Compressible Resistive MHD Research Articles

Secondary island induced during magnetic reconnection by an external sub-Alfvénic shear flow

Secondary tearing instability induced associated with sub-Alfvénic shear flow during magnetic reconnection processes is investigated using a compressible resistive MHD model. Compared to the without shear flow case, it is found that a secondary island can be built up during the reconnection process with an external sub-Alfvénic shear flow. For further investigation, we also found that the built-up island is not developed so larger due to the pairs of discontinuities formed in the inflow region of the reconnection. For the fixed initial asymptotic shear flow velocity v0, there existing a critical value λvc fastest to excite the secondary island. The critical value λvc may vary with different v0. Although, there is a significant gap for reconnection rates between the simulation results and observations, it can be deduced that the discontinuities can be formed in the situations with sheared flows associated with the magnetic reconnection. The results can be applied to interpret the multiple-X lines reconnections and discontinuities observations at the Earth's dayside magnetopause and magnetotail.

Generation of B y in Earth’s magnetotail with the effect of IMF B y during southward interplanetary magnetic field

Based on the three-dimensional compressible resistive MHD models, the Earth’s dipole magnetic field is employed to investigate IMF By penetration driven by the solar wind during southward interplanetary magnetic field (IMF) with uniform resistivity. It is found that the magnetic field By is built up in the central plasma sheet of the Earth’s magnetotail. When θ = 30° (where BIMFy = BIMF sin θ), the magnetic field By in the plasma sheet is the strongest and even larger than the initial imposed BIMFy. In addition, BIMFy promotes the reconnection process of dayside magnetopause. With a further increase in θ, the reconnection rate of dayside magnetopause and the magnetic field By decrease, and the structure changes significantly. The results can be used to analyze the observed data of IMF By penetration.

Configurations of Earth’s magnetosphere in response to variations in z component Solar-wind flow during the southward IMF

Based on the compressible resistive MHD models, the Earth’s dipole magnetic field is employed to investigate magnetic reconnection driven by the solar wind with southward interplanetary magnetic field. By including the z-component solar wind velocity vswz in a three-dimensional compressible global resistive MHD simulation with uniform resistivity, we found that vswz does not affect the location of magnetic reconnection on the dayside magnetopause in the interaction of southward magnetic field of the solar wind with the Earth’s dipole field. However, significant deviation of the central plasma sheet in the magnetotail from equatorial plane can occur. Detailed study also shows that vswz promotes magnetic reconnection at the dayside magnetopause, and the reconnection rate and deviation of magnetotail current sheet both increase with vswz. In particular, the deviation angle increases linearly with vswz. The results here can be useful for understanding observed substorm behavior in the magnetosphere.

Symplectic map and mathematica for calculations of magnetic field lines and compressible resistive MHD spectra in a tokamak with hydrogen plasma

This paper attempted to consider Symplectic mappings called the Tokamap to describe the magnetic field lines in the Poincaré map. These maps are compatible with the toroidal geometry and are considered in a tokamak with a large aspect ratio. The Tokamap depends on the two parameters ε and q, and with increasing ε chaos appears in the maps. In the current study, Tokamap and symmetric Tokamap are considered for two types of q, monotonic and non-monotonic. The non-monotonic is different from the original q in these mappings. The location of the created transport barriers depends on the q. Moreover, the compressible resistive MHD equations are solved for IR-T1 tokamak configuration with arbitrary currents and density mass profiles. The equations were linearized around an equilibrium state. Then, the eigenvalues and normal modes were obtained numerically by Mathematica software for homogeneous and inhomogeneous plasma. The results show that the eigenvalues are complex and lie on specific curves. Also, the normal modes are damped.

Slow shock formation and structure with sub‐Alfvénic shear flow in magnetic reconnection

Slow shock formation and structure associated with magnetic reconnection are investigated in the presence of sub‐Alfvénic shear flow using a compressible resistive MHD model. It is found for the first time that one or two pairs of the slow shocks are formed in the inflow region away from the reconnection separatrices within compressible resistive MHD. The distributions of the slow shocks depend largely on the plasma beta and the shear flow velocity that lead to the increase of magnetic reconnection rate. One pair of the slow shocks is formed for β = 0.2 and two pairs of the slow shocks are generated for β = 1.0 with the shear flow velocity in the range 0.6 VA to 0.9 VA. For high plasma beta (β = 5.0), there is no slow shock formed outside the reconnection separatrices. The results can be applied to interpret slow shock observations at the dayside magnetopause.

NUMERICAL SIMULATION OF SOLAR MICROFLARES IN A CANOPY-TYPE MAGNETIC CONFIGURATION

Microflares are small activities in solar low atmosphere, some are in the low corona, and others in the chromosphere. Observations show that some of the microflares are triggered by magnetic reconnection between emerging flux and a pre-existing background magnetic field. We perform 2.5D compressible resistive MHD simulations of magnetic reconnection with gravity considered. The background magnetic field is a canopy-type configuration which is rooted at the boundary of the solar supergranule. By changing the bottom boundary conditions in the simulation, new magnetic flux emerges up at the center of the supergranule and reconnects with the canopy-type magnetic field. We successfully simulate the coronal and chromospheric microflares, whose current sheets are located at the corona and the chromosphere, respectively. The microflare of coronal origin has a bigger size and a higher temperature enhancement than that of chromospheric origin. In the microflares of coronal origin, we also found a hot jet ($\sim$$1.8 \times 10^6$ K), which is probably related to the observational EUV/SXR jets, and a cold jet ($\sim$$10^4$ K), which is similar to the observational H$\alpha$/Ca surges, whereas there is only an H$\alpha$/Ca bright point in the microflares of chromospheric origin. The study of parameter dependence shows that the size and strength of the emerging magnetic flux are the key parameters which determine the height of the reconnection location, and further determine the different observational features of the microflares.

Magnetic Reconnection in a Canopy-type Magnetic Configuration for Solar Microflares

We performed 2.5D compressible resistive MHD simulations of magnetic reconnection with gravity considered. The background magnetic field is a canopy-type configuration which is rooted at the boundary of the solar supergranule. By changing the bottom boundary conditions in the simulations, an emerging flux rises up at the center of the supergranule and reconnects with the canopy magnetic field. We successfully simulate the coronal and chromospheric microflares, whose current sheets locate at the corona and chromosphere respectively. The coronal microflare is triggered by the reconnection at the corona, whose size and temperature enhancement is bigger and higher than the chromospheric one. We also found a hot jet (~1.8 × 106 K) relating to the observational EUV/SXR jet and a cold jet (~104 K) corresponding to the observational Hα /Ca surge or brightening in the coronal case. Whereas there is only Hα /Ca bright point in the chromospheric one.

Influences of sub-Alfvénic shear flows on nonlinear evolution of magnetic reconnection in compressible plasmas

Influences of sub-Alfvénic shear flows on the nonlinear evolution of the magnetic reconnection are studied in the framework of compressible resistive MHD and compressible Hall MHD. It is found for the first time that the sub-Alfvénic shear flow can either stabilize or destabilize magnetic reconnection, which is mainly determined by the plasma beta and the half thickness of the shear flow (λv). The shear flow exhibits a suppressing effect on magnetic reconnection and the boosting effect nearly disappears for the beta plasma β ≲1, which is associated with the presence of a pair of discontinuities in the upper and lower inflow region. The shear flow has the boosting effect on magnetic reconnection when the half thickness of the shear flow exceeds a critical value in the high beta plasma which is in a good agreement with the results from incompressible simulation. With the inclusion of the Hall effect, shear flow can still either stabilize or destabilize magnetic reconnection, but the boosting effect becomes weaker as the ion inertial length di increases.

NUMERICAL SIMULATIONS OF CHROMOSPHERIC MICROFLARES

With gravity, ionization, and radiation being considered, we perform 2.5D compressible resistive MHD simulations of chromospheric magnetic reconnection using the CIP-MOCCT scheme. The temperature distribution of the quiet-Sun atmospheric model VALC and the helium abundance (10%) are adopted. Our 2.5D MHD simulation reproduces qualitatively the temperature enhancement observed in chromospheric microflares. The temperature enhancement $\Delta T$ is demonstrated to be sensitive to the background magnetic field, whereas the total evolution time $\Delta t$ is sensitive to the magnitude of the anomalous resistivity. Moveover, we found a scaling law, which is described as $\Delta T/\Delta t \sim {n_H}^{-1.5} B^{2.1} {\eta_0}^{0.88}$. Our results also indicate that the velocity of the upward jet is much greater than that of the downward jet and the X-point may move up or down.

Current profile flattening and hot core shift due to non-linear development of resistive kink mode

A new and interesting phenomenon that the toroidal current profile, which at first exhibits peaking due to ohmic heating, flattens around the magnetic axis is obtained through a full compressible resistive MHD simulation for a 3-D toroidal geometry. It is concluded that the current flattening is caused by non-linear excitation of the unstable m=1/n=1 resistive kink mode, specifically by the quasi-linear effect of the coupling of the plasma velocity and the magnetic field of the n=+or-1 mode. The time-scale of the current profile flattening is of the order of the MHD time-scale. When the current profile is largely flattened, the plasma dynamic pressure due to the strongly excited kink mode pushes the hot core plasma in the radial kink flow direction and the hot core starts deviating from the magnetic surface owing to the dynamic pressure and the plasma compressibility. Because of the reduction of the magnetic shear due to the current flattening in the q<1 region, magnetic field reconnection is driven by the strong kink flow and leads to the destruction of the magnetic field structure within the q=1 rational surface. Subsequently, the magnetic field configuration recovers to an axisymmetric profile. This can explain the fast crash phase of sawteeth in tokamaks. The effect of the thermal conduction on the evolution of such a process is also discussed

On the efficiency of coronal loop heating by resonant absorption

The heating of solar coronal loops by resonant absorption of Alfven waves is investigated in the framework of linearized compressible resistive MHD. The resonant absorption of the waves incident on the coronal loops is numerically simulated in straight cylindrical, axisymmetric loop models externally excited by a periodic source. The stationary state of this driven system and the ohmic dissipation rate in this state are determined by a very accurate code based on the finite element technique. The efficiency of the heating mechanism and the energy deposition profile in this stationary state strongly depend on the characteristics of both the external driver and the equilibrium. It is shown that resonant absorption is very efficient for typical coronal loops as a considerable part of the energy supplied by the external source is actually dissipated ohmically and converted into heat. The heating rate is proportional to the square of the magnitude of the background magnetic field. 19 refs.

Undriven magnetic reconnection in an isolated current sheet

Magnetic reconnection in a plane current sheet is investigated by means of a two‐dimensional time dependent compressible resistive MHD code. The system length is large compared to the current sheet half thickness. A spatially limited resistivity is applied in the center of the current sheet. The resistivity falls off along the current sheet with some e‐folding distance xl. For sufficiently small xl, quasi‐steady reconnection with a small diffusion region develops. The reconnection exhibits all Petscheklike features, such as two pairs of slow mode shocks attached to the diffusion region, a strongly converging flow toward the field line reversal region, and a weak fast mode expansion of the inflowing plasma. At larger xl values, long current sheets develop; i.e., the length of the diffusion region is always such as to occupy the largest permitted space. The flow in the long current sheet cases is also of the fast mode expansion type. However, the flow turns in these cases upstream of the separatrices into a wedge‐shaped reconnection layer, whereas in the case with a small diffusion region the separatrices are well outside the reconnection layer. The reconnection rate measured in terms of the inflow Alfvén Mach number well upstream of the diffusion region decreases with increasing current sheet length and reaches the Sweet‐Parker rate for a current sheet corresponding to the system size. Starting the simulation with a small xl and increasing xl as a function of time to the total system size inevitably also leads to long extended current sheets with a correspondingly small reconnection rate. It is thus impossible to retain a diffusion region with a comparable width and length in a large‐sized system with spatially extended finite resistivity. By artificially limiting the length of the diffusion region, the maximum reconnection rate has been determined for several simulation runs with different magnetic Reynolds numbers Rm. Over a limited Rm range the numerically obtained rate is consistent with the classical Petschek rate.

Finite beta effects on tearing modes in the tokamak

Details are given of a numerical study of finite-beta tearing modes in the tokamak. The linear compressible resistive MHD equations are solved in full toroidal geometry with no ordering assumptions. The results show a strong stabilizing effect as beta is increased, arising from the average curvature within the resistive layer. This stabilizing effect is particularly pronounced for high conductivity temperatures and small aspect ratios.

A simulation study on reconnection and small‐scale plasmoid formation

Magnetic reconnection in a plane current sheet is investigated by means of a two‐dimensional time dependent compressible resistive MHD code. The system length is large compared to the current sheet half thickness. The anomalous resistivity is allowed to grow with either the electrical current density or the drift velocity. Reconnection is not forced, but is initiated by a small localized resistivity which is subsequently switched off. Fast reconnection develops self‐consistently with slow shocks extending from the X point and a fast mode expansion upstream. A slow mode expansion fan leads upstream of the slow mode shocks to a plasma flow toward the X point. In the case of current dependent resistivity the reconnection rate decreases again, which leads to a flattening of the separatrices and a long current layer. Secondary tearing produces a new pair of X points which are active sites of reconnection. For low plasma β the two developing plasmoids immediately merge into a single one. For high plasma β, reconnection proceeds at all three X points leading to a figure‐8 magnetic island structure. In the case of drift velocity dependent resistivity and low plasma β values the secondary tearing occurs at locations of low density along the x axis (large resistivity). The plasmoids merge, and new X points develop further out. Continuous development of plasmoids and their subsequent coalescence leads to a large‐scale plasmoid filling the whole computational box. For high plasma β values (small compressibility) the resistivity (and the reconnection rate) at the initial X point stays constant, the current sheet does not elongate, and no plasmoid develops, although the system length is large. The results are discussed in relation to recent observations by ISEE 3 in the distant tail.

The spectrum of resistive MHD modes in cylindrical plasmas

A numerical study of the normal modes of a compressible resistive MHD fluid in cylindrical geometry is presented. Resistivity resolves the shear Alfvén and slow magnetosonic continua of ideal MHD into discrete spectra and gives rise to heavily damped modes whose frequencies lie on specific lines in the complex plane. Fast magnetosonic waves are less affected but are also damped. Overstable modes arise from the shear Alfvén spectrum. The stabilizing effect of favourable average curvature is shown. Eigenfunctions illustrating the nature of typical normal modes are displayed.