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Published byἸώβ Ἡρακλείδης Βλαχόπουλος Modified over 6 years ago
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The Physics of the Collisionless Diffusion Region
Michael Hesse NASA GSFC
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Diffusion region basics – focus on component merging
Overview: Diffusion region basics – focus on component merging Thermal- or bulk inertia-based diffusion? Scaling of the electron diffusion region Particle orbit analysis Acknowledgements: J. Birn, M. Kuznetsova, K. Schindler, M. Hoshino, J. Drake
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Simulation Setup - 1-D “Harris” Equilibrium, Lx= 2Lz= 25.6 c/wpi
- Flux function: A = -ln cosh(z/a) - normal magnetic field perturbation (X type, 2.5% of lobe field) - 80% guide field - Sheet Full-Width a= c/wpi - we/We=2 - Ti/Te = 5 - mi/me=256 - 100x106 particles - 800x800 grid Results averaged over 60 plasma periods
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x z
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Change of symmetry By P. Pritchett
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Electric Field Equations
Electron eqn. of motion At reconnection site important? small, limited by me?
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Magnitude of Bulk Acceleration Contribution
Time derivative of (negative) electron velocity in y direction:
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Pxye Pyze
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-(vezBx-vexBz) -me(ve.grad vey)/e
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Scaling the pressure tensor evolution equation
Assume ignore heat flux…
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Pressure tensor approximations
Hesse, Kuznetsova, Hoshino, 2001
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Electron Pressure Tensors
approximation from simulation Pxye Pxye Pyze Pyze critical difference at reconnection site – need to include Q!
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Qxyze Qxxye
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Div Q|xy Pyza approximation
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Approximations for Qxyze
x,y,x component: Assume near gyrotropy, By>>Bx, Bz Leading order, Pii>>Pjk
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Approximations for Qxyze
From simulation: Approximation: Ok in center, difference due to 4-tensor?
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Scaling of diffusion region
=> 2 Scale lengths: Collisionless skin depth Electron Larmor radius in guide field
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coll. skin depth
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Physical Mechanism: Larmor orbit interacts with “anti-parallel” B components
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Straight Acceleration and Thermalization
Particle Picture: Straight Acceleration and Thermalization Question: Are electrons transiently accelerated while crossing the diffusion region, or is some of the energy thermalized? Relevance: straight acceleration -> thermalization -> Approach: Integrate 104 electron orbits in vicinity of reconnection region
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Parallel electric field Wit=16
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Idea: If Ey approximately constant, then, for each particle (electron): If there is no scattering, then all additional energy is deposited into: Approach: Plot total and “y” kinetic energy change vs. y-displacement for ensemble of electrons in diffusion region
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Approximately 6% of energy is thermalized
-0.5 0.5 1 1.5 2 -12 -10 -8 -6 -4 -2 kinetic energy change as function of delta y delta Ek y = e x R= delta y -0.5 0.5 1 1.5 2 -12 -10 -8 -6 -4 -2 delta y-component of kinetic energy vs. delta y delta Eyk y = x R= delta y Approximately 6% of energy is thermalized
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orbit( 6293): z-x acceleration phase
-0.08 -0.06 -0.04 -0.02 0.02 0.04 0.06 13.15 13.2 13.25 13.3 13.35 13.4 13.45 orbit( 6293): x-z plane x -0.08 -0.06 -0.04 -0.02 0.02 0.04 0.06 13.15 13.2 13.25 13.3 13.35 13.4 13.45 orbit( 6293): z-x acceleration phase z x
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Orbit of “typical electron” in poloidal magnetic field
Scale length: electron Larmor radius
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3D Modeling M. Scholer et al.: Formation of “2D” channel
J. Drake et al.: Buneman modes, electron holes, anomalous resistivity
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P. Pritchett: inertia important
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…and other limitations, such as
Finite (small) system size Finite (small) ion/electron mass ratio Finite (small) speed of light Periodicity …there is work to be done!
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Additional slides
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Electron Distribution Functions
F(vx,vy) F(vx,vz) F(vy,vz) vx vy vz
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..pressure tensor nearly(?) gyrotropic
But: if Bx, Bz=0 -> nongyrotropy important. How to estimate?
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