High Beta Cases Research Articles

Multidimensional nonlinear mirror‐mode structures in the Earth's magnetosheath

We performed two‐dimensional (2D) and three‐dimensional (3D) hybrid simulations in open boundary models to study the nonlinear mirror‐mode structures driven by the temperature anisotropy (T⊥/T∥> 1) of protons in the magnetosheath. In the open systems, because of the propagation of EMIC waves, we obtain the clearer non‐propagating mirror‐mode structures. We analyzed the relation between the mirror instability and the magnetic peaks and dips observed in the magnetosheath. In the 2D open boundary model with low beta (β∥ ≲ 1), we obtain fine structures of the magnetic dips at the nonlinear stage. In the 3D model, on the other hand, the mirror instability makes the magnetic peak structures with the same parameters. The parametric analysis indicates that the magnetic peaks also arise in both 2D and 3D high beta cases (β∥ ⪆ 1) as shown by the Cluster observations. In the high beta cases, the high mobility of the protons helps continuous coalescence of the diamagnetic currents inside the magnetic dips. The coalescence makes the magnetic dips larger and shallower. Between the large and shallow magnetic dips, the magnetic peaks appear in the high beta cases. In the 3D models, because degree of freedom increases in the perpendicular direction, the continuous coalescence can take place even in the low beta cases. Thus, the magnetic peaks appear in the 3D models in both cases.

ENERGY RELEASE AND TRANSFER IN SOLAR FLARES: SIMULATIONS OF THREE-DIMENSIONAL RECONNECTION

Using three-dimensional magnetohydrodynamic simulations we investigate energy release and transfer in a three-dimensional extension of the standard two-ribbon flare picture. In this scenario, reconnection is initiated in a thin current sheet (suggested to form below a departing coronal mass ejection) above a bipolar magnetic field. Two cases are contrasted: an initially force-free current sheet (low beta) and a finite-pressure current sheet (high beta), where beta represents the ratio between gas (plasma) and magnetic pressure. The energy conversion process from reconnection consists of incoming Poynting flux turned into up- and downgoing Poynting flux, enthalpy flux, and bulk kinetic energy flux. In the low-beta case, the outgoing Poynting flux is the dominant contribution, whereas the outgoing enthalpy flux dominates in the high-beta case. The bulk kinetic energy flux is only a minor contribution in the downward direction. The dominance of the downgoing Poynting flux in the low-beta case is consistent with an alternative to the thick target electron beam model for solar flare energy transport, suggested recently by Fletcher & Hudson, whereas the enthalpy flux may act as an alternative transport mechanism. For plausible characteristic parameters of the reconnecting field configuration, we obtain energy release timescales and energy output rates that compare favorably with those inferred from observations for the impulsive phase of flares. Significant enthalpy flux and heating are found even in the initially force-free case with very small background beta, resulting mostly from adiabatic compression rather than Ohmic dissipation. The energy conversion mechanism is most easily understood as a two-step process (although the two steps may occur essentially simultaneously): the first step is the acceleration of the plasma by Lorentz forces in layers akin to the slow shocks in the Petschek reconnection model, involving the conversion of magnetic energy to bulk kinetic energy. However, due to pressure gradient forces that oppose the Lorentz forces in approximate, or partial force balance, the accelerated plasma becomes slowed down and compressed, whereby the bulk kinetic energy is converted to heat, either locally deposited or transported away by enthalpy flux and deposited later. This mechanism is most relevant in the downflow region, which is more strongly governed by force balance; it is less important in the outflow above the reconnection site, where more energy remains in the form of fast bulk flow.

Proton acceleration in a single-loop disrupted during collision of two moving solitary magnetic kinks

We investigate a new model of single-loop flare based on the fact that a magnetic flux tube with axial current can be explosively disrupted during collision of two moving solitary magnetic kinks (MoSMaK), particularly paying attention to an acceleration mechanism of high energy protons. By using three-dimensional electromagnetic fields obtained from a resistive three-dimensional MHD equations during the single-loop flare, we investigate the orbit of many protons to obtain their energy spectra. We found that the protons can be accelerated to γ-ray-emitting energies (>1 MeV) with double power-law spectra up to about 25 MeV. There appears a breaking point of the index of the power-law spectra from 1.8 to 2.1 near 10 MeV. The protons are accelerated mainly in one direction along the loop by the electric field produced near the three-dimensional localized current associated with the magnetic reconnection process in the disrupted loop. We study the loop disruption for two different plasma beta in the center of the loop; and . In a high beta case (), the disruption of the loop is more violent than that of . We found that the proton acceleration for the case of occurs mainly at two different regions; one is inside the loop and the other is in the upper part of the disrupting loop. However, the energy spectra of protons are very similar for both cases.

Ion heating by kinetic cross-field streaming instability due to reflected ions at a quasiperpendicular shock

The present paper shows that the reflected ion at a supercritical quasiperpendicular shock wave can excite a purely growing m9de propagating parallel to the ambient magnetic field (k∥B0). To discuss the ion heating by such an unstable mode, the self-consistent quasilinear kinetic equation is solved with the assumption that the present purely growing mode is the dominant unstable mode in the system. In the quasilinear analysis of the instability, two particular cases are considered—the case of low initial ion beta [βi(0)=0.1] and that of a high initial ion beta [βi(0)=1]. For each case of low and high initial betas, two values of initial turbulence level are used. One corresponds to δB2(0)/B20=0.1 and the other corresponding to δB2(0)/B20 =0.1. It is shown that for both low and high beta cases, the ion heating at the shock becomes more efficient for a higher value of δB2(0)/B20.

ON THE SECOND STABILITY REGION OF TOKAMAK PLASMAS AGAINST HIGH-n BALLOONING MODES

The stability of a high-beta tokamak plasma having circular crosssection against the high-n ballooning modes is reconsidered. In the high-beta case, the poloidal magnetic field yields a rather strong driving term to the ballooning modes, leading to a substantial distortion of the structure of the second stability region. The various effects of the magnetic shear, pressure gradient and the poloidal magnetic field parameter on the eigenfunctions and the eigenvalues of these modes are calculated. The results obtained give a comprehensive indication in predicting the ideal MHD ballooning modes in circular tokamaks.