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Volume 12, Issue 1, January 2005
 LETTERS


Experimental observation of resonance overlap responsible for Hamiltonian chaos
View Description Hide DescriptionA test electron beam is propagated in a specially designed traveling wave tube. The beam intensity is low enough to ensure that beamplasma instabilities are ruled out. By recording the beam energy distribution at the output of the tube, we report the experimental observation of the resonant domain of a single wave and of the overlap of the resonance domains of two waves associated to the destruction of Kolmogorov–Arnold–Moser tori constituting barriers in phase space. This overlap mechanism is responsible for the transition to large scale chaos common to a large class of Hamiltonian systems.

 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

The electrostatic sheath in an electronegative dusty plasma
View Description Hide DescriptionBohm criterion for the electrostaticsheath in electronegative dusty plasmas, which are composed of electrons, negative and positive ions, as well as dust grains, is investigated with Sagdeev potential, taking into account the selfconsistent dust charge variation. The numerical solutions show that the dust and negative ion densities, as well as the positive ion and dust Bohm velocities, all have effects on the dust charge at the sheath edge. The positive ion and dust Bohm velocities increase with the growth of the dust density, while both of them decrease with the growth of negative ion density. Furthermore, the interactions between the two Bohm velocities are considered. The results are examined and found to be reliable by the quantitative analysis of Sagdeev potential.

Drift kinetic equation exact through second order in gyroradius expansion
View Description Hide DescriptionThe drift kinetic equation of Hazeltine [R. D. Hazeltine, Plasma Phys.15, 77 (1973)] for a magnetized plasma of arbitrary collisionality is widely believed to be exact through the second order in the gyroradius expansion. It is demonstrated that this equation is only exact through the first order. The reason is that when evaluating the secondorder gyrophase dependent distribution function, Hazeltine neglected contributions from the firstorder gyrophase dependent distribution function, and then used this incomplete expression to derive the equation for the gyrophase independent distribution function. Consequently, the secondorder distribution function and the stress tensor derived by this approach are incomplete. By relaxing slightly Hazeltine’s orderings one is able to obtain a drift kinetic equation accurate through the second order in the gyroradius expansion. In addition, the gyroviscous stress tensor for plasmas of arbitrary collisionality is obtained.

Extensions of adiabatic invariant theory for a charged particle
View Description Hide DescriptionThe standard theory of Hamiltonian dynamics of a charged particle is extended to allow electric and magnetic fields to vary across magnetic field lines or surfaces on the Larmor radius distance scale. After the development of the general theory, the special cases of toroidally nested magnetic surfaces and of axisymmetry are considered. In a further restriction the situation with spatially slowly varying static magnetic fields but spatially rapidly varying static bounded electrostatic potentials is treated. The dynamics of the perpendicular velocity is represented by a nonlinear oscillator. The adiabatic invariant and drift Hamiltonian are constructed near an point in the perpendicular velocity phase plane. Motion near a separatrix and point in physical space is also briefly explored.

Resonance between continuous spectra: Secular behavior of Alfvén waves in a flowing plasma
View Description Hide DescriptionConventional normal modeanalysis often falls short in predicting a variety of transient phenomena in a nonselfadjoint (nonHermitian) system. Laplace transform is capable of capturing all possible behavior in general systems. However, degenerate essential spectra require careful analysis. The Alfvén wave in a flowing plasma is an example in which the coalescence of the Alfvén singularities yields nonexponential growth of fluctuations. Invoking hyperfunction theory, rigorous expression of the Laplace transform leads to an accurate estimate of the asymptotic behavior of resonant singular modes.
 Nonlinear Phenomena, Turbulence, Transport

Modified Zakharov equations for plasmas with a quantum correction
View Description Hide DescriptionQuantum Zakharov equations are obtained to describe the nonlinear interaction between quantum Langmuir waves and quantum ionacoustic waves. These quantum Zakharov equations are applied to two model cases, namely, the fourwave interaction and the decay instability. In the case of the fourwave instability, sufficiently large quantum effects tend to suppress the instability. For the decay instability, the quantum Zakharov equations lead to results similar to those of the classical decay instability except for quantum correction terms in the dispersion relations. Some considerations regarding the nonlinear aspects of the quantum Zakharov equations are also offered.

Accelerated electron populations formed by Langmuir wavecaviton interactions
View Description Hide DescriptionDirect numerical simulations of electron dynamics in externally driven electrostatic waves have been carried out using a relativistic twofluid onedimensional Vlasov–Poisson code. When the driver wave has sufficiently large amplitude, ion density holes (cavitons) form. The interaction between these cavitons and other incoming Langmuir waves gives rise to substantial local acceleration of groups of electrons, and fine jetlike structures arise in electron phase space. We show that these jets are caused by wave breaking when finite amplitude Langmuir waves experience the ion density gradient at the leading edge of the holes, and are not caused by caviton burnout. An analytical twofluid model gives the critical density gradient and caviton depth for which this process can occur. In particular, the density gradient critically affects the rate at which a Langmuir wave, moving into the caviton, undergoes Landau damping. This treatment also enables us to derive analytical estimates for the maximum energy of accelerated electrons, and for the energy spectrum along a phasespace jet. These are confirmed by direct numerical simulations.

Bihelical magnetic relaxation and large scale magnetic field growth
View Description Hide DescriptionA unified, threescale system of equations accommodating nonlinear velocity driven helical dynamos, as well as timedependent relaxation of magnetically dominated unihelical or bihelical systems is derived and solved herein. When opposite magnetic helicities of equal magnitude are injected on the intermediate and small scales, the large scale magnetic helicity grows kinematically (independent of the magnetic Reynolds number) to equal that on the intermediate scale. For both free and driven relaxation large scale fields are rapidly produced. Subsequently, a dissipationlimited dynamo, driven by growth of small scale kinetic helicity, further amplifies the large scale field. The results are important for astrophysical coronae fed with bihelical structures by dynamos in their host rotators. The large scale for the rotator corresponds to the intermediate scale for the corona. That bihelical magnetic relaxation can produce global scale fields may help to explain the formation of astrophysical coronal holes and magnetohydrodynamic outflows.

Structure of reconnection layer with a shear flow perpendicular to the antiparallel magnetic field component
View Description Hide DescriptionA onedimensional resistivemagnetohydrodynamic(MHD) simulation of the Riemann problem is carried out for the structure of reconnection layer, i.e., outflow region of quasisteady magnetic reconnection, in the presence of a sheared flow tangential to the initial current sheet. Unlike previous studies, the shear flow is in the direction, perpendicular to the antiparallel component of the magnetic field, with a total change of flow across the current sheet. Cases with symmetric or asymmetric current sheet and various guide magnetic fields are investigated. The simulation shows that in the reconnection layer, the structure of MHDdiscontinuities changes significantly with the strength of the shear flow. The main findings are the following: (1) In the case initially with a zero guide field (, for the socalled “antiparallel reconnection”), the shear flow in produces a finite in the reconnection layer and two timedependent intermediate shocks with rotation angle of tangential magnetic field less than 180°. (2) For initial (the “component reconnection”) the sheared leads to very different magnetic field structures in the two outflow regions on the two sides of the line. (3) In the cases with the initial , the existence of the sheared can lead to the reversal of the rotation sense of tangential magnetic field through the reconnection layer. The critical value of for the occurrence of this field reversal is discussed. The general simulation results can be applied to space and laboratory plasmas.

Exact models for Hall current reconnection with axial guide fields
View Description Hide DescriptionThis paper employs an analytic reconnectionmodel to investigate the conditions under which Hall currents can influence reconnection and Ohmic dissipation rates. It is first noted that time dependent magnetohydrodynamic systems can be analyzed by decomposing the magnetic and velocity fields into guide field and reconnecting field components. A formally exact solution shows that Hall currents can speed up or slow down the reconnection rate depending on the strength and orientation of the axial guide field. In particular, merging solutions are developed in which the axial guide field is the dominant driver of the reconnection. The extent to which Hall currents can alleviate the buildup of back pressures in flux pileup reconnectionmodels is also examined. The analysis shows that, although enhancements of the merging rate can be expected under certain conditions, it is unlikely that Hall currents can completely undo the fundamental pressure limitations associated with flux pileup reconnection.

Large amplitude parallel propagating electromagnetic oscillitons
View Description Hide DescriptionEarlier systematic nonlinear treatments of parallel propagating electromagnetic waves have been given within a fluid dynamic approach, in a frame where the nonlinear structures are stationary and various constraining first integrals can be obtained. This has lead to the concept of oscillitons that has found application in various space plasmas. The present paper differs in three main aspects from the previous studies: first, the invariants are derived in the plasma frame, as customary in the Sagdeev method, thus retaining in Maxwell’sequations all possible effects. Second, a single differential equation is obtained for the parallel fluid velocity, in a form reminiscent of the Sagdeev integrals, hence allowing a fully nonlinear discussion of the oscilliton properties, at such amplitudes as the underlying Mach number restrictions allow. Third, the transition to weakly nonlinear whistler oscillitons is done in an analytical rather than a numerical fashion.

The role of high frequency oscillations in the penetration of plasma clouds across magnetic boundaries
View Description Hide DescriptionExperiments are reported where a collissionfree plasma cloud penetrates a magnetic barrier by selfpolarization. Three closely related effects, all fundamental for the penetration mechanism, are studied quantitatively: (1) anomalous fast magnetic field penetration (two orders of magnitude faster than classical), (2) anomalous fast electron transport (three orders of magnitude faster than classical and two orders of magnitude faster than Bohm diffusion), and (3) the ion energy budget as ions enter the potential structure set up by the selfpolarized plasma cloud. It is concluded that all three phenomena are closely related and that they are mediated by highly nonlinear oscillations in the lower hybrid range, driven by a strong diamagnetic current loop which is set up in the plasma in the penetration process. The fast magnetic field penetration occurs as a consequence of the anomalous resistivity caused by the wave field and the fast electron transport across magnetic field lines is caused by the correlation between electric field and density oscillations in the wave field. It is also found that ions do not lose energy in proportion to the potential “hill” they have to climb, rather they are transported against the dc potential structure by the same correlation that is responsible for the electron transport. The results obtained through direct measurements are compared to particle in cell simulations that reproduce most aspects of the high frequency wave field.

Conditions for plasmoid penetration across abrupt magnetic barriers
View Description Hide DescriptionThe penetration of plasma clouds, or plasmoids, across abrupt magnetic barriers (of the scale less than a few ion gyro radii, using the plasmoid directed velocity) is studied. The insight gained earlier, from detailed experimental and computer simulation investigations of a case study, is generalized into other parameter regimes. It is concluded for what parameters a plasmoid should be expected to penetrate the magnetic barrier through selfpolarization, penetrate through magnetic expulsion, or be rejected from the barrier. The scaling parameters are , , , , , and the width of the plasmoid. The scaling is based on a model for strongly driven, nonlinear magnetic fielddiffusion into a plasma which is a generalization of the earlier laboratory findings. The results are applied to experiments earlier reported in the literature, and also to the proposed application of impulsive penetration of plasmoids from the solar wind into the Earth’s magnetosphere.

Excitation of zonal flows by kinetic Alfvén waves
View Description Hide DescriptionNonlinear couplings between dispersive kinetic Alfvén waves (DKAWs) and electrostatic convective cells∕zonal flows are reexamined. A set of equations that exhibit nonlinear couplings between the scalar and parallel vector potentials of the DKAWs and the scalar potential of zonal flows that are reinforced by the Reynolds stresses of the DKAWs in a magnetized plasma is presented. The equations are then Fourieranalyzed to obtain the nonlinear dispersion relation. The latter exhibits modulational instabilities, which could be responsible for enhanced zonal flows in a uniform magnetized plasma. Zonal flows can regulate the transport of plasma particles in laboratory magnetoplasmas as well as in the Earth’s magnetosphere and in the solar corona.

Gyrokinetic simulation of the collisionless and semicollisional tearing mode instability
View Description Hide DescriptionThe evolution of collisionless and semicollisional tearing mode instabilities is studied using an electromagnetic gyrokineticparticleincell simulationmodel. Driftkinetic electrons are used. Linear eigenmode analysis is presented for the case of fixed ions and there is excellent agreement with simulation. A double peaked eigenmode structure is seen indicative of a positive . Nonlinear evolution of a magnetic island is studied and the results compare well with existing theory in terms of saturation level and electron bounce oscillations. Electronion collisions are included to study the semicollisional regime. The algebraic growth stage is observed and compares favorably with theory. Nonlinear saturation following the algebraic stage is observed.

Positron acceleration to ultrarelativistic energies by an oblique magnetosonic shock wave in an electronpositronion plasma
View Description Hide DescriptionPositron acceleration in a shock wave in a plasma consisting of electrons, positrons, and ions is studied with theory and simulations. From the relativistic equation of motion, it is found that an oblique shock wave can accelerate some positrons with the energy increase rate proportional to . They move nearly parallel to the external magnetic field, staying in the shock transition region for long periods of time. Then, this acceleration is demonstrated with onedimensional, relativistic, electromagnetic particle simulations with full particle dynamics. Some positrons have been accelerated to ultrarelativistic energies with this mechanism. Parametric study of this acceleration is also made.

Bernstein mode aided anomalous absorption of laser in a plasma
View Description Hide DescriptionA laser propagating through a plasma, in the presence of an electron Bernstein wave, undergoes nonlinear mode coupling, producing a beat mode (, ) where (, ) and (, ) are the frequency and wave number of the laser and the Bernstein mode. The oscillatory electron velocity associated with this beat mode couples with electron density perturbation due to the Bernstein wave to produce a nonlinear current at the laser frequency. When the beat mode is Landau damped on electrons, the nonlinear current at the laser frequency has an inphase component with the laser field, giving rise to anomalous resistivity. The normalized anomalous resistivity is found to be maximum for .

Nonplanar dustion acoustic shock waves with transverse perturbation
View Description Hide DescriptionThe nonlinear dustion acoustic shock waves in dusty plasmas with the combined effects of bounded cylindrical/spherical geometry, the transverse perturbation, the dust charge fluctuation, and the nonthermal electrons are studied. Using the perturbation method, a cylindrical/spherical Kadomtsev–Petviashvili Burgers equation that describes the dustion acoustic shock waves is deduced. A particular solution of the cylindrical/spherical Kadomtsev–Petviashvili Burgers equation is also obtained. It is shown that the dustion acoustic shock wave propagating in cylindrical/spherical geometry with transverse perturbation will be slightly deformed as time goes on.

A physical mechanism of nonthermal plasma effect on shock wave
View Description Hide DescriptionAn electric discharge is applied to generate a plasma spike in front of a wedge. Use of this plasma spike to modify the shock wave structure in a supersonic flow over the wedge is then studied. It is shown that the plasma spike can effectively deflect the incoming flow before the flow reaches the wedge; consequently, the shock structure in the interaction region is modified from an oblique to a curved shape. Moreover, the shock becomes detached as the strength of the plasma spike exceeds a critical level.

Linear and nonlinear stability analysis for twodimensional ideal magnetohydrodynamics with incompressible flows
View Description Hide DescriptionThe equilibrium and Lyapunov stability properties for twodimensional ideal magnetohydrodynamic (MHD) plasmas with incompressible and homogeneous (i.e., constant density) flows are investigated. In the unperturbed steady state, both the velocity and magnetic field are nonzero and have three components in a Cartesian coordinate system with translational symmetry (i.e., one ignorable spatial coordinate). It is proved that (a) the solutions of the ideal MHD steady state equations with incompressible and homogeneous flows in the plane are also valid for equilibria with the axial velocity component being a free flux function and the axial magnetic field component being a constant, (b) the conditions of linearized Lyapunov stability for these MHDflows in the planar case (in which the fields have only two components) are also valid for symmetric equilibria that have a nonplanar velocity field component as well as a nonplanar magnetic field component. On using the method of convexity estimates, nonlinear stability conditions are established.