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Jul 1988

Volume 31, Issue 7, pp. 1835-2056

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Particle image displacement velocimetry measurements of a three‐dimensional jet

L. Lourenco and A. Krothapalli

Phys. Fluids 31, 1835 (1988); http://dx.doi.org/10.1063/1.866679 (3 pages) | Cited 4 times

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A whole field experimental technique, commonly referred to as particle image displacement velocimetry (PIDV), is used for the measurement of the instantaneous two‐dimensional velocity fields in the transition region of a three‐dimensional jet issuing from a rectangular nozzle with aspect ratio 4. The experiments were performed using an air jet at a Reynolds number based on the hydraulic diameter of 3600. The rollup of the laminar shear layer into vortices and their subsequent interactions are examined.
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47.27.W- Boundary-free shear flow turbulence
47.80.-v Instrumentation and measurement methods in fluid dynamics

Weak solutions of the three‐dimensional vorticity equation with vortex singularities

G. Winckelmans and A. Leonard

Phys. Fluids 31, 1838 (1988); http://dx.doi.org/10.1063/1.866680 (2 pages) | Cited 4 times

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The use of a modified scheme for the dynamics of vortex singularities is shown to lead to a weak solution of the three‐dimensional inviscid incompressible vorticity equation.
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47.32.Ef Rotating and swirling flows
47.10.-g General theory in fluid dynamics

The effective thermal conductivity and elongational viscosity of a nondilute suspension of aligned slender rods

Andreas Acrivos and E. S. G. Shaqfeh

Phys. Fluids 31, 1841 (1988); http://dx.doi.org/10.1063/1.866681 (4 pages) | Cited 13 times

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The effective thermal conductivity and elongational viscosity of a nondilute suspension of infinitely conducting perfectly aligned slender rods of slenderness ratio ϵ≪1 are determined using an effective medium theory together with a self‐consistent scheme. The expressions thereby obtained cover the range in particle concentration c from infinite dilution c2≪1, to the semidilute regime, c2≫1, but c≪1. In the latter case, the present results agree to leading order with a formula derived by Batchelor [J. Fluid Mech. 46, 813 (1971)] even though the analyses employ physical arguments that appear to be quite distinct.
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47.55.Kf Particle-laden flows
51.10.+y Kinetic and transport theory of gases
66.10.C- Diffusion and thermal diffusion
47.10.-g General theory in fluid dynamics

Nonlinear growth of Kelvin–Helmholtz instability: Effect of surface tension and density ratio

R. H. Rangel and W. A. Sirignano

Phys. Fluids 31, 1845 (1988); http://dx.doi.org/10.1063/1.866682 (11 pages) | Cited 42 times

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The nonlinear evolution of initially small disturbances at an interface separating two fluids of different density and velocity, including surface tension effects, is investigated with the use of the vortex‐sheet discretization approach. The location of the interface is tracked in time by following the motion of each vortex under the combined influence of all other vortices. The influence of surface tension and density discontinuity is incorporated in an equation governing the evolution of the circulation of each vortex. Increasing the surface tension or the density ratio is shown to reduce the growth of the disturbance. For density ratios larger than 0.2 a critical wavenumber exists that divides the unstable part of the spectrum into a region where a vorticity singularity can develop (with interface rollup) and a region where two finite vortical centers are formed (with partial or no rollup). For lower density ratios this bifurcation phenomenon is not observed.
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47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.55.Kf Particle-laden flows
47.20.Dr Surface-tension-driven instability

Density of states of inviscid incompressible two‐dimensional fluid unit disk vortex systems

Darell J. Johnson

Phys. Fluids 31, 1856 (1988); http://dx.doi.org/10.1063/1.866683 (6 pages) | Cited 2 times

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The density of states of discrete line vortex fluids in cylindrical pipes is experimentally determined for low vortex number systems via a Monte Carlo numerical computer simulation calculation. The results indicate that the theoretical results of Pointin and Lundgren [Phys. Fluids 19, 1459 (1976)] are valid for very small vortex number systems.
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47.10.-g General theory in fluid dynamics
05.20.Gg Classical ensemble theory
05.45.-a Nonlinear dynamics and chaos

Experimental studies in vortex pair motion coincident with a liquid reaction

A. R. Karagozian, Y. Suganuma, and B. D. Strom

Phys. Fluids 31, 1862 (1988); http://dx.doi.org/10.1063/1.866684 (10 pages) | Cited 6 times

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An experimental examination of the coincidence of a liquid reaction (acid/base) with the formation of a vortex pair structure is described in which emphasis is placed on the evolution of the strained diffusion layer and reacted core structures. Flow visualization of the reaction process is achieved via the technique of chemically sensitive laser‐induced fluorescence. The observed growth of reacted core structures associated with each vortex is compared with theoretically predicted behavior published recently [Recent Advances in the Aerospace Sciences (Plenum, New York, 1985), p. 395; Combust. Sci. Technol. 49, 185 (1986)]. Vortex pair separation is also compared with theoretical correlations, and the relevance of the analogy between a fast liquid reaction (Sc≫1) and a gaseous reaction (Sc∼1) is discussed.
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47.70.Fw Chemically reactive flows
47.32.Ef Rotating and swirling flows

Stability of swirling gas flows

Lennart S. Hultgren

Phys. Fluids 31, 1872 (1988); http://dx.doi.org/10.1063/1.866685 (5 pages) | Cited 5 times

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The stability of inviscid swirling gas flows to small nonaxisymmetric perturbations is considered. For small Brunt–Väisälä frequencies, the problem reduces to the classical Sturm–Liouville form and the oscillation theorem can be applied. The resulting necessary and sufficient stability condition is compared to various criteria in the literature and a limited numerical study of isothermal rigidly rotating Poiseuille flow. For given azimuthal and axial wavenumbers, it is found numerically that the higher inertial modes become unstable for successively lower Rossby numbers and that this sequence of critical values approaches the theoretical value from above.
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47.20.-k Flow instabilities
47.32.Ef Rotating and swirling flows

Structure of rough‐wall turbulent boundary layers

Promode R. Bandyopadhyay and Ralph D. Watson

Phys. Fluids 31, 1877 (1988); http://dx.doi.org/10.1063/1.866686 (7 pages) | Cited 35 times

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Recent experiments have shown that, in rough‐wall turbulent boundary layers, drag varies systematically with the spanwise aspect ratio λz (span/height) of roughness elements. In this paper, the effect of λz on turbulence structure has been examined. Based on λz, the roughness in a transversely grooved surface (λz≫1) is the opposite extreme of model plant canopies (λz≪1) studied in wind tunnels, whereas sandgrain is an intermediate type [λz=O(1)]. Second‐, third‐, and fourth‐order turbulence moments have been measured in turbulent boundary layers over transversely grooved and smooth surfaces and compared with available turbulence structure measurements over other types of surfaces. The near‐wall turbulence structure is found to vary with λz. The instantaneous motions involved in the flux of shear stress near the wall in smooth and transversely grooved surfaces are opposite in sign to those in three‐dimensional roughness. The former is explained in terms of hairpin vortices alone while the latter group is modeled to have an additional vortex, viz., the so‐called necklace vortex which straddles a three‐dimensional roughness element near its base.
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47.27.N- Wall-bounded shear flow turbulence
47.27.T- Turbulent transport processes
92.60.Fm Boundary layer structure and processes
92.60.hk Convection, turbulence, and diffusion

Model consistency in large eddy simulation of turbulent channel flows

Ugo Piomelli, Parviz Moin, and Joel H. Ferziger

Phys. Fluids 31, 1884 (1988); http://dx.doi.org/10.1063/1.866635 (8 pages) | Cited 115 times

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Combinations of filters and subgrid scale stress models for large eddy simulation of the Navier–Stokes equations are examined by a priori tests and numerical simulations. The structure of the subgrid scales is found to depend strongly on the type of filter used, and consistency between model and filter is essential to ensure accurate results. The implementation of consistent combinations of filter and model gives more accurate turbulence statistics than those obtained in previous investigations in which the models were chosen independently from the filter. Results and limitations of the a priori test are discussed. The effect of grid refinement is also examined.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.N- Wall-bounded shear flow turbulence

Large‐eddy simulations of axisymmetric excitation effects on a row of impinging jets

Magdi H. Rizk and Suresh Menon

Phys. Fluids 31, 1892 (1988); http://dx.doi.org/10.1063/1.866636 (12 pages) | Cited 7 times

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Numerical simulations of a row of impinging jets are performed. Both the impinging jets and the fountains caused by the collision of the wall jets are modeled in the simulation. The problem considered contains the essential features of twin jets impinging on the ground, simulating the hovering configuration of a vertical takeoff and landing (VTOL) aircraft. The flow is assumed to be governed by the time‐dependent, incompressible Navier–Stokes equations. The large‐eddy simulation approach is followed. The present study focuses on the motion and dynamics of large‐scale structures that have been experimentally observed in jet flows. The behavior of the jets and the fountain caused by the introduction of axisymmetric disturbances at the jet exits are investigated.
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47.27.W- Boundary-free shear flow turbulence
02.70.-c Computational techniques; simulations

Direct mode–mode coupling observation in the fluctuations of nonstationary transparent fluid

D. Grésillon and M. S. Mohamed‐Benkadda

Phys. Fluids 31, 1904 (1988); http://dx.doi.org/10.1063/1.866637 (6 pages) | Cited 23 times

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An experimental method by which a given time and space fluctuating medium can be qualified as equilibrium (laminar), or turbulent, is presented. It employs an optical observation to obtain directly the complex amplitude of the space Fourier transform of mass density distribution in a transparent gas. This observation is provided by coherent Rayleigh scattering and heterodyne detection. Several Fourier modes with different wavenumbers and frequencies are observed simultaneously. Their nonlinear quadratic mode–mode coupling is analyzed by using third‐order moment statistics and the full space‐time bispectrum. An experiment using this double (optical and numerical) technique on the air density fluctuations in a round free‐jet is reported. Significant nonlinear coupling is observed in the mixing layer and in the fully developed turbulence zone.
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47.27.T- Turbulent transport processes
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.60.Kz Flows and jets through nozzles

Light‐gasdynamic‐induced refractive index changes and beam propagation in fast‐pumped high‐power photodissociation lasers

K. J. Witte and J. Krug

Phys. Fluids 31, 1910 (1988); http://dx.doi.org/10.1063/1.866638 (12 pages) | Cited 1 time

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In high‐power photodissociation lasers such as the iodine laser, spatially inhomogeneous pump light deposition causes temperature and pressure gradients. These gradients set the gaseous laser medium into motion, thereby changing its density and thus also its refractive index. These perturbations may seriously degrade the laser beam quality. A pulse propagation model is presented, which for the first time incorporates the gasdynamic disturbances in an appropriate manner. Thus any deterioration of the beam quality resulting from gasdynamic effects and diffraction can be precisely evaluated. The model is shown to compare well with experiment. It is also suited for predicting the performance of high‐power amplifier chains.
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42.60.Da Resonators, cavities, amplifiers, arrays, and rings
51.10.+y Kinetic and transport theory of gases
47.70.Fw Chemically reactive flows

Analysis of the interaction terms of the motion of a shock wave due to an intense explosion

M. Yousaf

Phys. Fluids 31, 1922 (1988); http://dx.doi.org/10.1063/1.866639 (8 pages) | Cited 1 time

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In this paper various interactions caused by different types of disturbances behind the shock are examined. The similarity solution of Sedov [Prikl. Mat. Mekh. 10, 241 (1946)] is used to find the five interaction terms at all points of the flow.
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47.40.Nm Shock wave interactions and shock effects
51.10.+y Kinetic and transport theory of gases

Lyapunov stability analysis of magnetohydrodynamic plasma equilibria with axisymmetric toroidal flow

Juan Antonio Almaguer, Eliezer Hameiri, Julio Herrera, and Darryl D. Holm

Phys. Fluids 31, 1930 (1988); http://dx.doi.org/10.1063/1.866640 (10 pages) | Cited 12 times

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Lyapunov stability conditions for ideal magnetohydrodynamic (MHD) plasmas with mass flow in axisymmetric toroidal geometry are determined in the Eulerian representation. Axisymmetric equilibrium solutions of ideal MHD are associated to critical points of a nonlinearly conserved Lyapunov functional consisting of the sum of the total energy and the following flux‐weighted quantities: the circulation along field lines, the angular momentum, the toroidal flux, and the mass content within each flux tube. Conditions sufficient for Lyapunov stability of these equilibria against axisymmetric perturbations are found by taking advantage of the Hamiltonian formalism for ideal MHD. In particular [see Eq. (60)], it is sufficient for Lyapunov stability under linearized dynamics that an axisymmetric equilibrium be subsonic in the appropriate rotating frame, lie in the first elliptic regime of the Bernoulli–Grad–Shafranov (BGS) system of equations, and satisfy one additional, more complicated, condition. Effects of boundary conditions, nonlinearity, and three‐dimensionality on MHD stability are also discussed.
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52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.30.-q Plasma dynamics and flow

Nonlinear gyrokinetic theory for finite‐beta plasmas

T. S. Hahm, W. W. Lee, and A. Brizard

Phys. Fluids 31, 1940 (1988); http://dx.doi.org/10.1063/1.866641 (9 pages) | Cited 134 times

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A self‐consistent and energy‐conserving set of nonlinear gyrokinetic equations, consisting of the averaged Vlasov and Maxwell’s equations for finite‐beta plasmas, is derived. The method utilized in the present investigation is based on the Hamiltonian formalism and Lie transformation. The resulting formulation is valid for arbitrary values of kρi and, therefore, is most suitable for studying linear and nonlinear evolution of microinstabilities in tokamak plasmas as well as other areas of plasma physics where the finite Larmor radius effects are important. Because the underlying Hamiltonian structure is preserved in the present formalism, these equations are directly applicable to numerical studies based on the existing gyrokinetic particle simulation techniques.
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52.25.Dg Plasma kinetic equations
52.35.Ra Plasma turbulence
52.25.Gj Fluctuation and chaos phenomena
52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)

Nonlinear, dispersive, elliptically polarized Alfvén waves

C. F. Kennel, B. Buti, T. Hada, and R. Pellat

Phys. Fluids 31, 1949 (1988); http://dx.doi.org/10.1063/1.866642 (13 pages) | Cited 88 times

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The derivative nonlinear Schrödinger (DNLS) equation is derived by an efficient means that employs Lagrangian variables. An expression for the stationary wave solutions of the DNLS that contains vanishing and nonvanishing and modulated and nonmodulated boundary conditions as subcases is then obtained. The solitary wave solutions for elliptically polarized quasiparallel Alfvén waves in the magnetohydrodynamic limit (nonvanishing, unmodulated boundary conditions) are obtained. These converge to the Korteweg–de Vries and the modified Korteweg–de Vries solitons obtained previously for oblique propagation, but are more general. It is shown there are no envelope solitary waves if the point at infinity is unstable to the modulational instability. The periodic solutions of the DNLS are charcterized.
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52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Sb Solitons; BGK modes
52.35.Ra Plasma turbulence

Three‐dimensional global numerical simulation of ion temperature gradient mode turbulence

R. E. Waltz

Phys. Fluids 31, 1962 (1988); http://dx.doi.org/10.1063/1.866643 (6 pages) | Cited 46 times

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Three‐dimensional global numerical simulations of ion temperature gradient mode turbulence in a sheared and curved magnetic field corresponding to tokamak geometry is obtained. The key result demonstrates that there is no significant dependence of the bulk heat transport on the edge safety factor q in agreement with analytic theories. The motivation for this question in relation to tokamak experiments is discussed.
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52.35.Ra Plasma turbulence
52.35.Kt Drift waves

Mode conversion and absorption of lower hybrid waves in inhomogeneous magnetic fields

Suwon Cho and D. G. Swanson

Phys. Fluids 31, 1968 (1988); http://dx.doi.org/10.1063/1.866644 (11 pages) | Cited 3 times

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When a cold lower hybrid wave propagates in an inhomogeneous plasma, it undergoes a total mode conversion to the warm wave which is then coupled with the ion Bernstein wave around ion cyclotron harmonic frequencies. Both types of linear mode conversion problems can be described by fourth‐order differential equations if the two processes are separated from each other. The combination of the two types of mode conversion when the lower hybrid turning point is in the vicinity of a cyclotron harmonic requires a sixth‐order equation with a quadratic coefficient, which is not solvable analytically nor numerically. Another type of sixth‐order equation, which has only linear coefficients and represents the three‐wave problem marginally, is solved analytically without including the absorption term. Finally, the damping and the absorption of the wave are compared for the unmagnetized dispersion relation, the full magnetized dispersion relation, and the mode conversion analysis as the wave propagates in a magnetically confined plasma with slab geometry.
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52.50.Gj Plasma heating by particle beams
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)

Simulation of oscillating field current drive on the reversed‐field pinch

Douglas S. Harned, D. D. Schnack, H. R. Strauss, and R. A. Nebel

Phys. Fluids 31, 1979 (1988); http://dx.doi.org/10.1063/1.866645 (9 pages) | Cited 5 times

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Oscillating field current drive on the reversed‐field pinch is simulated by using a three‐dimensional nonlinear resistive magnetohydrodynamic model in conjunction with a one‐dimensional hyper‐resistive model. When input from the three‐dimensional model is used for fluctuating fields in the hyper‐resistive equations, the two models are found to give similar relaxed profiles. Comparisons are made with experiments on the Los Alamos National Laboratory ZT‐40M reversed‐field pinch device [Nucl. Fusion 25, 1321 (1985)]. Simulation results indicate that the oscillation period must be much less than the resistive decay time, but should not be much less than the hyper‐resistive relaxation time, in order to maintain reversal without a steady‐state driving field.
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52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.65.-y Plasma simulation
52.55.Ez Theta pinch

‘‘Moderate‐m’’ ballooning modes in quadrapole stabilized tandem mirrors

W. M. Nevins and L. D. Pearlstein

Phys. Fluids 31, 1988 (1988); http://dx.doi.org/10.1063/1.866646 (11 pages) | Cited 14 times

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The beta limits on the central cells of nonaxisymmetric tandem mirrors due to moderate‐m ballooning modes are studied. Both finite Larmor radius (FLR) effects and corrections associated with the finite extent of the ballooning modes in the plane perpendicular to B are retained. The assumption of short perpendicular wavelength together with the large ellipticity of the flux surfaces near the magnetohydrodynamic (MHD) anchor cells allows a reduction of the three‐dimensional problem into a sequence of three one‐dimensional problems. The marginal stable boundary for the Mirror Fusion Test Facility (MFTF‐B) (National Technical Information Service Document Nos. 82020108 and UCID‐19359) is calculated and compared with that obtained from a low mode number calculation.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
28.52.Av Theory, design, and computerized simulation
52.55.-s Magnetic confinement and equilibrium

Theory of the presheath in a weakly ionized plasma with hot neutrals

S. Biehler, G. Ecker, and K.‐U. Riemann

Phys. Fluids 31, 1999 (1988); http://dx.doi.org/10.1063/1.866647 (7 pages) | Cited 21 times

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In this paper a kinetic theory of the boundary layer of a weakly ionized plasma in contact with a perfectly absorbing wall is presented. The ion kinetics is governed by charge exchange collisions with neutrals of finite temperature; the collision frequency is constant. Based on the assumption that the Debye length is small compared with all other lengths of the system, a self‐consistent two scale (presheath–sheath) analysis is performed. In contrast to Emmert’s analysis [Phys. Fluids 23, 803 (1980)] of the corresponding collision‐free system, the sheath edge shows the usual field singularity. It is shown that in the case where the electron and neutral temperatures are of the same order a large fraction of ions enters the sheath with a multiple of the electron thermal energy.
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52.40.Hf Plasma-material interactions; boundary layer effects
52.20.Hv Atomic, molecular, ion, and heavy-particle collisions
52.25.Dg Plasma kinetic equations

The influence of damping on the ion hose instability

R. A. Bosch and R. M. Gilgenbach

Phys. Fluids 31, 2006 (1988); http://dx.doi.org/10.1063/1.866648 (3 pages) | Cited 3 times

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The ion hose instability in the ion‐focused regime is analyzed using a rigid beam model with phenomenological damping terms. Values of the instability wavelength, e‐folding length, and group velocity are calculated and compared with numerical results. The impulse response function for this model is also obtained.
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41.75.Ht Relativistic electron and positron beams
84.70.+p High-current and high-voltage technology: power systems; power transmission lines and cables

Experimental studies of divertor stabilization in an axisymmetric tandem mirror

J. A. Casey, B. G. Lane, J. H. Irby, K. L. Brau, S. N. Golovato, W. C. Guss, J. Kesner, R. S. Post, E. Sevillano, and J. Zielinski

Phys. Fluids 31, 2009 (1988); http://dx.doi.org/10.1063/1.866649 (8 pages) | Cited 15 times

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A divertor coil set has been installed on the Tara tandem mirror [Nucl. Fusion 22, 549 (1982); Plasma Physics and Controlled Nuclear Fusion Research 1984 (IAEA, Vienna, 1985), Vol. 2, p. 285] for stabilization of m=1 flutelike modes. The effectiveness of divertor stabilization is discussed in experiments where m=1 modes are driven to instability by plug electron cyclotron heating (ECH) in an ion cyclotron heated (ICH) plasma. The instability onset is characterized by thresholds in ECH power, fueling rate, ICH power, and mapping radius of the divertor null. In general, the stability is enhanced by mapping the null radially inwards into the plasma. The interdependence of these parameters and their effect on equilibrium profiles and stability boundaries are discussed.
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28.52.Av Theory, design, and computerized simulation
52.55.-s Magnetic confinement and equilibrium
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Experimental observations of the tearing of an electron current sheet

W. Gekelman and H. Pfister

Phys. Fluids 31, 2017 (1988); http://dx.doi.org/10.1063/1.866650 (9 pages) | Cited 23 times

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A neutral magnetic sheet, in which the current is carried mainly by the electrons, is set up in a laboratory plasma. By forcing the current through a thin slot, the ratio of the length to height t of the sheet may be varied; the current is observed to tear when t≳30. The structure of the magnetic islands and their associated currents is fully three dimensional, although a linear two‐dimensional theory gives a very good estimate of the tearing mode growth time. Tearing is accompanied by the generation of significant Hall currents, and magnetic disturbances are observed to propagate at the whistler wave speed.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)

Diagnosing superstrong turbulence in plasma by forbidden line measurements

David Levron, Gregory Benford, Andrei Ben‐Amar Baranga, and James Means

Phys. Fluids 31, 2026 (1988); http://dx.doi.org/10.1063/1.866651 (4 pages) | Cited 15 times

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Observations of satellites of forbidden helium lines yield a new diagnostic of superstrong turbulence in a relativistic beam–plasma system. Comparing the satellite‐to‐allowed line intensities allows estimates of the volume fraction of atoms that experience high Langmuir fields, i.e., 〈E2〉≥4πnTe. An independent estimate follows from counting the total number of events, and using the calculated optical efficiency of the system, this ratio is estimated independently—agreement is good. This ratio may be the packing fraction of high field cavitons. Its value (∼0.1) implies that collision processes may be important to caviton dynamics.
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52.35.Ra Plasma turbulence
52.40.Mj Particle beam interactions in plasmas
52.70.Kz Optical (ultraviolet, visible, infrared) measurements
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