Analytical model of magnetic reconnection in the presence of shock waves attached to a current sheet

MHD discontinuities in solar flares: Continuous transitions and plasma heating

“…Later on, Bezrodnykh et al (2007) constructed a two-dimensional analytical model of reconnection in a plasma with a strong magnetic field that included a thin current layer (CL) and four discontinuous MHD flows of finite length R attached to its endpoints. L is a halfwidth of the current layer.…”

“…Then the boundary condition for the function B is formulated as follows: B y = 0 on the current layer and surface (x = 0); B x sin α + B y cos α = −β on the discontinuity surface; B x = 0 on the surface (y = 0, x > L) and B = iγz + o(1) at z → ∞. Bezrodnykh et al (2007) constructed the sought-for analytic function in an explicit form by the method of the conformal mapping of the domain outside the system of sections onto the half-plane. Figure 9 shows magnetic field lines calculated in the special case of reconnection (L = 1, R = 1, α = 45…”

“…The advantage of an analytical model is the possibility to investigate more general patterns that do not depend on the detailed assumptions of a physical reconnection model. Consider some of the properties of discontinu- Figure 8: The configuration of electric currents (thick straight segments) consists of a current layer (CL) and four segments (discontinuity surfaces) of finite length R attached to its endpoints; L is the current layer half-width (Bezrodnykh et al, 2007). Figure 9: Magnetic field lines (thin curves) with an indication of the values of the vector potential.…”

“…The regions of direct and reverse currents inside the current layer (the thick horizontal straight segment) are seen. The magnetic field undergoes a jump on the attached discontinuity surfaces (inclined straight segments) (Bezrodnykh et al, 2007). Figure 10: Distribution of the angles θ 1 and θ 2 at the attached shock.…”

“…Figure 10: Distribution of the angles θ 1 and θ 2 at the attached shock. The variable l is the distance measured from the current layer endpoint along the discontinuity surface (Bezrodnykh et al, 2011). ous flows in the vicinity of a current layer predicted by the analytical model of Bezrodnykh et al (2007).…”