bluuebunny/crossref_metadata_2025 huggingface dataset:
A fast contour dynamics method for many-vortex calculations in two-dimensional flows
Authors: Dritschel David G.
Published: July 2002

A new computational method extending the contour dynamics/surgery (CS) algorithm is announced which gives typical speed-up factors of two orders of magnitude in calculations of flows involving many interacting vortices. The method makes use of an alternative expression for the velocity field in the exterior of a vortex that takes the form of a rapidly convergent series. Each term in this series can be expressed as a complex coefficient divided by the complex distance x+iy from the vortex center. The complex coefficient, or moment, is a real number pair that describes shape characteristics of the vortex (e.g., circulation, eccentricity, etc.). In numerical calculations, where accuracy is necessarily limited, it is frequently sufficient to retain only the leading-order terms in this series, particularly for a gas of well-separated vortices. The real computational gain is made, however, by reexpanding the series of all vortices that are sufficiently separated from a given vortex as a single, truncated series in positive powers of the complex distance from this vortex’s center. The coefficients of this series involve only the moments of the other vortices and their centroid separation from the given vortex. The leading-order truncation, for instance, simply gives point vortex dynamics, except that self- or close-range interactions are computed using the full contour integral expression of contour dynamics (hence, all vortices retain nontrivial spatial structure, vital to a proper dynamical description of close-range interactions). In general, the optimal truncation depends on a dynamic balance between the cost of all moment computations and the cost of all contour integrations. This method, called ‘‘moment-accelerated contour surgery,’’ which is briefly outlined above for the planar case, has a direct analog in spherical geometry. There are also extensions to generalized two-dimensional (2-D) flows having more general linear operator relationships between streamfunction and vorticity. Details are provided for quasigeostrophic flow.
Propagation of small-amplitude displacement waves on a vortex in the center of a circular tube
Authors: Rusak Z. , Seginer A.
Published: July 2002

The propagation of three-dimensional small-amplitude long waves on a vortex filament running down the center of a circular tube is investigated analytically. The vortex flow is idealized by an infinite concentrated potential vortex filament immersed in an axial uniform flow that is displaced from the axis of the tube by a small three-dimensional perturbation. The rigid walls of the tube are represented by a potential surface source distribution that also has the nature of a small perturbation. A linearization of the flow-field equations, with respect to the basic state of a straight filament along the tube axis, results in an eigenvalue problem. The analytical solution shows that the vortex in the center of the tube is stable and the disturbances propagate as constant amplitude displacement waves along the vortex line and as source-intensity fluctuations along the inner surface of the tube wall. Two different basic modes of either a helical or rotating sinusoidal wave can propagate along the vortex filament. A ‘‘supercritical’’ state is defined by the characteristics of the flow in which waves can propagate only downstream. It is shown from available experimental data that vortex flows in tubes that experienced vortex breakdown farther downstream, were ‘‘supercritical’’ at the tube inlet.
Global confinement and discrete dynamo activity in the MST reversed-field pinch
Authors: Hokin S. , Almagri A. , Assadi S. , Beckstead J. , Chartas G. , Crocker N. , Cudzinovic M. , Den Hartog D. , Dexter R. , Holly D. , Prager S. , Rempel T. , Sarff J. , Scime E. , Shen W. , Spragins C. , Sprott C. , Starr G. , Stoneking M. , Watts C. , Nebel R.
Published: July 2002

Results obtained on the Madison Symmetric Torus (MST) reversed-field pinch [Fusion Technol. 19, 131 (1991)] after installation of the design poloidal field winding are presented. Values of βθe0≡2μ0ne0Te0/B2θ(a)∼12% are achieved in low-current (I=220 kA) operation; here, ne0 and Te0 are central electron density and temperature, and Bθ(a) is the poloidal magnetic field at the plasma edge. An observed decrease in βθe0 with increasing plasma current may be due to inadequate fueling, enhanced wall interaction, and the growth of a radial field error at the vertical cut in the shell at high current. Energy confinement time varies little with plasma current, lying in the range of 0.5–1.0 msec. Strong discrete dynamo activity is present, characterized by the coupling of m=1, n=5–7 modes leading to an m=0, n=0 crash (m and n are poloidal and toroidal mode numbers). The m=0 crash generates toroidal flux and produces a small (2.5%) increase in plasma current.
Ellipticity induced Alfvén eigenmodes
Authors: Betti R. , Freidberg J. P.
Published: July 2002

It is shown that noncircularity of tokamak flux surfaces leads to frequency gaps in the magnetohydrodynamic Alfvén continuum. Within these gaps discrete modes having macroscopic structure are shown to exist and have many common features with toroidicity induced Alfvén eigenmodes. The present work focuses on ellipticity. Since κ−1>ε in many tokamaks the ellipticity induced Alfvén eigenmode may indeed be a more robust mode. The most global mode couples the m=1, n=1 and m=3, n=1 ‘‘cylindrical’’ eigenmodes. The region of strong coupling occurs at the q(r)=2 surface and the width of the coupling region is finite and of order (κ−1)a. Furthermore, for typical limiter q(r) profiles satisfying 1≲q≲3, the dominant mode harmonics do not intersect the continuum Alfvén spectrum.
Theory of neoclassical ion temperature-gradient-driven turbulence
Authors: Kim Y. B. , Diamond P. H. , Biglari H. , Callen J. D.
Published: July 2002

The theory of collisionless fluid ion temperature-gradient-driven turbulence is extended to the collisional banana-plateau regime. Neoclassical ion fluid evolution equations are developed and utilized to investigate linear and nonlinear dynamics of negative compressibility ηi modes (ηi≡d ln Ti/d ln ni). In the low-frequency limit (ω<μi, where ω is the mode frequency and μi is the neoclassical viscous damping frequency), neoclassical effects modify the sonic ηi mode by introducing strong viscous damping of parallel flows, which renders the long wavelength response dissipative rather than inertial. Also, the linear and nonlinear polarization drifts are enhanced by a factor of B2t/B2p. As a result of these modifications, growth rates are dissipative, rather than sonic, and radial mode widths are broadened [i.e., γ∼k2∥c2s(ηi −(2)/(3) )/μi, Δx∼ρs(Bt/Bp) (1+ηi)1/2, where k∥, cs, and ρs are the parallel wave number, sound velocity, and ion gyroradius, respectively]. In the limit of weak viscous damping, enhanced neoclassical polarization persists and broadens radial mode widths. Linear mixing length estimates and renormalized turbulence theory are used to determine the ion thermal diffusivity in both cases. In both cases, a strong favorable dependence of ion thermal diffusivity on Bp (and hence plasma current) is exhibited. Furthermore, the ion thermal diffusivity for long wavelength modes exhibits favorable density scaling. The possible role of neoclassical ion temperature-gradient-driven modes in edge fluctuations and transport in L-phase discharges and the L to H transition is discussed.
Anomalous decay of Langmuir turbulence
Authors: Benford Gregory , Zhai Xiaoling , Levron David
Published: July 2002

A Stark effect diagnostic yields measurements of the electric field distribution of Langmuir waves, P(E), in beam–plasma turbulence. When the destabilizing beam abruptly cuts off, the form of P(E)∝ exp(−E2) discovered earlier persists, with amplitude decaying exponentially in a microsecond. Strong fields last much longer than other time scales in strong turbulence theory. Exponential decay disagrees with recent power law scalings deduced from cascade theory. A possible explanation envisions Langmuir energy persisting at long wavelengths, slowly coalescing around nucleation density wells left by previous, ‘‘burnt-out’’ solitons.
Experimental investigations of second-harmonic spectra and Langmuir wave collapse
Authors: Dahmani Faiz , Ghobrini Djamel , EL-Mahdaoui Malek
Published: July 2002

Two kinds of experimental results obtained from time-resolved second-harmonic spectra for 1.06 μm laser-produced plasma are presented. At moderate laser intensities (≤2×1014 W/cm2) the results are explained with parametric and electron decay instabilities. Whereas, at high laser intensities (≥6×1014 W/cm2) the Langmuir strong turbulence is used to explain experimental results. In addition to results obtained by Briand et al. [Phys. Fluids B 2, 160 (1990)], a second sequence of collapses is observed.
Analytic study of the sideband instability in free electron laser oscillators
Authors: Riyopoulos Spilios
Published: July 2002

The steady-state distribution of a bunched electron beam in a resonator with a large-amplitude carrier signal is obtained self-consistently and for arbitrary injected distribution. It is then employed to analyze the stability of operation for free electron laser (FEL) oscillators fed by a continuous electron beam. The dielectric response to small perturbations (sidebands) includes the nonuniformity from the aperiodic beam bunching and the cross-coupling among symmetric upper and lower sidebands caused by the unharmonic (nonlinear) nature of the trapped particle trajectories. The dominant contribution comes from resonances of the sideband frequency detuning δ=‖ωs−ω0‖ with harmonics of the Doppler-upshifted synchrotron (bounce) frequency ωb, δ≂2γ2znωb. The instability is triggered by the gradients, both across, ∂F/∂J, and around, ∂F/∂θ, the bunched beam distribution F(J,θ), where the action J parametrizes the distance from, and θ, the angle around, the center of the trapped particle island. When the wiggler length becomes much longer than the synchrotron period, the contribution from the nonuniformity around θ phase mixes to zero; one then recovers the results for a FEL amplifier [Phys. Fluids 31, 1708 (1988)]. It is also shown that when the nonlinear shift of the carrier frequency is considerable, upper and lower sidebands decouple, because symmetric sideband frequencies correspond to asymmetric wave numbers.
Brillouin limit in cylinders and torus with shaped cross sections
Authors: Avinash K. , Bhattacharyya S. N.
Published: July 2002

The Brillouin limit for non-neutral plasma is calculated in cylindrical and toroidal traps with shaped cross section. In particular, the effect of ellipticity and D-shaping is considered. Perturbative solutions of equilibrium equations are constructed in powers of inverse aspect ratio. It is found that ellipticity and D-shaping both enhance the storage efficiency and Brillouin limit of cylindrical traps. In case of toroidal traps it is found that the ellipticity enhances the storage efficiency. The D-shaping also enhances the storage efficiency provided the vertex of the D shape is toward the major axis.
Alpha-Alfvén local dispersion relation and solutions
Authors: Hedrick C. L. , Leboeuf J.-N. , Spong D. A.
Published: July 2002

The local dispersion relation for shear and kinetic Alfvén waves is derived for arbitrary alpha particle distribution functions and analyzed for a set of representative distribution functions. Including both the velocity dependence of magnetic drift and temperature gradients is found to have the most striking effect on the partial growth rate associated with alpha particles for shear Alfvén waves. Parallel electric field effects are included and found to make significant changes in the damping associated with electrons and ions. The formalism parallels that used in reduced magnetohydrodynamics, so that it can be readily extended to calculations incorporating more detailed and realistic equilibrium geometry.
Nonlinear evolution of resistive tearing mode instability with shear flow and viscosity
Authors: Ofman L. , Morrison P. J. , Steinolfson R. S.
Published: July 2002

The nonlinear evolution of the tearing mode instability with equilibrium shear flow is investigated via numerical solutions of the resistive magnetohydrodynamic (MHD) equations. The two-dimensional simulations are in slab geometry, are periodic in the x direction, and are initiated with solutions of the linearized MHD equations. The magnetic Reynolds number S was varied from 102 to 105, a parameter V that measures the strength of the flow in units of the average Alfvén speed was varied from 0 to 0.5, and the viscosity as measured by the Reynolds number Sν satisfied Sν≥103. When the shear flow is small (V≤0.3) the tearing mode saturates within one resistive time, while for larger flows the nonlinear saturation develops on a longer time scale. The two-dimensional spatial structure of both the flux function and the streamfunction distort in the direction of the equilibrium flow. The magnetic energy release decreases and the saturation time increases with V for both small and large resistivity. Shear flow decreases the saturated magnetic island width, and generates currents far from the tearing layer. The validity of the numerical solutions was tested by verifying that the total energy and the magnetic helicity are conserved. The results of the present study suggest that equilibrium shear flow may improve the confinment of tokamak plasma.
Toroidal drift mode stability in a contaminated plasma
Authors: Jarmén A. , Fröjdh M.
Published: July 2002

Toroidal drift mode features and stability are studied, using a fluid description, for a plasma with two ion species: impurity and main ions. Impurity and main ion temperature gradient (ITG) modes dominate for larger temperature gradients, ηi≳1, while dissipative trapped electron (DTE) and impurity-induced modes are present also for ηi<1. Simple analytical expressions for the stability thresholds are derived from conditions given by the impurity and main ion fluids.
Stochastic transport of MeV ions by low-n magnetic perturbations*
Authors: Mynick H. E.
Published: July 2002

Recent progress toward understanding two transport phenomena of importance to fusion reactors is described, in the framework of a theory of the stochastic transport of energetic ions in low-frequency, low-n perturbations. These are the observed enhancement of fusion product loss by magnetohydrodynamic (MHD) perturbations, and a new possible mechanism for ash removal and burn control. Significant features of the theory bearing on both problems are the variety of transport scalings with energy possible from perturbations of differing structure, and the contribution to the transport from perturbing ‘‘grad-B’’ drifts, neglected in earlier studies, but that can be dominant for MeV ions. Numerical evidence is presented substantiating these analytic expectations. The transition from above to below the global stochastic threshold, and some remaining disparities between experimental observations and numerical/theoretical results, are discussed.
The magnetoacoustic cyclotron instability of an extended shell distribution of energetic ions
Authors: Dendy R. O. , Lashmore-Davies C. N. , Kam K. F.
Published: July 2002

The magnetoacoustic cyclotron instability is a mechanism by which waves on the perpendicular fast Alfvén-ion Bernstein branch can be excited through cyclotron resonance with an energetic ion population. It is a candidate emission mechanism for the superthermal ion cyclotron radiation, apparently associated with the products of fusion reactions, that has been observed from tokamak plasmas. In the present paper, an extended shell model is adopted for the energetic ion distribution function, fα(v)∼nα exp[−(v−v0)2/vT2]. An analytical formulation of the dispersion relation is obtained, whose numerical solution yields quantitative information on the role of vT in stabilizing wave growth at ion cyclotron harmonics. The results show that, for typical plasma parameters of interest, the degree of instability is significantly depressed, relative to its level for vT=0, once vT/v0≂0.1. Gaps appear in typical multiple cyclotron harmonic excitation patterns for 0.1≤vT/v0≤0.2, and most harmonics are stable for vT/v0≥0.25. Thus the energetic ion shell-driven magnetoacoustic cyclotron instability typically occurs only when the shell is relatively narrow in velocity space.
Macroscopic behavior and discrete dynamo in high-Θ reversed-field pinch discharges
Authors: Arimoto H. , Nakamura A. , Sato K. I. , Nagata A. , Ando T. , Kubota S. , Masamune S. , Nagatsu M. , Tsukishima T.
Published: July 2002

The magnetohydrodynamic (MHD) activity and the discrete dynamo in high-Θ reversed-field pinch (RFP) discharges are studied through comparisons with those in normal-Θ RFP discharges, where Θ=Bθ(a)/〈Bz〉 is the pinch parameter. In high-Θ RFP discharges, the mode coupling of m=1 is enhanced by the high magnetic shear configuration, and the MHD activity is more turbulent as compared with that in normal-Θ RFP discharges. Furthermore, the discrete increase of the toroidal magnetic flux is obviously observable. The increase of the toroidal magnetic flux generated by the discrete dynamo, which has an asymmetric structure in the toroidal direction, is only 1%–2% of the whole toroidal magnetic flux. The experimental results indicate that the discrete dynamo does not play an essential role in the RFP dynamo.
Experimental and computational equilibria of field-reversed configurations
Authors: Spencer R. L. , Tuszewski M.
Published: July 2002

Experimental measurements on the field-reversed configurations produced in the FRX-C device (Plasma Phys. 26, 991 (1984)]are compared to corresponding measurements on numerically computed magnetohydrodynamic equilibria. Good agreement between experiment and theory is obtained for magnetohydrodynamic (MHD) equilibria with separatrix betas of about 0.6. The experimental measurements indicate that the separatrix is more elliptical and that the flux surfaces are distributed more gently in the axial direction than in the equilibria computed previously. A sharp spike in dp/dψ at the separatrix is found to produce computed equilibria similar to those observed experimentally. The effect of end mirrors and toroidal field on equilibrium properties is also discussed.
Nonlinear slowly varying finite depth standing waves
Authors: Roskes G. J.
Published: July 2002

Nonlinear, slowly-varying, finite-depth standing waves over a flat bottom are shown to exhibit sideband instabilities at third order when the depth parameter h is larger than 1.022.
Collapse and amplification of a vortex filament
Authors: Siggia Eric D.
Published: July 2002

A single filament with a variable core size parameter is used to model how a vortex tube breaks down in the Euler equations. The first singularity is a self-similar collapse which brings two antiparallel pieces of filament together at a point. This pairing then quickly encompasses a finite fraction of the initial data and the arclength begins to grow faster than exponential. A local model should exist which would allow one to understand the stage of rapid stretching in terms of simpler processes.
Compressibility as a feature of field reversal maintenance in the reversed-field pinch
Authors: Aydemir A. Y. , Barnes D. C. , Caramana E. J. , Mirin A. A. , Nebel R. A. , Schnack D. D. , Sgro A. G.
Published: July 2002

Five different codes have been used to simulate the identical problem in reversed-field pinch (RFP) dynamics using the resistive magnetohydrodynamic (MHD) model in three dimensions with the same set of initial and boundary conditions. Three codes are compressible, while two are incompressible. The assumption of incompressibility was made in the spirit of reducing the model so that, for example, the codes would run faster while retaining the relevant physics. The results show that the three compressible codes agree quite well with each other and the two incompressible codes agree with each other also, but the compressible and incompressible models show qualitatively different behavior. Most importantly, for a certain set of boundary and initial conditions, the compressible codes predict field reversal maintenance while the incompressible codes do not. Thus compressibility is an important feature of RFP physics. This is in contrast to tokamak physics where the strong toroidal field enforces incompressibility at low poloidal beta.
Relativistically covariant warm charged fluid beam modeling
Authors: Amendt Peter , Weitzner Harold
Published: July 2002

A relativistically covariant moment description of the relativistic Vlasov equation is presented and is applied to a warm charged particle beam. Two truncation schemes of the moment equations are proposed yielding models that are distinct both mathematically and physically. The first simply neglects the heat flow tensor S μνλ and recovers what is essentially the model of Newcomb. The distinctions between Newcomb’s formulation and the formulation presented in this paper are described. The second method incorporates fully one of the relativistic constraints on the moments and assumes S μνλ nonzero, but no fourth moments are introduced. The first leads to a hyperbolic system of partial differential equations, whereas the second is partially elliptic and partially hyperbolic. Thus, although the second system appears better on physical grounds, it leads to a mathematically ill-posed system and cannot be used. The second model is rejected. The first system is used to analyze anew the Bennett pinch and space-charge neutral steady flows. It is found that the usual assumptions regarding particular elements of the pressure tensor Θij are incomplete and require modification. For the nonrotating and rigidly rotating Bennett pinch steady flows, it is found that the beam rest frame pressure tensor is diagonal if and only if all of the diagonal elements are equal. Only when the axial and radial pressures are equal can one invoke the standard assumption of isotropy in a plane perpendicular to the axial guide magnetic field. For rigidly rotating space-charge neutral steady flows, the same conclusion holds but now from the perspective of the laboratory frame. For both types of steady flows in the case of rotational shear, Θij is generally nondiagonal and anisotropic in the respective reference frames. An arbitrary warm beam steady flow must satisfy the constraints imposed by the generalized ‘‘equations of state’’ given in this paper in order to be physically legitimate.
Trapped particle destabilization of the internal kink mode
Authors: White R. B. , Chen L. , Romanelli F. , Hay R.
Published: July 2002

The internal kink mode is destabilized by trapped high-energy particles, leading to a new branch of the internal kink dispersion relation with a real frequency near the average trapped-particle precession frequency and a growth rate of the same magnitude. This trapped particle branch of the dispersion relation is investigated numerically for a variety of particle distributions. Mode growth rate and frequency is found as a function of plasma β, density, and trapped-particle energy and distribution. The high-energy trapped particle sources considered are neutral beam injection, ion-cyclotron heating, and fusion alpha particles. Relevance for various plasma heating schemes is discussed.
The dynamo effect in fusion plasmas
Authors: Strauss H. R.
Published: July 2002

A set of reduced magnetohydrodynamic equations for mean and fluctuating fields is derived and applied to the dynamo effect in reversed field pinch (RFP) and tokamak plasmas. There are two dynamo effects, the first arising from mean field equilibrium, and the second from the fluctuations. The dynamo effect does not drive a net current in steady state. The quasilinear dynamo caused both by growing and stationary tearing modes is calculated and found to be consistent with field reversal in RFP’s. Numerical solutions of the equations are presented, which are in qualitative agreement with experiment and other computations.
Magnetohydrodynamic equilibrium and stability of rotating field-reversed configurations with excluded multipole fields
Authors: Spencer R. L. , Tuszewski M.
Published: July 2002

The rotational instability in field-reversed configurations (FRC’s) is observed experimentally to be suppressed by the application of multipole fields. In this paper the equilibrium and stability of a FRC with multipole fields that do not penetrate into the plasma are studied. It is shown that two rotating magnetohydrodynamic (MHD) equilibria are possible for a long FRC in a multipole field. One is nearly circular while the other is cusp shaped. Experiments and hybrid simulations indicate that cusp-like equilibria are usually obtained. The effect of helical multipole fields on the equilibrium is also discussed. The stability of such a configuration has been previously studied by using the MHD model on a circular plasma and by using a hybrid simulation code. In the important quadrupole case, the two calculations disagree: the simulation shows that the mode is stabilized while the circular MHD calculation predicts that it remains unstable. A close look at the MHD calculation shows that stability is strongly influenced by the shape of the equilibrium. Simple estimates indicate that the cusp-like equilibrium should be more stable than the circular one.
Microstability properties of the sheath region of a field-reversed configuration
Authors: Gladd N. T. , Sgro A. G. , Hewett D. W.
Published: July 2002

An analysis of the microstability properties of the sheath region of a field-reversed configuration is performed. Attention is focused on the lower-hybrid-drift instability, a mode known to be important in devices with similar parametric conditions. This mode is thought to play a significant role in determining the confinement properties of a field-reversed configuration. Specifically, a model profile characteristic of the sheath region is constructed and analyzed in detail, both theoretically, by means of a nonlocal kinetic theory, and computationally, by means of a hybrid simulation technique. The lower-hybrid-drift is found to be unstable under typical sheath conditions. The theoretically predicted growth rate and the variation of the growth rate with wavenumber is found to be in good agreement with the growth characteristics deduced from the simulation. By means of the hybrid simulation technique, the lower-hybrid-drift has been simulated at drift velocities as low as 0.2vi with mi/me =100 and 0.3vi with mi/me =3672.
Toroidally linked mirrors
Authors: Strauss H. R. , Friedland L. , Kishinevsky M.
Published: July 2002

Mirrors linked by toroidal segments may be stabilized by ponderomotive force produced by electromagnetic waves at the ion-cyclotron frequency. This may provide a simple alternative to tandem mirrors and bumpy tori. Approximate calculations of equilibrium, stability, and diffusion are given.
Magnetic flux trapping during field reversal in the formation of a field-reversed configuration
Authors: Steinhauer Loren C.
Published: July 2002

The flow of plasma and magnetic flux toward a wall is examined in a slab geometry where the magnetic field is parallel to the wall. Magnetohydrodynamic (MHD) flow with a quasisteady approximation is assumed that reduces the problem to three coupled ordinary differential equations. The calculated behavior shows that a thin current sheath is established at the wall in which a variety of phenomena appear, including significant resistive heating and rapid deceleration of the plasma flow. The sheath physics determines the speed at which flux and plasma flow toward the wall. The model has been applied to the field-reversal phase of a field-reversed theta pinch, during which the reduced magnetic field near the wall drives an outward flow of plasma and magnetic flux. The analysis leads to approximate expressions for the instantaneous flow speed, the loss of magnetic flux during the field reversal phase, the integrated heat flow to the wall, and the highest possible magnetic flux retained after reversal. Predictions from this model are compared with previous time-dependent MHD calculations and with experimental results from the TRX-1 [Proceedings of the 4th Symposium on the Physics and Technology of Compact Toroids, 27–29 October 1981 (Lawrence Livermore National Laboratory, Livermore, CA, 1982), p. 61] and TRX-2 [Proceedings of the 6th U.S. Symposium on Compact Toroid Research, 20–23 February, 1984 (Princeton Plasma Physics Laboratory, Princeton, NJ, 1984), p. 154] experiments.
Helical and straight quadrupole stabilization of the n=2 rotational instability in translated field-reversed configurations
Authors: Rej D. J. , Armstrong W. T. , Barnes G. A. , Chrien R. E. , Hugrass W. N. , Klingner P. L. , McKenna K. F. , Siemon R. E. , Tuszewski M. , Harned Douglas S.
Published: July 2002

The n=2 rotational instability has been completely suppressed on translated field-reversed configurations (FRC’s) in the FRX-C/T device [Phys. Fluids 29, 852 (1986)] by the application of either helical or straight quadrupole fields. Quadrupole field thresholds approximately equal to 7% and 9% of the external confinement field are required for stabilization with straight and helical coils, respectively. Comparisons with linearized magnetohydrodynamic (MHD) theory and 2 1/2 -dimensional hybrid simulations are made. The influence of quadrupoles on translation and plasma confinement is also reported.
One-dimensional transport models with local and nonlocal lower-hybrid-drift waves in field-reversed configurations
Authors: Hamasaki S. , Gladd N. T. , Krall N. A.
Published: July 2002

The one-dimensional transport theory for field-reversed configurations has been reexamined taking into account global lower-hybrid-drift turbulence. Extending previous work for nonlocal electrostatic lower-hybrid-drift theory, the spatial character of lower-hybrid-drift eigenmodes have been determined in the separatrix region of a field-reversed configuration. Surprisingly, it has been found that the transport model based on the more comprehensive ‘‘global’’ theory of the lower-hybrid-drift theory results in transport coefficients which are very similar to those based on the simple ‘‘local’’ lower-hybrid-drift theory. The reason for this is as follows. The nonlocal theory of the lower-hybrid-drift predicts a sequence of eigenmodes with differing eigenvalues and spatial extent. It is found that if a particular eigenmode is considered and the radial points which mark its radial extent are noted, then the eigenfrequency and growth rate associated with that eigenmode will have approximately the same value as the frequency and the growth rate naively calculated on the basis of the local conditions at the radial edges of the eigenmode.
Plasma stability of a nearly spherical field-reversed configuration
Authors: Nakata Shuhei , Sekiguchi Tadashi , Seki Hirohumi , Yamamoto Kouji
Published: July 2002

A nearly spherical field-reversed configuration (FRC) is created by employing a combination of a double-cusp bias magnetic field and laser-produced plasma, and its plasma stability is studied. The FRC equilibrium configuration is found to last for 20–25 μsec, which is not determined by any plasma instability in the present experiment and is estimated to be longer than the Alfvén time by a factor of more than 40. That is, the occurrence of neither the n=2 rotational instability nor the active magnetohydrodynamic (MHD) (tilting) mode is observed during this time period. The stabilization of the rotational mode may be attributed to the effect of magnetic field line bending. Although the exact reason for stabilizing the tilting mode is not known, it has become clear that the geometry of an equilibrium FRC has no significant effect on its stability, based upon comparison with the other experimental results obtained thus far from theta-pinch-based FRCs with a very elongated cross section. It is suggested that the ion kinetic, nonadiabatic effect may be largely responsible for this stability.
Two-dimensional drift vortices and their stability
Authors: Laedke E. W. , Spatschek K. H.
Published: July 2002

Drift vortices in plasmas described by the Petviashvili equation in the case of strong temperature inhomogeneities or by the Hasegawa–Mima equation in the case of density gradients are investigated. Both equations allow for two-dimensional vortex solutions. The models are reviewed and the forms of the vortices are discussed. In the temperature-gradient case, the stationary solutions are only known numerically, whereas in the density gradient case analytical expressions exist. The latter are called modons; here the ground states are investigated. The result of a stability calculation is that both types of two-dimensional solutions, for the Petviashvili equation as well as the Hasegawa–Mima equation, are stable. The methods used to prove this result are either direct (constructing Liapunov functionals) or indirect, and then based on variational principles.
A search for lower-hybrid-drift fluctuations in a field-reversed configuration using CO2 heterodyne scattering
Authors: Carlson Arthur W.
Published: July 2002

An upper bound of (ñe/ne) <10−4 for frequencies and wavenumbers relevant to the lower-hybrid-drift (LHD) instability is set on fluctuations in field-reversed configurations (FRC’s) produced by TRX-2 [Fusion Techn. 9, 48 (1986)]. LHD is a well-studied microinstability that is often invoked to explain particle loss rates in FRC’s. The conventional technique of CO2 laser scattering with heterodyne detection is here modified to compensate for severe refraction. The calibration of the system is verified by scattering from acoustic waves in salt. The measured bound is two orders of magnitude below both the fluctuation level usually predicted and the level needed to account for observed particle loss rates. Electron collisionality is identified as the most likely LHD stabilization mechanism. Some alternative explanations of anomalous loss rates are discussed.
Anchor stabilization of trapped particle modes in mirror machines
Authors: Berk H. L. , Roslyakov G. V.
Published: July 2002

It is shown that for trapped particle modes in tandem mirrors, the pressure of the passing particles in the anchor region introduces a stabilizing term proportional to the sum of the anchor’s field line curvature and total diamagnetic pressure gradient. The theory is applied to the proposed gas dynamic trap experiment.
Field-reversed configuration profiles and resistivities inferred from the radial line-integral density profile
Authors: Chrien R. E. , Okada S.
Published: July 2002

The beta and magnetic field profiles of field-reversed configurations (FRC’s) can be inferred from the radial profile of the line-integral density together with a temperature model. When these profiles are combined with the particle and flux decay times, the plasma resistivities at the field null and separatrix can also be deduced. This method is applied to a class of FRC’s formed in the FRX-C/LSM device [in Proceedings of the Seventh US–Japan Workshop on Compact Toroid Research, 1985 (Spectra Technology, Inc., Bellevue, WA, 1985), p. 33; in Plasma Physics and Controlled Nuclear Fusion Research, 1986 (IAEA, Vienna, 1986), Vol. 2, p. 673]. The inferred beta profile shows an average beta that is larger than expected for elongated FRC equilibria in a straight coil, indicating that the FRC equilibrium is influenced by the mirror fields at the ends of the coil. The resistivity at the separatrix is consistent with classical plus lower hybrid drift resistivity, while the resistivity at the field null is anomalous and larger than that at the separatrix by about a factor of 3.
Influence of impurities on the plasma parameters and stability of a field-reversed configuration
Authors: König R. , Kolk K.-H. , Kunze H.-J.
Published: July 2002

Atoms of solid elements were injected into a theta-pinch discharge from both coil ends shortly before the start of the preionization discharge by a ruby-laser driven ablation from solid targets. The ablation process itself and the subsequent distribution of the impurities during the different stages of the discharge were studied experimentally as well as theoretically. The injection of aluminum from only one coil end resulted in an axial drift of the whole field-reversed configuration (FRC) at 5 cm/μsec. By injecting it from both ends it was again possible to keep the whole plasma configuration stable in the coil’s midplane but at a reduced equilibrium plasma length. Small changes in the plasma parameters of the FRC were observed that are interpreted to be the consequence of a better ionization of the initial plasma and of a delay in the highly dynamic reconnection process. This delay is most probably caused by the increased mass density of the plasma.
Exponential Taylor states in circular cylinders
Authors: Schaffer Michael J.
Published: July 2002

Solutions to the Woltjer–Taylor relaxed plasma equation ∇×B=μB, with μ a constant, inside an infinitely long, circular cylinder with magnetically impermeable walls and no net axial magnetic flux, are obtained for complex k, where modal spatial dependence is exp i(mθ−kz). Complex k yields the continuum of externally driven states between μ=0 (currentless) and the finite ‖μ‖ free-states. The continuum states are related to formation of plasma from magnetized electrode sources.
The structure of the sideband spectrum in free electron lasers
Authors: Riyopoulos S. , Tang C. M.
Published: July 2002

The one-dimensional, fast time averaged Hamiltonian is derived in a free electron laser (FEL) for electrons passing through a constant parameter wiggler and a radiation field. The exact unperturbed orbits without sidebands are obtained for all particles and arbitrary strength of the main signal. Integration, in action-angle variables, of the linearized kinetic equation with perturbing sidebands over the unperturbed orbits yields the sideband growth rate including both trapped and untrapped particles. The structure and scaling of the unstable spectrum are different from previous results obtained for electrons localized at the bottom of the ponderomotive well. It is found that upper and lower sidebands that are symmetric relative to the FEL frequency have opposite growth rates. There is no differentiation in the magnitude of the gain between upper and lower sidebands. The stability is determined by the sign of df0/dωb, the relative population of quantized oscillators with energy quantum ℏωb, where ωb is the synchrotron frequency in resonance with the sideband. The shear dωb/dJ, where J is the action variable, is stabilizing and distributions with gradients df0/dJ localized near the separatrix have the minimum growth rates.
Nonlinear dynamics of tearing modes in the reversed field pinch
Authors: Holmes J. A. , Carreras B. A. , Diamond P. H. , Lynch V. E.
Published: July 2002

The results of investigations of nonlinear tearing-mode dynamics in reversed field pinch plasmas are described. The linear instabilities have poloidal mode number m=1 and toroidal mode numbers 10≲n≲20, and the resonant surfaces are therefore in the plasma core. The nonlinear dynamics result in dual cascade processes. The first process is a rapid m=1 spectral broadening toward high n, with a simultaneous spreading of magnetic turbulence radially outward toward the field-reversal surface. Global m=0 perturbations, which are driven to large amplitudes by the m=1 instabilities, in turn trigger the m=1 spectral broadening by back coupling to the higher n. The second process is a cascade toward large m and is mediated by m=2 modes. The m=2 perturbations have the structure of localized, driven current sheets and nonlinearly stabilize the m=1 modes by transferring m=1 energy to small-scale dissipation. The calculated spectrum has many of the qualitative features observed in experiments.
Hydrodynamic instability in an ablatively imploded target irradiated by high power green lasers
Authors: Nishimura H. , Takabe H. , Mima K. , Hattori F. , Hasegawa H. , Azechi H. , Nakai M. , Kondo K. , Norimatsu T. , Izawa Y. , Yamanaka C. , Nakai S.
Published: July 2002

Time evolution of the ablation front displacement between concave and convex regions of a surface corrugated spherical target was observed by flash x-ray radiography. The results are compared with calculations based on the linearized fluid equation combined with a one-dimensional simulation to describe the ambient fluid motion. In the analysis, perturbation of the fluid is scaled up to kδ∼2π (k is the perturbation wavenumber and δ is the perturbation amplitude) for the acceleration phase with perturbation mode numbers of l=20 and 30. The practical perturbation of the target requires a relaxation time to form the nominal eigenstate of the Rayleigh–Taylor instability, which results in time delay of instability growth onset.
Hydrodynamic simulations of bubble collapse and picosecond sonoluminescence
Authors: Moss William C. , Clarke Douglas B. , White John W. , Young David A.
Published: July 2002

Numerical hydrodynamic simulations of the growth and collapse of a 10 μm air bubble in water were performed. Both the air and the water are treated as compressible fluids. The calculations show that the collapse is nearly isentropic until the final 10 ns, after which a strong spherically converging shock wave evolves and creates enormous temperatures and pressures in the inner 0.02 μm of the bubble. The reflection of the shock from the center of the bubble produces a diverging shock wave that quenches the high temperatures (≳30 eV) and pressures in less than 10 ps (full width at half maximum). The picosecond pulse widths are due primarily to spherical convergence/divergence and nonlinear stiffening of the air equation of state that occurs at high pressures. The results are consistent with recent measurements of sonoluminescence that had optical pulse widths less than 50 ps and 30 mW peak radiated power in the visible.
Observations of a cavitation bubble interacting with a solid boundary as seen from below
Authors: Jin Y. H. , Shaw S. J. , Emmony D. C.
Published: July 2002

We present a schlieren photographic sequence of a laser generated cavity in water interacting with a solid boundary as seen from the boundary’s perspective looking through the bubble. Previous studies have photographed the collapsing bubble from the side and it is unclear from these photographs once a bubble becomes toroidal how the central hole develops. Our schlieren sequence displays the jet first penetrating the lower bubble surface and then follows the evolution of the central channel as the bubble contracts and reexpands. It is felt that the bubble shapes recorded add further knowledge to the possible damage mechanisms of cavitation.
Thermocapillary mobility of a suspension of droplets in a fluid
Authors: Felderhof B. U.
Published: July 2002

The effective thermocapillary mobility of a suspension of viscous, heat conducting droplets in a fluid of different shear viscosity and thermal conductivity is studied in the framework of the theory of linear transport coefficients of heterogeneous media. The fluid velocity and the temperature field are combined conveniently into a single four-vector field. This allows a multiple scattering analysis and calculation of the thermocapillary mobility in terms of a renormalized cluster expansion. A mean field result is derived that reduces to the Clausius-Mossotti formula in the case of bubbles. Correlation corrections are calculated in pair approximation.
The viscous modulation of Lamb’s dipole vortex
Authors: van de Fliert B. W.
Published: July 2002

A description of the adiabatic decay of the Lamb dipolar vortex is motivated by a variational characterization of the dipole. The parameters in the description are the values of the entrophy and linear momentum integrals, which change in time due to the dissipation. It is observed that the dipole dilates during the decay process [radius R∼(νt)1/2], while the amplitude of the vortex and its translation speed diminish in time proportional to (νt)−3/2 and (νt)−1.
Effect of viscosity on the stability of an interface subjected to high-frequency magnetic fields
Authors: Ramos Antonio , Castellanos Antonio
Published: July 2002

Natural frequencies and stability criterion for an interface between a liquid metal and an insulating gas subjected to a parallel alternating magnetic field are obtained, with particular attention to the influence of the small viscosity of the liquid metal. The governing equations are derived under the assumption of small magnetic Reynolds number and the neglect of thermal effects. Results indicate that when the liquid metal is above the insulating gas the viscous-magnetic terms may play the role of a negative viscosity, leading to overstability close to the nonviscous critical solution of Rayleigh–Taylor type. Thus, the criterion of stability changes. Apart from this region of overstability the natural frequencies of the nonviscous and viscous solutions are very similar, the changes being of the order of the nondimensional viscosity. Similarly, the velocity perpendicular to the interface does not deviate appreciably from the nonviscous solution. On the contrary, the tangential velocity differs markedly from the nonviscous solution.
Non-continuum anomalies in the apparent viscosity experienced by a test sphere moving through an otherwise quiescent suspension
Authors: Almog Y. , Brenner H.
Published: July 2002

A comparison is made of the ‘‘apparent viscosity’’ (as defined by Stokes law) between two different cases of a test sphere moving slowly through an unbounded, otherwise quiescent, globally homogeneous, dilute suspension of identical, neutrally buoyant spherical particles dispersed in an incompressible Newtonian liquid. In case I the force on the test sphere is maintained constant for all time (and the torque-free sphere allowed to rotate) — corresponding to the so-called ‘‘falling ball’’ case — and its instantaneous velocity allowed to vary with proximity to each suspended sphere encountered during its trajectory; in case II the non-rotating test sphere is towed with a uniform (instantaneous) velocity through the suspension and the force experienced by it allowed to vary with proximity to each suspended sphere. Allowing for two-body hydrodynamic interactions between the ball and a suspended particle, the ensemble-average velocity of the test sphere is calculated in case I and ensemble-average force in case II, and Stokes law used to calculate the apparent viscosity of the suspension from the ensemble-averaged, linear force/velocity ratio obtained. In each case the ‘‘apparent suspension viscosity’’ coefficient attains, as expected, the limiting, continuum, Einstein value of 2.5 when the test sphere is much larger than the freely suspended particle. However, in the case of disparate relative sizes, the apparent viscosity is found to be significantly larger in case II than in case I. The difference arises from the locally inhomogeneous nature of the suspension and points up a fundamental non-continuum aspect of suspension behavior above and beyond the expected test/suspended-sphere size ratio ‘‘Knudsen’’ non-continuum effect.
Kolmogorov flow in three dimensions
Authors: Shebalin John V. , Woodruff Stephen L.
Published: July 2002

A numerical study of the long-time evolution of incompressible Navier-Stokes turbulence forced at a single long-wavelength Fourier mode, i.e., a Kolmogorov flow, has been completed. The boundary conditions are periodic in three dimensions and the forcing is effected by imposing a steady, two-dimensional, sinusoidal shear velocity which is directed along the x-direction and varies along the z-direction. A comparison with experimental data shows agreement with measured cross-correlations of the turbulent velocity components which lie in the mean-flow plane. A statistical analysis reveals that the shear-driven turbulence studied here has significant spectral anisotropy which increases with wave number.