bluuebunny/crossref_metadata_2025 huggingface dataset:
Continuous iteration of dynamical maps
Authors: Aldrovandi R. , Freitas L. P.
Published: July 2002

A precise meaning is given to the notion of continuous iteration of a mapping. Usual discrete iterations are extended into a dynamical flow which is a homotopy of them all. The continuous iterate reveals that a dynamic map is formed by independent component modes evolving without interference with each other. An application to turbulent flow suggests that the velocity field assumes nonseparable values.
Higher dimensional Painlevé integrable models from the Kadomtsev–Petviashvili equation
Authors: Lou Sen-yue , Xu Jian-jun
Published: July 2002

After embedding the Kadomtsev–Petviashvili equation in higher dimensions and extending the Painlevé analysis approach to a new form such that the coefficients of the expansion around the singular manifold possess conformal invariance and contain explicit new space variables, we can get infinitely many Painlevé integrable models in (3+1)-dimensions and higher dimensions. Some concrete higher dimensional modified Korteweg–de Vries type of extensions are given. Whether the models are Lax integrable or integrable under other meanings remain still open.
On the geometric structure of thermodynamics
Authors: Chen M.
Published: July 2002

In this paper we consider symmetry transformations of the generalized entropy function that preserve the Gibbs one-form (Gibbs relation). We show that this symmetry consideration naturally leads to the geometric structure of thermodynamics in terms of contact geometry. We also construct an example based on the van der Waals’ fluid to illustrate the method discussed in the paper.
Nonunitary representations of the SU(2) algebra in the Dirac equation with a Coulomb potential
Authors: Martı́nez-y-Romero R. P. , Salas-Brito A. L. , Saldaña-Vega Jaime
Published: July 2002

A novel realization of the classical SU(2) algebra is introduced for the Dirac relativistic hydrogen atom defining a set of operators that allow the factorization of the problem. An extra phase is needed as a new variable in order to define the algebra. We take advantage of the operators to solve the Dirac equation using algebraic methods. A similar path to the one used in the angular momentum case is used; hence, the radial eigenfunctions so calculated comprise nonunitary representations of the algebra. One of the interesting properties of such nonunitary representations is that they are not labeled by integer nor by half-integer numbers, as occurs in the usual angular momentum representation.
Physical properties of quantum field theory measures
Authors: Mourão J. M. , Thiemann T. , Velhinho J. M.
Published: July 2002

Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with different masses is studied. We apply the same methods to study the Ashtekar–Lewandowski (AL) measure on spaces of connections. In particular we prove that the diffeomorphism group acts ergodically, with respect to the AL measure, on the Ashtekar–Isham space of quantum connections modulo gauge transformations. We also prove that a typical, with respect to the AL measure, quantum connection restricted to a (piecewise analytic) curve leads to a parallel transport discontinuous at every point of the curve.
New generalized coherent states
Authors: Penson K. A. , Solomon A. I.
Published: July 2002

We construct a new family of boson coherent states using a specially designed function which is a solution of a functional equation dε(q,x)/dx=ε(q,qx) with 0⩽q⩽1 and ε(q,0)=1. We use this function in place of the usual exponential to generate new coherent states |q,z〉 from the vacuum, which are normalized and continuous in their label z. These states allow the resolution of unity, and a corresponding weight function is furnished by the exact solution of the associated Stieltjes moment problem. They also permit exact evaluation of matrix elements of an arbitrary polynomial given as a normally-ordered function of boson operators. We exemplify this by showing that the photon number statistics for these states is sub-Poissonian. For any q<1 the states |q,z〉 are squeezed; we obtain and discuss their signal to quantum noise ratio. The function ε(q,x) allows a natural generation of multiboson coherent states of arbitrary multiplicity, which is impossible for the usual coherent states. For q=1 all the above results reduce to those for conventional coherent states. Finally, we establish a link with q-deformed bosons.
Invariance groups of transformations of basic hypergeometric series
Authors: Van der Jeugt J. , Srinivasa Rao K.
Published: July 2002

We show that certain two-term transformation formulas between basic hypergeometric series can easily be described by means of invariance groups. For the transformations of nonterminating φ23 series, and those of terminating balanced φ34 series, these invariance groups are symmetric groups. For transformations of φ12 series the invariance group is the dihedral group of order 12. Transformations of terminating φ23 series are described by means of some subgroup of S6, and finally the invariance group of transformations of very-well-poised nonterminating φ78 series is shown to be isomorphic to the Weyl group of a root system of type D5.
Anisotropic self-avoiding walks
Authors: Borgs Christian , Chayes Jennifer , King Christopher , Madras Neal
Published: July 2002

We consider a model of self-avoiding walks on the lattice Zd with different weights for steps in each of the 2d lattice directions. We find that the direction-dependent mass for the two-point function of this model has three phases: mass positive in all directions; mass identically −∞; and masses of different signs in different directions. The final possibility can only occur if the weights are asymmetric, i.e., in at least one coordinate the weight in the positive direction differs from the weight in the negative direction. The boundaries of these phases are determined exactly. We also prove that if the weights are asymmetric then a typical N-step self-avoiding walk has order N distance between its endpoints.
The one-dimensional spinless relativistic Coulomb problem
Authors: Lucha Wolfgang , Schöberl Franz F.
Published: July 2002

Motivated by a recent analysis that presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a (“hard-core amended”) Coulomb interaction potential in one dimension. We prove the existence of a critical coupling constant (which contradicts the assertions of the previous analysis) and give analytic upper bounds on the energy eigenvalues. These upper bounds seem to disprove the previous explicit solution.
Becchi–Rouet–Stora–Tyutin invariant formulation of spontaneously broken gauge theory in a generalized differential geometry
Authors: Okumura Yoshitaka
Published: July 2002

Noncommutative geometry (NCG) on a discrete space successfully reproduces the Higgs mechanism of the spontaneously broken gauge theory, in which the Higgs boson field is regarded as a kind of gauge field on the discrete space. People also know how to construct the generalized differential geometry (a GDG) as one version of NCG on a discrete space M4×ZN where ZN denotes the N points discrete space. A GDG is a direct generalization of the differential geometry on the ordinary manifold into the discrete one. In this paper, we attempt to construct the Becchi–Rouet–Stora–Tyutin (BSRT) invariant formulation of spontaneously broken gauge theory based on a GDG and obtain the BSRT invariant Lagrangian with the ’t Hooft–Feynman gauge fixing term.
A bistatic inverse scattering problem for electromagnetic waves
Authors: Wang Jenn-Nan
Published: July 2002

In this paper we discuss a bistatic inverse scattering problem for Maxwell’s equations. We show that both the electric permittivity and magnetic permeability can be uniquely recovered from the knowledge of S(s,θ,θ′) for all s∈R and special pairs of orthonormal vectors (θ,θ′) provided that they are close to constants, where S(s,θ,θ′) is the scattering kernel associated with Maxwell’s equations. In other words, in this scattering experiment, measurements are made on a set of a priori arranged pairs of incoming and reflected directions.
Counterexamples to Parker’s theorem
Authors: Bogoyavlenskij Oleg I.
Published: July 2002

Two families of exact global solutions to the equations of plasma equilibrium are derived. These solutions have no singularities, are localized, and are quasiperiodic in variable z; each family depends on an arbitrary number of free parameters. The solutions model a wide variety of magnetic field phenomena that might occur in laboratory plasmas, in astrophysical jets, and in solar corona. The same solutions describe global equilibria of an ideal incompessible fluid. In addition, these families provide counterexamples to a well-known theorem of Parker.
The generalized Casimir operator and tensor representations of groups
Authors: Gladush V. D. , Konoplya R. A.
Published: July 2002

A new method of the constructing of the basic functions for spaces of tensor representations of the Lie groups, with the help of the generalized Casimir operator, has been proposed. In the definition of the operator there we used the Lie derivatives instead of the corresponding infinitesimal operators. When introducing the generalized Casimir operator we used the metric for which a group being considered will be isometry that follows from the invariance condition for the generalized Casimir operator. This allows us to formulate the eigenvalue and eigenfunction problems correctly. The invariant projection operators have been constructed in order to separate irreducible components. The cases of the Bianchi type G3IX and G3II groups are considered as examples.
Conjugation in braided C*-categories and orthogonal quantum groups
Authors: Lance E. C. , Paolucci A.
Published: July 2002

We consider braided C*-categories with conjugates and the notion of dimension. If the braid is a Birman–Wenzl–Murakami symmetry then we characterize the compact orthogonal quantum groups.
Generalized bc-systems based on Hermitian vector bundles
Authors: Schork Matthias
Published: July 2002

A generalized bc-system associated to a Hermitian vector bundle over a Riemann surface is introduced in close analogy to the usual rank one case. Some of the geometric analogies to the well-known case are studied. In particular, if there are no zero-modes, the “non-Abelian” theta divisor appears. In the general case where zero-modes exist, it seems to be more difficult to find a natural description. It is discussed in detail why no such system exists in low genus that is on the Riemann sphere and on elliptic curves.
High Marangoni number convection in a square cavity: Part II
Authors: Carpenter Bradley M. , Homsy G. M.
Published: July 2002

Steady thermocapillary flow is examined in a square two-dimensional cavity with a single free surface and differentially heated side walls. The numerical solutions are obtained with a finite difference method applied to a streamfunction-temperature formulation. This work investigates the Prandtl number dependence, structure, and stability of high Marangoni number flow. It is found that the character of thermocapillary flow is highly sensitive to the value of the Prandtl number over a range of Marangoni numbers exceeding 1×105 for 1≤Pr≤50, the magnitude of the flow showing nonmonotonic dependence on the Marangoni number for Pr≤∼10. A complete structural analogy is observed between flow in a cavity driven by a moving lid and thermocapillary flow in the boundary layer limit, and it is found that all the solutions, spanning a wide range of Marangoni and Prandtl numbers, are linearly stable to a restricted class of disturbances.
The average rotation rate of a fiber in the linear flow of a semidilute suspension
Authors: Koch Donald L. , Shaqfeh Eric S. G.
Published: July 2002

Shaqfeh and Fredrickson [Phys. Fluids A 2, 7 (1990)] renormalized the multiple reflection expansion for hydrodynamic fiber interactions in a semidilute suspension, nl3≫1 and φ≪1, where φ is the fiber volume fraction, n is the number of fibers per unit volume, and l is the fiber half-length. We use the results of Shaqfeh and Fredrickson to obtain the average rotation rate of a fiber in linear shear flows of a semidilute suspension. Specific results are obtained for the case where most of the fibers are oriented in a preferred direction, as occurs in simple shear and extensional flows. The correction to the O(γ̊) Jeffrey rotation rate [Proc. R. Soc. London Ser. A 102, 161 (1922); J. Fluid Mech. 14, 284 (1962)] due to hydrodynamic interactions is shown to be O[γ̊/ln(1/φ)], where γ̊ is the shear rate.
The effect of electromagnetic fields on the stability of a uniformly elongating plastic jet
Authors: Littlefield David L. , Powell John D.
Published: July 2002

In this paper the stability characteristics of an infinitely long, uniformly elongating metal jet are investigated. The application to a metallic jet formed from an explosive charge, or shaped-charge jet, is of particular interest. The effect of an axial electric current on the stability of the jet is determined. The jet is assumed to be perfectly plastic, perfectly conducting, nonswirling, and isothermal. The governing equations are solved to determine the idealized motion of the jet, which is then perturbed by an arbitrary three-dimensional disturbance. The resulting first-order equations are solved numerically for the time evolution of this perturbation. For a given initial condition, the growth rate of the disturbance depends on the relative importance of the inertial, electrical, and plastic forces. The details of growth rate characteristics are explained in terms of the appropriate physical principles.
Analysis of viscous dissipation in disk storage systems and similar flow configurations
Authors: Humphrey J. A. C. , Schuler C. A. , Iglesias I.
Published: July 2002

Flows in rotating magnetic disk storage systems and similar devices are prone to instabilities and the viscous generation of heat. Serious degradation in the performance of disk storage systems occurs when differential thermal expansion, due to the maldistribution of heat, and flow-induced vibrations result in track misregistration by the magnetic read/write heads. Submicron flying heights and micron track widths exacerbate such alignment difficulties. High rotation speeds, also characterizing the emerging disk storage technology, impose significant torque requirements. Experimental measurements of torque obtained by Daily and Nece [J. Basic Eng. Trans ASME 82, 217 (1960)] for a single disk, and by Hudson and Eibeck [J. Fluids Eng. 113, 648 (1991)] for a disk stack with and without obstructions, both in cylindrical enclosures, are found in this study to be correctly correlated by the analytically derived equation, TNo≡Ttotρ/Nμ2R2 = (2C1 + C2H/R2) × [Re/(1 − tL/HR2)]3/2+m, where TNo is a newly defined dimensionsless torque number, Re is the Reynolds number of the interdisk flow; H, R2, t, and L are geometrical length scales; and, C1, C2, and m are experimentally determined constants of order unity.

Regressions to the experimental data of these authors yield values for C1, C2, and m in this equation which offer a combination of accuracy and universality not previously available. Moderate amounts of imposed radially directed flows in the spaces between unobstructed pairs of corotating disks are shown, via numerical calculation, to affect the interdisk flow fields quite notably. Analysis of results obtained solving the Navier–Stokes equations, assuming unsteady, axisymmetric, streamlined flow at low speeds of rotation shows that sucking air radially inward in the interdisk space, rather than blowing it radially outwards, substantially reduces the torque required to rotate the disks relative to the unventilated condition. Notwithstanding, depending on how the sucking condition is implemented, in obstructed geometries the reduction in torque may come at the expense of flow instabilities that could affect magnetic head read/write performance, a problem requiring close attention in the application of present findings to the improved design of disk storage systems.
Convective instability of autocatalytic reaction fronts in vertical cylinders
Authors: Vasquez Desiderio A. , Wilder Joseph W. , Edwards Boyd F.
Published: July 2002

Linear stability analysis predicts that the onset of convection for an ascending autocatalytic reaction front in a vertical cylinder corresponds to a nonaxisymmetric mode. This mode consists of a single convective roll confined to the region near the reaction front, with fluid rising in half of the cylinder and falling in the other half. Experiments show a flat front below the onset of convection and an axisymmetric front well above the onset of convection. New experiments are called for to closely examine the onset of convection in order to test this prediction.
Eddy Rossby wave frequency in β-plane turbulence
Authors: Galperin Boris , Sukoriansky Semion , Staroselsky Ilya
Published: July 2002

The concept of eddy viscosity is generalized to include an ‘‘eddy β-term’’ that accounts for the effect of unresolved turbulence and Rossby waves on the resolved modes in the subgrid-scale representation of β-plane turbulence.
The balance of momentum and energy at an interface between colliding and freely flying grains in a rapid granular flow
Authors: Jenkins James T. , Hanes Daniel M.
Published: July 2002

A steady rapid flow of a granular material down an incline is considered and attention is focused on the relatively narrow region of transition between a concentrated regime of colliding grains and a more dilute regime of freely flying grains. Momentum and energy are balanced over a control volume with surfaces in each flow regime, the solid volume fraction is determined at the interface, and the boundary condition on the energy of the velocity fluctuations at the top of the collisional regime is obtained.
Self-adjoint formulation of plasma heating in the ion-cyclotron range of frequencies
Authors: Romero H. , Morales G. J.
Published: July 2002

It is shown that second-order (ρ/L) corrections in the expression for the equilibrium distribution function are required to obtain a self-adjoint system of equations for ion cyclotron range of frequencies (ICRF) wave propagation in a nonuniform plasma (ρ denotes the ion-Larmor radius and L the gradient scale length). Self-adjointness results in energy conservation in the absence of absorption mechanisms, as expected. A Lagrangian density is obtained, which yields both the wave operator and its adjoint, and directly results in the conservation law of the truncated system.
Electron cyclotron power absorption and current drive in the lower hybrid heating regime
Authors: Farina Daniela , Pozzoli Roberto
Published: July 2002

The power deposition and the current drive by electron cyclotron waves interacting at the downshifted cyclotron resonance with the suprathermal electrons in a lower hybrid heating tokamak regime is analyzed. The power absorption is evaluated in the framework of the relativistic linear theory, using a suitable model electron distribution to describe the lower hybrid sustained plasma; the driven current is computed by means of the adjoint method. Top and equatorial launch have been explored for a wide range of plasma parameters and propagation angles. A favorable scaling of the driven current with the magnetic field is found with a proper choice of launching conditions. The results are interpreted in terms of single-particle efficiencies for absorption and current drive, location of resonant regions in momentum and physical space, and characteristics of the ray trajectories.
Numerical study of resistive magnetohydrodynamic modes in high-temperature plasma of general toroidal geometry
Authors: Kim Jin-Yong , Choi Duk-In
Published: July 2002

The linearized resistive magnetohydrodynamic (MHD) boundary layer equations in general toroidal geometry are numerically solved to investigate ETG (the effect of temperature gradient coupled with thermal conduction and transport) on the linear stability of the three resistive MHD modes (ballooning, tearing, and interchange). The present model is more realistic than usual for high-temperature plasma in that it includes ETG in addition to the effects from electron diamagnetic drift and compression. It is found that ETG gives substantial stabilization to the resistive ballooning mode, as well as to the tearing mode, while the resistive interchange mode is destabilized by this effect. Though most of the findings are in good agreement in their essential points with existing work, the conclusion associated with the resistive ballooning mode appears to be in disagreement with some aspects of previous work. An analysis of the reasons for this discrepancy is presented.
Boundary conditions for the Darwin model
Authors: Weitzner H. , Lawson W. S.
Published: July 2002

The ambiguity in boundary conditions for the Darwin model is considered in depth. While no single boundary condition seems dictated by physical considerations alone, one set of boundary conditions is presented which has several desirable properties. These include a minimum error principle, numerical tractability, a well-behaved Poynting theorem, and a conservation law for the boundary charge density. The consequences of the boundary conditions are worked out for several simple geometries which are common in computational work.
Theory of weak ion temperature gradient-driven turbulence near the threshold of instability
Authors: Mattor N. , Diamond P. H.
Published: July 2002

In this paper a theory of weak ion temperature gradient-driven turbulence near the threshold of instability is presented. The model considers kinetic ions and adiabatic electrons in a sheared slab geometry. Linear theory shows that for ηth<ηi≲ηth+(1+Ti/Te) Ln/Ls (where ηth=0.95 is the instability threshold and Ln/Ls≪1) then γ≪ω and a weak turbulence theory applies. The nonlinear wave kinetic equation indicates that ion Compton scattering is the dominant nonlinear saturation process, and it is shown that the energy scatters to the linearly stable low ky modes. The resulting fluctuation spectrum (peaked about k⊥ρi≂1) is much lower than that suggested by naive extrapolation from the strong turbulence regime. The resulting ion thermal conductivity is also extremely low, so that strong ion heating can be expected to drive the ion temperature gradient to a level where this weakly turbulent threshold regime is surpassed. Thus the critical ηi relevant to magnetic confinement experiments is not the linear instability threshold but the point where the diminutions of the weak turbulence regime vanish, and the transport increases to the strong fluid turbulence level.
Toroidal field generation and magnetic field relaxation in a conical-theta-pinch-generated configuration
Authors: Wira K. , Pietrzyk Z. A.
Published: July 2002

The configurations generated by conical theta pinches (CθP’s) of angles 10° and 18° were studied experimentally. The hydrogen plasma density and temperature were approximately 1–3×1015 cm−3 and 5 eV, respectively. The magnetic field structure was measured by four three-dimensional magnetic probes. The magnetic helicity and energy of the configuration were calculated directly from the measured magnetic field through algorithms that were independent of the chosen coordinate and configuration axis. The magnetic fluxes were calculated after the axis was located. Single-fluid model equations predict that the toroidal field can be generated by effects that are normally neglected in the simple Ohm’s law, of which the Hall effect is the most important. The average toroidal field generation was measured to vary quadratically with the cone angle of the CθP, and this field could be accounted for by the Hall effect alone. The time histories of the magnetic helicity and energy decay and poloidal to toroidal flux conversion indicated that the relaxation of the configuration had occurred in agreement with the Taylor hypothesis. The relaxation time history indicated that the relaxation behaved like a turbulent relaxation process. Therefore a spheromaklike configuration could either be generated directly by the CθP (if the generated toroidal and poloidal field had an appropriate distribution) or through relaxation (if only small amount of toroidal field was generated).
Influence of an energetic ion population on tokamak plasma stability
Authors: White R. B. , Romanelli F. , Bussac M. N.
Published: July 2002

The stability of a tokamak plasma to ideal and resistive internal kink modes in the presence of an energetic trapped-particle population is analyzed. Domains of stability are found for both slowing-down and Maxwellian particle distributions. The stable domains are at moderately high plasma beta and involve a significant, but easily obtainable high-energy trapped-particle density.
Stationary flow model of ablatively imploded spherical shells
Authors: Montierth L. M. , Morse R. L.
Published: July 2002

The stationary flow model of spherical ablation is extended to shells, solutions with a density discontinuity at the critical surface, and charged-particle-beam-driven ablation. Parameter studies of the shell solutions show the relationship between shell aspect ratio, relative ablative mass removal or burnthrough, laser power, and shell material type. The discontinuous solutions are shown to occur when the critical surface and sonic surface coalesce. The relationship of these discontinuous solutions to particular physical situations is shown to be ambiguous in a way that must be resolved by microscopic transport calculations. Charged-particle-driven ablative implosion processes are shown to resemble laser-driven ablation. However, qualitatively different ablation processes occur in different regimes of the power and particle range of the incident beam. Procedures are described by which stationary solutions can be used to predict and interpret the results of experiments and numerical simulations.
Symmetry breaking bifurcations of a current sheet
Authors: Parker R. D. , Dewar R. L. , Johnson J. L.
Published: July 2002

Using a time evolution code with periodic boundary conditions, the viscoresistive hydromagnetic equations describing an initially static, planar current sheet with large Lundquist number have been evolved for times long enough to reach a steady state. A cosh2 x resistivity model was used. For long periodicity lengths Lp, the resistivity gradient drives flows that cause forced reconnection at X point current sheets. Using Lp as a bifurcation parameter, two new symmetry breaking bifurcations were found: a transition to an asymmetric island chain with nonzero, positive, or negative phase velocity, and a transition to a static state with alternating large and small islands. These states are reached after a complex transient behavior, which involves a competition between secondary current sheet instability and coalescence.
The effect of the ion transit resonance on the resistive magnetohydrodynamic modes
Authors: Romanelli Francesco , Chen Liu
Published: July 2002

The stability of resistive interchange and ballooning modes is analyzed taking into account the kinetic effects associated with the ion transit resonance. In the parallel compressible limit, it is found that kinetic effects yield an unstable localized mode driven by inverse ion Landau damping. In addition, no threshold is found for the resistive ballooning mode even in the presence of average good curvature, with the effect of the ion transit resonance being destabilizing.
A practical limitation on transport by ripple-trapped ions
Authors: Gentle K. W. , Hazeltine R. D.
Published: July 2002

Ripple in the toroidal field of tokamaks is predicted to enhance ion transport at low collisionality because ions trapped in the magnetic wells are prevented from moving poloidally along field lines; their grad-B drift then can generate a large radial step for diffusion. However, tokamaks generally have radial electric fields that will drive poloidal motion even for ripple-trapped ions, thereby moderating the transport. For typical parameters, electric field effects enter for collisionalities only somewhat smaller than ripple effects themselves. This suggests that ripple effects will not seriously degrade thermal ion transport. High-energy populations remain subject to strong effects of ripple.
Large gyroradius m=1 Alfvén modes and energetic particles
Authors: Pegoraro F. , Porcelli F. , Schep T. J.
Published: July 2002

Nonmagnetohydrodynamic effects, caused by a minority population of energetic particles and/or by the large gyroradii of the main ion population, strongly modify the stability of a high temperature toroidal plasma against m=1 internal modes. It is shown that the enhanced stability due to the presence of the energetic particles is reduced in the large gyroradius regime, where the width of the transition layer of the mode is determined by the gyroradius of the main ions. This modification results from the presence of a discrete spectrum of resistively damped Alfvén-type modes which can be destabilized through the resonance with the energetic particles.
Inverse energy cascades in three-dimensional turbulence
Authors: Hossain Murshed
Published: July 2002

Fully three-dimensional magnetohydrodynamic (MHD) turbulence at large kinetic and low magnetic Reynolds numbers is considered in the presence of a strong uniform magnetic field. It is shown by numerical simulation of a model of MHD that the energy inverse cascades to longer length scales when the interaction parameter is large. While the steady-state dynamics of the driven problem is three-dimensional in character, the behavior has resemblance to two-dimensional hydrodynamics. These results have implications in turbulence theory, MHD power generator, planetary dynamos, and fusion reactor blanket design.
Magnetohydrodynamic equilibria in the vicinity of an X-type neutral line specified by footpoint shear
Authors: Finn John M. , Lau Yun-Tung
Published: July 2002

Results pertaining to two-dimensional (∂/∂z=0) magnetohydrodynamic equilibria in the presence of an X-type neutral line are presented. Naive analyses indicate that there may be tangential discontinuities in B, specifically discontinuities in Bz across the separatrix connected to the X line. However, such analyses indicate an infinite z component of footpoint displacement (or safety factor q in the toroidal case) at the separatrix. The solutions presented here allow the specification of footpoint displacement (or safety factor q) that is finite as the separatrix is approached. These solutions are scale-invariant, or similarity, solutions. They are appropriate near the X line on length scales intermediate between the boundary layer width because of resistivity (or other nonideal effects) and the macroscopic length scale. Force balance across the separatrix implies identical radial dependence in all four quadrants and continuity of B2z across the separatrix. The latter shows that there are two classes of solutions: those with Bz continuous across the separatrix and those with ‖Bz‖ continuous but with a sign change in Bz. The former class has fractional power-law singularities at the separatrix. The latter class has, in addition, a sheet current along the separatrix in the x-y plane associated with the jump in Bz. Detailed properties of these solutions are explored. In particular, sheetlike one-dimensional solutions are found to be limiting cases of the general solutions. Except for one special case, these sheet solutions cannot have finite footpoint displacement if they are force free, but can in the presence of pressure gradient. The general solutions can have arbitrary separatrix angle and ratio of flux between the quadrants. Discussion is presented regarding the matching of these solutions to the physical conditions on boundaries where the field lines leave the system, e.g., the photospheric surface in the solar coronal context.
Enhanced slow-wave beach heating of mirror plasmas with two-ion species
Authors: Roberts D. R. , Hershkowitz N.
Published: July 2002

Plasma heating in the ion-cyclotron range of frequencies has been examined in a beach-heating configuration of the central cell of the Phaedrus-B tandem mirror [Phys. Rev. Lett. 51, 1955 (1983)] during scans of the ion species ratio of hydrogen–helium (H–He) and hydrogen–deuterium (H–D) plasmas. Observed changes in the radial profiles of wave magnetic field and plasma parameters during the scans provide evidence of varied fast- and slow-wave eigenmode excitation and absorption. These changes are shown to be in agreement with those expected from wave accessibility considerations. Optimal peak parameters in the plasma core, ne=1.0×1013 cm−3, Te∥=20 eV, Ti∥=140 eV, Ti⊥=450 eV, and β=0.26 at midplane, were obtained for moderate helium or deuterium ion fractions (puffed nHe/ne=nD/ne ∼0.25). These parameters represent a significant increase in plasma energy density over that obtained under the same conditions with ‘‘pure’’ hydrogen plasmas: ne=7.0×1012 cm−3, Te∥=25 eV, Ti∥=80 eV, Ti⊥=300 eV, and β=0.12.
Wave breaking in cold plasma
Authors: Wang Jin-Gen , Payne G. L. , Nicholson D. R.
Published: July 2002

Strongly nonlinear plasma oscillations in a cold plasma are investigated in the wave breaking regime using the two-fluid model. The electrons are described in Lagrangian coordinates; the ions are described by the usual Eulerian coordinates. The model is extended to describe the motion after wave breaking has occurred. Numerical solutions are followed up to and beyond wave breaking for both driven and undriven cases. In a driven cold plasma, the plasma waves are excited from fluctuations by the modulational instability, growing to very large amplitudes, which leads to wave breaking. For the undriven cold plasma, large initial perturbations are assumed, which also lead to wave breaking. Multistreams and the generation of fast electrons are observed for both cases after wave breaking.
Particle simulation of the magnetized rf plasma sheath
Authors: Paes A. C. J. , Sydora R. D. , Dawson J. M.
Published: July 2002

In the sheath regions strong electric fields can develop that accelerate ions to sufficient energy to cause sputtering and increase the plasma impurities to an intolerable level. Simulations of these sheaths are performed with a one-and-two-half-dimensional (y,vx,vy,vz) electrostatic particle model with a homogeneous magnetic field tilted in relation to y; guiding-center electrons and full dynamic ions are used. The plasma is taken to be bounded by metallic walls in which a time-dependent potential difference V(t) is applied and the average energies and flux of ions hitting the walls are computed. The results show that the magnetic fields inhibits the sputtering caused by D atoms. Comparisons of the present model with previous work, which used a Vlasov model and fluid approach, are also made with good agreement in the appropriate regime.
Single-mode operation of a submillimeter wave gyrotron at the third-harmonic resonance
Authors: Idehara T. , Tatsukawa T. , Ogawa I. , Wada S. , Yoshizue K. , Inoue F. , Brand G. F.
Published: July 2002

If gyrotrons are to attain higher frequencies, high harmonic operation is necessary. In this Letter, the single-mode operation of a submillimeter wave gyrotron at the third harmonic of the electron cyclotron frequency is reported.
Spitzer or neoclassical resistivity: A comparison between measured and model poloidal field profiles on PBX-M
Authors: Kaye S. M. , Levinton F. M. , Hatcher R. , Kaita R. , Kessel C. , LeBlanc B. , McCune D. C. , Paul S.
Published: July 2002

Direct measurements of the radial profile of the magnetic field line pitch on PBX-M [Phys. Fluids B 2, 1271 (1990)], coupled with model predictions of these profiles allow a critical comparison with the Spitzer and neoclassical models of plasma parallel resistivity. The measurements of the magnetic field line pitch are made by motional Stark effect polarimetry, while the model profiles are determined by solving the poloidal field diffusion equation in the transp transport code using measured plasma profiles and assuming either Spitzer or neoclassical resistivity. The measured field pitch profiles were available for only seven cases, and the model profiles were distinguishable from each other in only three of those cases due to finite resistive diffusion times. The data in two of these three were best matched by the Spitzer model, especially in the inner-half of the plasma. Portions of the measured pitch profiles for these two cases and the full profiles for other cases, however, departed significantly from both the Spitzer and neoclassical models, indicating a plasma resistivity profile different from either model.
The effect of displacement current on whistler propagation of a fast-rising magnetic field
Authors: Gomberoff K. , Fruchtman A.
Published: July 2002

The effect of the displacement current on the magnetic field propagation into plasmas in the form of a whistler wave is studied. For times between the electron and the ion cyclotron periods and if the plasma is tenuous so that the electron plasma frequency is smaller than the cyclotron frequency, the magnetic field is shown to be governed by the Telegraph equation with complex coefficients. The propagation of a fast-rising magnetic field is examined and at early times the magnetic field is shown to propagate as a left-polarized wave with the light velocity. At a later time the magnetic field propagates as the dispersive whistler wave and is governed by the diffusion equation with a complex coefficient [Fruchtman and Maron, Phys. Fluids B 3, 1546 (1991)]. As expected, the front of the wave keeps propagating with the finite velocity of light. The effect of collisional resistivity is also considered.
Absolute instabilities in gyropeniotron amplifiers
Authors: Ganguly A. K. , Lau Y. Y. , Ahn S.
Published: July 2002

The critical current, oscillation frequency, and characteristic wave number for the excitation of absolute instability in gyropeniotron amplifiers are calculated from the linear dispersion relation by following the Briggs–Bers criterion. Numerical results are presented for some cases of interest.
Some parametric decay instabilities of fast magnetosonic waves in the ion cyclotron harmonic frequency regime
Authors: Sharma R. P. , Kumar A. , Hadi Al. Janabi A. , Kumar Raj
Published: July 2002

In the present paper, some possible parametric decay instabilities of fast magnetosonic waves (FMSW) near the second harmonic of ion cyclotron frequency have been considered in one-ion species hydrogen plasmas. The decay channels of FMSW include an ion Bernstein wave as a high-frequency decay wave and a low-frequency decay wave either as an ion-acoustic wave or kinetic Alfvén wave. Applications have been pointed out to the ASDEX [Plasma Phys. Controlled Fusion 28, 235 (1986)] and ACT-1 [Rev. Sci. Instrum. 53, 4 (1982)] toroidal devices where parametric decay instabilities of FMSW near the second harmonic of ion cyclotron frequency have been observed in the scrape-off layer and near the edge plasma. It has been shown that the growth rate is sufficiently high at the edge and may thus contribute to the energy deposition to the edge plasma. A comparison between various decay processes has been discussed for different toroidal devices. Applications have also been pointed out to Earth’s magnetospheric plasmas where some magnetic fluctuations have been observed.
Dynamic property of spontaneous toroidal field in field-reversed configuration plasmas
Authors: Shiokawa A. , Goto S.
Published: July 2002

The toroidal field in the translated field-reversed configuration (FRC) plasma has been measured, although the FRC plasma has sometimes been described as having only the poloidal field. Measurements of the toroidal field distribution during the plasma translation clarify the location where the toroidal field originates. The experimental results show that the flux of poloidal and toroidal components decays monotonically in time after the beginning of the translation. This indicates that the toroidal field occurs just after the FRC formation without further production during the translation.
Statistical theory of wave propagation and multipass absorption for current drive in tokamaks
Authors: Kupfer K. , Moreau D. , Litaudon X.
Published: July 2002

In this work the effect of ray stochasticity on the multipass absorption of lower-hybrid waves, used to drive current in tokamaks, is considered. In toroidal geometry, stochasticity arises as an intrinsic property of the Hamiltonian ray trajectories for lower-hybrid waves. Based on the wave kinetic equation, a diffusion equation is derived, with damping and sources, for the wave energy density in the stochastic layer. This equation is solved simultaneously with the electron Fokker–Planck equation to describe the quasilinear flattening of the electron distribution function and the subsequent modification of the wave damping. Steady-state solutions of this system (obtained numerically) indicate that the spectral gap is filled in a self-regulating manner, so that the boundaries of the diffused wave spectrum are independent of the level of ray stochastic diffusion. This allows the development of a simple (semianalytic) model for the self-consistent wave spectrum and the radial profile of absorbed power.
Stimulated Brillouin scattering in picosecond time scales: Experiments and modeling
Authors: Baldis H. A. , Villeneuve D. M. , La Fontaine B. , Enright G. D. , Labaune C. , Baton S. , Mounaix Ph. , Pesme D. , Casanova M. , Rozmus W.
Published: July 2002

This paper presents an experimental and theoretical study of stimulated Brillouin scattering (SBS) in laser produced plasma using a laser pump with a duration of 8–10 psec. The experiments were performed in a preformed plasma to minimize the flow velocity and have the same plasma conditions over a large range of laser intensities. The reflectivity was then compared to theoretical results over an intensity range of 1013–2×1015 W/cm2. A short pulse was used so that the SBS was in the temporally growing regime and saturation was not an issue.
Experimental study of charge state distribution from KrF and ruby laser-produced plasmas
Authors: Tsui Y. Y. , Fedosejevs R. , Offenberger A. A.
Published: July 2002

The detailed angular charge distributions of the asymptotic plasma produced from carbon and aluminum targets by UV and visible laser pulses in the intensity range of 1011–1013 W cm−2 and pulselength range of 1–20 nsec have been measured using a single shot electrodynamic charge analyzer. The observed variation of average charge state as a function of velocity was determined from measurement and has been found to be approximately linear with no apparent dependence on angle of observation. For similar irradiation conditions, shorter-wavelength radiation produces lower final charge states, as expected, from the higher interaction density in the initial laser produced plasma leading to enhanced recombination in the early stages of expansion of the plasma. The characteristics of the angular charge distribution can be qualitatively explained by considering the flow of the source plasma mapping different regions of the focal spot into different angles, relative to the target normal, in the expanding plasma.
H mode in the TUMAN-3 tokamak triggered by edge plasma perturbations*
Authors: Askinazi L. G. , Golant V. E. , Lebedev S. V. , Levin L. S. , Rozhansky V. A. , Tendler M.
Published: July 2002

Several types of edge plasma perturbations in the TUMAN-3 tokamak [Proceedings of the 13th International Atomic Energy Agency Conference on Plasma Physics and Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 509] have been demonstrated to trigger the Ohmic H-mode transition. It is shown that three different methods, (1) radial electric field of either sign imposed by an electrode biased up to 500 V, (2) perturbation of the edge plasma density by strong gas puffing, and (3) LiD pellet injection, bring about the Ohmic H mode. In biasing experiments, the degree of improvement of particle and energy confinement depends on the polarity of the electric field and is higher for negative biasing. The evaporation of a LiD pellet (V∼150 m/sec, size ∼0.3 mm, density perturbation∼50%) in the peripheral region of the plasma column can also lead to the H-mode transition. Experimental results are shown to be in reasonable agreement with the theory of radial electric fields in tokamaks.
Symmetry breaking of quasihelical stellarator equilibria
Authors: Weening R. H.
Published: July 2002

A mean-field Ohm’s law is used to determine the effects of the bootstrap current on quasihelically symmetric stellarator equilibria. The Ohm’s law leads to the conclusion that the effects of the bootstrap current break the quasihelical stellarator symmetry at second order in an inverse aspect ratio expansion of the magnetic field strength. The level of symmetry breaking suggests that good approximations to quasihelical stellarator fusion reactors may not be attainable.
Scaling study of potential in the end region of a tandem mirror based on end-loss electron measurement
Authors: Saito T. , Kiwamoto Y. , Kurihara K. , Cho T. , Inutake M. , Miyoshi S. , Tamano T. , Yatsu K.
Published: July 2002

An empirical scaling for the potential difference between the plug potential ΦP and the floating potential ΦEP of an endplate is obtained in terms of end-loss electron temperatures. Results from the GAMMA 10 tandem mirror [Phys. Rev. Lett. 55, 939 (1985)] indicate that ΔΦ=ΦP−ΦEP scales much better with an effective temperature Teff≡(1−β)TeL+βTeH than with a single temperature TeL or TeH, where TeL and TeH are temperatures of the bulk and the high-energy tail components of the end-loss electrons and β denotes the flux fraction of the TeH component. Moreover, the observed scaling is consistent with a recently developed theoretical model [K. Kurihara et al., J. Phys. Soc. Jpn. 61, 3153 (1992)].
A covariant derivation of the ponderomotive force
Authors: Manheimer Wallace M.
Published: July 2002

Using the covariant equations of motion, an expression for the ponderomotive force is obtained for relativistic particles in an arbitrary three-dimensional field configuration.
Enhanced lower-hybrid heating caused by frequency modulation
Authors: Riyopoulos Spilios
Published: July 2002

The effect of frequency modulation during stochastic ion heating induced by lower-hybrid waves is examined. The modulation occurs either in the ion-cyclotron frequency because of the variation of the magnetic field in toroidal devices, or it can be externally imposed on the frequency of the lower-hybrid waves. It has already been observed numerically [Phys. Fluids 27, 184 (1984)] that a small variation in the ion-cyclotron frequency can induce velocity diffusion for wave amplitudes well below the stochasticity threshold in a uniform magnetic field. Here a detailed study reveals that to the lowest order in the small parameters, the modulational effects can be incorporated in a two-dimensional Hamiltonian. This allows the derivation of the new stochasticity thresholds. It is found that a small amount of modulation, Δω/ω≲1%, produces an order of magnitude reduction in the stochasticity threshold relative to the constant frequency case. The stochastic regime in velocity space also grows in size, resulting in a considerable increase of number of heated particles in the case of devices with modest aspect ratio. Both ion-cyclotron and wave-frequency modulation lead to similar results. The modulation of the wave frequency offers the ability to control and optimize the modulation parameters and is proposed as a method to enhance radio frequency (rf) heating.