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Abstract

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  1. Electronbehaviour in three-dimensional collisionless magnetic reconnectionA. Perona1, D. Borgogno2 , D. Grasso2,31CFSA, DepartmentofPhysics, UniversityofWarwick, UK2Burning Plasma Research Group, Politecnico di Torino, Italy3Istituto deiSistemiComplessi-CNR, Roma, Italy

  2. Abstract Aim of this project, still in progress, is to investigate the behaviour of an electron population during the evolution of a spontaneous collisionless magnetic reconnection event reproduced by a fluid formulation in a three-dimensional geometry. In this 3D setting the magnetic field lines become stochastic when islands with different helicities are present1. The reconstruction of the test electron momenta, in particular, can assess the small scale behaviour shown by the fluid vorticity and by the current density during the nonlinear phase of the reconnection process even in the presence of chaoticity. We present here preliminary results of the numerical tool developed on this purpose. 1D. Borgogno et al., “Aspects of three-dimensional magnetic reconnection”, Phys. Plasmas, Vol. 12, 032309, (2005). 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

  3. The fluid model for collisionless magnetic reconnection • We consider a fluid model that describes drift-Alfvén perturbations in a plasma immersed in a strong, uniform, externally imposed magnetic field. • Effects related to the electron temperature, through the sonic Larmor radius, and to the electron density, through the electron inertia, are retained. • Modes with different helicities can be present. They evolve independently during the linear phase, while a strong interaction occurs during the nonlinear stage of the process. • The set of equationsis closed by assuming constant temperatures for both the ions and the electrons. 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

  4. The fluidmodelforcollisionlessmagneticreconnection B = B0 ez+ (x,y,z,t) ez magnetic field with B0=const. and |B0|>>|B| ( = 8p2/B2 <<1),  magnetic flux function,  stream function. T. J. Schep, F. Pegoraro, B. N. Kuvshinov, Phys. Plasmas, Vol. 1, 2843, (1994) Two scale lengths: Fluid velocity: v=ez+ electron skin depth sound Larmor radius 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

  5. The magneticreconnectionmodel: simulation of the reconnectionprocess We adopt a static, linearly unstable magneticequilibrium Single-helicity initial perturbation nonlinear linear Island width vs time 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

  6. Single-helicity case (kz0): the ‘fluid’ parallelelectricfield Linear phase: monopole structure peaked at the X-point of the magnetic island. 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

  7. The electron model In ordertoverifywhether the parallelelectricfieldgenerated during the reconnectionleads tosuprathermalenergetic generation, a relativisticHamiltonianformulation*of the electron guiding-centerdynamicshasbeenchosen. The unperturbed relativistic guiding-centre phase-space Lagrangian can be written in terms of the guiding-centre coordinates as where * A. J. Brizard, A. A. Chan,Phys. Plasmas 6, 4548 (1999) 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

  8. The electron model The relativisticHamiltonianis magnetic moment: The equations of motion follow from the Hamiltonian in the usual manner where the conjugate momenta to the y and z coordinates are given by 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

  9. The electron equations 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

  10. The fapproach • A fapproachhas been adopted in order to reduce the number of particles required while resolving small fluctuations in the electron distribution function. • The distribution function is decomposed in an analytically described background component and the remaining component • In each cell labeled by i in the real space, we calculate • the electron density • the current density • and the mean longitudinal kinetic energy of electrons 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

  11. Kinetic simulations • The electron equationshavebeenimplemented in a 3-D code, whichreads at eachtimestep the fluidfieldsprovidedby the reconnection code1. • The kinetic code evolves the spatialcoordinates, the parallelvelocity and the change in the weightof the markersaccordingto the fluidfields. • We assume periodicboundaryconditionsalongy and z for the flux and for the streamfunction. • The resultspresentedhavebeenobtainedloading 2.5x106electrons in the 5-D phasespace (x,y,z,p|| , p). • The code hasbeenparallelizedbydistributingmarkersamongprocessersusingMessagePassingInterface (MPI) librairies. 1 A. Perona, L-G Eriksson, D. Grasso, Phys. Plasmas 17, 042104 (2010) 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

  12. Kinetic simulations:single particle trajectory The Poincaré plot of a single test electron crossing the X-point maps the magnetic island as expected. magneticsurface electron electron trajectory (kz=0 case) 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

  13. Numerical simulations: kinetic results (kz0) During the linear phase the electron and fluid current density evolve in good agreement, while the velocity distribution becomes thinner and the amount of electrons in the tails increases. Linear phase: Kinetic current density Fluid current density 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

  14. Numerical simulations: kinetic current density Linear phase Nonlinear phase Linear growth rate: fluid current * kinetic current Good agreement with the toroidal current of small Tokamaks such as T-3 (a ≈ 10-1 m, It=100 kA). 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

  15. Further steps • The behaviour of the electron population will be followed during the nonlinear phase of the single-helicity case (kz0) in order to confirm the agreement with the fluid results, as already observed in the 2D case. • The test electron distribution function will be reconstructed in the presence of multiple-helicity fluid fields. This will allow us to assess the structures of the electron and current density in the stochastic fields that develop during the nonlinear phase of the reconnection process. • In order to analyse the influence of the magnetic chaoticity on the electron transport we plan to compare the test electron distribution and the magnetic barriers detected through the analysis of the finite-time Lyapunov exponent ridges1. 1D. Borgogno et al., “Barriers in the transition to global chaos in collisionless magnetic reconnection”, in press Phys. Plasmas (2011). 14th European Fusion Theory Conference, Frascati, September 26-29, 2011

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