Non linear evolution of 3D magnetic reconnection in slab geometry

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Presentation transcript:

Non linear evolution of 3D magnetic reconnection in slab geometry M. Onofri, L.Primavera, P. Veltri, F. Malara University of Calabria, 87036 - Rende - Italy Summer school on Turbulence - Chalkidiki, September 23rd-28th 2003

Magnetic reconnection as a driver for turbulence The presence of current sheets and magnetic reconnection are seen to enhance the level of turbulence both in astrophysical and plasma machines context Earth magnetotail (Savin et al.) Earth magnetosphere (Hoshino et al.)

Understanding turbulence dynamics during the reconnection process Open questions: are the growth rates foreseen by the linear theory still valid when several modes are initially excited? saturation levels of the instability? nonlinear dynamics of the 3D reconnection: inverse cascade, coalescence of islands, etc.(Malara, Veltri, Carbone, 1992) Our approach: numerical simulations

Description of the simulations: equations and geometry Incompressible, viscous, dimensionless MHD equations: Magnetic reconnection in a current layer in slab geometry with the plasma confined between two conducting walls: Periodic boundary conditions along y and z directions Dimensions of the domain: -lx < x < lx, 0 < y < 2ply, 0 < z < 2plz

Description of the simulations: the initial conditions Equilibrium field: plane current sheet (a = c.s. width) Incompressible perturbations superposed:

Description of the simulations: the numerical code Boundary conditions: periodic boundaries along y and z directions in the x direction, conducting walls give: Numerical method: FFT algorithms for the periodic directions (y and z) fourth-order compact differences scheme along the inhomogeneous direction (x) third order Runge-Kutta time scheme code parallelized using MPI directives to run on a 16-processor Compaq a -server

Numerical results: characteristics of the runs Magnetic reconnection takes place on resonant surfaces defined by the condition: modenumber along y safety factor modenumber along z The growth rates of the instability depend on the position of the resonant surfaces According to the linear theory, the m=0 (bidimensional) modes are the most unstable ones!

Numerical results: instability growth rates Parameters of the run: Perturbed wavenumbers: -4  m  4, 0  n  12 Resonant surfaces on both sides of the domain!

Numerical results: spectrum along z for m=0

Numerical results: spectrum along z for m=1

Numerical results: B fieldlines and current at y=0

Numerical results: B fieldlines and current at y=0.79

Numerical results: B fieldlines and current at y=3.14

Numerical results: B fieldlines and current at y=15.70

Numerical results: time evolution of the spectra

Conclusions The two-dimensional modes (m=0) are not the most unstable ones Initially,the modes with n=3 (m=0,1) grow faster At later times an inverse cascade transports the energy towards longer wavelengths This corresponds, in the physical space, to a cohalescence of the magnetic islands The spectrum of the fluctuations, which is initially growing mainly along the z direction rotates towards higher values of m/n.