Index of content:
Volume 3, Issue 3, March 1996

Sawteeth and energy confinement in the Madison Symmetric Torus reversed‐field pinch
View Description Hide DescriptionMost Madison Symmetric Torus (MST) [Fusion Technol. 19, 131 (1991)] reversed‐field pinch discharges exhibit sawtooth oscillations with a period of 2–5 ms, corresponding to magnetohydrodynamic(MHD)instability and increased transport. However, in discharges where the plasma‐facing wall has been boronized, the plasma resistivity is reduced, and sawteeth are often suppressed for periods up to 20 ms. The energy confinement time during these sawtooth‐free periods is triple the normal value, corresponding to a higher plasma temperature and lower Ohmic input power. In addition, the steady growth of the dominant magnetic fluctuations normally observed between sawtooth crashes is absent.

Rapid current transition in a crossed‐field diode
View Description Hide DescriptionThe transmitted current in a crossed‐field gap has been characterized analytically by a number of authors. Using a one dimensional PIC simulation, we explore the behavior of the crossed‐field diode at B=B _{ Hull }. For mono‐energetic (cold) emission, a rapid reduction of transmitted current is observed when the injected current exceeds the critical current by just 1%. The addition of a small electron temperature normal to the cathode eliminates the transition, even for kT/V∼10^{−5} (V=10 kV, gap = 1 cm, B=337 G, J=1.69 A/cm^{2}), while an isotropic velocity distribution accelerates the transition.

Thomas–Fermi‐like and average atom models for dense and hot matter
View Description Hide DescriptionAll the Thomas–Fermi approaches to the thermodynamics and atomic physicsproperties of dense and ionized matter consisting of a single element are systematically derived and compared within a density‐functional theoretical framework. The corresponding results are contrasted to those of the average atom model by using similar approximations for exchange, correlation, and gradient corrections. Emphasis is led on equations of state,ionization, level shifts, and radial moments. The same numerical algorithms are used to unravel similar trends or identify specific ones, in terms of density and temperature variations. The most sophisticated Thomas–Fermi–Dirac–Weizäcker method yields the closest results to the hybrid average atom model using quantized bound states. Parameters ranges of potential interest for inertially confined thermonuclear fusion stress out density in the 0.1–10 times the solid, and temperature up to 10 keV.

Electromagnetic instability in nonuniform resistive electron magnetohydrodynamics
View Description Hide DescriptionA local dispersion relation for electromagnetic modes in a nonuniform collisional magnetized electron plasma with fixed ion background is derived, taking into account equilibrium magnetic field and pressure gradients, as well as impurity radiation losses. The dispersion relation is then analyzed both analytically as well as numerically. It is found that for a low‐β plasma, the principal source for the generation of unstable modes is the impurity radiation loss; whereas for a high‐β plasma, the various effects such as the electron streaming, the electron–ion collisions, finite electron thermal conductivity, and impurity radiation losses are shown to be responsible for unstable perturbations. The results should be useful in the interpretation of nonthermal electromagnetic fluctuations in nonuniform collision‐dominated magnetoplasmas with impurities.

Variational structure for dissipationless linear drift‐wave equations
View Description Hide DescriptionA derivation from first principles of the Lagrangian density for the dissipationless linear drift‐ wave equation recently introduced by Mattor and Diamond [Phys. Plasmas 1, 4002 (1994)] is presented. An exact wave‐action conservation law for linear drift waves propagating in a rotating magnetized plasma is then derived from the Lagrangian density without requiring the use of the eikonal representation for the wave fields.

Modes of spheroidal ion plasmas at the Brillouin limit
View Description Hide DescriptionThe confinement properties and collective modes of single‐component plasmas are investigated in a quadrupole Penning trap. Brillouin‐density pure ion plasmas are generated by electron‐beam ionization of a low‐pressure gas. Large, spheroidal, steady‐state plasmas are produced, extending out to contact one or more of the trap electrodes. With the density fixed at the Brillouin limit by the high ion production rate, the electrode potentials determine the plasma shape. The frequencies of azimuthally propagating cyclotron and diocotron modes are found to vary significantly with the plasma aspect ratio. For oblate plasmas, the frequencies are in good agreement with a simple fluid model.

The structure of three‐dimensional magnetic neutral points
View Description Hide DescriptionThe local configurations of three‐dimensional magnetic neutral points are investigated by a linear analysis about the null. It is found that the number of free parameters determining the arrangement of field lines is four. The configurations are first classified as either potential or non‐potential. Then the non‐potential cases are subdivided into three cases depending on whether the component of current parallel to the spine is less than, equal to or greater than a threshold current; therefore there are three types of linear non‐potential null configurations (a radial null, a critical spiral and a spiral). The effect of the four free parameters on the system is examined and it is found that only one parameter categorizes the potential configurations, whilst two parameters are required if current is parallel to the spine. However, all four parameters are needed if there is current both parallel and perpendicular to the spine axis. The magnitude of the current parallel to the spine determines whether the null has spiral, critical spiral or radial field lines whilst the current perpendicular to the spine affects the inclination of the fan plane to the spine. A simple method is given to determine the basic structure of a null given M the matrix which describes the local linear structure about a null point.

Creation of a resonant diocotron mode
View Description Hide DescriptionThe modal structure for linearized waves in a magnetron or a crossed‐field amplifier (CFA) is shown to be very sensitive to the profile of the electron density at the edge of the electron sheath. As is well known, with the classical Brillouin density profile, no propagating diocotron mode can exist. Furthermore, in the parameter regime at which these devices operate (ω=kv _{ d } where ω is the frequency, k is the wave vector and v _{ d } is the drift velocity at the top of the sheath), there are no unstable modes. However if we replace the Brillouin density profile with a ‘‘ramped’’ density profile (where the discontinuity is replaced by a finite, but large, negative density gradient), then we can show that any mode in the operating regime will become weakly unstable. However these weakly unstable modes in the presence of the strong density gradient at the edge of the ramped density profile combine to generate a quasilinear diffusion of order unity. Thus, after a time on the order of a few cyclotron periods, the original density profile will become modified. This modification is expected to generate a plateau on the edge of the sheath at which time a resonant propagating diocotron mode can exist. Implications of these results and their predictions for magnetron and CFA operation are discussed.

Magnetic topology and the problem of its invariant definition
View Description Hide DescriptionThe evolution of an ideal plasma conserves magnetic lines of force and hence magnetic topology. However, magnetic topology, i.e. the structure and linkage of magnetic flux, is a property of the magnetic field alone. Therefore, the conservation of topology can also be a property of non‐ideal plasmas for which the plasma flow is not line conserving. A general definition of magnetic topology is given and it is shown that it yields a large set of non‐ideal topology‐conserving systems. In the application of the notion of magnetic topology to real plasmas problems arise concerning the stability of topology.Instability may inhibit one from defining the topology of a given real, i.e. not exactly prescribed, magnetic field configuration and makes it difficult to detect changes of magnetic topology, such as reconnection processes. This problem of structural instability of magnetic topology also appears in connection with changes of the frame of reference. A change of the frame of reference may lead to a transition in topology especially for topological unstable, non‐ideal systems.

Stopping power of ions in a strongly magnetized plasma
View Description Hide DescriptionThe energy loss of heavy ions in a strongly magnetized plasma is studied by means of Vlasov and Particle‐in‐Cell (PIC) simulations. The topic is of importance for many practical applications, as for example in the electron cooling of heavy ion beams. Measurements of the longitudinal cooling force show strong deviations from the well known linear theories. Moreover, the possibility of heavy ions to reach high charge states Z _{ p } increases the interest in understanding the plasma regime with coupling parameter Z _{ p }/N _{ D }≳1 (N _{ D } is the number of electrons in a Debye sphere), when nonlinear phenomena are important. In this regime a linearization of the drift kinetic Vlasov–Poisson system is not possible, so that a fully nonlinear numerical approach is unavoidable. Comparisons between the two numerical schemes are made for the stopping power and the potential created in the plasma by a moving ion, together with the dielectrictheory of ion stopping. Our results show strong deviations from the dielectrictheory, and our investigations show the importance of the role played by the electrons trapped in the potential troughs excited by the ion in the stopping process.

On the conical refraction of hydromagnetic waves in plasma with anisotropic thermal pressure
View Description Hide DescriptionA phenomenon analogous to the conical refraction widely known in crystalo‐optics and crystalo‐acoustics is discovered for the magnetohydrodynamical waves in a collisionless plasma with anisotropic thermal pressure. Angle of the conical refraction is calculated for the medium under study which is predicted to be 18°26′. Possible experimental corroboration of the discovered phenomenon is discussed.

Relativistic theory of cross‐field transport and diffusion in a plasma
View Description Hide DescriptionA modified Chapman–Enskog analysis is employed to solve the relativistic Boltzmann transport equation. This is in the context of binary Coulomb encounter in a weakly coupled and fully ionized nondegenerate electron–ion plasma across a magnetic field. Specific formulas concerning transport coefficients are derived analytically in the various limits of temperatures, viz., nonrelativistic, moderately relativistic, and ultrarelativistic temperatures. Early classical results are equally recovered. The dependence of coefficients on thermal regimes is quantitatively discussed and their markedly diminishing trends are analyzed.

Strongly anomalous diffusion in sheared magnetic configurations
View Description Hide DescriptionThe statistical behavior of magnetic lines in a sheared magnetic configuration with reference surface x=0 is investigated within the framework of the kinetic theory. A Liouville equation is associated with the equations of motion of the stochastic magnetic lines. After averaging over an ensemble of realizations, it yields a convection‐diffusion equation within the quasilinear approximation. The diffusion coefficients are space dependent and peaked around the reference surface x=0. Due to the shear, the diffusion of lines away from the reference surface is slowed down. The behavior of the lines is asymptotically strongly non‐Gaussian. The reference surface acts like an attractor around which the magnetic lines spread with an effective subdiffusive behavior. Comparison is also made with more usual treatments based on the study of the first two moments equations. For sheared systems, it is explicitly shown that the Corrsin approximation assumed in the latter approach is no longer valid. It is also concluded that the diffusion coefficients cannot be derived from the mean square displacement of the magnetic lines in an inhomogeneous medium.

Multisplitting and collapse of self‐focusing anisotropic beams in normal/anomalous dispersive media
View Description Hide DescriptionThree‐dimensional self‐focusing light pulses in normal and anomalous dispersive media are investigated by means of a waveguideinstability analysis, a Lagrangian approach, and a quasi‐self‐similar analysis. In the case of normal dispersion for which no localized ground state exists, it is shown that a high‐intensity elongated beam cannot self‐similarly collapse. Even when the incident beam power widely exceeds the critical power for a two‐dimensional self‐focusing, the beam is shown to split into multiple cells that ultimately disperse when their individual mass lies below the critical power. The mechanism underlying this fragmentation process is described in terms of a stretching of the self‐focusing beam along its propagation axis. The focal point, where the splitting process develops, is identified. Finally, it is shown that the longitudinal dynamical motions of self‐focusing elongated pulses also play an important role in an anomalous dispersive medium. In this case, unlike the former one, the beam self‐contracts along its propagation axis and reconcentrates its shape back toward the center where it ultimately collapses in a finite time.

Coalescence of two parallel current loops in a nonrelativistic electron–positron plasma
View Description Hide DescriptionThe coalescence of two parallel current loops in an electron–positron plasma is investigated by a three‐dimensional electromagnetic relativistic particle code. Instead of mixing uniformly in the dissipation region as observed for current coalescence in an electron–ion plasma,electrons and positrons initially in the loops are driven to move separately by the magnetic gradient drift. Redistribution of the current‐carrying electrons and positrons creates new current loops, which coalesce again, if the initial drift velocities remain greater than a critical value after coalescence. It was found that the energy stored in the current loops dissipates gradually through several coalescences. Consequently, the electrons and positrons near the current loops are heated through the coalescence. This process is qualitatively different from the explosive energy release during coalescence in an electron–ion plasma.

Computer studies on the spontaneous fast reconnection mechanism in three dimensions
View Description Hide DescriptionThe spontaneous evolution of fast reconnection is studied in three dimensions by extending (in the z direction) the previous two‐dimensional model that considered only the x‐y plane [M. Ugai, Phys. Fluids B 4, 2953 (1992)]. It is demonstrated that the reconnection development strongly depends on three‐dimensional effects; only when the central current sheet is sufficiently long in the z direction, say more than a few times larger than the current sheet width, the fast reconnection mechanism fully develops by the self‐consistent coupling between the global reconnection flow and the current‐driven anomalous resistivity. In this case, the reconnection flow can grow so powerfully as to enhance the current density (the current‐driven resistivity) locally near an X line; otherwise, such a vital reconnection flow cannot be caused. The resulting quasisteady fast reconnection mechanism is significantly confined in the z direction, where a strong (Alfvénic) plasma jet results from standing switch‐off shocks; accordingly, a large‐scale plasmoid is formed and propagates in the middle of the system. It is concluded that the well‐known two‐dimensional spontaneous fast reconnection model can reasonably be extended to three dimensions.

Fluid models for kinetic effects on coherent nonlinear Alfvén waves. I. Fundamental theory
View Description Hide DescriptionCollisionless regime kinetic models for coherent nonlinear Alfvén wave dynamics are studied using fluid moment equations with an approximate closure anzatz. Resonant particle effects are modeled by incorporating an additional term representing dissipation akin to parallel heat conduction. Unlike collisional dissipation, parallel heat conduction is presented by an integral operator. The modified derivative nonlinear Schrödinger equation thus has a spatially nonlocal nonlinear term describing the long‐time evolution of the envelope of parallel‐propagating Alfvén waves, as well. Coefficients in the nonlinear terms are free of the (1−β)^{−1} singularity usually encountered in previous analyses, and have a very simple form that clarifies the physical processes governing the large‐amplitude Alfvénic nonlinear dynamics. The nonlinearity appears via coupling of an Alfvénic mode to a kinetic ion‐acoustic mode. Damping of the nonlinear Alfvén wave appears via strong Landau damping of the ion‐acoustic wave when the electron‐to‐ion temperature ratio is close to unity. For a (slightly) obliquely propagating wave, there are finite Larmor radius corrections in the dynamical equation. This effect depends on the angle of wave propagation relative to B _{0} and vanishes for the limit of strictly parallel propagation. Explicit magnetic perturbation envelope equations amenable to further analysis and numerical solution are obtained. Implications of these models for collisionless shock dynamics are discussed.

Statistical description and transport in stochastic magnetic fields
View Description Hide DescriptionThe statistical description of particle motion in a stochastic magnetic field is presented. Starting form the stochastic Liouville equation (or, hybrid kinetic equation) associated with the equations of motion of a test particle, the probability distribution function of the system is obtained for various magnetic fields and collisional processes. The influence of these two ingredients on the statistics of the particle dynamics is stressed. In all cases, transport properties of the system are discussed.

Compressibility and rotation effects on transport suppression in magnetohydrodynamic turbulence
View Description Hide DescriptionCompressibility and rotation effects on turbulenttransports in magnetohydrodynamic(MHD)flows under arbitrary mean field are investigated using a Markovianized two‐scale statistical approach. Some new aspects of MHDturbulence are pointed out in close relation to plasma compressibility. Special attention is paid to the turbulent electromotive force, which plays a central role in the generation of magnetic and velocity fluctuations. In addition to plasma rotation, the interaction between compressibility and magnetic fields is shown to bring a few factors suppressing MHDfluctuations and, eventually, density and temperaturetransports, even in the presence of steep mean density and temperature gradients. This finding is discussed in the context of the turbulence‐suppression mechanism in the tokamak’s high‐confinement modes.

Scattering of electromagnetic waves by counter‐rotating vortex streets in plasmas
View Description Hide DescriptionThe scattering of electromagnetic waves from counter‐rotating vortex streets associated with nonlinear convective cells in uniform plasmas has been considered. The vortex street solution of the Navier–Stokes or the Hasegawa–Mima (and of the ‘‘sinh‐Poisson’’) equation is adopted as a scatterer. Assuming arbitrary polarization and profile function for the incident electromagnetic field, a compact expression for the scattering cross section has been obtained. Specific results for the differential cross section are obtained for the case in which the incident beam has a Gaussian profile and propagates as an ordinary mode. The results show that when the characteristic wavelength of the vortex street (λ_{ v }=2π/a) is larger than that of the incident electromagnetic wave (λ_{ i }=2π/k _{ i }), the differential cross section dσ/dΩ has a very well‐defined angular periodicity; in fact, it is a collection of Gaussians varying as exp[−f(k _{ iw })^{2}], where w is the waist and f is a function expressing a kind of ‘‘Bragg condition.’’ On the other hand, for λ_{ i }≳λ_{ v } the incident electromagnetic beam is unable to distinguish the periodic structure of the vortex street. The effects of the vortex street as well as the incident beam parameters on the scattering cross section are examined.