Electron
This presentation is the property of its rightful owner.
Sponsored Links
1 / 15

Abstract PowerPoint PPT Presentation


  • 60 Views
  • Uploaded on
  • Presentation posted in: General

Download Presentation

Abstract

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Abstract

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


Abstract

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


The fluid model for collisionless magnetic reconnection

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


The fluid model for collisionless magnetic reconnection1

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


The magnetic reconnection model s imulation of the reconnection process

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


Single helicity case k z 0 the fluid parallel electric field

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


The electron model

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


The electron model1

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


The electron equations

The electron equations

14th European Fusion Theory Conference, Frascati, September 26-29, 2011


The f approach

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


Kinetic simulations

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


Kinetic simulations single particle trajectory

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


Numerical simulations kinetic results k z 0

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


Numerical simulations kinetic current density

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


Further steps

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


  • Login