Transcript Acceleration at Shocks Without Particle Scattering

Acceleration at Shocks
Without Particle Scattering
J. R. Jokipii and Joe Giacalone
University of Arizona
Shimada et al, 1999
• Observations of shockaccelerated electrons
Mewaldt et al, 2005
Shock Acceleration of Electrons
• In principle, there is no difference between
electrons and ions in the basic picture of
diffusive shock acceleration
– What scatters the electrons?
– We need a low-energy electron accelerator
• Importance of large-scale fluctuations
– Electrons move rapidly (nearly) along magnetic lines
of force that can intersect the shock in multiple
locations
What is the Electron Accelerator?
Surprisingly few mechanisms have
been proposed:
1. Somehow, the relevant fluctuations
are produced.
2. Stochastic acceleration (or
injection).
Acceleration by a Meandering
Magnetic Field Line
• Large-scale field line
meandering leads to
multiple connections at
the shock (compression)
– Electrons are fast enough
to cross the shock several
times by following along
these meandering fields
• This process will be most
effective at a
perpendicular shock.
The Process of Adiabatic
Acceleration
• A particle moving nearly along the local magnetic field,
with a pitch angle close to 0 degrees, conserving its first
adiabatic invariant, will closely follow a magnetic field
line.
• As the x-component of the particle velocity changes, its
energy increases or decreases in the observer's frame
because of the motion of the magnetic field line with the
local flow speed.
Sample Electron Trajectory
• This electron
gains energy as it
crosses and recrosses the shock
– Similar to 1st-orderFermi acceleration,
but does not involve
resonant scattering
• The particles move only along the local magnetic field,
so we expect that the rate of energy change will go to
zero as the field line meandering goes to zero and the
particles can only move normal to the flow direction.
• For finite field meandering, the acceleration rate should
be
• Where α = <(δBx/B)2>. Note that for an isotropic
distribution of field-line directions, <(δBx/B)2>=1/3, and
we recover the normal rate (Parker, 1965).
• By analogy with the Parker transport equation,
we can write for the distribution function of
particles f(x,z,p,t).
• Applying this to particles injected at some low momentum at a narrow
compression yields a time-asymptotic spectrum of accelerated
particles similar to that found in standard diffusive shock acceleration:
• where the power law index becomes
• where rsh is the shock ratio U1/U2 and 1 and 2 are the values
evaluated upstream and downstream of the compression, respectively.
Test-Particle Numerical Simulations
• We follow the trajectories of an
ensemble of electrons
• The upstream random magnetic
field is obtained by a discrete sum of
individual waves
• Satisfies Maxwell’s equations
• The amplitudes A(kn) are determined
from a power spectrum
Computed Spectrum
Shock-accelerated electrons:
downstream distribution function
• The simulated distribution
of accelerated electrons is
steeper than the
prediction (diffusive shock
acceleration) at low
energies, but approaches
it asymptotically at high
energies
Including shock microstructure
• Generally, this mechanism will work at any
compression. A shock-like discontinuity is not required
• Including the microstructure is difficult because in
addition to the cross-shock electric field, we must also
include the rotation of the magnetic field out of the
plane of coplanarity
– This would vary along the shock since it depends on the local
shock normal angle (as known from past studies)
Results using ad-hoc scattering in the shock
transition region
• Fully kinetic particle simulations
reveal that electrons can be
efficiently accelerated/scattered
by electromagnetic fluctuations
inside the shock layer
• This is modeled using ad-hoc
scattering when the electron
exists within the shock layer
• The scattering time is taken to
be 100 electron gyroperiods
(independent of energy).
Conclusions
1.
New simulations and theory show that electrons can be
efficiently accelerated by shocks
They move along meandering magnetic
field lines and interact with the shock (or
compression) several times. They gain energy,
even though resonant scattering is not required.
2.
This process is most effective at nearlyperpendicular shocks.
Diffusive shock
acceleration has
proved to be a very
robust and attractive
mechanism for ion
acceleration.
Acceleration and Transport of
Energetic Particles at CIRs
Joe Giacalone,University of Arizona
(W ith thanks to Randy Jokipii and Jozsef K ota)
1.
2.
Shocks are ubiquitous
in space
The spectrum is
narrowly constrained
and is what is needed
SHINE 2006
Zermatt Resort, Utah