Transcript Shock drift acceleration

Electron Acceleration in
Perpendicular Collisionless shocks
with preexisting magnetic field
fluctuations
Fan Guo and Joe Giacalone
With thanks to Dr. Randy Jokipii & Dr. David Burgess
Lunar and Planetary Laboratory, University of Arizona
Los Alamos National Lab 6/30/2010
Electron acceleration throughout the universe
Heliospheric Termination shock
frequency
Solar flare
Type II bursts
Supernova remnants
time
How can shock accelerate particles?
<u2>
<u1>
n
θBn
shock
<B1>
<B2>
shock
• Energy source: a large amount of bulk flow energy dissipates at
the shock layer
• Physics: The motion of particles is dominated by electric field
and magnetic field (collisionless plasma)
• The distinction between perpendicular shock and parallel shock
Shock acceleration
• Diffusive shock acceleration (DSA) (Krymsky 1977, Axford et al.
1977, Bell 1978, Blandford & Ostriker 1978)
1. The energy comes from upstream and downstream velocity
difference
2. The theory predicts a power-law spectrum
3. The acceleration rate depends on shock normal angle (Jokipii 1987)
Quantitative results of DSA can be calculated by solving Parker
transport equation (Parker 1965)
advection
diffusion
drift
energy change
The transport equation is valid when the anisotropy of particles is
small enough!
injection problem
Shock acceleration
• Shock drift acceleration (SDA) (fast-fermi) (Wu [1984], Leroy &
Mangeney [1984] discussed electrons)
1. The energy comes from particle drift in -v x B/c electric field
2. In a planar shock, scattering-free limit, the acceleration is limited (e.g.
Ball 2001)
3. In a perpendicular shock, diffusion process, shock drift acceleration is
equal to diffusive shock acceleration (Jokipii 1982)
Normal Incidence frame
Decker (1988)
E/E0
Diffusive shock acceleration
x
Decker (1988)
Type II bursts and their fine Herringbone
structures
• Type II bursts
1. driven by accelerated electron beams
come from the shock.
2. frequency and their drift indicate
the speed of the shock.
3. The common way to get accelerated
electrons is SDA (scattering-free limit).
• Herringbone structures
frequency
1. Very rapid frequency drift rate
2. May drift to higher or lower frequencies
3. ~89% HB structures have drift velocity
0.05c-0.5c (1.3keV-130keV)
Cairns & Robinson (1987)
How to accelerate electrons to
these energies?
time
Electron injection problem for DSA
• Cyclotron resonance
condition is hard to be
satisfied. Electron gyroradii re
is (mp/me)1/2 times smaller
than proton gyroradii.
• Electron DSA seems to work
at the Termination Shock and
a few interplanetary shocks
(oblique, large-scale,
turbulent/dynamical).
Shimada et al. (1999)
How these electron get injected ?
Decker et al. 2008
Coronal shocks:
Q-perp VS Q-parallel shock
• Particle acceleration theory for
parallel shocks mainly focused on
ions (Lee and colleagues, and Ng
and colleagues, etc.)
• New theory for particle
acceleration is required?
• Role of perpendicular shocks has
to be considered.
Cliver (2010)
Electron injection problem
• Jokipii & Giacalone (2007)
provided an interesting solution
for electron acceleration at
perpendicular shocks
• Electrons can travel along
meandering magnetic field lines,
and cross shock many times…
• The energy is from the
difference between upstream
and downstream velocities.
Note: This process does not include SDA,
which will make the acceleration more
efficient.
Jokipii & Giacalone (2007)
Shock is rippled …
Shock is rippled in a variety of scales (by
magnetic field or density fluctuations)
Interplanetary shocks have the characteristic
irregular structure in the same scale with the
coherence length of the interplanetary
turbulence Neugebauer & Giacalone(2005).
The shock ripples in different scales may contribute to
the acceleration of particles.
If Lc = 0.01 AU, d|| = 0.18Lc,
0.07Lc, 0.1Lc
Bale et al. 1999 GRL,
Pulupa & Bale 2008 ApJ
Electron accelerated by ion-scale ripples
D. Burgess 2006 ApJ
The current work
The effects of preexisting
magnetic fluctuation and shock
ripples.
The method is to employ the
hybrid simulation combined
with test particle simulation.
The dimension is limited in 2-D,
thus all particles are tied on
their original field lines.
Our approach to study this problem
• Consideration: Interaction between magnetic turbulence
and collisionless shock is very complicated. There is no
way to capture all the physics analytically.
• Suitable self-consistent simulation has to be used. The
scale has to be large enough to include large scale preexisting turbulence, and the resolution has to be small
enough to capture shock microphysics (ion scale).
• Approach: Hybrid simulation + electron test particle
• hybrid simulation (kinetic ions, fluid electron) gives
electric and magnetic fields
• Test particle electrons: assume no feed back on the
electric and magnetic field.
Hybrid simulation
• The simplified 1-D magnetic fluctuations are assumed for
the pre-existing turbulence.
• The fluctuating component contains an equal mixture of
right- and left-hand circularly polarized, forward and
backward parallel-propagating Alfven waves. The
amplitude of the fluctuations is determined from a 1D
Kolmogorov power spectrum:
• <ΔB2> = 0.3B02
Note: In 1-D or 2-D hybrid simulations, the particles are tied
on their original field lines! (Jokipii 1993)
Test Particle simulation
• Integrate the equation of motion for an ensemble of testparticle electrons with non-relativistic motions assumed
• Use second order interpolation of fields to make sure the
smoothness and avoid artificial scattering
• Bulirsh-Stoer method (see Numerical Recipes):
Highly accurate and conserves energy well
Fast when the fields are smooth
Adjustable time-step method based on the evaluation of
local truncation error.
• Test-particle electron
release ~106 test particles uniformly upstream with a
isotropic mono-energetic distribution (100eV) after the
shock is fully developed
Box size:Lx X Lz = 400(c/ωpi) X 1024(c/ωpi)
MA0 = 4.0, Ωci/ωpi = 8696, <θbn> =/2
Shock is rippling in a variety of scales.
The rippling of the shock and varying
upstream magnetic field lead to a varying
local shock normal angle along the shock
front.
Electron distribution (E>10E0) after the initial release
Effect of shock ripples on electron acceleration
Dependence on different shock normal angle
• Efficient electron acceleration
is found after consider the
magnetic fluctuations in quasiperpendicular shock.
• The acceleration efficiency
decreases as averaged shock
normal angle decreases
• Perpendicular shocks are the
most important in electron
acceleration
Dependence on different shock normal angle
• Large shock normal angle permits field lines crossing
shock multiple times
• The energy spectrum of electrons does not evolve after
the field lines convecting downstream completely.
Upstream electron: compared with the observations
simulation
observation
θBn=81.3o
θBn= 92o
Simnett et al. (2005)
• Profile of number of accelerated electrons shows similar
features with observations.
<ΔB2>/B02 = 0.1, 0.3, 0.5
• The field line wandering is
important for acceleration to
higher energies
Future works
• 1. Electron and proton acceleration in 3-D collisionless
shocks. In the system with at least one ignorable coordinate,
particles are artificially tied on their original field lines. Particle
transport normal to the mean magnetic field is suppressed
[Jokipii et al. (1993)].
Giacalone (2009)
Future works
• 2. Electron acceleration in shock with other structures
The interaction between preexisting turbulence/current sheets
and collisionless shocks could change the picture of particle
acceleration. The possible application will be the observation
in Earth’s bow shock interacting with interplanetary
discontinuity structures.
Shock interact with current sheet
(Thomas et al., 1991)
Conclusions
• After including preexisting turbulence, the electron can
be efficiently accelerated by quasi-perpendicular shock.
• The acceleration mechanism is drift acceleration
including acceleration by ripples and multiple reflection
taken by large scale field line random walk.
• The limitation of drift acceleration is probably associated
with the scale of shock and structure in y-direction.
• The diffusive acceleration is suppressed by 2-D
calculation, which require the consideration of 3-D
magnetic field, or artificial cross-field diffusion.
Shock Drift (Fast Fermi) Acceleration
deHoffmann-Teller frame
Wu (1984)