Magnetohydrodynamic simulation of a solar flare: 1. Current sheet in the corona

The results of modeling the preflare situation in the solar corona, obtained using a numerical solution for a complete set of three-dimensional MHD equations, are reviewed. Any assumptions concerning the flare development character or the active region’s behavior before a flare are not introduced. The initial and boundary conditions on the photosphere are specified from magnetic field measurements before a flare. The photospheric field sources are approximated by magnetic dipoles. The usage of the PERESVET program indicated that a current sheet is formed in the vicinity of a singular magnetic field line in the corona. The sheet is formed due to disturbances coming from the photosphere. The energy necessary for a flare is stored in the current sheet magnetic field during 2–3 days. The main construction principles of the PERESVET program, which makes it possible to use the maps of a measured photospheric field as boundary conditions, are presented.     

Numerical MHD simulations of the appearance of a series of current sheets above the active region AR 0365

The first attempt at numerical MHD simulations of the appearance of several current sheets above an active region before a series of elementary flares is described. Energy accumulates in the field of each sheet that can be released during one of the flares. The computations started three days before the appearance of a series of flares, i.e., before the emergence of a new magnetic flux in the active region. The initial (potential) magnetic field was calculated by solving the Laplace equation with an oblique derivative. The boundary conditions on the photosphere were specified from maps of the measured magnetic field in the active region for various instants of time. The Peresvet program solving the full system of MHD equations with dissipative terms was used in the computations. An absolutely implicit scheme conservative relative to the magnetic flux was used. The problem of properly choosing the size of the computational domain and finding the positions of singular magnetic field lines is discussed.     

Localized auroral disturbance in the morning sector of topside ionosphere as a standing electromagnetic wave

An intense, localized auroral disturbance observed by Intercosmos-Bulgaria-1300 satellite in the morning sector at the altitude 850 km is analyzed in detail. The disturbance is characterized by strong “jumps” of electric and magnetic fields reaching ～ 80 mV/m and ～ 100 nT, fluctuations of ion density (Δn/n ～ 70%) and bursts of downward and upward energetic electron fluxes. Electric and magnetic disturbances display a distinct spatial-temporal relationship typical for the standing quasi-monochromatic wave ($\text{? ～ 1}\text{Hz}\text{, λ}{}_{\mathrm{x}}\text{～ 10}\text{km}$). The ratio of amplitudes of electric and magnetic fluctuations is equal to Alfvén velocity (ΔE/ΔB ～ v_A/c). However, a strong parallel component of the electric field (～ 30 mV/m) and large ion density fluctuations indicate significant changes of plasma properties (the effects of anomalous resistivity are possible).     

On the possibility of the solar flare energy accumulation in the vicinity of a singular line

The energy of a solar flare can be accumulated as the magnetic energy of the current sheet created in the vicinity of a magnetic field singular line by the focusing of disturbances. Conditions which define the singular line in general were obtained using the properties of a singular line as it focuses disturbances. Numerical simulations and an analytical model show the possibility of the creation of a stable current sheet which becomes unstable after a quasistationary evolution. The nonlinear development of the instability leads to a fast reconstruction of the magnetic field with the release of a substantial part of the magnetic energy. The longitudinal magnetic field in our experiment increases the sheet thickness by at most a factoring of ten.     

Current sheet creation by a super-Alfvénic jet in a bipolar field

Energy accumulation in a current sheet (CS) can occur during the injection of a fast plasma jet in a perpendicular magnetic field. A similar situation can occur in the solar corona when a flux of plasma appears under a magnetic arch. The flare can be produced at the CS disruption. The CS creation during plasma jet interaction with the magnetic field is demonstrated by numerical MHD simulation. The choice of dimensionless parameters Re, Re_m,, II, which are suitable for simulation of coronal phenomena, is discussed. When jet injection ceases, the CS evolution produces an unstable state and fast magnetic energy dissipation is observed.     

On the problem of the formation of the Greenland sea convective gyre

The transformation of the interfaces of a rotating three-layer fluid is described through a simple hydrodynamic model using the shallow-water approximation. Using the Greenland sea gyre as an example, it is shown that a cyclonic circulation results in the oncoming deflection of the upper and lower layers, which favours the development of deep convection.Translated by Mikhail M. Trufanov.     

Magnetic flux in an active solar region and its correlation with flares

The correlation between the magnetic flux in an active solar region and associated powerful solar flares is studied. The behavior of the active regions AR 10486 and AR 10365 is considered. These regions produced a series of class X flares as they crossed the solar disk. The flares appeared when the magnetic flux exceeded 10²² Mx. The magnetic flux remained constant during all the flares except for one. During this flare, the flux decreased by about 10%; this impulsive decrease of the flux was also recorded in the absence of flares. No energy flux from the photosphere to the corona at the time of the flare was observed. The behavior of the photospheric field in AR 10486 and AR 10365 is consistent with a slow accumulation of energy in the corona and the explosive release of energy stored in the magnetic field of a current sheet above an active region during the flare.     

The possibility of energy accumulation in a current sheet above the NOAA 9077 active region prior to the flare on 14 July 2000

Current sheet (CS) creation and energy accumulation above the NOAA 9077 active region have been numerically simulated. The magnetic spots are approximated by vertical dipoles placed under the photosphere, and the system of resistive 3D MHD equations is solved for compressible plasma with anisotropic thermal conduction. Two neutral magnetic lines are present in the corona above the NOAA 9077 active region, and a vertical CS emerges in the vicinity of one of them. The energy accumulated in this CS is about 5×10³² erg. The j×B/c force in it accelerates plasma upward. The other neutral line is not suitable for CS creation.     

Possibility of real time scale MHD simulation above an active region

The MHD simulations of preflare situation in the corona above the real active region (AR) are performed without any assumptions about the solar flare mechanism. All conditions for simulation are taken from observations. Such approach is directed to understand the flare mechanism. The observed SOHO MDI magnetic maps are used. The special numerical methods are developed and realized in the PERESVET code for numerical simulation in the real time scale. The first results of real time scale MHD simulation during several first minutes are presented. Initiation of current sheet (CS) creation in the vicinity of the magnetic field X-line is shown. The possibilities of real time scale MHD simulation of preflare situation on modern computers using the developed mathematical methods are discussed.