are due to an enhancement of the thermal source strength for frequencies near the eigenfrequencies of weakly damped normal modes.
Quasi-recurring energy leakage in the two-space-dimensional nonlinear Schrödinger equation
Authors: Martin David U. , Yuen Henry C.
Published: March 2003

The relationship between initial condition and long time evolution observed by Yuen and Ferguson for the one-space dimensional nonlinear Schrödinger equation has been extended to two-space dimensions. In the case where the instability region is infinite in extent, it is found that the energy initially contained in low modes can leak to unstable higher harmonics in a quasi-recurring fashion.
Kelvin–Helmholtz instability in supersonic and super-Alfvénic fluids
Authors: Tajima T. , Leboeuf J. N.
Published: March 2003

A magnetohydrodynamic particle code is used to simulate highly nonlinear stages of the Kelvin–Helmholtz instability. Without a magnetic field, a supersonic flow with sonic Mach number Ms creates a stream of vortices which turn into a series of structured shock fronts with shock angle sin−1 (1/Ms). With a magnetic field, a super-Alfvénic flow results in substantial bending of the magnetic field lines.
Propagation of intense ion beams in straight and tapered z-discharge plasma channels
Authors: Ottinger P. F. , Mosher D. , Goldstein Shyke A.
Published: March 2003

A preformed z-discharge plasma channel can be used to transport focused ion beams appropriate for a pellet fusion device. During transport, the beam can be compressed axially by time-of-fight bunching when appropriate ion accelerating voltage waveforms are employed. Single-particle orbits in such channels are expressible in terms of simple harmonic functions for small ion injection angles. In this work, orbit analysis is used to investigate how nonuniformities or tapering of the channel and electric fields present in the channel affect radial beam confinement and power multiplication by bunching.
Steady-state response of the electron distribution function to an applied electric field
Authors: Wiley J. C. , Hinton F. L.
Published: March 2003

Steady-state solutions to the linearized Fokker–Planck equation have been numerically investigated using two models. The Kulsrud model, in which the electron-electron collision term is simplified by evaluating the integrals using a Maxwellian distribution, is considered first. It is shown that steady-state solutions of the Kulsrud model, obtained by long time integrations of the time dependent equation, can be obtained more easily by considering a separable solution. A more physically reasonable steady-state model, which consistently describes both the thermal and runaway regimes and is readily solved numerically, is developed. The resistivity, in agreement with Spitzer and Härm, and runaway production rates, in agreement with the Kulsrud model, are obtained.
Production of plasma from diatomic gases by relativistic electron beams
Authors: Cary John R.
Published: March 2003

The theory of the production of plasma by the interaction of a relativistic electron beam with a diatomic gas is presented. The theory includes atomic species as well as molecular species; this is shown to be necessary when nearly fully ionized plasma are produced. In addition, the theory models magnetic field diffusion by an effective time constant, which allows extensive parameter studies to be performed. The dependence of the production process on the beam intensity and width and the gas pressure is presented. It is shown that the thin beams produced by foil-less diodes are not capable of ionizing high pressure (≳ 3 Torr) targets.
Ekman compatibility conditions in Wedemeyer spin-up model
Authors: Kitchens Clarence W.
Published: March 2003

Numerical solutions of the Navier–Stokes equations are used to assess compatibility conditions used in the Wedemeyer model for impulsive spin-up from rest in a circular cylinder. A monotonic, nonlinear compatibility condition is proposed based on this work.
A shear stabilized cylindrically symmetric mirror plasma
Authors: Manheimer Wallace M.
Published: March 2003

The possibility of shear stabilization of a cylindrically symmetric mirror plasma is examined.
Effect of a horizontal plane boundary on a falling horizontal cylinder at low Reynolds number
Authors: Chen Yang-Jen , Hussey R. G.
Published: March 2003

Experimental results are presented for the change in velocity of a slender cylinder with its axis horizontal as it falls through a viscous fluid toward a horizontal plane boundary. When the boundary influence is strong, the deceleration of the cylinder is observed to be constant, and the velocity extrapolates to zero at the boundary. When the relative change in velocity is small (<20%), it is observed to depend inversely on the square of the distance from the boundary. The Reynolds number based on cylinder diameter ranges from 2.9 to 0.015 and the Reynolds number based on cylinder length ranges from 122 to 0.16.
Errors in simultaneous measurements of temperature and velocity in the outer part of a heated jet
Authors: Antonia R. A. , Chambers A. J. , Hussain A. K. M. F.
Published: March 2003

Simultaneous measurements of velocity and temperature fluctuations in the outer part of a heated circular jet discharged into still air may be in error as a result of reverse flow regions and the inevitable contamination of the cold (temperature) wire signal by the thermal wake of the hot wire. The error in mean and rms temperature is estimated for the case of two standard hot wire-cold wire arrangements. At the half-temperature radius, the mean and rms temperature are overestimated by about 16% and 46%, respectively. Conditional measurements of velocity fluctuations are also presented as a first attempt to obtain velocity statistics without the effect of reverse flow regions. Measured normalized moments of the velocity fluctuation are larger than the ’’corrected’’ values, the difference increasing with the order of the moment and with radial distance in the outer part of the jet.
Effects of very high collision frequencies on the electron density fluctuation spectrum of plasmas
Authors: Theimer O. , Sandalov A. N. , Theimer M. M.
Published: March 2003

This is a generalization of an earlier theory for calculating the electron density fluctuations in a plasma containing strongly ionized impurities. This earlier theory is based on the simplifying assumption that the collision parameter yμ is small so that only linear terms of first order in yμ have to be kept in the formalism. The present theory removes this unnecessary and unrealistic limitation and shows that a theory, nonlinear in yμ, can be deduced from the general principles of density fluctuations as easily as the linear theory. Some numerical results are presented which illustrate the difference between the linear and nonlinear theory.
Variational principles and canonical theory for many-component plasmas with self-consistent field
Authors: Wilhelm H. E.
Published: March 2003

The Lagrangian L=ℱℱℱL(qs,∂qs/∂t,∇⋅qs)d3 r and Hamiltonian H=ℱℱℱℋ(ps,qs,∇⋅qs)d3r for many-component plasmas with self-consistent field interactions are derived. The canonical fields ps(r,t) and qs(r,t) are defined by ps=msvs and ∂qs/∂t=nsvs, respectively, where ns(r,t) is the density and vs(r,t) is the velocity of the component s, s=1,2,...,N. Based on the action principle, the Lagrange and Hamilton equations of motion for the components (s) are presented as functional derivatives of L and H with respect to the canonical momenta ps and qs. It is shown that the new formulations of many-component plasma dynamics have mathematical advantages compared with the conventional variational principles and hydrodynamic equations.
Effect of flux-limited thermal conduction on the jump conditions of the laser-plasma critical surface
Authors: Mayer F. J. , Berger R. L. , Max Claire E.
Published: March 2003

The effects of flow, radiation pressure, and flux-limited thermal conduction on the plasma profile near the critical surface are examined. When the absorbed flux is deposited locally and the thermal conduction is inhibited, the density profile and plasma flow are determined by the flux limit because the self-consistent plasma pressure is larger than the radiation pressure.
Mode conversion of lower-hybrid waves
Authors: Chan V. S. , Chiu S. C. , Guest G. E.
Published: March 2003

In an inhomogeneous plasma, partial conversion of lower-hybrid waves to ion plasma waves can occur for a range of plasma parameters, even in the absence of a reflection layer. Nonetheless, mode conversion may be significantly reduced if the plasma is sufficiently dissipative. If electron Landau damping is a dominant dissipation mechanism, the quasi-linear behavior of the electron distribution function can introduce a strong rf power dependence into the mode conversion efficiency. At low rf power levels the damping may be too large to permit effective mode conversion, while above some critical power level, the quasi-linear flattening of the distribution function may sufficiently reduce the damping to permit strong mode conversion.
Exact Vlasov equilibria for field-reversing rings
Authors: Channell Paul J.
Published: March 2003

A technique is developed for finding exact Vlasov equilibria for field-reversing rings. An infinite class of equilibria can be generated in which the plasma is confined to a finite region of space. A variety of ring cross sectional shapes can be found.
Slow viscous rotation of a sphere on the axis of a circular cone
Authors: Kim Moon-Uhn
Published: March 2003

Slow viscous flow due to the rotation of a small sphere on the axis of a circular cone of an arbitrary vertex angle is investigated on the basis of the Stokes’ approximation. The torque and force on the sphere are determined to the first-order effects of the boundary.
Relativistic gasdynamics in two dimensions
Authors: Königl Arieh
Published: March 2003

Steady two-dimensional flow of an ideal compressible fluid is studied in the context of special-relativistic gasdynamics. The Newtonian equations for potential flow, including the equation of characteristics, Chaplygin’s equation, and the Euler–Tricomi equation, are generalized. It is found that these equations can have the same form in the Newtonian and the relativistic regimes if their parameters are defined in the local rest-frame of the fluid. The Mach number thus defined, ℳ≡[β/(1−β2)1/2]×[βs/(1−β2s)1/ 2]−1, where β and βs are, respectively, the speed of the fluid and the speed of sound relative to the fluid (in units of the speed of light), is shown to have the same properties as M=β/βs in Newtonian theory. The Newtonian expressions for oblique plane shock waves in a perfect gas can similarly be generalized in certain cases (which include, in particular, the extreme-relativistic limit), and it is shown that the adiabatic index Γ in these expressions is generalized by Γ̂≡ Γ/(1−β2s). Some applications of these results are discussed. In addition, it is shown that the analogy between Newtonian sound speeds and the corresponding relativistic proper speeds extends to the expressions for hydromagnetic wave speeds.
Second-order asymptotic solution for laminar separation
Authors: Ragab S. A. , Nayfeh Ali H.
Published: March 2003

The method of matched asymptotic expansions is used to obtain a second-order triple-deck solution for the case of constant wall temperature. It includes the problem of an adiabatic wall as a special case. The theory is applied to the case of a supersonic flow over a compression ramp with laminar separation. A numerical procedure is presented for solving the lower-deck equations by using the Crank–Nicolson finite-difference scheme. A modification of the boundary conditions for an adiabatic wall made it possible to solve for the total second-order solution instead of solving for the different orders in succession. Sample results and comparisons with other solutions are presented. The region of separation predicted by the second-order theory is larger than that predicted by the first-order theory. Moreover, for the case of cooled walls, the second-order theory predicts negative temperatures and densities, depending on the Reynolds number and the degree of cooling, thus indicating a breakdown of the theory.
Spreading of energy in solutions of the nonlinear Schrödinger equation
Authors: Martin David U. , Yuen Henry C.
Published: March 2003

Theoretical bounds on the spreading of energy in physical systems describable by the nonlinear Schrödinger equation are compared to numerical results for the development of solutions of this equation. The theoretical bounds are verified, but it is found that they are not sharp for the cases considered.
Nonlinear estimates of Brillouin scatter in plasma
Authors: Kruer W. L.
Published: March 2003

Simple models are used to provide nonlinear estimates of Brillouin scatter in several complementary regimes. Some applications to laser plasma interactions are given.
Collisionless flow and end loss from a high-energy theta-pinch plasma
Authors: McKenna K. F. , Bartsch R. R. , Commisso R. J. , Ekdahl C. , Quinn W. E. , Siemon R. E.
Published: March 2003

End-loss experiments on the high-energy (Te+Ti=3.3 keV, ne=1.5×1016 cm−3) 5 m Scylla IV-P theta pinch are reported. The evolution of the theta-pinch plasma parameters in the presence of axial losses and the behavior of the exhausting plasma near the ends of the device have been investigated. The measured decay of the theta-pinch plasma electron temperature agrees with code predictions based on classical axial thermal conduction losses. However, the axial ion heat flux is found to be unmeasurably small in the collisionless ion plasma. Energy-line-density measurements at the coil midplane also agree with code predictions and provide evidence of inward traveling rarefaction-like waves. At the theta-pinch ends, the exhausting plasma is comprised of a collimated plasma core which remains radially confined for tens of centimeters, strongly convects magnetic fields, and contains the bulk of the ejected plasma. This collimated core is surrounded by a plasma annulus that expands rapidly to the walls after leaving the theta-pinch coil. The radially confined exhaust plasma is successfully modeled as one-dimensional flow through a converging-diverging nozzle. The new results obtained in Scylla IV-P have led to a re-analysis of the particle end-loss data obtained in previous experiments. The subsequent comparison of experiments and theory shows that the normalized particle end-loss time is independent of both the plasma beta and collisionality regime.
Energy loss of a modified Korteweg–de Vries solitary wave in a varying medium
Authors: Kuehl H. H. , Pereira N. R.
Published: March 2003

The energy loss from a solitary wave governed by the modified Korteweg–de Vries equation with a slowly varying coefficient is found numerically to be in good agreement with recent perturbation theory.
Heat flux limitation by ion-acoustic instability
Authors: Monchicourt P. , Holstein P. A.
Published: March 2003

The heat flux limit coefficient at the threshold of the ion-acoustic instability is given for the Spitzer–Härm distribution and is shown to be 5 to 10 times higher than the usual values [e.g., (Zme/mi)1/2] which are derived from a very approximate distribution.
Amplification of ion cyclotron waves via high frequency electron plasma wave turbulence
Authors: Huba J. D. , Chaturvedi P. K. , Papadopoulos K.
Published: March 2003

It is shown that the presence of high frequency electron plasma wave turbulence can nonlinearly amplify obliquely propagating, electrostatic, ion cyclotron modes.
Energy stability of the Eulerian-mean motion in the upper ocean to three-dimensional perturbations
Authors: Leibovich S. , Paolucci S.
Published: March 2003

The stability of the wind-driven unidirectional current solution of the Craik–Leibovich equations for the Eulerian-mean flow in the upper layers of a deep stratified ocean or lake is investigated using the energy method. The energy stability limit for three-dimensional disturbances of arbitrary amplitude is found to correspond to two-dimensional disturbances. Thus, convective roll disturbances with roll axes parallel to the current have the greatest rate of energy growth; this is consistent with field and laboratory observations of Langmuir circulations.
Numerical integration of the gasdynamic equations
Authors: Chong T. H. , Sirovich L.
Published: March 2003

The gasdynamic equations are transformed to new coordinates based on particle paths and an appropriate set of characteristics. The numerical integration of the transformed equations is accomplished by a scheme which is accurate, rapidly convergent, and free from shock oscillations. Complete flow solutions are presented in graphical form for several cases.
Cross-field electron transport due to thermal electromagnetic fluctuations
Authors: Lin A. T. , Dawson J. M. , Okuda H.
Published: March 2003

The cross-field electron particle and energy transport for a high β thermal plasma is investigated using a magnetostatic particle code. The diffusion process due to magnetic fluctutations alone is observed to have a Bohm-like scaling. However, when both electrostatic convective cells and magnetic fluctuations are allowed, there is interference between the two diffusive processes; the diffusion takes on the character of strong turbulence for the interaction between these static modes. The resulting diffusion is smaller than would be the case when assuming that these modes are independent.
Raman backscatter in high temperature, inhomogeneous plasmas
Authors: Kruer W. L. , Estabrook Kent , Lasinski B. F. , Langdon A. B.
Published: March 2003

The behavior of Raman backscatter of intense laser light in a high temperature, inhomogeneous plasma is examined in theory and simulations. Plasma conditions thought to be characteristic of recent long pulse length experiments are considered. Significant levels of reflected light are found near ω0/2, a frequency which is not commonly monitored in experiments. It is shown that the plasma temperature leads to a sizable shift of the spectrum to frequencies below ω0/2. Conditions for significant Raman backscatter at densities much less than one-fourth the critical density are also briefly considered.
Brillouin and Raman scattering of an extraordinary mode in a magnetized plasma
Authors: Grebogi Celso , Liu C. S.
Published: March 2003

The effects of magnetic field on the stimulated Brillouin and Raman scattering processes are studied. The formalism applies to plasmas produced by CO2 lasers and to electron cyclotron heating of toroidal systems by an extraordinary electromagnetic wave. In the case of laser fusion the plasma is magnetized due to the self-generated dc magnetic field, while in toroidal plasmas it is due to the external magnetic field. The magnetic field greatly reduces the threshold for Brillouin backscattering by the lower hybrid wave. The Raman scattering by the upper hybrid wave has substantial growth rate even for large kλD because of the reduction of linear Landau damping due to the magnetic field.
Electron cyclotron emission from tokamak plasmas with mildly superthermal electrons
Authors: Fidone I. , Granata G. , Meyer R. L. , Jornada E. H. , Schneider R. S. , Ziebell L. F.
Published: March 2003

The emission of cyclotron radiation from a tokamak plasma in the presence of a high toroidal current is investigated. For the fundamental frequency, a theory of the radiation which consistently includes the hot plasma polarization effects is developed. The high current density electron system is described by a distribution function which is the sum of two Maxwellian functions representing the body of the electron population and a small fraction of superthermal drifting electrons, respectively. The emission of the ordinary and extraordinary modes in the equatorial plane of the torus for quasi-perpendicular propagation is investigated numerically. It is found that the radiation temperature deduced from the emission of radiation on the high Bt side of the torus differs from that on the low Bt side, where Bt is the confining magnetic field.
Converging nonlinear resonance cone trajectories
Authors: Kuehl H. H.
Published: March 2003

The trajectory of the converging resonance cone due to a circular ring exciter in a weakly nonlinear plasma is derived. The analysis applies to all frequencies for which resonance cones exist, and the nonlinearity is assumed to be due to the ponderomotive force. It is shown that the nonlinear focal shift is either toward or away from the exciter, depending on the frequency and the plasma parameters.
An eikonal expansion of the Vlasov–Maxwell equations valid near cyclotron resonance
Authors: Weitzner Harold , Batchelor D. B.
Published: March 2003

In the usual formulations of geometrical optics, the physics of the medium enters the equations through a conductivity tensor operator σ. An essential assumption in the subsequent expansion is that the magnitude of σH, the Hermitian part of σ, is much smaller than σA, the anti-Hermitian part. In a finite temperature plasma with ωpe∼‖Ωe‖, this condition is always violated sufficiently close to cyclotron resonance, even though in many cases the waves are weakly damped and k is slowly varying. Simultaneously expanding the Vlasov equation and Maxwell equations and taking explicit account of the relative magnitude of the electric field components in the ordering scheme yields a formalism in terms of real rays, real eikonal functions, and slowly varying amplitude that is valid at cyclotron resonance. It is assumed that ωpe∼‖Ωe‖∼ω are large, that ω≃‖Ωe‖, and that vek/ω is small. It is shown that when the waves are weakly damped at cyclotron resonance, the ray trajectories are, to leading order, exactly those of cold plasma theory. A Poynting theorem that can be put into the standard form is obtained by taking the expansion to first order. Care must be taken, however, to include finite temperature effects in calculating the zero-order electric field. The theory is also applied to ion cyclotron resonance.
Stability of mode-converted lower-hybrid solitons
Authors: Himmell Lewis C.
Published: March 2003

The stability of planar mode-converted, lower-hybrid solitons to transverse perturbations is investigated in parametric regions well seperated from mode conversion points. Two classes of modes are found. In lowest order, the stability of each class is related to a particular term of the equation governing the nonlinear evolution of these waves.
Intense electron beam propagation between two plane conductors
Authors: Uhm Han S. , Sternlieb A.
Published: March 2003

The properties of an intense relativistic electron beam propagating between two grounded plane conductors, including the important influence of an ion current, are examined. The steady-state and time-averaged equilibrium properties are obtained analytically by employing a one-dimensional model. It is shown that the ratio of the final forward ion current to the electron current can be expressed in terms of the electron energy, the potential depth of the last virtual cathode, and the electron-to-ion-mass ratio, although the forward electron current itself is a complicated function of the system parameters. Based on this investigation, it is found that the forward electron current is significantly reduced as the distance between the two conductors is increased. However, by introducing an ion current into the system and allowing a number of virtual anodes in the region between the two plane conductors, the forward electron current can be substantially enhanced.
Magnetoacoustic heating by ion Landau damping
Authors: Turner Leaf
Published: March 2003

There have been recent experimental observations of collisionless damping of Alfvén waves and m=0, k=0 magnetoacoustic waves at high beta. In the absence of microinstabilities and for nonzero k, it will be shown that collisionless absorption can provide a heating mechanism when an equilibrium plasma column is pumped by oscillations of the confining magnetic field at a frequency near the oblique (i.e., k ≠ 0) magnetoacoustic frequency. In particular, the dynamics of a sharp-boundary, Vlasov-fluid screw pinch are studied analytically using the following ordering scheme: σ=rL/r0, ω/ωc=O(σ), kr0=O(1), ω/kvth =O(1), local beta=O(1), r0∇⊥=O(1). The resulting equations keep ion kinetic effects along magnetic field lines while retaining only ion fluid effects transverse to the field lines. To leading order all finite-Larmor-radius effects are absent. However, Landau damping leads to collisionless absorption of energy by the ions for k ≠ 0 at an oblique magnetoacoustic resonance. An example of a resonance line profile along with the associated heating time scale and induced rf electric field will be presented.
Particle orbits in ion rings: Ergodic or not?
Authors: Larrabee D. A. , Lovelace R. V.
Published: March 2003

An analytic and numerical study has been made of the single-particle orbits in self-consistent, large gyroradii ion ring Vlasov equilibria. In most of the cases studied the numerically computed orbits are nonergodic, indicating the existence of a constant of the motion, 𝒦, in addition to the Hamiltonian, ℋ, and the canonical angular momentum, 𝒫ϑ. An analytic method for understanding the occurrence of nonergodic orbits is obtained from an analysis of the orbital stability of the class of particles which have orbits lying near the midplane of the ring. Finally, a discussion is given of an illustrative case of a distribution function f dependent on three constants of the single-particle motion, ℋ, 𝒫ϑ, and 𝒦. In this case there may be a toroidal self-magnetic field in contrast with conventional equilibria.
Existence of a time-dependent heat flux-related ponderomotive effect
Authors: Schamel H. , Sack Ch.
Published: March 2003

The existence of a new ponderomotive effect associated with high-frequency waves is pointed out. It originates when time-dependency, mean velocities, or divergent heat fluxes are involved and it supplements the two effects known previously, namely, the ponderomotive force and fake heating. Two proofs are presented; the first is obtained by establishing the momentum equations generalized by including radiation effects and the second by solving the quasi-linear-type diffusion equation explicitly. For a time-dependent wave packet the solution exhibits a new contribution in terms of an integral over previous states. Owing to this term, the plasma has a memory which leads to a breaking of the time symmetry of the plasma response. The range, influenced by the localized wave packet, expands during the course of time due to streamers emanating from the wave active region. Perturbations, among which is the heat flux, are carried to remote positions and, consequently, the region accessible to wave heating is increased. The density dip appears to be less pronounced at the center, and its generation and decay are delayed. The analysis includes a self-consistent action of high-frequency waves as well as the case of traveling wave packets. In order to establish the existence of this new effect, the analytical results are compared with recent microwave experiments. The possibility of generating fast particles by this new ponderomotive effect is emphasized.
Radiation from a localized Langmuir oscillation in a uniformly magnetized plasma
Authors: Freund H. P. , Papadopoulos K.
Published: March 2003

The electromagnetic radiation at the first and second harmonics of the electron plasma frequency from a localized Langmuir perturbation is computed for the case of a uniformly magnetized plasma. It is assumed that the localized perturbations in both the electrostatic field and plasma density have cylindrical symmetry about the direction of the ambient magnetic field. The analysis is initially performed for such an arbitrary localized perturbation, and then applied to treat the case of a quasi-planar Langmuir soliton propagating in the direction of the magnetic field. An extensive numerical study of the angular dependence of the radiation spectrum as a function of the ratio of the electron plasma and cyclotron frequencies is described.
Theory of the resistive hose instability in relativistic electron beams
Authors: Uhm Han S. , Lampe M.
Published: March 2003

A theory of the resistive hose instability is developed for an infinitely long relativistic electron beam propagating parallel to an applied axial magnetic field. Complete space-charge neutralization by the ambient plasma and paraxial flow (p2z≳≳p2r+p2ϑ) are assumed. An integro-differential eigenvalue equation is derived from Vlasov–Maxwell theory for the general case, and this equation is reduced to an ordinary differential equation by using a model in which the class of beam electrons with a given transverse energy displaces as a rigid component. The model introduced spread betatron frequency in a natural way that includes correlations to radial position. Using a variational technique, an approximate dispersion relation is found for arbitrary density profile and is evaluated in closed form for either the Bennett or square profile. Stability properties are illustrated and discussed in detail for a square profile, including the influence of the applied magnetic field (stabilizing), proximity to a conducting guide (stabilizing), and partial current neutralization (destabilizing).
Low-frequency flute instabilities in intense nonneutral electron and ion beams
Authors: Uhm Han S. , Davidson Ronald C.
Published: March 2003

The stability properties for low-frequency flute perturbations in a relativistic nonneutral electron beam are investigated within the framework of the Vlasov–Maxwell equations. It is assumed that ν/γb<<1, where ν is Budker’s parameter and γbmc2 is the characteristic electron energy. The analysis is carried out for the rigid-rotor equilibrium distribution function in which all electrons have the same value of energy in a frame rotating with angular velocity ωb and the same value of axial canonical momentum. Strong instability is found for aximuthally symmetric perturbations (∂/∂ϑ=0) with radial mode numer n=2 and rotational frequency ωb=0.5 ωcb, where ωcb is the electron cyclotron frequency. However, the instability can easily be stabilized by slightly detuning the rotational frequency from the value ωb=0.5 ωcb. The transverse stability properties of an intense ion beam in a quadrupole magnetic field are also investigated by analogy with the electron beam stability analysis, including the important influence of rotational effects on stability behavior. It is found that the rotational motion also plays an important role in determining the stability properties of intense ion beams.
Bubble or drop distortion in a straining flow in two dimensions
Authors: Vanden-Broeck Jean-Marc , Keller Joseph B.
Published: March 2003

The distortion of a two-dimensional bubble (or drop) in a straining flow of an inviscid imcompressible fluid is examined theoretically. Far from the bubble the stream function of the flow is assumed to be αxy, where α is a constant. Within the bubble the pressure is assumed to be a constant pb, and the bubble surface is assumed to have a surface tension σ. Then, the shape of the bubble depends upon the single dimensionless constant γ=2(pb−ps)/(2σα)2/3ρ1/3, where ρ is the fluid density, ps is the stagnation pressure of the flow, and the size of the bubble is proportional to (2σ/ρα2)1/3. For γ large, it is found that the bubble tends to a circle of radius (2σ/ρα2)1/3 γ−1. As γ decreases, numerical solutions show that the bubble at first becomes a square with rounded corners. Then, it develops four horns or spikes with large curvature near their ends. Finally at γ∼−1.8, the two sides of each spike touch each other near the tip and enclose a small bubble there. It is also found that there is a maximum value of the Weber number above which there is no steady solution.
Power-driven and adiabatic expansions into vacuum
Authors: Farnsworth Archie V.
Published: March 2003

Analytical solutions are obtained for the planar, cylindrical, and spherical expansions into vacuum of matter initially concentrated at a plane, a line, or a point. Both power-driven and adiabatic expansions are considered, where in the power-driven case, the specific power is deposited uniformly in space, but may vary in time according to a power law. These problems are found to be self-similar. The non-self-similar motion of matter during the adiabatic expansion that follows a power pulse of finite duration has also been addressed and a solution has been obtained.
Diffusion of rarefied gas mixtures in a circular tube under the existence of pressure gradients
Authors: Kanki Tatsuo , Iuchi Satoru , Yamamoto Yuji
Published: March 2003

A simple and general expression for nonuniform pressure diffusion of a binary mixture in a circular tube is obtained by applying locally uniform distributions of molecular velocity plus a new physical model on the molecular transport of momentum in the Knudsen layer, which is derived from the momentum balance considerations including the influence of wall interactions of molecules, to Maxwell’s transport equation. The theory predicts some striking phenomena, the Kramers–Kistemaker pressure effect, the Hoogschagen flux ratio, Knudsen minimum, and so on. In order to check the validity of the theory, the flux of a component gas in the Stefan tube and the pressure difference which accompanies it are determined experimentally for Hg-He and Hg-Ar mixtures and found to be in good agreement with those predicted from theory.
Theoretical multiple beam overlap from channel transport of intense particle beams
Authors: Wright Thomas P. , Halbleib John A.
Published: March 2003

The overlap of intense particle beams transported in current-carrying plasma channels for inertial confinement fusion has been studied. Basic geometric considerations suggest an upper bound on the current density gain of N/4 due to the overlap of N uniform beams that are transported to the overlap region in channels. For ’’hot’’ electron beams this limit is seldom approached. For ’’cold’’ ions beams with radial distributions peaked on channel axes, this limit can be attained and even exceeded. From the standpoint of channel energetics, it is desirable to minimize the transverse energy of the ions in the channel which is quantified by the average ion angle ϑ. In order to optimize the ion overlap it is necessary to satisfy ϑ<2N−1/2. A spherical multi-’’disk’’ model of converging plasma channels is developed with the constraint that the geometrical overlap radius (where the incoming channels touch each other) remain as small as possible in order to avoid excessive beam expansion in the overlap region. Details of electron transport and escape are explained using adiabatic drift theory.
Relativistic-electron-beam/target interaction in plasma channels
Authors: Halbleib John A. , Wright Thomas P.
Published: March 2003

A model describing the transport of relativistic electron beams in plasma channels and their subsequent interaction with solid targets is developed and applied to single-beam and multiple-beam configurations. For single beams the targets consist of planar tantalum foils and, in some cases, cusp fields on the transmission side of the foils are employed to improve beam/target coupling efficiency. In the multi-beam configurations, several beams are arranged in wagon-wheel fashion so as to converge upon cylindrical targets, consisting of either hollow tantalum or solid graphite cylinders, located at the hub. For 0.3-cm beam radii that are less than or equal to the channel radii, mean specific power depositions up to about 17 TW/g per MA of injected beam current are obtained for single beams; 12-beam results are typically an order-of-magnitude less. The corresponding enhancements are up to five times the collisional stopping power for either single or multiple beams. Substantial improvement is predicted for the multi-beam interaction should future channel technology permit transport at higher current densities in smaller channels.
Bifurcation of sharp boundary β=1 multipole equilibria
Authors: Spencer Ross L.
Published: March 2003

The bifurcation of sharp boundary magnetohydrodynamic equilibria in linear multipoles of arbitrary order is studied using the hodograph method. In the low pressure limit, simple formulae are obtained for the shapes of multipole cusp equilibria. In the high pressure limit the equilibria are found to bifurcate; two different equilibria may exist for the same values of the external parameters. It is conjectured that a similar bifurcation will be encountered in the calculation of diffuse multipole equilibria at high beta.
Time behavior of nonlinear plasma oscillations
Authors: Dewandre Thierry , Simon Albert
Published: March 2003

The time behavior of a single weakly damped electron mode is analyzed. Analytic expressions for the time-dependent mode damping and frequency shift equivalent to those of O’Neil and to those of Morales and O’Neil are obtained, but in a much simpler form since there are no sums.
Rate of electron heating in a multidipole plasma
Authors: Leung K. N. , Kribel R. E.
Published: March 2003

The rate of increase in electron temperature in a multidipole device due to the interaction of a group of test electrons with an argon plasma is determined.
Variational corrections to ELMO Bumpy Torus neoclassical ion plateau transport
Authors: Spong D. A. , Hedrick C. L.
Published: March 2003

Low collisionality corrections to ELMO Bumpy Torus (EBT) ion plateau transport coefficients are calculated using a variational method. Using a bounce-averaged drift kinetic equation and a drift orbit model appropriate to collisionless EBT ion transport, a solution is obtained that is accurate to first order in ε(Ω0/ν0)2/3 (ε is the inverse aspect ratio, ν0 is the 90° deflection frequency, and Ω0 is the average poloidal gradient B drift frequency). This is substituted into a variational principle (valid over both the plateau and banana regimes) from which particle and energy fluxes are obtained. The sensitivity of the transport rates with respect to variations in the radial and poloidal components of the ambipolar electric field and with respect to variations in the poloidal drift frequency scale length is examined. The transition from plateau to crescent orbit scaling occurs at approximately ν0/Ω0=ε3/2.