Particle Acceleration in Multiple Dissipation Regions

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Particle Acceleration in Multiple Dissipation
Regions

• Kaspar Arzner (PSI/ETHZ)
• Loukas Vlahos, Heinz Isliker, Fabio Lepreti
  (AUTH)
• Bernard Knaepen, Daniele Carati, Nicolas Denewet
  (ULB)

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Acceleration environment
hot spots with E.jgt0

• True MHD turbulence Gauss proxy

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Gauss Proxy for Dissipation Regions
magnetic field lines
Sample trajectory

• B0 20G, dBx dBy 20G, dBz 100G
• Outer scales
• lxly1km, lz20km
• Matern class PSD with index a1.5
• Threshold current jcencs exceeded in 5 of
  volume

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Simulations at PSI

• Merlin cluster
• 56 nodes
• Myrinet / Ethernet
• code f90
• MPI / MPICH

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Diagnostics Anomaleous Diffusion

• What quantity to consider? P mgv is a good
  candidate since it is unbounded and incremented
  by the equation of motion.
• For initially Maxwellian protons (T106K) we find
• EW / ED lt 103 ordinary diffusion.
• EW / ED gt 5 .103 subdiffusion.

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EW / ED 2.102 ltP2gt t
100 keV
EW / ED 105 ltP2gt t0.8
time
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Proton acceleration efficiency
200 ms
Terminal Proton Energy
rms dissipative field
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Proton lifecycle in the presence of an adiabtic
invariant Py
Reason ltvyEygt lt(Ay - Py)DAygt f(e,Py)
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Electron Acceleration
sample
mean
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Distribution of Energy Jumps
Simulation
Best-fit Levy stable distribution
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Close-up dominant B field direction is z
(x,y) Brown motion OK z jump/drift
dominated
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Also existing, and definitifely not Brownian
Adiabatic/bounded trajectories
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Velocity vs. Waiting time
Prob(Dt) f(Dt L/v)
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Shape of f(Dt v / L)
Exponential 1D Poisson nearest-neighbour
distance. (1D because of ltdBz2gt 10 ltdBx,y2gt)
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Summary

• Conversion of electromagnetic energy to other
  forms implies j.E gt 0. The j-parallel component
  of E is responsible for acceleration.
• Present study super-Dreicer test particles in a
  Gauss proxy for strong resistive MHD turbulence
• Cross - (rms) field diffusion
• (rms) field-aligned jumps
• Fokker-Planck may be insufficient

References
Arzner, K. Vlahos, L., ApJ (2004) 605, L69
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-gt Montroll-Weiss type jump model
(Vlahos, Isliker, Lepreti 2003)
P(v,t -gt v,t) Pv(v-v) Pt(t-t)/t(v)/t(v)
t(v) collision time with dissipation regions
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Some exact Results (last-but-one slide!)
(q1/t )
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Resumee

• Super-Dreicer electrons perform energy jumps
  when dissipation regions are encountered
• On macroscopic (observable!) time scales, their
  orbit is thus a jump process rather than Brownian
  motion with continuous sample paths.

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EW / ED 105
t 0.8
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Normal Diffusion
100 keV
Initially maxwellian protons with T 106 K.