Volume 20, Issue 6, June 2013

From spacecraft data, it is evident that electron pressure anisotropy develops in collisionless plasmas. This is in contrast to the results of theoretical investigations, which suggest this anisotropy should be limited. Common for such theoretical studies is that the effects of electron trapping are not included; simply speaking, electron trapping is a nonlinear effect and is, therefore, eliminated when utilizing the standard methods for linearizing the underlying kinetic equations. Here, we review our recent work on the anisotropy that develops when retaining the effects of electron trapping. A general analytic model is derived for the electron guiding center distribution of an expanding flux tube. The model is consistent with anisotropic distributions observed by spacecraft, and is applied as a fluid closure yielding anisotropic equations of state for the parallel and perpendicular components (relative to the local magnetic field direction) of the electron pressure. In the context of reconnection, the new closure accounts for the strong pressure anisotropy that develops in the reconnection regions. It is shown that for generic reconnection in a collisionless plasma nearly all thermal electrons are trapped, and dominate the properties of the electron fluid. A new numerical code is developed implementing the anisotropic closure within the standard twofluid framework. The code accurately reproduces the detailed structure of the reconnection region observed in fully kinetic simulations. These results emphasize the important role of pressure anisotropy for the reconnection process. In particular, for reconnection geometries characterized by small values of the normalized upstream electron pressure, , the pressure anisotropy becomes large with and strong parallel electric fields develop in conjunction with this anisotropy. The parallel electric fields can be sustained over large spatial scales and, therefore, become important for electron acceleration.
 LETTERS


Advances in target normal sheath acceleration theory
View Description Hide DescriptionA theoretical model of the Target Normal Sheath Acceleration (TNSA) process, able to go beyond the limits of available descriptions, is developed. It allows to achieve a more satisfactory interpretation of TNSA. The theory, also supported by two dimensional particleincell simulations, elucidates the role played by the main laser and target parameters. Comparison between model predictions and experimental data related to the target thickness dependence of the maximum ion energy is discussed, showing satisfactory agreement. The model can be used as a simple but effective tool to guide the design of future experiments.
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 SPECIAL TOPIC: ADVANCES IN MAGNETIC RECONNECTION RESEARCH IN SPACE AND LABORATORY PLASMAS—PART II



A review of pressure anisotropy caused by electron trapping in collisionless plasma, and its implications for magnetic reconnection
View Description Hide DescriptionFrom spacecraft data, it is evident that electron pressure anisotropy develops in collisionless plasmas. This is in contrast to the results of theoretical investigations, which suggest this anisotropy should be limited. Common for such theoretical studies is that the effects of electron trapping are not included; simply speaking, electron trapping is a nonlinear effect and is, therefore, eliminated when utilizing the standard methods for linearizing the underlying kinetic equations. Here, we review our recent work on the anisotropy that develops when retaining the effects of electron trapping. A general analytic model is derived for the electron guiding center distribution of an expanding flux tube. The model is consistent with anisotropic distributions observed by spacecraft, and is applied as a fluid closure yielding anisotropic equations of state for the parallel and perpendicular components (relative to the local magnetic field direction) of the electron pressure. In the context of reconnection, the new closure accounts for the strong pressure anisotropy that develops in the reconnection regions. It is shown that for generic reconnection in a collisionless plasma nearly all thermal electrons are trapped, and dominate the properties of the electron fluid. A new numerical code is developed implementing the anisotropic closure within the standard twofluid framework. The code accurately reproduces the detailed structure of the reconnection region observed in fully kinetic simulations. These results emphasize the important role of pressure anisotropy for the reconnection process. In particular, for reconnection geometries characterized by small values of the normalized upstream electron pressure, , the pressure anisotropy becomes large with and strong parallel electric fields develop in conjunction with this anisotropy. The parallel electric fields can be sustained over large spatial scales and, therefore, become important for electron acceleration.

Magnetic reconnection in a weakly ionized plasma
View Description Hide DescriptionMagnetic reconnection in partially ionized plasmas is a ubiquitous phenomenon spanning the range from laboratory to intergalactic scales, yet it remains poorly understood and relatively little studied. Here, we present results from a selfconsistent multifluid simulation of magnetic reconnection in a weakly ionized reacting plasma with a particular focus on the parameter regime of the solar chromosphere. The numerical model includes collisional transport, interaction and reactions between the species, and optically thin radiative losses. This model improves upon our previous work in Leake et al. [“Multifluid simulations of chromospheric magnetic reconnection in a weakly ionized reacting plasma,” Astrophys. J. 760, 109 (2012)] by considering realistic chromospheric transport coefficients, and by solving a generalized Ohm's law that accounts for finite ioninertia and electronneutral drag. We find that during the two dimensional reconnection of a Harris current sheet with an initial width larger than the neutralion collisional coupling scale, the current sheet thins until its width becomes less than this coupling scale, and the neutral and ion fluids decouple upstream from the reconnection site. During this process of decoupling, we observe reconnection faster than the singlefluid SweetParker prediction, with recombination and plasma outflow both playing a role in determining the reconnection rate. As the current sheet thins further and elongates, it becomes unstable to the secondary tearing instability, and plasmoids are seen. The reconnection rate, outflows, and plasmoids observed in this simulation provide evidence that magnetic reconnection in the chromosphere could be responsible for jetlike transient phenomena such as spicules and chromospheric jets.

The transfer between electron bulk kinetic energy and thermal energy in collisionless magnetic reconnection
View Description Hide DescriptionBy performing twodimensional particleincell simulations, we investigate the transfer between electron bulk kinetic and electron thermal energy in collisionless magnetic reconnection. In the vicinity of the X line, the electron bulk kinetic energy density is much larger than the electron thermal energy density. The evolution of the electron bulk kinetic energy is mainly determined by the work done by the electric field force and electron pressure gradient force. The work done by the electron gradient pressure force in the vicinity of the X line is changed to the electron enthalpy flux. In the magnetic island, the electron enthalpy flux is transferred to the electron thermal energy due to the compressibility of the plasma in the magnetic island. The compression of the plasma in the magnetic island is the consequence of the electromagnetic force acting on the plasma as the magnetic field lines release their tension after being reconnected. Therefore, we can observe that in the magnetic island the electron thermal energy density is much larger than the electron bulk kinetic energy density.

The influence of intense electric fields on threedimensional asymmetric magnetic reconnection
View Description Hide DescriptionA threedimensional particleincell simulation of magnetic reconnection in an asymmetric configuration without a guide field and with temperature ratio demonstrates that intense perpendicular electric fields are produced on the lowdensity side of the current layer where there is a strong gradient in the plasma density. The simulation shows that the 3D reconnection rate is unaffected by these intense electric fields, that the electron current layer near the X line remains coherent and does not break up, but that localized regions of strong energy dissipation exist along the lowdensity separatrices. Near the X line the dominant term in the generalized Ohm's law for the reconnection electric field remains the offdiagonal electron pressure gradient . On the lowbeta separatrix, however, the anomalous drag makes an equally important contribution to that of the pressure gradient to the average Ey field.

The adiabatic phase mixing and heating of electrons in Buneman turbulence
View Description Hide DescriptionThe nonlinear development of the strong Buneman instability and the associated fast electron heating in thin current layers with is explored. Phase mixing of the electrons in wave potential troughs and a rapid increase in temperature are observed during the saturation of the instability. We show that the motion of trapped electrons can be described using a Hamiltonian formalism in the adiabatic approximation. The process of separatrix crossing as electrons are trapped and detrapped is irreversible and guarantees that the resulting electron energy gain is a true heating process.

Effects of the nonuniform initial environment and the guide field on the plasmoid instability
View Description Hide DescriptionEffects of nonuniform initial mass density and temperature on the plasmoid instability are studied via 2.5dimensional resistive magnetohydrodynamic (MHD) simulations. Our results indicate that the development of the plasmoid instability is apparently prevented when the initial plasma density at the center of the current sheet is higher than that in the upstream region. As a result, the higher the plasma density at the center and the lower the plasma β in the upstream region, the higher the critical Lundquist number needed for triggering secondary instabilities. When , the critical Lundquist number is higher than 104. For the same Lundquist number, the magnetic reconnection rate is lower for the lower plasma β case. Oppositely, when the initial mass density is uniform and the Lundquist number is low, the magnetic reconnection rate turns out to be higher for the lower plasma β case. For the high Lundquist number case ( ) with uniform initial mass density, the magnetic reconnection is not affected by the initial plasma β and the temperature distribution. Our results indicate that the guide field has a limited impact on the plasmoid instability in resistive MHD.

On phase diagrams of magnetic reconnection
View Description Hide DescriptionRecently, “phase diagrams” of magnetic reconnection were developed to graphically organize the present knowledge of what type, or phase, of reconnection is dominant in systems with given characteristic plasma parameters. Here, a number of considerations that require caution in using the diagrams are pointed out. First, two known properties of reconnection are omitted from the diagrams: the history dependence of reconnection and the absence of reconnection for small Lundquist number. Second, the phase diagrams mask a number of features. For one, the predicted transition to Hall reconnection should be thought of as an upper bound on the Lundquist number, and it may happen for considerably smaller values. Second, reconnection is never “slow,” it is always “fast” in the sense that the normalized reconnection rate is always at least 0.01. This has important implications for reconnection onset models. Finally, the definition of the relevant Lundquist number is nuanced and may differ greatly from the value based on characteristic scales. These considerations are important for applications of the phase diagrams. This is demonstrated by example for solar flares, where it is argued that it is unlikely that collisional reconnection can occur in the corona.

Development of multihierarchy simulation model with nonuniform space grids for collisionless driven reconnection
View Description Hide DescriptionA multihierarchy simulation model aimed at magnetic reconnection studies has been developed, in which macroscopic and microscopic physics are solved selfconsistently and simultaneously. In this work, the previous multihierarchy model by these authors is extended to a more realistic one with nonuniform space grids. Based on the domain decomposition method, the multihierarchy model consists of three parts: a magnetohydrodynamics algorithm to express the macroscopic global dynamics, a particleincell algorithm to describe the microscopic kinetic physics, and an interface algorithm to interlock macro and micro hierarchies. For its verification, plasma flow injection is simulated in this multihierarchy model and it is confirmed that the interlocking method can describe the correct physics. Furthermore, this model is applied to collisionless driven reconnection in an open system. Magnetic reconnection is found to occur in a micro hierarchy by injecting plasma from a macro hierarchy.

Excitation and propagation of electromagnetic fluctuations with ioncyclotron range of frequency in magnetic reconnection laboratory experiment
View Description Hide DescriptionLargeamplitude electromagnetic fluctuations of ioncyclotronfrequency range are detected in a laboratory experiment inside the diffusion region of a magnetic reconnection with a guide field. The fluctuations have properties similar to kinetic Alfvén waves propagating obliquely to the guide field. Temporary enhancement of the reconnection rate is observed during the occurrence of the fluctuations, suggesting a relationship between the modification in the local magnetic structure given by these fluctuations and the intermittent fast magnetic reconnection.

Aspects of collisionless magnetic reconnection in asymmetric systems
View Description Hide DescriptionAsymmetric reconnection is being investigated by means of particleincell simulations. The research has two foci: the direction of the reconnection line in configurations with nonvanishing magnetic fields; and the question why reconnection can be faster if a guide field is added to an otherwise unchanged asymmetric configuration. We find that reconnection prefers a direction, which maximizes the available magnetic energy, and show that this direction coincides with the bisection of the angle between the asymptotic magnetic fields. Regarding the difference in reconnection rates between planar and guide field models, we demonstrate that a guide field can provide essential confinement for particles in the reconnection region, which the weaker magnetic field in one of the inflow directions cannot necessarily provide.

The plasmoid instability during asymmetric inflow magnetic reconnection
View Description Hide DescriptionTheoretical studies of the plasmoid instability generally assume that the reconnecting magnetic fields are symmetric. We relax this assumption by performing twodimensional resistive magnetohydrodynamic simulations of the plasmoid instability during asymmetric inflow magnetic reconnection. Magnetic asymmetry modifies the onset, scaling, and dynamics of this instability. Magnetic islands develop preferentially into the weak magnetic field upstream region. Outflow jets from individual Xpoints impact plasmoids obliquely rather than directly as in the symmetric case. Consequently, deposition of momentum by the outflow jets into the plasmoids is less efficient, the plasmoids develop net vorticity, and shear flow slows down secondary merging between islands. Secondary merging events have asymmetry along both the inflow and outflow directions. Downstream plasma is more turbulent in cases with magnetic asymmetry because islands are able to roll around each other after exiting the current sheet. As in the symmetric case, plasmoid formation facilitates faster reconnection for at least small and moderate magnetic asymmetries. However, when the upstream magnetic field strengths differ by a factor of 4, the reconnection rate plateaus at a lower value than expected from scaling the symmetric results. We perform a parameter study to investigate the onset of the plasmoid instability as a function of magnetic asymmetry and domain size. There exist domain sizes for which symmetric simulations are stable but asymmetric simulations are unstable, suggesting that moderate magnetic asymmetry is somewhat destabilizing. We discuss the implications for plasmoid and flux rope formation in solar eruptions, laboratory reconnection experiments, and space plasmas. The differences between symmetric and asymmetric simulations provide some hints regarding the nature of the threedimensional plasmoid instability.

Electromagnetic instability of thin reconnection layers: Comparison of threedimensional simulations with MRX observations
View Description Hide DescriptionThe influence of currentaligned instabilities on magnetic reconnection in weakly collisional regimes is investigated using experimental observations from Magnetic Reconnection Experiment (MRX) [M. Yamada et al., Phys. Plasmas 4, 1936 (1997)] and largescale fully kinetic simulations. In the simulations as well as in the experiment, the dominant instability is localized near the center of the reconnection layer, produces large perturbations of the magnetic field, and is characterized by the wavenumber that is a geometric mean between electron and ion gyroradii . However, both the simulations and the experimental observations suggest the instability is not the dominant reconnection mechanism under parameters typical of MRX.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Temporal evolution of bubble tip velocity in classical RayleighTaylor instability at arbitrary Atwood numbers
View Description Hide DescriptionIn this research, the temporal evolution of the bubble tip velocity in RayleighTaylor instability (RTI) at arbitrary Atwood numbers and different initial perturbation velocities with a discontinuous profile in irrotational, incompressible, and inviscid fluids (i.e., classical RTI) is investigated. Potential models from Layzer [Astrophys. J. 122, 1 (1955)] and perturbation velocity potentials from Goncharov [Phys. Rev. Lett. 88, 134502 (2002)] are introduced. It is found that the temporal evolution of bubble tip velocity [u(t)] depends essentially on the initial perturbation velocity [u(0)]. First, when the , the bubble tip velocity increases smoothly up to the asymptotic velocity ( ) or terminal velocity. Second, when , the bubble tip velocity increases quickly, reaching a maximum velocity and then drops slowly to the . Third, when , the bubble tip velocity decays rapidly to a minimum velocity and then increases gradually toward the . Finally, when , the bubble tip velocity decays monotonically to the . Here, the critical coefficients , and , which depend sensitively on the Atwood number (A) and the initial perturbation amplitude of the bubble tip [h(0)], are determined by a numerical approach. The model proposed here agrees with hydrodynamic simulations. Thus, it should be included in applications where the bubble tip velocity plays an important role, such as the design of the ignition target of inertial confinement fusion where the RichtmyerMeshkov instability (RMI) can create the seed of RTI with , and stellar formation and evolution in astrophysics where the deflagration wave front propagating outwardly from the star is subject to the combined RMI and RTI.

Ion acoustic shock waves in plasmas with warm ions and kappa distributed electrons and positrons
View Description Hide DescriptionThe monotonic and oscillatory ion acoustic shock waves are investigated in electronpositronion plasmas (epi) with warm ions (adiabatically heated) and nonthermal kappa distributed electrons and positrons. The dissipation effects are included in the model due to kinematic viscosity of the ions. Using reductive perturbation technique, the KadomtsevPetviashviliBurgers (KPB) equation is derived containing dispersion, dissipation, and diffraction effects (due to perturbation in the transverse direction) in epi plasmas. The analytical solution of KPB equation is obtained by employing tangent hyperbolic (Tanh) method. The analytical condition for the propagation of oscillatory and monotonic shock structures are also discussed in detail. The numerical results of two dimensional monotonic shock structures are obtained for graphical representation. The dependence of shock structures on positron equilibrium density, ion temperature, nonthermal spectral index kappa, and the kinematic viscosity of ions are also discussed.

Experimental evidence of ion acoustic soliton chain formation and validation of nonlinear fluid theory
View Description Hide DescriptionWe perform onedimensional fluid simulation of ion acoustic (IA) solitons propagating parallel to the magnetic field in electronion plasmas by assuming a large system length. To model the initial density perturbations (IDP), we employ a KdV soliton type solution. Our simulation demonstrates that the generation mechanism of IA solitons depends on the wavelength of the IDP. The short wavelength IDP evolve into two oppositely propagating identical IA solitons, whereas the long wavelength IDP develop into two indistinguishable chains of multiple IA solitons through a wave breaking process. The wave breaking occurs close to the time when electrostatic energy exceeds half of the kinetic energy of the electron fluid. The wave breaking amplitude and time of its initiation are found to be dependent on characteristics of the IDP. The strength of the IDP controls the number of IA solitons in the solitary chains. The speed, width, and amplitude of IA solitons estimated during their stable propagation in the simulation are in good agreement with the nonlinear fluid theory. This fluid simulation is the first to confirm the validity of the general nonlinear fluid theory, which is widely used in the study of solitary waves in laboratory and space plasmas.

Stimulated Raman back scattering of extraordinary electromagnetic waves from periodically magnetized nanoparticle lattice
View Description Hide DescriptionStimulated Raman back scattering of extraordinary electromagnetic waves from the nanoparticle lattice is investigated in the presence of the static magnetic field. In the context of macroscopic theory, dispersion relation and growth rate of extraordinary mode for different values of static magnetic field and lattice parameters are derived and analyzed. It is found that when the static magnetic field is off, dispersion relation has two branches. These branches are related to the plasmonic and body wave branches of the plane polarized wave. Low frequency branch of the pump wave is not involved in the instability while the other branch is not stable, and the growth rate of Raman back scattered wave has one peak. If the electrons have cyclotron frequency by static magnetic field, dispersion has three branches. These branches are related to the plasmonic and body wave branches of left and right hand circularly polarized waves. In this situation, it is found that low frequency lower branch of the pump wave is stable while other branches are not stable, and the growth rate of Raman back scattered wave has three peaks. Numerical study of growth rate in various cyclotron frequencies shows that the growth rate increases and the instability band width decreases with increasing static magnetic field.

Errorfield penetration in reversed magnetic shear configurations
View Description Hide DescriptionErrorfield penetration in reversed magnetic shear (RMS) configurations is numerically investigated by using a twodimensional resistive magnetohydrodynamic model in slab geometry. To explore different dynamic processes in locked modes, three equilibrium states are adopted. Stable, marginal, and unstable current profiles for double tearing modes are designed by varying the current intensity between two resonant surfaces separated by a certain distance. Further, the dynamic characteristics of locked modes in the three RMS states are identified, and the relevant physics mechanisms are elucidated. The scaling behavior of critical perturbation value with initial plasma velocity is numerically obtained, which obeys previously established relevant analytical theory in the viscoresistive regime.

Comparison of kinetic and extended magnetohydrodynamics computational models for the linear ion temperature gradient instability in slab geometry
View Description Hide DescriptionWe perform linear stability studies of the ion temperature gradient (ITG) instability in unsheared slab geometry using kinetic and extended magnetohydrodynamics (MHD) models, in the regime . The ITG is a parallel (to B) sound wave that may be destabilized by finite ion Larmor radius (FLR) effects in the presence of a gradient in the equilibrium ion temperature. The ITG is stable in both ideal and resistive MHD; for a given temperature scale length , instability requires that either or be sufficiently large. Kinetic models capture FLR effects to all orders in either parameter. In the extended MHD model, these effects are captured only to lowest order by means of the Braginskii ion gyroviscous stress tensor and the ion diamagnetic heat flux. We present the linear electrostatic dispersion relations for the ITG for both kinetic Vlasov and extended MHD (twofluid) models in the local approximation. In the low frequency fluid regime, these reduce to the same cubic equation for the complex eigenvalue . An explicit solution is derived for the growth rate and real frequency in this regime. These are found to depend on a single nondimensional parameter. We also compute the eigenvalues and the eigenfunctions with the extended MHD code NIMROD, and a hybrid kinetic code that assumes sixdimensional Vlasov ions and isothermal fluid electrons, as functions of and using a spatially dependent equilibrium. These solutions are compared with each other, and with the predictions of the local kinetic and fluid dispersion relations. Kinetic and fluid calculations agree well at and near the marginal stability point, but diverge as or increases. There is good qualitative agreement between the models for the shape of the unstable global eigenfunction for and 20. The results quantify how far fluid calculations can be extended accurately into the kinetic regime. We conclude that for the linear ITG problem in slab geometry with unsheared magnetic field when , the extended MHD model may be a reliable physical model for this problem when and .