bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonlinear tearing modes in the reversed field pinch
Authors: Miller Guthrie
Published: July 2002

Finite-amplitude islands, which are the saturated states of tearing modes in the reversed field pinch, are calculated. These states are bifurcated noncylindrical equilibrium states. With σ(r) (σ≡j ⋅ B/B2) nonuniform across the plasma, as is consistent with experiment, a variety of m=1 and m=0 bifurcated equilibria are possible, instead of just the m=1 helix calculated for uniform σ(r) by Taylor [in Pulsed High Beta Plasmas, edited by D. Evans (Pergamon, Oxford, 1976), p. 59]. Assuming the magnetic field lines in the reversed field pinch are weakly stochastic, the growth time of an unstable tearing mode is on the inertial time scale, as in the Taylor model, in constrast to growth on the resistive time scale predicted from nonlinear tearing mode theory when magnetic surfaces exist. The dependence of the saturated island width on radius of a conducting shell is investigated. Islands in the reversed field pinch often have magnetic wells in the island interior, which may result in improved confinement in the island regions.
The ion temperature gradient instability in a linear machine
Authors: Mathey O. , Sen A. K.
Published: July 2002

It is shown that anisotropy in the ion temperature gradient has a substantial effect on the ion temperature gradient driven mode. A gradient in the parallel temperature is needed for an instability to occur and a gradient in the perpendicular temperature gradient further enhances the instability indirectly as long as the frequency of the mode is near ion resonance. The physical reason for this important role difference is presented. The Columbia Linear Machine (CLM) [Phys. Rev. Lett. 57, 1729 (1986)] is being redesigned to produce and identify the ion temperature gradient driven ηi mode. Using the expected parameters, detailed predictions of the mode characteristics in the CLM have been developed. These include growth rate and real frequency as a function of the azimuthal number m, the drive parameter ηi ≡d(ln Ti)/d(ln n), and the parallel wavenumber k∥. Strong multimode instabilities are expected. Because the ion parallel and perpendicular ion temperature gradients are expected to differ significantly, the roles of ηi∥ and ηi⊥ are differentiated, and this difference is exploited for a stabilization scheme of the mode. Since all gradients are significantly variable over the expected radial wavelength of the mode, a nonlocal radial differential equation has been derived. With some approximations, this can be reduced to a Weber-type equation, which has been solved.
Three-dimensional gyrokinetic particle simulation of low-frequency drift instabilities
Authors: Sydora R. D.
Published: July 2002

The nonlinear behavior of drift-wave fluctuations driven unstable by trapped particles and pressure gradients is studied using three-dimensional gyrokinetic plasma simulation methods. In the linear stages of instability, the growth rates and the radial and poloidal ballooning mode structures agree reasonably well with theory. Saturation of the unstable modes occurs principally through quasilinear profile modification and mode coupling. Results of the growth and saturation phase of the instability are compared with a bounce-averaged electron drift model. The resultant anomalous particle and energy diffusion are estimated using the saturated mode spectrum.
Overview of results from the JET tokamak using a beryllium first wall
Authors: Keilhacker M. ,   the JET team
Published: July 2002

In this paper results from the initial operation of the JET tokamak [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1985), Vol. 1, p. 11] with beryllium are summarized. JET was first operated with an evaporated Be coating on the walls and graphite limiters in June 1989. In August the graphite limiter tiles were replaced with the Be tiles, and a three week experimental campaign was conducted in September/October. In the first phase oxygen was reduced to a negligible level and the carbon flux halved. In the second phase, for limiter mode operation, carbon was reduced by another factor of 5, and Be became the dominant impurity. High-power, long-pulsed additionally heated limiter mode discharges with Zeff <1.5 were achieved, and density limits were increased by a factor of up to 2. Ion cyclotron resonance frequency (ICRF)-produced H modes were obtained in X-point operation (double null). The combination of Be gettering with new operational procedures to delay the strong influx of carbon from the X-point tiles enables the achievement of record fusion parameters in H-mode discharges including a transient ndTiτE value of 9×1020 m−3 keV sec, corresponding to a QDT equivalent of about 0.8.
Deflection of electron beams by ground planes
Authors: Fernsler R. F. , Lampe M.
Published: July 2002

Analytic methods are used to determine the effect of a nearby ground plane on the trajectory of a relativistic electron beam passing through dense gas. The beam is shown to respond to the ground plane in one of two distinct modes, determined by beam current and energy. Low-power beams deflect from the ground plane and tear longitudinally. High-power beams do not deflect or tear but tilt, i.e., the beam axis is no longer parallel to the direction of propagation. This conclusion is reached by computing the net beam force as a superposition of the ‘‘bare’’ ground-plane forces, the shielding forces from the beam-generated plasma, the body coupling forces induced by beam tilt, and the force that arises as the beam separates from the plasma. Effects from electromagnetic retardation and ground resistivity are shown to be negligible in typical cases of interest, and the interaction between ground planes and other external forces is discussed as well.
Stationary drift vortices with large amplitude
Authors: Nycander J.
Published: July 2002

Stationary drift vortices in plasmas are studied analytically. It is demonstrated how to obtain explicit monopole vortex solutions of this kind. They contain a core region with closed streamlines, and have an arbitrary radial profile. A simple expression giving the propagation velocity of the vortices is obtained, and it is found that for the vortices to be stationary, the velocity should not be close to the phase velocity of linear waves. This requires a large amplitude.
Resonant magnetohydrodynamic modes with toroidal coupling. Part II: Ballooning-twisting modes
Authors: Connor J. W. , Hastie R. J. , Taylor J. B.
Published: July 2002

This is Part II of a study of resonant perturbations, such as resistive tearing and ballooning modes, in a torus. These are described by marginal ideal magnetohydrodynamic (MHD) equations in the regions between resonant surfaces; matching across these surfaces provides the dispersion relation. Part I [Phys. Fluids B 3, 1532 (1991)] described how all the necessary information from the ideal MHD calculations could be represented by a so-called E matrix. The calculation of this E matrix for tearing modes (even parity in perturbed magnetic field) in a large-aspect-ratio torus was also described. There the toroidal modes comprise coupled cylinder tearing modes and the E matrix is a generalization of the familiar Δ′ quantity in a cylinder. In the present paper, resistive ballooning, or twisting modes, which have odd parity in perturbed magnetic field, are discussed. Unlike the tearing modes, these odd-parity modes are intrinsically toroidal and are not directly related to the odd-parity modes in a cylinder. This is evident from the analysis of the high-n limit in ballooning space, where the twisting mode exhibits a singular transition at large aspect ratio when the interchange effect is small (as in a tokamak). Analysis of the high-n limit in coordinate space, rather than ballooning space, clarifies this singular behavior. It also yields a prescription for treating low-n twisting modes and a method for calculating an E matrix for resistive ballooning modes in a large-aspect-ratio tokamak in the limit the interchange term vanishes. The elements of this matrix are given in terms of cylindrical tearing mode solutions.
Fully three-dimensional ideal magnetohydrodynamic stability analysis of low-n modes and Mercier modes in stellarators
Authors: Fu G. Y. , Cooper W. A. , Gruber R. , Schwenn U. , Anderson D. V.
Published: July 2002

The terpsichore three-dimensional linear ideal magnetohydrodynamic (MHD) stability code [Theory of Fusion Plasmas, Proceedings of the Joint Varenna–Lausanne International Workshop, Chexbres, Switzerland, 1988 (Editrice Compositori, Bologna, Italy, 1989), p. 93; Controlled Fusion and Plasma Heating, Proceedings of the 17th European Conference, Amsterdam, The Netherlands (European Physical Society, Petit-Lancy, Switzerland, 1990), Vol. 14B, Part II, p. 931; Theory of Fusion Plasmas, Proceedings of the Joint Varenna–Lausanne International Workshop, Valla Monastero, Varenna, Italy, 1990 (Editrice Compositori, Bologna, Italy, 1990), p. 655] has been extended to the full MHD equations. The new code is used to calculate the physical growth rates of nonlocal low-n modes for l=2 torsatron configurations. A comprehensive investigation of the relation between the Mercier modes and the low-n modes has been performed. The unstable localized low-n modes are found to be correlated with the Mercier criterion. Finite growth rates of the low-n modes correspond to finite values of the Mercier criterion parameter. Near the Mercier marginal stability boundary, the low-n modes tend to be weakly unstable with very small growth rates. However, the stability of global-type low-n modes is found to be decorrelated from that of Mercier modes. The low-n modes with global radial structures can be more stable or more unstable than Mercier modes.
Anomalous energy exchange in the gBL and quasilinear theories
Authors: Mynick H. E.
Published: July 2002

The rate of turbulence-induced energy exchange Ẇ0 between species is computed in the framework of the quasilinear and generalized Balescu–Lenard (gBL) transport theories, and the relationship between these two similar theories is thereby elucidated. For both theories, general formal expressions for Ẇ0 are developed and then applied to the trapped electron mode for illustration. The general expressions for Ẇ0 in the two theories are formally closely related, but can yield predictions of very different magnitude in concrete applications. The fact that quasilinear theory is not valid for saturated steady-state turbulence gives rise to certain peculiarities in its predictions for this normal experimental situation, such as permitting energy to flow from the cooler to the hotter species, even in the limit of thermal equilibrium, where real-space gradients vanish. The gBL theory may be viewed as a modification of quasilinear theory to be valid for steady-state turbulence, keeping extra terms due to the self-consistent back reaction of particles on the fluctuations, which are just such as to eliminate these peculiarities.
Linearized Vlasov–Poisson equations for the planar magnetron
Authors: Kaup D. J. , Thomas Gary E.
Published: July 2002

The linearized Vlasov–Poisson equations are obtained for the planar magnetron in the form ∂2yφ̂1+(V−k2)φ̂1=0, where V∝(∂yn0)Z(ζ), (∂yn0) is the density gradient and Z(ζ) is usual plasma dispersion function. The form for ζ, the ratio of the shifted phase velocity to the thermal velocity, is very strongly density dependent. One may understand this by considering the thermal velocity to be density dependent. In the interior of the sheath, the wave–particle resonance is very broad, corresponding to a high effective temperature. Just outside the sheath, this effective temperature drops to very low values (proportional to the electron density), leaving very narrow wave–particle resonances. The cold-fluid limit of this equation is also obtained.
Diffusion of charged particles in tokamak-like stochastic magnetic and electric fields
Authors: Coronado M. , Vitela E. J. , Akcasu A. Z.
Published: July 2002

In this paper the diffusion of guiding centers induced by stochastic magnetic and electric field fluctuations, with both time and space dependence, is analyzed for the case of tokamak plasmas. General experimental results on tokamak fluctuations are used to derive guiding-center equations that properly describe the particle motion. These equations assume uniform average magnetic and electric fields with random stationary Gaussian fluctuations that constitute a homogeneous and cylindrically symmetric turbulence. By applying Novikov’s theorem, a Fokker–Planck equation for the probability distribution function is derived and an expression for the guiding-center diffusion coefficient is obtained. This coefficient not only contains the standard terms due to the stochastic wandering of the magnetic lines and the stochastic electric drift, but also new terms due to the stochastic curvature and ∇B drifts. The form of these terms is shown explicitly in terms of the correlation functions of the fields.
Electric field and thermal diffusivity profiles of a compact helical system heliotron/torsatron plasma in a plateau regime
Authors: Ida K. , Yamada H. , Iguchi H. , Hidekuma S. , Sanuki H. , Yamazaki K. ,   the CHS Group
Published: July 2002

The radial electric field profiles are derived from poloidal rotation velocity for a plateau regime plasma heated by a neutral beam in a CHS device. The measured electric field is more negative than the neoclassical prediction especially near the plasma periphery. However, the negative radial electric field is not directly related to the reduction of thermal diffusivity.
Plasma production by multiphoton ionization: Density inhomogeneities due to ponderomotive effects
Authors: Marquès J. R. , Amiranoff F. , Dyson A. , Matthieussent G. , Benkheiri P. , Gregory C. , Jacquet F. , Miné Ph. , Montes B. , Poilleux P. , Stenz C. , Mora P. , Gouédard C.
Published: July 2002

The generation of long and homogeneous plasmas by multiphoton ionization of low-pressure gases—H2, D2, and N2 at pressures of a few Torr—with a high-power laser at λ=0.53 μm and intensities of the order of 1015 W/cm2 has been studied. The temperature and density of the plasma are measured by Thomson thermal scattering. After the initial full ionization the hydrodynamic density evolution with time is observed. The comparison with a simple model shows that this evolution is mainly due to the ponderomotive force of the laser beam itself. Typical density variations range from 1% to 5% per 100 psec.
Integral eigenmode analysis of shear flow effects on the ion temperature gradient mode
Authors: Artun M. , Reynders J. V. W. , Tang W. M.
Published: July 2002

Previous numerical and analytic kinetic studies have investigated the influence of velocity shear on the ion temperature gradient (ITG) mode. These studies relied on a differential approximation to study mode structures with k⊥ρi≪1. A recently developed gyrokinetic integral code is here used to explore the effects of sheared flows on the ITG mode for arbitrary values of k⊥ρi in sheared slab geometry. It is found that both the mode structure and eigenfrequencies predicted by the integral code can differ from the results obtained by the differential approach, even in the kyρi≪1 limit. Although some trends predicted by the differential approximation are recovered by the integral approach, there are some significant differences. For example, the slight destabilizing effect observed for small values of the perpendicular velocity shear at k⊥ρi≪1 is amplified when the integral approach is applied. In dealing with the higher radial eigenmodes, which can often exhibit the largest growth rates, it is emphasized that their finer radial structure usually dictates that the integral equation analysis is required. Results from the integral code are presented together with comparisons with results from the differential approach.
Effects of anisotropic ηi and collisions on the mixed slab and toroidal ITG mode
Authors: Song H. , Sen A. K.
Published: July 2002

The effects of collisions and anisotropy in the ion temperature gradient on the ion-temperature-gradient-driven (ITG) mode are investigated with dissipative trapped electrons and fully kinetic ions, in the presence of both transit and magnetic drift resonances. For the slab and toroidal modes, electron collisions stabilize the ion branch but destabilize the electron branch. For the mixed slab and toroidal mode, a coupling effect is found that causes a split of the stability region in the ηi∥-ηi⊥ plane. A second stability region at large ηi⊥ with electron collisions may provide a possible stabilization scheme for ITG instabilities.
Effect of a poloidal electric field on neoclassical transport in a multispecies tokamak plasma
Authors: Indireshkumar K. , Stacey W. M.
Published: July 2002

The effects of a poloidal potential variation of order ε, which is likely to be produced during high-power cyclotron wave heating or neutral beam injection, upon neoclassical particle transport and plasma current are studied theoretically, for a realistic tokamak plasma with significant impurity content. Using an approximate collision operator, an analytic procedure is employed to calculate the transport coefficients in the low collisionality regime for a large aspect ratio tokamak. In the presence of carbon impurity, the ion diffusion coefficients are generally found to increase by a factor of ∼2. Inclusion of the effects of a poloidal electric field is found to result in an increase in the bootstrap current if the potential on the outside of the tokamak is greater than that on the inside [as during ion cyclotron resonance heating (ICRH) or neutral beam injection (NBI)] and the density profiles are more peaked than roughly the square root of the temperature profiles.
Toroidal coupling of disparate helical tearing modes
Authors: Li Ding , Huo Yuping
Published: July 2002

An analytical model has been developed for toroidal coupling of tearing modes with different helicities in the low-β and large aspects ratio tokamaks. A standard characteristic value problem has been naturally composed according to the structure of magnetohydrodynamic (MHD) solutions. The explicit general dispersion relation has been obtained by the asymptotic matching. The growth rates (characteristic values) and corresponding flux perturbations (characteristic functions) of the toroidal tearing mode have been derived. The toroidal coupling plays a role mainly through the correction for the ideal MHD solutions. Without loss of generality, variation tendency of growth rates has been analyzed for a toroidal tearing mode with cylindrical components m/n and (m+1)/n, the results indicate that (1) The toroidal coupling has a destabilizing effect on the tearing modes; (2) the ‘‘beating’’ of the growth rates of two components leads to strong coupling, even if the coupling parameter C is quite small, and the coupling effect does not explicitly rely on magnitude of Δ′(0)m of cylindrical component, so that Δ′(0)m ∼ ε is neither a necessary nor sufficient condition for strong coupling.
Multiple-gap theory of toroidal Alfvén waves with kinetic effects
Authors: Zhang X. D. , Zhang Y. Z. , Mahajan S. M.
Published: July 2002

The stability of kinetic toroidal Alfvén waves with multigap coupling is analyzed by using the two-dimensional ballooning transform. An alternate convergence scheme, based on the smallness of the inverse aspect ratio, is devised. The resulting wave functions are oscillatory and do not balloon in contrast to the wave functions of conventional ballooning theory. It is shown that the single-gap theory is a special, weak shear (s→0) limit of the formalism. Analytical and numerical results for the two fundamental branches, the ideal toroidal Alfvén eigenmode (TAE), and the kinetic toroidal Alfvén eigenmode (KTAE), are presented and discussed.
Finite Larmor radius effects in stimulated Raman scattering
Authors: Boyd T. J. M. , Gardner G. A. , Rankin R.
Published: July 2002

Stimulated Raman scattering from a magnetized plasma has been examined using the set of Vlasov–Maxwell equations. The incident laser light, propagating in the form of an extraordinary mode, decays into a scattered extraordinary mode together with electron-Bernstein waves. For sufficiently strong magnetic fields and high electron temperatures, the growth rates of these waves become comparable to the field-free values. At relatively low plasma densities the magnetic field can result in scattered light at ω0/2 (where ω0 is the laser frequency), a frequency associated with radiation emitted from the quarter-critical density region of unmagnetized plasmas. We have compared the results from the kinetic theory analysis with observations from numerical experiments using a 1 1/2 -D electromagnetic particle code and found them to be in good agreement.
Some bifurcation diagrams for Taylor vortex flows
Authors: Meyer-Spasche Rita , Keller H. B.
Published: July 2002

The numerical continuation and bifurcation methods of Keller [H. B. Keller, in Applications of Bifurcation Theory (Academic, New York, 1977), pp. 359–384] are used to study the variation of some branches of axisymmetric Taylor vortex flow as the wavelength in the axial direction changes. Closed ‘‘loops’’ of solutions and secondary bifurcations are determined. Variations with respect to Reynolds number show the same phenomena. The results presented here show that Taylor vortices with periodic boundary conditions exist in a wider range of wavelengths, λ, than observed in the Burkhalter/Koschmieder experiments [Phys. Fluids 17, 1929 (1974)]. They also show that there is possibly a λ subinterval within the neutral curve of Couette flow such that there are no Taylor vortex flows with smallest period in this interval.
Kinetic stability theorem for relativistic non-neutral electron flow in a planar diode with applied magnetic field
Authors: Davidson Ronald C.
Published: July 2002

A kinetic stability theorem is developed for relativistic non-neutral electron flow in a planar high-voltage diode with applied magnetic field. The effects of strong inhomogeneities and intense self-electric and self-magnetic fields are retained in the analysis in a fully self-consistent manner. Use is made of global (spatially averaged) conservation constraints satisfied by the fully nonlinear Vlasov–Maxwell equations, assuming electromagnetic perturbations with extraordinary-mode polarization, and space-charge-limited flow with E0x(x=0)=0 at the cathode. It is also assumed that the y-averaged, x-directed net flux of particles, y momentum, and energy, vanish identically at the cathode (x=0) and at the anode (x=d). It is shown that the class of self-consistent Vlasov equilibria f0b(H,Py) is stable for small-amplitude perturbations, provided f0b is a monotonic decreasing function of H−VbPy, i.e., provided ∂f0b/∂(H−VbPy)≤0. Here, H is the energy and Py is the canonical y momentum. The generality of this sufficient condition for stability should be emphasized. First, the derivation of the stability theorem has not been restricted to a specific choice of f0b(H−VbPy). Moreover, the fully non-neutral electron equilibria are generally characterized by strong spatial inhomogeneities and intense self-electric and self-magnetic fields. For the class of equilibria with ∂f0b/∂(H−VbPy)≤0, it is also shown that the density profile n0b(x)=∫ d3p f0b and x–x pressure profile P0b(x) =∫ d3p vxpxf0b decrease monotonically from the cathode (x=0) to the anode (x=d) provided the applied magnetic field at the anode (Ba) is sufficiently strong that (Vb/c)Ba ≥4πe ∫d0 dx′ n0b(x′).
Collisionless tearing instability in a non-Maxwellian neutral sheet: An integrodifferential formulation
Authors: Chen J. , Lee Y. C.
Published: July 2002

An integro-differential formalism is developed to study the collisionless tearing instability in a non-Maxwellian neutral sheet. The exact unperturbed particle orbits are used analytically in the orbit integrals. The treatment is linear, self-consistent, and kinetic for both ions and electrons. The analysis is carried out for low-frequency, purely growing electromagnetic perturbations (‖ω‖≪ωci). Using the Galerkin method, the integro-differential equation is solved to obtain the dispersion relation and the eigenmode structure. A sufficient condition for instability is given on the basis of a quadratic form and the eigenvalues of a self-adjoint integro-differential operator. The formalism is applied to a specific model distribution. For the case where the electrons and ions are both non-Maxwellian, it is found that the instability is dominated by the axis-crossing electrons and that the eigenmode is strongly localized to a region of the order of ( ρezp)1/2 at the null plane, where  ρe is a measure of the electron gyroradius in the asymptotic magnetic field and zp is the sheet thickness. It is shown that the growth rate can be enhanced by several orders of magnitude over the isotropic case and that short wavelength perturbations are strongly preferred. The dispersion relation has the general form γ/kve∥=const where k∥B0 and ve∥ is the electron thermal velocity along B0, the equilibrium magnetic field.
Effect of the laser flux on the field generating thermal instability in laser-produced plasmas
Authors: Kumar Ajit , Tripathi V. K. , Saikia P.
Published: July 2002

The effect of the laser flux on the field generating thermal instability in a laser-produced plasma is investigated taking into account the thermoelectric term also. It is found that the thermoelectric term does not change the basic features of the thermal instability studied by Tidman and Shanny [Phys. Fluids 17, 1207 (1974)]. However, it is found that in a plasma (with particle density ∼4×1020 and temperature ∼1 KeV) with classical resistivity the laser flux tends to stabilize the instability by influencing the process of collisional heating of electrons. The threshold value of the laser power for the suppression of the instability is of the order of 2.7×1015 W/cm2 for an Nd–glass laser when the density and temperature scale lengths are of the order of 10 μm. In the case when the plasma has anomalous resistivity because of ion-acoustic turbulence the flux tends to enhance the instability further.
Dynamic breakup of liquid–liquid jets
Authors: Richards John R. , Lenhoff Abraham M. , Beris Antony N.
Published: July 2002

The axisymmetric, dynamic breakup of a Newtonian liquid jet injected vertically into another immiscible Newtonian liquid at various Reynolds numbers is investigated here. The full transient from jet start-up to breakup into drops was simulated numerically by solving the time-dependent axisymmetric equations of motion and continuity using an algorithm based on the Volume of Fluid (VOF) method that was previously proven successful in simulations of steady-state liquid jets (i.e., of the jet region close to the nozzle before breakup). The algorithm has been further refined here based on its performance on transient problems such as the solution of the free liquid–liquid capillary jet breakup problem. The comparison of the simulation results with previous experimental measurements of jet length under conditions where all forces, i.e., viscous, inertial, buoyancy, and surface tension, are important, can be judged satisfactory given the sensitive dependence of the results on details of the experimental setup that are not available. The comparison involves the jet length till breakup as well as the jet and drop shapes, often far from regular. In comparison with experiment, the results of the present numerical method show a greater sensitivity of the jet length to the Reynolds number than the best predictions previously available based on the linear stability analysis of the free liquid–liquid capillary jet breakup problem.
Unsteady low Reynolds number shock boundary layer interactions
Authors: Loth E. , Matthys Mark W.
Published: July 2002

Finite element methods were used to perform an investigation of the interaction between a reflected shock wave and a low Reynolds number laminar boundary layer in Mach 2 flow. The finite element scheme makes use of the time-accurate flux-corrected transport technique and a fully unstructured mesh, which is adaptive to both viscous and gasdynamic effects. A boundary layer transformation was employed to eliminate both the upstream pressure gradient and resolution issues of the leading edge flow. Shock wave/boundary layer interactions were simulated for four different shock intersection Reynolds numbers: 600, 2400, 9600, and 24 000. While significant amounts of flow separation were found for all Reynolds numbers, the character and size of the separated region varied significantly. It was also noted that separation bubble lengths when normalized by the distance from the leading edge to the shock intersection point decreased as the Reynolds number increased for the conditions considered herein. However, the most interesting observation was the inherent unsteadiness found for the higher Reynolds numbers. This led to separation bubble instability and vortex shedding for the two highest Reynolds number cases. The results indicated a natural shedding frequency of 1.3 based on ambient velocity and primary separation bubble length for these two cases.
Hydrostatics and oscillatory flows of magnetic fluid under a nonuniform magnetic field
Authors: Shliomis Mark I. , Kamiyama Shinichi
Published: July 2002

A nonuniform magnetic field induces an inhomogeneous ferroparticle distribution in a magnetic fluid (MF). As a consequence the magnetic field influences MF flows. In particular, we consider an oscillatory pipe flow in a stationary nonuniform magnetic field subject to the quasielastic magnetic force. Concentration inhomogeneities can be formed from both single particles and many-particle drops, which appear as a result of the field-induced MF phase separation. Kinematic considerations show that only the drops contribute to the magnetic force. Our theory is in good agreement with recent experimental results.
Boundary layer instability over compliant walls: Comparison between theory and experiment
Authors: Lucey A. D. , Carpenter P. W.
Published: July 2002

Theoretical studies have shown that compliant walls are able to attenuate the Tollmien–Schlichting waves that lead to conventional two-dimensional boundary-layer transition. This phenomenon was demonstrated in towing-tank tests conducted by Gaster et al. The results of these experiments also featured a different and very dramatic form of boundary-layer breakdown. We contend that this type of breakdown was due to a hydroelastic mode of instability, namely traveling-wave flutter. In this paper we model the two-layer viscoelastic compliant wall of Gaster et al. and its interaction with the boundary-layer flow using the asymptotic theory of Carpenter and Gajjar; en-type calculations are carried out for the traveling-wave flutter. Excellent agreement is found between the stability characteristics of the TWF mode and the measurements of the new form of breakdown found in the experiments; thus a complete understanding of the physical features found in the experiments is now available. Such understanding is essential for progress to be made in the technological development of compliant panels for transition delay.
Velocity autocorrelations of decaying isotropic homogeneous turbulence
Authors: Huang Mei-Jiau , Leonard Anthony
Published: July 2002

Velocity autocorrelations and the mean-square displacements of fluid particles are obtained for decaying, isotropic homogeneous turbulence by numerical simulation of the flow field, using 1283 and 2563 grids, and tracking several tens of thousands of fluid particles, using a third-order interpolation scheme. A self-preserving Lagrangian velocity autocorrelation coefficient is found in terms of a dimensionless time variable s, defined by ds=dt/𝒯s(t), under the observation of a power-law energy decay and the assumption that 𝒯s(t) is proportional to the Lagrangian integral timescale 𝒯ℒ. This timescale is in turn assumed to be proportional to the length scale of the energy-containing eddies ℒe∼K3/2/ε divided by the turbulent velocity u′, where K=3/2u′2 is turbulent energy and ε is the energy dissipation rate.
Three-dimensional vortex/wall interaction: Entrainment in numerical simulation and experiment
Authors: Chang Tae Y. , Hertzberg Jean R. , Kerr Robert M.
Published: July 2002

Three-dimensional interactions between an elliptic vortex ring and two no-slip parallel walls are visualized in a numerical simulation and an experiment. The vortex ring induces a surface vorticity layer on the wall which reconnects with the vortex ring. During the interaction core-area-varying axial waves are generated and carry the surface layer away from the wall. The vortex ring then becomes two tornado-like structures with strong upward helical flows near the wall surface, which provides entrainment of the surface fluid into the vortex structure. Similarities between the entrainment mechanisms of vorticity in the simulation and dye in the experiment from the surface layer are identified.
On the symmetry breaking instability leading to vortex shedding
Authors: Tang Shaojie , Aubry Nadine
Published: July 2002

It is well known that at early stages an impulsively started flow past a circular cylinder consists of twin vortices which are images of one another by reflection through the mid-plane. While the twin vortices are stable for Reynolds numbers below the critical Reynolds number value (Rec≃48), they become unstable above the critical Reynolds number. At Re>Rec, the flow keeps its symmetric recirculating bubble structure for a short time, undergoes a symmetry-breaking instability, and develops into a Karman vortex street. Föppl’s vortex model is studied here as a low-dimensional model for the symmetric bubble. The stability analysis of a fixed bubble in the model shows that there are two asymmetric eigenmodes, a stable mode and an unstable one. In this paper, we show by two-dimensional direct numerical simulations (DNS) of the impulsively started flow past a circular cylinder how the instability properties of the model qualitatively mimic those of the real flow.
The linear stability of thermally stratified rotating channel flow
Authors: Sha Weiming , Tsuchiya Kenichi , Nakabayashi Koichi
Published: July 2002

A linear stability analysis has been made of the hydrodynamic stability of viscous flow in a thermally stratified rotating channel. To understand the competition mechanism of the flow stabilization and destabilization, an inviscid stability criterion including effects of the rotation and stratification was first formulated for indicating the stable and unstable regimes of the flow. Then, an eigenvalue problem was derived for the viscous flow and solved using a shooting method. The combined effect of the Coriolis force and centrifugal-type buoyancy force on the longitudinal roll-cell instability was examined. For Prandtl number 7.11, the critical Reynolds number, corresponding critical wave number, and induced cell pattern of the longitudinal vortices are shown for various values of the rotation number and rotational Rayleigh number. Based on the analytical results, we predict the onset of the longitudinal roll-cell instability in this nonisothermal rotating channel flow. As compared to the isothermal rotating channel flow case, not only the critical Reynolds number but also the onset mode of the roll cell are altered significantly by the centrifugal-type buoyancy force. It is found that the flow may be stabilized or destabilized depending on the rotation and stratification of the channel. In the presence of a positive rotational Rayleigh number, the flow becomes more stable as compared with the isothermal rotating channel flow, otherwise, the flow becomes more unstable.
An experimental study of boundary-layer transition over a rotating, compliant disk
Authors: Colley A. J. , Thomas P. J. , Carpenter P. W. , Cooper A. J.
Published: July 2002

An experimental study is described which investigates the laminar-turbulent transition of the boundary layer over rigid and compliant disks rotating under water. Hot-film data are presented and analyzed to produce neutral-stability curves. It appears to be the first time that such data has become available for a compliant disk. Our experiments employing a rigid disk essentially confirm the results of previous authors. For the flow over the compliant disk the turbulence levels in the transitional and fully turbulent flow regimes are found to be considerably lower than the corresponding levels for the rigid disk. The analysis of our experimental data suggests that wall compliance has a stabilizing influence in the frequency range associated with the Type I cross-flow instability. Nevertheless, compliance is found to have an overall destabilizing effect on the boundary-layer flow. This results in a substantially lower transitional Reynolds number compared to the case of the rigid disk. The experimental observations are in qualitative agreement with our theoretical predictions. It is argued that the reduced transitional Reynolds number for the compliant disk might indicate that transition for such a disk results from a convective-instability mechanism and not from an absolute-instability mechanism as has recently been suggested in the literature to be the case for a rigid disk.
Experimental study of Taylor’s hypothesis in a turbulent soap film
Authors: Belmonte Andrew , Martin Brian , Goldburg Walter I.
Published: July 2002

An experimental study of Taylor’s hypothesis in a quasi-two-dimensional turbulent soap film is presented. A two-probe laser Doppler velocimeter enables a nonintrusive simultaneous measurement of the velocity at spatially separated points. Using the cross correlation between a pair of points displaced in both space and time, the velocity coherence is measured to be better than 90% for scales less than the integral scale. Taylor’s hypothesis is confirmed insofar as the lower moments of the longitudinal velocity difference are equal whether measured with or without invoking the hypothesis. A quantitative study of the decorrelation beyond the integral scale is also presented.
Propagation of radius-tailored laser pulses over extended distances in a uniform plasma*
Authors: Krall J. , Esarey E. , Sprangle P. , Joyce G.
Published: July 2002

A Maxwell-fluid model is described, which allows simulation of laser pulses over extended distances (multiple diffraction lengths) in an underdense plasma. This model is used to simulate radius-tailored laser pulses, which can propagate over such distances with minimal distortion in a uniform plasma. Theoretical model equations governing the choice of radius tailoring are also given. A radius-tailored pulse has constant power approximately equal to the critical power for relativistic guiding over the length of the pulse and a spot size at focus that varies over the length of the pulse. A laser pulse configuration of this type can be constructed from a series of ultrashort Gaussian pulses.
Impact of dissociation and ionization on properties of iodine vapor
Authors: Holbrook Robert T. , Kunc Joseph A.
Published: July 2002

The partition functions are calculated for the 127I127I iodine molecule, the 127I atom, and the corresponding singly charged atomic ion and are subsequently used in calculating the dissociation and ionization degrees as well as the thermodynamic functions in iodine vapor in local thermal equilibrium in the temperature range of 700≤T≤12 000 K. It was found that at densities greater than 1014 cm−3 iodine dissociates at rather low temperatures (T<3000 K) and only achieves significant ionization at high temperatures (T≳10 000 K). This makes iodine a convenient model gas for studying chemical nonequilibrium in diatomic gases.
Continuum damping of ideal toroidal Alfvén eigenmodes
Authors: Zhang X. D. , Zhang Y. Z. , Mahajan S. M.
Published: July 2002

A perturbation theory based on the two-dimensional (2-D) ballooning transform is systematically developed for ideal toroidal Alfvén eigenmodes (TAEs). A formula, similar to the Fermi golden rule for decaying systems in quantum mechanics, is derived for the continuum damping rate of the TAE; the decay (damping) rate is expressed explicitly in terms of the coupling of the TAE to the continuum spectrum. Numerical results are compared with previous calculations. It is found that in some narrow intervals of the parameter mε̂, the damping rate varies very rapidly. These regions correspond precisely to the root missing intervals of the numerical solution by Rosenbluth et al. [Phys. Fluids B 4, 2189 (1992)].
Phase space evolution in linear instabilities
Authors: Pantellini F. G. E. , Burgess D. , Schwartz S. J.
Published: July 2002

A simple and powerful way to investigate the linear evolution of particle distribution functions in kinetic instabilities in a homogeneous collisionless plasma is presented. The method can be applied to any kind of instability, provided the characteristics (growth rate, frequency, wave vector, and polarization) of the mode are known and can also be used to estimate the amplitude of the waves at the end of the linear phase of growth. Two didactic examples are used to illustrate the versatility of the technique: the Alfvén Ion Cyclotron (AIC) instability, which is electromagnetic, and the Electron Ion Cyclotron (EIC) instability, which is electrostatic.
Ion orbit loss and the poloidal electric field in a tokamak
Authors: Xiao H. , Hazeltine R. D. , Valanju P. M.
Published: July 2002

Monte Carlo simulation studies for ion orbit loss in limiter tokamaks show a poloidal asymmetry in ion loss arising from differences in ion orbit geometry. Since electron loss to the limiter is uniformly distributed because of its tiny orbit width, the nonuniform ion loss could cause a poloidal electric field that would tend to make the ion loss to the limiter more uniform. A simple analytical derivation of this poloidal electric field and a discussion of its effects on ion movement and transport are also presented.
Density, temperature, and potential fluctuation measurements by the swept Langmuir probe technique in Wendelstein 7-AS
Authors: Giannone L. , Balbín R. , Niedermeyer H. , Endler M. , Herre G. , Hidalgo C. , Rudyj A. , Theimer G. , Verplanke Ph. ,   the W7-AS Team
Published: July 2002

In the Wendelstein 7-AS stellarator (W7-AS) [Plasma Phys. Controlled Fusion 33, 1591 (1991)], current-voltage characteristics of the Langmuir probe at sweep frequencies in the range 400 kHz to 1 MHz were measured and it was found that the mean and fluctuation values of the ion saturation current, floating potential, and electron temperature were independent of the sweep frequency. A radial scan in the vicinity of the velocity shear layer was performed. The simultaneous sweeping of 3 probe tips showed a statistically significant spatial coherence of the fluctuations in the poloidal direction and a decrease in spatial coherence of the fluctuations with increasing tip separation could be demonstrated. The observation of a change in the propagation direction of fluctuations as the shear layer was crossed and a calculation of the transport spectrum show that the swept probe method is capable of reproducing known results. Apparent temperature fluctuations, due to variations of density and potential during a sweep, are shown by simulations to be only of importance at frequencies above half the Nyquist frequency.
On electromagnetic ballooning modes in fluid and kinetic descriptions
Authors: Fröjdh M. , Nordman H. , Jhowry B.
Published: July 2002

A comparison between two-fluid, gyrofluid, and gyrokinetic descriptions of the collisionless ballooning mode in the toroidal limit is performed. The two-fluid model [A. Jarmén et al., Nucl. Fusion 27, 941 (1987)] is reactive and expanded in the finite-Larmor radius (FLR), in contrast to the gyrofluid model [R. E. Waltz et al., Phys. Fluids B 4, 3138 (1992)], which is dissipative and includes finite-Larmor-radius effects to all orders. The eigenmode differential equation is derived and solved numerically. It is shown that the fluid models are able to reproduce the gyrokinetic result, at least qualitatively. The role of the ion magnetic drift resonance and the ion FLR terms, in the fluid and kinetic descriptions, is discussed.
Plasma flow resulting from electron cyclotron resonance heating on a magnetic hill
Authors: Hooper E. B.
Published: July 2002

The flow of low collisionality plasma down a magnetic hill during electron cyclotron resonance heating is analyzed using a particle-in-cell code that follows both the electron and ion guiding centers. The analysis is applied to the formation of an ion beam by plasma expansion in a magnetic nozzle, of interest for plasma thrusters and other applications. The ambipolar electric potential that accelerates the ions is enhanced by effects of the magnetic forces on the electrons that are heated perpendicular to the magnetic field. Comparison with flow in the presence of isotropic heating demonstrates an increase in the efficiency of the particle and energy fluxes down the field relative to those that flow up the field to a wall at a large mirror ratio. The increases are reduced somewhat if particles recycle near the wall, but are still significant.
Vacuum flux surfaces produced by inclined coils
Authors: Moroz Paul E.
Published: July 2002

The detailed analysis of the vacuum magnetic field structure produced by the inclined toroidal field (TF) coils is presented. This configuration has a potential for adding stellarator properties to the tokamak configuration while maintaining the simplicity of planar coils. Parameters of the system are identified that result in significant stellarator-like effects: large vacuum flux surfaces and appreciable rotational transform. Two sets of closed flux surfaces with opposite helicity are studied: the internal one and the external one. It is found that the external set of flux surfaces possesses a magnetic well and, hence, is favorable for the magnetohydrodynamic (MHD) stability. Also, it has larger enclosed volume and rotational transform. It is, hence, preferential in our studies, in comparison with the internal set that usually features a magnetic hill. Analysis of the flux surface structure and the helical harmonic spectrum yields optimization rules required for the configuration to be of practical interest for possible fusion applications. In a few examples it is demonstrated what occurs if the parameters are set differently than optimal. It is found that toroidal inhomogeneity is a key factor and vacuum flux surfaces disappear in the limit of a very high number of TF coils. The important role of the poloidal field (PF) coil system is stressed, and the possibility of the compensated PF system (with zero total current) is found.
A model for a scrape-off-layer low-high (L-H) mode transition
Authors: Cohen Ronald H. , Xu Xueqiao
Published: July 2002

Increasing the radial mode number has a stabilizing effect on the conducting-wall and curvature-driven interchange modes in a tokamak scrape-off layer (SOL), arising from the increased polarization response. Such an effect is naturally imposed as the SOL width is decreased, and for a narrow-enough SOL, the stabilizing effect is stronger than the increase in the instability drives. By combining a mixing-length estimate for the thermal diffusivity with energy conservation and heat conduction equations and the condition of continuity of the heat flux at the separatrix, it is found that the resultant turbulence-transport system admits two solutions, one stable and one unstable, at different SOL widths; the inclusion of additional physics can add a second stable root at lower width. These roots are plausibly identified with SOL behavior in low (L) and high (H) modes. Particularly when a model is introduced for finite-β, finite-k∥ effects on the modes, a power threshold for transition to the narrower root is obtained, suggesting a possible L-H transition mechanism. The non-monotonic dependence of the turbulent heat flux vs SOL width and the possibility of multiple solutions for the equilibrium SOL width are verified with nonlinear simulations.