Electron Acceleration in Perpendicular Collisionless shocks

with preexisting magnetic field fluctuations

Fan Guo and Joe GiacaloneWith thanks to Dr. Randy Jokipii & Dr. David BurgessWith thanks to Dr. Randy Jokipii & Dr. David BurgessLunar and Planetary Laboratory, University of Arizona

Los Alamos National Lab 6/30/2010

Electron acceleration throughout the universe

Solar flare

Type II bursts

Heliospheric Termination shock

Supernova remnants

freq

uenc

y

time

How can shock accelerate particles?

<u1><u2>

• 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

θBn

<B1>

<B2>

shock shock

n

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)

Diffusive shock acceleration

Decker (1988)

E/E

0

x

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 structures1. Very rapid frequency drift rate2. May drift to higher or lower frequencies3. ~89% HB structures have drift velocity

0.05c-0.5c (1.3keV-130keV) Cairns & Robinson (1987)

How to accelerate electrons to these energies?

freq

uenc

y

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).

Decker et al. 2008

Shimada et al. (1999)

How these electron get injected ?

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.

Jokipii & Giacalone (2007)

Note: This process does not include SDA, which will make the acceleration more efficient.

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 pre-existing 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.

• 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

Hybrid simulation

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 test-

particle 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> =π/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 quasi-perpendicular shock.

• The acceleration efficiency decreases as averaged shock normal angle decreases

• Perpendicular shocks are the most important in electron acceleration

• Large shock normal angle permits field lines crossing shock multiple times

Dependence on different shock normal angle

• The energy spectrum of electrons does not evolve after the field lines convecting downstream completely.

• Profile of number of accelerated electrons shows similar features with observations.

Simnett et al. (2005)

Upstream electron: compared with the observations

θBn=81.3o θBn= 92o

observationsimulation

• The field line wandering is important for acceleration to higher energies

<ΔB2>/B02 = 0.1, 0.3, 0.5

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.

(Thomas et al., 1991)

Shock interact with current sheet

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

Wu (1984)deHoffmann-Teller frame