bluuebunny/crossref_metadata_2025 huggingface dataset:
On self-consistent ray-tracing and Fokker–Planck modeling of the hard x-ray emission during lower-hybrid current drive in tokamaks
Authors: Bizarro João P. , Peysson Yves , Bonoli Paul T. , Carrasco Joël , de Wit Thierry Dudok , Fuchs Vladimir , Hoang Gia T. , Litaudon Xavier , Moreau Didier , Pocheau Christine , Shkarofsky Issie P.
Published: July 2002

A detailed investigation is presented on the ability of combined ray-tracing and Fokker–Planck calculations to predict the hard x-ray (HXR) emission during lower-hybrid (LH) current drive in tokamaks when toroidally induced ray stochasticity is important. A large number of rays is used and the electron distribution function is obtained by self-consistently iterating the appropriate power deposition and Fokker–Planck calculations. It is shown that effects due to radial diffusion of suprathermal electrons and to radiation scattering by the inner wall can be significant. The experimentally observed features of the HXR emission are fairly well predicted, thus confirming that combined ray-tracing and Fokker–Planck codes are capable of correctly modeling the physics of LH current drive in tokamaks.
A two-nonlinearity model of dissipative drift wave turbulence
Authors: Liang Y.-M. , Diamond P. H. , Wang X.-H. , Newman D. E. , Terry P. W.
Published: July 2002

A simple, one-field, two-nonlinearity, drift wave model equation is derived to describe the dynamics of a nonuniform magnetized plasma by taking into account the effects of dissipative trapped electron response in the turbulence dynamics. Because of the nonadiabatic response of trapped electrons, mode couplings by both the E×B drift and the polarization drift nonlinearities are present. In this work, the statistical dynamics for this dissipative drift wave turbulence is investigated using the EDQNM (eddy-damped quasinormal Markovian) closure scheme. In particular, apart from the eddy viscosity, a large nonlinear frequency shift is shown to be induced by cross coupling of the two nonlinearities. Thus instability drive is modified by this turbulent back reaction. By taking into account this self-consistency effect, a wave kinetic equation is derived, and the density fluctuation spectrum is obtained in different parameter ranges. The results show that the dynamics of dissipative drift wave turbulence is fundamentally different from that of the familiar Hasegawa–Mima model, because E×B drift nonlinearity blocks the low-k condensation of fluctuation energy. It is shown that both the E×B drift nonlinearity and the nonlinear frequency shift effect transfer energy nonlocally from large to small scales and, in contrast to the predictions of dimensional analysis, their contribution to the nonlinear transfer processes are actually of the same order as that of the polarization drift nonlinearity, even within the Hasegawa–Mima regime. This results in a significant modification of the Hasegawa–Mima spectrum for the short-wavelength drift waves.
A simple model for driven islands in tokamaks
Authors: Jensen T. H. , Leonard A. W. , Hyatt A. W.
Published: July 2002

The problem modeled is that of a surface of magnetic islands, which, because of flow of plasma relative to the islands, is exposed to a viscous force. Such a model is needed for describing the effects of error fields on a rotating plasma or to describe the effects of deliberately imposed, moving island surfaces on the plasma. The latter may be a useful tool to establish desirable rotation velocity profiles in tokamak plasmas, possibly resulting in better confinement. The model described is simple in that results may be obtained analytically and comprehensive in that it can account both for ‘‘locking’’ circumstances, under which plasma inside islands is almost at rest in the island frame, and ‘‘slipping’’ circumstances under which plasma slips rapidly in and out of islands. It can also account for discontinuous transitions between ‘‘locking’’ and ‘‘slipping’’ circumstances.
Impact of multiple-frequency heating on the formation and control of diamagnetic electron rings in an axisymmetric mirror
Authors: Quon B. H. , Dandl R. A. , DiVergilio W. , Guest G. E. , Lao L. L. , Lazar N. H. , Samec T. K. , Wuerker R. F.
Published: July 2002

High-beta, hot-electron plasmas have been produced by electron-cyclotron heating in the SM-1 axisymmetric mirror using closely-spaced multiple frequencies. The relativistic electrons produce annular distributions (ELMO rings) with as much as ten times more stored energy than with single-frequency heating. While larger frequency separations (Δf/f∼0.1) provide some control of the ring size, the dominant effects are associated with an improvement in heating efficiency which persists to very small frequency separations (Δf/f∼10−3). Details of the reconstruction of the ring distribution (both in steady state and during build-up), the influence of multiple frequency heating on fluctuations, axial electron losses, and a scaling of these effects with power are presented.
An algorithm to solve the linear mode conversion problem in a weakly inhomogeneous plasma
Authors: Gambier D. J. , Swanson D. G.
Published: July 2002

In a previous article, the wave equation for electromagnetic and electrostatic waves propagating in a weakly inhomogeneous plasma was studied assuming an ordinary differential equation of the Laplace type. An algorithm was developed, based on the contour integral formalism, that gives a prescription for calculating the connection formulas between the set of fast and slow propagating waves. Physical problems connected to the evanescent solutions were not treated, however, so the complete set of solutions was not obtained. In this paper, the method is extended to include both propagating and nonpropagating waves so that a complete set of solutions is obtained, permitting the construction of the Green function and the inclusion of localized sources or sinks.
Nonlinear dynamics of magnetic islands with curvature and pressure
Authors: Kotschenreuther M. , Hazeltine R. D. , Morrison P. J.
Published: July 2002

Curvature and finite pressure are known to have a dramatic influence on linear magnetic tearing stability. An analytic theory of the nonlinear resistive growth of magnetic islands in tokamaks that includes the interchange driving term in presented here. A Grad-Shafranov equation to describe the magnetohydrodynamic (MHD) equilibrium of thin islands is derived. The resistive evolution of these islands is then obtained. Interchange effects are found to become progressively less important with increasing island width.
Low-frequency density fluctuations in a tokamak plasma
Authors: Watterson R. L. , Slusher R. E. , Surko C. M.
Published: July 2002

CO2 laser scattering and correlation techniques are used to study low-frequency density fluctuations in plasmas in the Alcator C tokamak. Using crossed-beam correlation techniques, these fluctuations are found to have largest amplitudes near the plasma edge. In discharges with mean plasma densities n̄≳2×1014 cm−3, the normalized fluctuation amplitude is ñ/n≂0.5 and peaks at the limiter radius; however, at lower plasma densities, ñ/n peaks in the plasma interior at a normalized minor radius r/a≂0.75 (where a is the limiter radius). The radial and poloidal wave vectors of the fluctuations are comparable, with mean wavenumbers k̄∼20 cm−1. At any given k, the observed frequency spectrum is broad. For plasma densities n̄≲1.5×1014 cm−3, the poloidal group propagation velocity vθ of the fluctuations is measured to be approximately 2×105 cm/sec in the electron diamagnetic drift direction, while at plasma densities n̄≳2×1014 cm−3, vθ≂9×104 cm/sec in the ion diamagnetic drift direction. The nature of these fluctuations is also studied in discharges exhibiting a boundary-layer instability (i.e., ‘‘marfes’’).
Emission of light at half-integer harmonics of the laser frequency
Authors: Berger R. L. , Powers L. V.
Published: July 2002

Calculations have been made of the spectrum of light emitted at half-integer harmonics of the laser light frequency ω0. The emitted light results from either the Raman scattering of laser light by Langmuir waves or by the direct conversion of Langmuir waves to light. The Langmuir wave amplitude is calculated from convective instability theory for two-plasmon decay in an inhomogeneous, plane-stratified medium. The Raman scattering process generates harmonics at (n/2) ω0 where n=1,3,5 ...; however, only for n=1 and 3 is the emission level significant. The conversion process produces (1/2) ω0 light with a comparable efficiency to the Raman scattering process near the two-plasmon instability threshold. Results of the calculation are in agreement with the general features of measured emission spectra.
Free unsteady expansion of a polytropic gas: Self-similar solutions
Authors: Schmalz R. F.
Published: July 2002

A new class of generalized self-similar solutions for the problem of one-dimensional unsteady outflow of a gas into a vacuum is found. It allows a unified and comprehensive description of plane, cylindrical, and spherical symmetric flows for arbitrary polytropic index. A key property is a moving inner boundary. Relative to this, subsonic and supersonic outflows are possible in certain parameter regions. Simple analytic expressions are found near the boundaries and an extensive parameter discussion is presented. The asymptotic solutions are of specific importance. As an application, it is shown that the isothermal corona of a laser-generated plasma is in part described by one of these asymptotic solutions.
A generalized Langevin model for turbulent flows
Authors: Haworth D. C. , Pope S. B.
Published: July 2002

A Langevin model appropriate to constant property turbulent flows is developed from the general equation for the fluid particle velocity increment proposed by Pope in an earlier paper [Phys. Fluids 26, 404 (1983)]. This model can be viewed as an analogy between the turbulent velocity of a fluid particle and the velocity of a particle undergoing Brownian motion. It is consistent with Kolmogorov’s inertial range scaling, satisfies realizability, and is consistent with second-order closure models. The objective of the present work is to determine the form of a second-order tensor appearing in the general model equation as a function of local mean quantities. While the model is not restricted to homogeneous turbulence, the second-order tensor is evaluated by considering the evolution of the Reynolds stresses in homogeneous flows. A functional form for the tensor is chosen that is linear in the normalized anisotropy tensor and in the mean velocity gradients. The resulting coefficients are evaluated by matching the modeled Reynolds stress evolution to experimental data in homogeneous flows. Constraints are applied to ensure consistency with rapid distortion theory and to satisfy a consistency condition in the limit of two-dimensional turbulence. A set of coefficients is presented for which the model yields good agreement with available data in homogeneous flows.
Macroscopic extraordinary-mode stability properties of relativistic non-neutral electron flow in cylindrical geometry
Authors: Davidson Ronald C. , Tsang Kang T.
Published: July 2002

Use is made of a macroscopic model based on the cold-fluid-Maxwell equations to investigate the extraordinary-mode stability properties of relativistic non-neutral electron flow in a cylindrical diode with the cathode located at r=a and the anode located at r=b. The equilibrium radial electric field E0r (r)êr and axial magnetic field B0z (r)êz induce an azimuthal flow of electrons with velocity V0θb (r)=ωb(r)r. Assuming flute perturbations (∂/∂z=0) with extraordinary-mode polarization, the eigenvalue equation is derived for the effective potential Φ(r)=(ir/l)δ ̂Eθ(r). Here, l is the azimuthal mode number, and perturbations are about the general class of equilibrium profiles E0r (r), B0z (r), ωb(r), and n0b (r), consistent with the steady-state cold-fluid-Maxwell equations. For prescribed equilibrium profiles, the extraordinary-mode eigenvalue equation is solved numerically for the eigenfunction Φ(r) and complex eigenfrequency ω. As a general remark, the numerical results show that detailed stability properties exhibit a sensitive dependence on cylindrical effects. For example, at low values of the mode number l, the properties of the eigenfunction Φ(r) are qualitatively different from the planar case, and from the cylindrical case for large l values. Furthermore, it is found that the instability growth rate Im ω exhibits a sensitive dependence on the layer aspect ratio A=a/(rb−a), particularly when the electron flow is relativistic and centrifugal effects play an important role in modifying the equilibrium profiles. (Here, r=rb denotes the outer edge of the electron layer.)
Stochastic electron motion in magnetically insulated diodes
Authors: Desjarlais M. P. , Sudan R. N.
Published: July 2002

The transition to stochasticity is investigated for electron motion in the field configuration of a magnetically insulated diode. The model system is planar and periodic. The equilibria studied are nonrelativistic with constant electron density across the sheath. This class of equilibria includes the Brillouin flow equilibrium as a limit. Action-angle variables are introduced that facilitate the nonlinear analysis. It is found that small periodic perturbations of the equilibrium potential may lead to stochastic motion of the sheath electrons. It is shown that the critical perturbation amplitude for global stochasticity goes to zero as the Brillouin limit is approached for a variety of perturbations. A global stochasticity diagram is presented that gives a simple characterization of the electron motion in the allowed phase space of a magnetically insulated diode. A piecewise linear map is introduced that allows an efficient study of the electron dynamics in the stochastic regions.
Inertial range of two-dimensional turbulence in a Lagrangian renormalized approximation
Authors: Kaneda Yukio
Published: July 2002

The inertial range structure of two-dimensional turbulence is studied on the basis of a deductive Lagrangian renormalized approximation. The approximation is consistent with the energy spectra E(k)=Cε2/3 k−5/3 in the energy-transfer range and E(k)=C′β2/3 k−3 ×[ln(k/k1)]−1/3 (k≫k1) in the enstrophy-transfer range, and yields the estimates C=5.88 and C′=1.44. Here E(k) is the usual energy spectrum, ε and β are, respectively, the rates of energy and enstrophy transfer per unit mass, and k1 is the bottom of the enstrophy-transfer range.
Poloidal electric field generated by electron cyclotron heating in a collisional tokamak plasma
Authors: Chan V. S. , Wong S. K.
Published: July 2002

The poloidal electric field generated by electron heating in a collision dominated tokamak plasma is calculated by the adjoint method. The physical mechanism is elucidated as due to a combination of the Doppler shifted cyclotron resonance and magnetic field inhomogeneity. For uniform rf field on a flux surface, the normalized electrostatic potential is found to be much smaller than the inverse aspect ratio for realistic power levels.
Thermally driven convective cells and tokamak edge turbulence
Authors: Thayer D. R. , Diamond P. H.
Published: July 2002

A unified theory for the dynamics of thermally driven convective cell turbulence is presented. The cells are excited by the combined effects of radiative cooling and resistivity gradient drive. The model also includes impurity dynamics. Parallel thermal and impurity flows enhanced by turbulent radial diffusion regulate and saturate overlapping cells, even in regimes dominated by thermal instability. Transport coefficients and fluctuation levels characteristic of the saturated turbulence are calculated. It is found that the impurity radiation increases transport coefficients for high density plasmas, while the parallel conduction damping, elevated by radial diffusion, in turn quenches the thermal instability. The enhancement due to radiative cooling provides a resolution to the dilemma of explaining the experimental observation that potential fluctuations exceed density fluctuations in the edge plasma (eΦ/Te >n/n0).
Stability of a one-dimensional plasma in slab geometry
Authors: Jensen Torkil H. , Thompson William B.
Published: July 2002

Stability of a one-dimensional slab of plasma is considered for the simplest case of a static equilibrium with negligible pressure. A special class of deformations is considered that satisfies a magnetohydrodynamic (MHD) constraint except in a particular surface. These deformations, which resemble those considered for tearing modes, form a continuous path away from the equilibrium. The deformed configurations are not equilibria and their magnetic energies are, therefore, always larger than those of associated equilibria. It is shown that except for a special class of equilibria [previously discussed by Taylor, Phys. Rev. Lett. 33, 1139 (1974)] there exist deformations for which the magnetic energy is continuously decreasing, a result that is interpreted as showing that only this class is stable. The arguments, though asymptotic, are simple, essentially geometric, and do not require linearization. The results differ from those of the traditional linear tearing mode calculation [Furth, Killeen, and Rosenbluth, Phys. Fluids 6, 459 (1963)], making the class of stable equilibria smaller.
Simulation of oscillating field current drive on the reversed-field pinch
Authors: Harned Douglas S. , Schnack D. D. , Strauss H. R. , Nebel R. A.
Published: July 2002

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.
Electron acceleration using intense electromagnetic waves
Authors: Menyuk C. R. , Drobot A. T. , Papadopoulos K. , Karimabadi H.
Published: July 2002

Electron acceleration by an intense electromagnetic wave incident obliquely to the ambient magnetic field in a plasma is considered. It is shown that the wave amplitude has a stochasticity inducing threshold. Although substantial acceleration can be achieved below this threshold, it is limited to the trapping width of a single resonance. Above threshold, the electrons can accelerate from resonance to resonance. It is also shown that when the parallel phase velocity of the electromagnetic waves is supraluminous, the Hamiltonian surfaces describing the wave–particle interaction are topologically open. In this case, electrons gain large amounts of energy. The mechanism is quite robust, being weakly sensitive to changes in the wave parameters and the electron’s initial energy; as a result, it is an ideal mechanism for space applications. As an application, the conditions are obtained for accelerating electrons to energies of several MeV using ground-based transmitters.
Radial fluctuation scale of ion temperature gradient driven turbulence
Authors: Terry P. W. , Leboeuf J. N. , Diamond P. H. , Thayer D. R. , Sedlak J. E. , Lee G. S.
Published: July 2002

It is shown that ion temperature gradient driven turbulence supports fluctuations with broader radial scales than those inferred previously on the basis of mixing length arguments derived from the eigenfunction with lowest radial eigenmode number. These fluctuations of greater radial extent are more strongly excited and are shown to result in fluctuation levels and transport coefficients that can be considerably larger than those previously predicted. It is expected that transport of this nature would maintain ion temperature and density profiles near marginal stability in neutral beam heated and ion cyclotron resonance heated plasmas.
Numerical study on two-dimensional spin-up in a rectangle
Authors: Suh Yong K.
Published: July 2002

Two-dimensional spin-up in a rectangular geometry is examined by a numerical computation of the Navier–Stokes equations. Cells are, in most cases, created by the vorticity generated on the top and bottom boundaries. Further, the movement and interaction of those vortices play a key role in establishing the cell pattern in the quasisteady state. The critical phenomenon in the cell-pattern selection (a small perturbation can result in a completely different cell pattern) observed by previous investigators turns out to be caused by the critical movement of vortices; that is, a pair of vortices, for instance, can merge with or part away from each other by a small perturbation. The final quasisteady flow decays slowly at high Reynolds numbers having a linear relationship between the streamfunction and the vorticity in the core inviscid region.
Intense vortical structures in grid-generated turbulence
Authors: Villermaux E. , Sixou B. , Gagne Y.
Published: July 2002

This paper presents a set of experiments aimed at investigating the features and the statistical frequency of intense vortical structures (sometimes called ‘‘filaments’’, or ‘‘worms’’) as manifested by a migrating bubble technique in a mean shear free, homogeneous, isotropic, stationary turbulence generated by oscillating grids in a water tank for Rλ reaching up to 300. It is found that the nucleation of filaments at the surface of the walls of the tank, where boundary layers are liable to destabilize is much more frequent than in the homogeneous bulk of the tank where one filament is typically detected each hundred large scale turnover time. This distinction between the wall surface and the bulk activity, supplemented with the fact that the size of the filaments and their lifetime compare with the length and time-scales of the largest structures of the flow leads us to formulate an elementary model explaining the origin and the geometrical features of these intense vortical structures in turbulent flows for arbitrary Reynolds numbers.
Numerical simulation of spatially evolving Ekman layer instability
Authors: Marlatt Stuart W. , Biringen Sedat
Published: July 2002

The spatial development of Type II instabilities in the laminar Ekman layer is studied by means of direct numerical simulation. At a relatively low Reynolds number, a quasisteady, saturated, two-dimensional equilibrium state is obtained, while at a higher Reynolds number, the existence of an explosively growing, obliquely oriented secondary instability is demonstrated.
Chaotic mixing and heat transfer between confocal ellipses: Experimental and numerical results
Authors: Saatdjian E. , Midoux N. , Gastou Chassaing M. I. , Leprevost J. C. , André J. C.
Published: July 2002

The annular region between two concentric, confocal ellipses is a new geometry which is particularly effective for either mixing of viscous fluids or heat transfer enhancement in the important limit of a high Péclet number. This geometry is in many respects similar to the annular space between two eccentric, rotating cylinders although it possesses two (instead of one) axes of symmetry. The recently obtained analytical solution of the Stokes flow equations in this geometry shows that at steady state and for counter-rotation of the inner and outer ellipses, two opposite saddle points (connected by two different streamlines) appear in the region of minimum gap. This flow characteristic is also exhibited by the eccentric cylinder system for some cases of co-rotation. The Poincaré sections obtained when the inner and outer ellipses are displaced using a discontinuous velocity protocol show that a more effective long term mixing is obtained for the counter-rotating case, this is confirmed by the experimental data we have obtained. The opposite conclusions (more effective mixing for co-rotation) have been given in the eccentric cylinder geometry.

Photographs of the fluorescent dye after 5 periods are compared with remarkable success to numerical blob deformation experiments. Experimental results also confirm previous results based on an analysis of Poincaré sections. In particular, better mixing is obtained when the inner ellipse displacement per period increases. Finally, this geometry is shown to be particularly effective as a heat exchanger. For steady, counter-rotation of the two boundaries, the recirculation zones can lead to a heat transfer rate increase of 80% over that of pure conduction at high Péclet numbers, and, by an appropriate sinusoidal modulation of the angular velocity of one boundary, the heat transfer rate can be more than double that of pure conduction. Since an analysis of the experimental data also suggests that the mixing rate for a sinusoidal modulation of the angular velocity of the boundaries is better than for a discontinuous velocity protocol, we propose that the average Nusselt number per period could be one of the several useful tools in the global optimization of the mixing protocol.
Pair dispersion over an inertial range spanning many decades
Authors: Elliott Frank W. , Majda Andrew J.
Published: July 2002

New numerical results on scalar pair dispersion through an inertial range spanning many decades are presented here. These results are achieved through a new Monte Carlo algorithm for synthetic turbulent velocity fields, which has been developed and validated recently by the authors [J. Comput. Phys. 117, 146 (1995)]; this algorithm is capable of accurate simulation of a Gaussian incompressible random field with the Kolmogoroff spectrum over 12–15 decades of scaling behavior with low variance. The numerical results for pair dispersion reported here are within the context of random velocity fields satisfying Taylor’s hypothesis for two-dimensional incompressible flow fields. For the Kolmogoroff spectrum, Richardson’s t3 scaling law is confirmed over a range of pair separation distances spanning eight decades with a Richardson constant with the value 0.031±0.004 over nearly eight decades of pair separation, provided that the longitudinal component of the velocity structure tensor is normalized to unity. Remarkably, in appropriate units this constant agrees with the one calculated by Tatarski’s experiment from 1960 within the stated error bars. Other effects on pair dispersion of varying the energy spectrum of the velocity field and the degree of isotropy, as well as the importance of rare events in pair separation statistics, are also developed here within the context of synthetic turbulence satisfying Taylor’s hypothesis.
Spin-up in a rectangular tank with a discontinuous topography
Authors: van de Konijnenberg J. A. , van Heijst G. J. F.
Published: July 2002

The spin-up from rest to a state of solid-body rotation in a tank with one or more stepwise changes in depth is studied experimentally. Since flow across the steps is counteracted by the rotation acquired by the fluid in the course of the spin-up process, eventually the flow is forced into a cellular pattern determined by the position of the steps. However, if the initial flow field has little resemblance with the quasisteady pattern imposed by the topography, most of the energy of the flow may be dissipated before the organization into the preferred pattern is complete.
Transition flow in an impact pressure probe: Relevance of gas–wall interaction
Authors: Hartmaier Alexander , Urbassek Herbert M. , Sack Werner
Published: July 2002

Impact pressure probes may be used to measure the stagnation pressure of a spacecraft vehicle during reentry into the atmosphere. We model the flow in an impact pressure probe in the collision-free and transition regime using a kinetic simulation scheme of the Boltzmann equation. It is shown that, depending on the gasdynamic properties density, velocity, temperature of the inflow into the impact pressure probe, the measured pressure may deviate by almost a factor 2 from the stagnation pressure. Furthermore, we study the dependence of the flow in the impact pressure probe on the gas–wall interaction. The models by Maxwell, Cercignani and Lampis, and by Lord are implemented. The influence of the gas–wall interaction is sensible for small accommodation coefficients; it is more pronounced, however, for temperature and density than for the pressure.
The conformation change of model polymers in stochastic flow fields: Flow through fixed beds
Authors: Mosler Alisa B. , Shaqfeh Eric S. G.
Published: July 2002

Simulations of the conformation change of model polymers in various steady, anisotropic Gaussian random flow fields are presented. These flow fields have been chosen because they are models for the flow through porous media and have been predicted to be “stochastic strong flows” according to the criteria developed by Shaqfeh and Koch [J. Fluid Mech. 244, 17 (1992)]. To be specific, beyond a certain Deborah number (based on the sampling time of a velocity fluctuation), large average conformation change in the polymer is predicted. In our simulations, the polymers are modeled as dumbbells, but beyond this restriction, the assumptions of the theory by Shaqfeh and Koch are removed. Many realizations of the Gaussian fields are synthesized spectrally following a modified version of the method developed by Kraichnan [Phys. Fluids 13, 22 (1970)]. Moreover, the ratio of the mean “plug” flow to the amplitude of the fluctuations is varied from mean-dominant to fluctuation-dominant flows. The simulated conformation change shows that, in fact, these flows are “strong” in the sense that the average second moment of the end-to-end distance becomes large (relative to equilibrium) beyond a critical value of the fluctuation Deborah number. Although qualitatively capturing these trends, the theory by Shaqfeh and Koch underestimates the strength of the flows and thus overestimates the critical Deborah number. We present a new theory which includes spring relaxation and Brownian motion in the sampling of a velocity fluctuation (two factors which were neglected in the existing theory), thereby breaking the fore–aft symmetry of the sampling, thus increasing the average polymer stretch. The new theory quantitatively predicts the simulation results. To the authors knowledge, this is the first evidence via direct simulation that these random flows can produce large conformation change in model polymer molecules, even when the mean flow would produce no such change.
Azimuthal and streamwise disturbances in a fluid layer flowing down a rotating cylinder
Authors: Ruiz-Chavarrı́a G. , Dávalos-Orozco L. A.
Published: July 2002

In this paper an extensive investigation is done of the linear stability of a film falling down a vertical rotating cylinder. Two cases are considered: flow in the outside and flow in the inside of the cylinder. To this end, a system of differential equations which describe the instability is solved numerically with the Runge–Kutta fourth and sixth order methods. We show that in different circumstances the azimuthal disturbances become the most unstable when the rotation is taken into account. Moreover, a splitting of the azimuthal modes appears due to the Coriolis force. In the case of flow in the inside there is a threshold in the centrifugal force above which the flow is linearly stable. Besides, new results for the nonrotating case are also obtained.
Instabilities of a liquid layer locally heated on its free surface
Authors: Favre E. , Blumenfeld L. , Daviaud F.
Published: July 2002

We report experimental results concerning patterns in a model experiment built to study buoyant-thermocapillary-driven flows. The fluid is situated in a cooled cylindrical container and locally heated on its free surface. The resulting temperature gradient induces a basic flow which draws the surface fluid from the hot center toward the cold boundary. When the gradient is increased and depending on the height of liquid, the basic flow destabilizes into different stationary patterns. Above a second threshold, the patterns become time-dependent. These different instabilities are characterized and compared to recent theoretical results.
Buoyant flows with low-frequency jitter
Authors: Grassia P. , Homsy G. M.
Published: July 2002

A slot with applied temperature stratification is considered when mean gravity is directed along its length and weak quasistatic jitter is applied in the spanwise direction, but when there is no component of gravity in the vertical. The behavior of the slot is governed by a number of factors: The sense of the mean gravity with respect to the applied stratification, the spanwise and lengthwise Rayleigh numbers, the Prandtl and Biot numbers, and the spanwise–lengthwise aspect ratio of the slot. A perturbation expansion of the governing equations is performed for weak spanwise jitter. At the first order of perturbation there is a circulation around the slot, producing an advected temperature field with spanwise gradients. At second order there are inflows or outflows in both the spanwise and lengthwise directions, along with a vertical redistribution of fluid. There is also a temperature field with lengthwise gradients, which typically competes with the applied temperature gradient. Equations are derived governing the vertical structure of all these fields and are solved in terms of a set of special basis functions. A parametric study is performed for the solutions. When lengthwise buoyancy forces are absent (the lengthwise Rayleigh number is zero), it is comparatively easy to deduce the required fields. However, finite lengthwise Rayleigh numbers couple the momentum and thermal equations thereby affecting the structure of the fields. Interesting behavior is predicted for small Biot numbers, when convected heat is effectively trapped in the slot: Infinitessimal flows can produce finite advected temperatures. The limits of small Biot number and small lengthwise Rayleigh number are found to be noninterchangeable. At large lengthwise Rayleigh number, boundary layers occur for stable applied stratification and layered cellular structures occur for unstable stratification. For the stable case at moderately small Biot number, the temperature jump across the boundary layer is small compared with the depth independent temperature in the bulk. Then by exploiting the boundary layer nature of the solutions, it becomes simple to predict the bulk fluid temperatures, interfacial heat fluxes and the circulations associated with the buoyant flows. Turning to the unstably stratified case, it is demonstrated that runaways can occur at first order in the spanwise jitter, and these correspond to resonant excitation of three-dimensional, stationary, long wave Rayleigh–Bénard modes. It is demonstrated how the Biot number and the spanwise–lengthwise aspect ratio of the slot influence the lengthwise Rayleigh number at which these resonances occur. There is in addition a set of two-dimensional Rayleigh–Bénard modes, which can potentially become excited at second order. When the Biot number and the spanwise–lengthwise aspect ratio are not too large, the Rayleigh numbers corresponding to the two sets of modes are nearly coincident. The second-order system will then be strongly forced near resonance, causing it to have a disproportionately large response.
Incompressible turbulence and minimum Fisher information: Correlations between velocity and pressure
Authors: Cocke W. J. , Spector M. D.
Published: July 2002

The principle of minimum Fisher information (MFI) and the theory of random Gaussian fields are used to work out the joint distribution function of the density and velocity in homogeneous, isotropic, stationary, nearly incompressible turbulence, in the case where the velocity and pressure are correlated. The appropriate Fisher variables seem to be the mass flux, the density, and the generalized heat function (enthalpy) or pressure head. It is shown that simple constraints on the minimization may be chosen to give a good fit to the pressure distribution function found in recent direct numerical simulations and experiments, where the PDF is exponential for negative p and roughly exp[−(p/p0)3/2]p−1/2 for positive p. In this case, the fit is an improvement on a past MFI calculation, in which the correlations between p and u were not accounted for. In addition, the form of the conditional average 〈p|u〉 as found from direct numerical simulations is taken into consideration. The theory of random Gaussian velocity fields predicts 〈p|u〉=〈p|0〉−βu2, where u2≡u⋅u and β⩽1/8 is a constant. In conjunction with this theory, MFI predicts a specific dependence of the conditional average 〈ux2|p〉 on p, where ux is a typical velocity component. The conditional PDF P(ux|p) is slightly non-Gaussian, but P(ux) is Gaussian. The relation 2〈u2δp〉2=〈u2〉[〈u2(δp)2〉−〈u2〉〈(δp)2〉] is predicted.
Random forcing of three-dimensional homogeneous turbulence
Authors: Alvelius K.
Published: July 2002

A method of using a fully random force to numerically generate statistically stationary homogeneous turbulence has been developed. The forcing is implemented in spectral space where it is concentrated at small wave numbers. Hence, the power input is introduced into the flow at large scales. The randomness in time makes the force neutral, in the sense that it does not directly correlate with any of the time scales of the turbulent flow, and it also makes the power input determined solely by the force-force correlation. This means that it is possible to generate different desirable turbulence states, such as axisymmetric turbulence, where the degree of anisotropy of the forcing can be chosen a priori through forcing parameters. In particular, the total amount of power input from the forcing can be set to balance a desired dissipation at a statistically stationary state. In order to only get a contribution from the force-force correlation to the input power in the discrete equations, the force is determined so that the velocity-force correlation vanishes for each Fourier mode. In direct numerical simulations (DNS) of forced isotropic turbulence, universality of the small scales is shown for the kinetic energy spectrum at different Reynolds numbers and the velocity derivative skewness obtains the value −0.5. The forcing method is used in a large eddy simulation (LES), where it is compared with a simulation of decaying turbulence to show the importance of having a statistically stationary flow if well known inertial laws are to be recovered at moderate Reynolds numbers.
A note on nonlinear corrections to the Ekman layer pumping velocity
Authors: Hart J. E.
Published: July 2002

High order corrections to the Ekman pumping formula are derived analytically by a regular perturbation expansion in the external flow Rossby number. General shear lines V(x) and general circular vortices V(r) are considered. The results extend previous calculations based on the assumption of constant vorticity in the exterior fields. At each order in the expansion, higher derivatives of the basic external flow are introduced, thus rendering the pumping more and more nonlocal as additional orders in Rossby number are included. For general profiles of exterior velocity, the constant vorticity similarity and perturbation solutions may be corrected using the formulas presented here.
Phase advance for an intense charged particle beam propagating through a periodic quadrupole focusing field in the smooth-beam approximation
Authors: Davidson Ronald C. , Qian Qian
Published: July 2002

The envelope equations for a uniform-density Kapchinskij–Vladimirskij (KV) beam equilibrium are used to derive a transcendental equation for the phase advance of an intense charged particle beam propagating through a periodic quadrupole focusing lattice, κq(s)=κq(s+S). The analysis is carried out for the case of a matched beam in the smooth-beam approximation, and precise estimates of the phase advance are obtained for a wide range of system parameters and choices of lattice function κq(s). Introducing the quadratic measure, σ20/S2 = 〈[∫s0sds κq(s)]2〉, of the average quadrupole focusing field squared, a detailed analysis of the transcendental equation for the phase advance σ is used to quantify the range of validity of the approximate estimate of the phase advance obtained from the simple quadratic equation (σ/S)2+(K/ε)(σ/S)=(σ0/S)2. Here, σ=εS/r̄2b is the phase advance for a circular beam with average radius r̄b, ε is the unnormalized beam emittance, S is the periodicity length of the lattice, and K is the self-field perveance. For σ0≲30°, it is found that the (approximate) quadratic expression for σ gives an excellent estimate of the phase advance over the entire range of KS/ε, and the quadratic estimate for σ is accurate to within 5% for values of σ0 approaching σ0=60°.
Response to ‘‘Comment on ‘Critique of atomic physics instability mechanisms: Ionization-driven and radiative microinstabilities in the tokamak edge plasma’ ’’ [Phys. Plasmas 1, 2806 (1994)]
Authors: Ross David W.
Published: July 2002

Both the nonlinear theory and the numerical calculations of atomic-driven turbulence demostrate that a solution to the radative microinstability is the tokamak edge plasma exists which is required to establish the validity of the equation used and the existance of stationary turbulence. (AIP)
Upstream structure of collisionless perpendicular shocks
Authors: Simerský Mojmír , Simerská Carmen
Published: July 2002

A full set of Vlasov–Maxwell equations describing a stationary perpendicular collisionless shock has been solved in the asymptotic case x→±∞, where x is the spatial coordinate of the one dimensional (1-D) shock geometry. The perpendicular magnetic field in the upstream region has been found to vary asymptotically as Bz(x)−Bz(−∞)∼exp(−bx/Rp), where b(MA,βp,βe)<0 is a function of the Alfvén Mach number, MA, and the proton and electron betas; Rp is the proton Larmor radius. The electron and proton distribution functions are expressed as one-dimensional integrals to be evaluated numerically. Two general results are derived: (i) there occurs an instability, in the sense that the distribution functions are not unique, for −b/MA=(mp/me)1/2, where mp and me are the proton and the electron mass, respectively. Numerical computations show that the lowest value of MA fulfilling this instability condition is Mc≊6.5. (ii) The perpendicular shock cannot develop if MA≤(1+βp+βe)1/2. Moreover, it was found that for MA, βp, and βe from a certain range, the proton distribution function exhibits a peak of reflected particles, with vx≊0 and vy≊2.33v0, i.e., with an energy of about 5.4 times that of the incident flux.
Cyclotron subharmonics resonant (CSR) heating
Authors: Abe Hirotada
Published: July 2002

Corresponding to the experiment done with the JIPPT-II-U device [Phys. Rev. Lett. 54, 2339 (1985)], the cyclotron subharmonics resonant (CSR) heating mechanism is studied using particle simulation codes with an emphasis on the relationship between CSR and the nonlinear Landau damping.
Poloidal spin-up of tokamak plasmas from poloidal asymmetry of particle and momentum sources
Authors: Hassam A. B. , Antonsen T. M.
Published: July 2002

Transport equations for particle density, toroidal angular momentum, and poloidal rotation are derived in the presence of strong particle and momentum sources in general axisymmetric toroidal geometry. It is shown that the state with no poloidal rotation is unstable on flux surfaces where the local particle source rate is sufficiently poloidally asymmetric and, roughly, more rapid than the damping rate of poloidal rotation from magnetic pumping. In agreement with earlier results, it is also shown that a toroidally injected momentum source can drive poloidal rotation if the momentum deposition is poloidally asymmetric. Thus poloidal rotation could be induced in tokamaks by asymmetric particle fueling.
The effect of electron beam on the electron hole in a plasma
Authors: Sayal V. K. , Jain S. L. , Sharma S. R.
Published: July 2002

An electron hole is discussed theoretically in an electron beam–plasma system. The nonlinear dispersion relation for the electron hole along with the conditions on the existence of the electron hole is investigated numerically. It is found that depending upon the beam parameters and radial boundary there are two regions where the electron hole can be formed. It is also seen that the upper limit on Mach number of the electron hole does not vanish even in the presence of the electron beam. The electron holes of high Mach number are possible only in the presence of an electron beam.
Nonlinear saturation of curvature induced low-frequency instability
Authors: Dwivedi C. B.
Published: July 2002

Analytical analysis of the nonlinear saturation of the Rayleigh–Taylor (R–T) instability has been carried out and an appropriate physical model has been proposed for the saturation mechanism. Stationary wave formalism and initial value approach have been applied for the analysis. In the former case, a linear superposition model has been forwarded to understand the nonlinear saturation process, whereas in the latter, the mode–mode coupling model. Parallel friction due to shear effect and ion polarization drift are identified as the basic sources of the nonlinearity. Utility of the results in laboratory plasmas are highlighted.
A kinetic model of pulsed sheaths
Authors: Keiter E. R. , Hitchon W. N. G. , Goeckner M. J.
Published: July 2002

The ion distribution function is calculated as a function of time, self-consistently with the electrostatic potential in two spatial coordinates for a pulsed sheath experiment. Such pulsed sheaths are used for a variety of purposes, including modification of material surfaces. The accuracy of the model is established by comparing the time varying ion density with experimental measurements. Additionally, the first reported prediction of the ion velocity distribution in this kind of pulsed sheath is given. This is important because the velocity distribution of the ions striking the surface determines how the surface material is modified.
Linear and nonlinear dynamics of Alfvén eigenmodes in tokamaks
Authors: Vlad G. , Kar C. , Zonca F. , Romanelli F.
Published: July 2002

Linear and nonlinear dynamics of various toroidicity induced global Alfvén eigenmodes is investigated by means of an initial value numerical code. The code uses the reduced magnetohydrodynamic (MHD) model expanded to the third order in the inverse aspect ratio parameter ε (ε ≡ a/R0, with a the minor radius of the plasma column and R0 the major radius of the vacuum chamber). Nonlinear saturation is shown to occur due to the excitation of a perturbation to the nonlinear mode structure, which dissipates energy on very short scales. In particular, the nonlinear saturation of the Toroidal Alfvén Eigenmodes (TAE) and of the Resistive Periodic Shear Alfvén Eigenmodes (RPSAE) due to MHD nonlinearities is investigated and compared with analytical predictions.
A topological approach to the problem of charged particle trajectories in a toroidal axisymmetric configuration
Authors: Doloc C. M. , Martin G.
Published: July 2002

This paper proposes a new approach for solving the general problem of Charged Particle Orbits in an axisymmetric toroidal configuration. This method is based upon the guiding center theory and gives a general and ‘‘a priori’’ classification of the topological properties of the trajectories. For a typical tokamak plasma, fifteen topological classes of orbits and their boundaries in a Constant-Of-Motion-space are found without any trajectory computation. The confinement of these energetic orbits into the plasma region is then discussed. The method remains useful for any arbitrary toroidal axisymmetric configuration, as X-points, doublets, etc., being strictly independent of the equilibrium mathematical form. This new approach may be applied mainly to charged fusion products and runaway electrons produced during disruptions.