Nessun titolo diapositiva

1
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
2
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.)
3
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
4
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 lt x lt lx, 0 lt y lt
2ply, 0 lt z lt 2plz
5
Description of the simulations the initial
conditions
Equilibrium field plane current sheet (a c.s.
width)
Incompressible perturbations superposed
6
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

7
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 m0
(bidimensional) modes are the most unstable ones!
8
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!
9
Numerical results spectrum along z for m0
10
Numerical results spectrum along z for m1
11
Numerical results B fieldlines and current at y0
12
Numerical results B fieldlines and current at
y0.79
13
Numerical results B fieldlines and current at
y3.14
14
Numerical results B fieldlines and current at
y15.70
15
Numerical results time evolution of the spectra
16
Conclusions

• The two-dimensional modes (m0) are not the most
  unstable ones
• Initially,the modes with n3 (m0,1) 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.