nonlinear particle acceleration at nonrelativistic shocks
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Nonlinear Particle Acceleration at Nonrelativistic Shocks Don Ellison, North Carolina State University. Magnetic Field Amplification (MFA) from cosmic ray streaming instability Emphasize nonlinear connection between : First-order Fermi Particle acceleration Shock structure - PowerPoint PPT PresentationTRANSCRIPT
Nonlinear Particle Acceleration at Nonrelativistic ShocksDon Ellison, North Carolina State University
Nonlinear Particle Acceleration at Nonrelativistic ShocksDon Ellison, North Carolina State University
Don Ellison, Cracow Oct 2008
1) Magnetic Field Amplification (MFA) from cosmic ray streaming instability
2) Emphasize nonlinear connection between :a) First-order Fermi Particle accelerationb) Shock structurec) Production of magnetic turbulenced) Calculation of diffusion coefficient from turbulencee) Influence of amplified B-field on maximum CR energy
3) Particular emphasis on role of escaping particles.
4) Only discuss non-relativistic shocks
This is NOT a formal review. Magnetic Field Amplification in shock acceleration is an active field with work being done by many people.
Important Points:
1) Collisionless shocks and the nonthermal particles they produce are widespread in astrophysics (and they are important)
a) In some sources, a sizable fraction of energy budget is in relativistic particles !
2) Diffusive Shock Acceleration (DSA) mechanism is well-studied
a) Works as expected in some sources (e.g. Earth bow shock, Interplanetary shocks)
b) DSA is inherently efficient !
3) In order for DSA to work, shocks must self-generate magnetic turbulence.
a) Magnetic field most important parameter in DSA
b) There is evidence that DSA amplifies turbulent magnetic fields by large factors: B/B >> 1 (e.g., Tycho; B-field in Cas A >500 G)
4) High acceleration efficiency means Magnetic Field Amplification (MFA) and Diffusive Shock Acceleration (DSA) are coupled and must be treated self-consistently
Don Ellison, Cracow Oct 2008
3 /( 1) 4 2( ) , or, ( )( ) r rf p p p N E E
Test-particle power law for Non-relativistic shocks (Krymskii 76; Axford, Leer &
Skadron 77; Bell 78; Blandford & Ostriker 78):
Power law index is:
Independent of any details of diffusion
Independent of shock Obliquity (geometry)
But, for Superthermal particles only
Ratio of specific heats, , along with Mach number, determines shock
compression, r
For high Mach number shocks:
( ) is phase space density
is compression ratio
f p
r
u0 is shock speed
So-called “Universal” power law from shock acceleration
! 41)3/5(
1)3/5(
1
1~
r
skprr Vuvppf
0)1/(3 if )(
BUT clearly Not so simple!
Consider energy in accelerated particles assuming NO maximum momentum cutoff and r ~ 4 (i.e., high Mach #, non-rel. shocks)
injinj
2 4 /p
p
Ep p dp dp p
)()( 2 pfppN
injln |pp
Diverges if r = 4
If produce relativistic particles < 5/3 compression ratio increases
The spectrum is harder Worse energy divergence Must have high energy cutoff in spectrum to obtain steady-state particles must escape at cutoff !!
But, if particles escape, compression ratio increases even more . . . Acceleration becomes strongly nonlinear with r >> 4 !!
►Bottom line: Strong shocks will be efficient accelerators with large comp. ratios even if injection occurs at modest levels (1 ion in 104)
1
1
rBut
Don Ellison, Cracow Oct 2008
Efficient particle acceleration
Amplification of magnetic fields
Efficient particle acceleration
Amplification of magnetic fields
Evidence for High magnetic fields in SNRs (all indirect):
1) Broad-band fits: Same distribution of electrons produces synchrotron radio and inverse-Compton TeV -rays
2) Spectral curvature in continuum spectra: prediction of NL shock acceleration
3) Sharp X-ray edges: High B large synch losses short electron lifetime and short diffusion lengths narrow X-ray structures.
Bottom line: Inferred B-fields (200-500 G) are much larger than can be expected from simple compression of BISM
Bshock >> 10 G x 4 ~ 40 G
Amplification factor ~ 5 -- 50
Note: Evidence for Bshock >> compressed BISM reasonably convincing, but still room for doubtNote: Evidence for Bshock >> compressed BISM reasonably convincing, but still room for doubt
Don Ellison, Cracow Oct 2008
Tycho’s Supernova Remnant
Warren et al 2005
Chandra
Sharp edge X-ray edges
Blue is synchrotron emission from TeV electrons.
Radial cuts: Sharp decline high B-field
Sharp X-ray synchrotron edges in SNRs : one piece of evidence for high Magnetic fields
Tycho’s SNR, 4-6 keV surface brightness profiles at outer blast wave (non-thermal emission)
Don Ellison, Cracow Oct 2008
Tycho’s SNR
Radio synchX-ray synch
Cassam-Chenai et al. 2007
Tycho’s SNR
Radio edge not sharp magnetic field is large:
Bds~ 100 – 300 G
(Note: authors more conservative in conclusions)
Ironically, evidence for large B-fields and MFA is obtained exclusively from radiation from electrons, but The NL processes that produce MFA are driven by efficient acceleration of protons or other ions
Don Ellison, Cracow Oct 2008
Nonlinear coupling of DSA and MFA is a difficult plasma physics problem
1) Strong turbulence (or dissipation) cannot yet be treated analytically
2) Observations of shocks in heliosphere :
a) Self-generated turbulence is seen in heliospheric shocks, BUT
b) Weak & small heliospheric shocks don’t produce relativistic particles with high enough efficiency for MFA (as seen in SNRs) to be apparent
3) Particle-in-Cell (PIC) simulations of non-relativistic shocks (e.g., SNRs):
a) To model SNRs, require acceleration of non-relativistic particles to relativistic energies in non-relativistic shock hard to do with PIC
b) PIC size and run-time requirements beyond current capabilities, but
c) PIC simulations are essential to understand magnetic field production and thermal particle injection
4) To make progress must use approximate methods:
a) Monte Carlo (Vladimirov, Ellison & Bykov 2006,2008)
b) Semi-analytic, kinetic technique based on diffusion-convection approximation (Amato & Blasi & co-workers)
Here I discuss Monte Carlo work done with Andrey Vladimirov (NCSU) and Andrei Bykov (St. Petersburg)
Here I discuss Monte Carlo work done with Andrey Vladimirov (NCSU) and Andrei Bykov (St. Petersburg)
max
thermal
9TeV10
keV
E
E
Energy range:
Length scale (number of cells in 1-D):
Run time (number of time steps):
Requirements for PIC simulations to do “entire” SNR problem. That is, go from injection at keV to TeV energies in non-relativistic shock
Problem difficult because TeV protons influence injection and acceleration of keV protons and electrons: NL feedback between TeV & keV
Plus, must do PIC simulations in 3-D (Jones, Jokipii & Baring 1998)
PIC simulations will only be able to treat limited, but very important, parts of problem, i.e., initial B-field generation, test-particle injection
To cover full dynamic range, must use approximate methods: Monte Carlo, Semi-analytic (e.g., Berezhko & co-workers; Blasi & co-workers)
10
pe
10)/( depth, skin electron
proton TeV LengthDiff
c
141-
pe
10TeV toTime Accel
Shocks set up converging flows of ionized plasmaBlast wave, i.e., Forward Shock
Vsk = u0VDS
Post-shock gas Hot, compressed, dragged along with speed VDS < Vsk
charged particle moving through turbulent B-field
Particles make nearly elastic “collisions” with magnetic field gain energy when cross shock bulk kinetic energy of converging flows is put into individual particle energy
Convert to shock rest frame
u2 = Vsk - VDS
SN explosion
rtot=u0/u2
Some of the most energetic particles leave at “Free escape boundary”
FEB
Don Ellison, Cracow Oct 2008
X
subshock
Flow speed, u test particle shock
modified shock
upstream diffusion length
If acceleration is efficient, shock becomes smooth from backpressure of CRs:
High momentum particles “feel” a larger compression ratio this produces a concave spectrum
Injection at subshock, and maximum momentum, must be treated self-consistently
effr
plot: p4 f(p) vs. p
Test-particle power law for superthermal particles only. No normalization
Shock Structure and particle distributions in nonlinear DSA:
Highest energy particles must escape from the shock in steady state
Don Ellison, Cracow Oct 2008
1) Main features of NL-DSA (Concave spectrum, Compression ratio > 7, Decrease in temperature of shocked plasma as acceleration efficiency increases) result from momentum dependence of diffusion coefficient.
2) If D(p) increases rapidly enough with momentum, these features occur regardless of details of wave-particle interactions. (This has been known for some time, e.g., Eichler 1984, ApJ, V. 277)
3) Why are details of diffusion coefficient, D(p), important?1) D(p) determines injection of thermal particles may set overall
acceleration efficiency may determine if NL effects occur at all2) The production of magnetic turbulence that creates D(p) may also
produce strong Magnetic Field Amplification (MFA)3) If MFA occurs, the maximum particle energy a shock can produce will
increase4) The number and spectral shape of escaping particles will be a strong
function of the detailed form of D(p)5) Obliquity effects will depend on details6) Electron to proton injection ratio will depend critically on diffusion
details
Don Ellison, Cracow Oct 2008
Magnetic Field Amplification (MFA) in Nonlinear Diffusive Shock Acceleration using Monte Carlo methods
Work done with Andrey Vladimirov & Andrei Bykov
Discuss Non-relativistic shocks only here
Don Ellison, Cracow Oct 2008
Bell & Lucek 2001 apply Q-linear theory when B/B >> 1; Bell 2004 non-resonant streaming instabilities
Amato & Blasi 2006; Blasi, Amato & Caprioli 06,08; Vladimirov, Ellison & Bykov 2006, 2008
How do you start with BISM 3 G and end up with B 500 G at the shock?
Basic assumptions:
1) Large B-fields exist and efficient shock acceleration produces them
2) Assume cosmic ray streaming instability is responsible, but hard to model correctly difficult plasma physics (e.g., non-resonant interactions etc)
3) Connected to efficient CR production, so nonlinear effects essential
4) Make approximations to estimate effect as well as possible
}
See references for details
calculations coupled to nonlinear particle accel.
growth of magnetic turbulence energy density, W(x,k), as a function of position, x, and wavevector, k
energetic particle pressure gradient as function of position, x, and momentum, p
VG(x,k) parameterizes a lot of complicated plasma physics
Make approximations for VG and proceed (if quasi-linear
approximation applies, VG is Alfvén speed)
Phenomenological approach: Growth of magnetic turbulence driven by cosmic ray pressure gradient (so-called streaming instability) e.g., McKenzie & Völk 1982
Determine diffusion coefficient, D(x,p), from W(x,k) Use diffusion coefficient in Monte Carlo simulation
Iterate
)(res
CR ),(),(
stream kG
ppdk
dp
x
pxPVkxW
dt
d
Don Ellison, Cracow Oct 2008
Don Ellison, Cracow, Oct 2008
Once turbulence, W(x,k), is determined from CR pressure gradient, determine diffusion coefficient from W(x,k). Must make approximations here:
1) Bohm diffusion approximation: Find effective Beff by integrating over turbulence spectrum (Vladimirov, Ellison & Bykov 06)
2) Resonant diffusion approximation (e.g., Bell 1978; Amato & Blasi 06):
3) Hybrid approach – Non-resonant approximation: In progressFor a particle of momentum, p, have waves with scales larger and smaller than gyro-radius. How is diffusion coefficient determined?
0
2eff ),(
2
1
8
)(dkkxW
xB
),(
3
1),( ,),(
eff
pxvpxDeB
cppx
1)(0
res0res eB
pckBrk g
),(
11),(
res2
22
2 kxWe
cppx
Determine steady-state, shock structure with iterative, Monte Carlo technique
Position relative to subshock at x = 0
[ units of convective gyroradius ]
Upstream Free escape boundary
Unmodified shock with r = 4
Self-consistent, modified shock
with rtot ~ 11 (rsub~ 3)
Energy Flux (only conserved when escaping particles taken into account)
Momentum Flux conserved (within few %)
Flow speed
Don Ellison, Cracow Oct 2008
Energy flux in thermal particles
Energy flux in Cosmic Rays Total Energy flux
Energy flux in Escaping particles
Upstream Free escape boundary
Position relative to subshock at x = 0[ units of convective gyroradius ]
Effective, amplified magnetic field, ~ 100 x upstream field
B
eff [
G] Beff
Don Ellison, Cracow Oct 2008
~ 50% of energy flux in CR spectrum
~ 35% of energy flux in escaping particles
Position relative to subshock at x = 0
[ units of convective gyroradius ]
Total acceleration efficiency ~ 85%
Energy flux in Cosmic Rays
Total Energy flux
When the acceleration is efficient, a large fraction of energy ends up in escaping particles
Don Ellison, Cracow Oct 2008
Escaping particles in Nonlinear DSA:
1)Highest energy particles must scatter in self-generated turbulence. a) At some distance from shock, this turbulence will be weak enough that
particles freely stream away.b) As these particles stream away, they generate turbulence that will scatter next
generation of particles
2)In steady-state DSA, there is no doubt that the highest energy particles must decouple and escape – No other way to conserve energy.
a) In any real shock, there will be a finite length scale that will set maximum momentun, pmax. Above pmax, particles escape.
b) Lengths are measured in gyroradii, so B-field and MFA importantly coupled to escape and pmax
c) The escape reduces pressure of shocked gas and causes the overall shock compression ratio to increase (r > 7 possible).
3)Even if DSA is time dependent and has not reached a steady-state, the highest energy particles in the system must escape.
• In a self-consistent shock, the highest energy particles won’t have turbulence to interact with until they produce it.
• Time-dependent calculations (i.e., PIC sims.) needed for full solution.
Monte Carlo results for Bohm vs. Resonant approximations for diffusion coefficient
Preliminary results:Andrey Vladimirov, Ellison & Andrei Bykov, in preparation
Don Ellison, Cracow Oct 2008
upstream
DS
Show distributions and wave spectra at various positions relative to subshock
subshock
Shock structure, i.e., Flow speed vs. position
Position relative to subshock at x = 0[ units of convective gyroradius]
Don Ellison, Cracow Oct 2008
0
2eff ),(
2
1
8
)(dkkxW
xB
),(
3
1),( ,),(
effpxvpxD
eB
cppx Bohm approx.
k W(k,p)p4 f(p)
D(x,p)/p
Don Ellison, Cracow Oct 2008
Iterate:
D(x,p)f(p)
W(k,p)upstream
),(
11),(
res2
22
2 kxWe
cppx
Resonant approx.
Diffusion in resonantly amp. turb. as well as compressed seed turb.
Seed turbulence ∝ 1/k
Diffusion in non-amplified but compressed seed turb. No particles resonant here
k W(k,p)p4 f(p)
D(x,p)/p
Don Ellison, Cracow Oct 2008
D(x,p) very different from Bohm case
Sold curves : downstream Dashed curves : upstream near FEBSold curves : downstream Dashed curves : upstream near FEBD(x,p) is very different in the two cases, BUT, the shock structure & amplified B-field are adjusting to compensate for changes in D(x,p). Downstream, the particle distributions are very similar. Near the free escape boundary, large difference occur.
Red: Bohm Blue: Resonant
k W(k,p)
p4 f(p)
Diffusion coefficient
Flow speed
Beff
near FEB
DSDS
near FEB
Red: BohmBlue: Resonant
Escaping particles ~35% of total energy flux escapes out front of shock
Energy flux calculated downstream from the shock ~50% in CRs
Energy flux in shock frame : Zero indicates isotropic flux. +1 indicates total incoming energy flux
Importance of escaping particles discussed in recent paper: Caprioli, Blasi & Amato 2008 Our Monte Carlo results for nonlinear MFA are reasonably consistent with semi-analytic results of Blasi, Amato & co-workers
Importance of escaping particles discussed in recent paper: Caprioli, Blasi & Amato 2008 Our Monte Carlo results for nonlinear MFA are reasonably consistent with semi-analytic results of Blasi, Amato & co-workers
Don Ellison, Cracow Oct 2008
No B-amp
B-amp
Shocks with and without B-field amplification
The maximum CR energy a given shock can produce increases with B-amp
BUT
Increase is not as large as downstream Bamp/B0 factor !!
Monte Carlo Particle distribution functions f(p) times p4
All parameters are the same in these cases except one has B-amplification
p
4 f
(p)
For this example,
Bamp/B0 = 450G/10G = 45
but increase in pmax only ~ x5
Maximum electron energy will be determined by largest B downstream. Maximum proton energy determined by some average over precursor B-field, which is considerably smaller
protons
Switch gears from a Monte Carlo model of a steady-state, plane shock, to a spherically symmetric model of an expanding SNR
Use semi-analytic model for nonlinear DSA from P. Blasi and co-workers Combined in VH-1 hydro code (from J. Blondin)
No MFA in the following examples
Don Ellison, Cracow Oct 2008
Contact Discontinuity
Forward Shock
Reverse Shock
Shocked Ejecta material : Strong X-ray emission lines, but expect no radio if B is diluted progenitor field
Shocked ISM material :
Weak X-ray lines; Strong Radio
1-D CR-hydro model couples eff. DSA to SNR hydrodynamics
e.g. Ellison, Decourchelle & Ballet 2004
SNR
Forward Shock
Reverse Shock
Shocked ISM material :
Weak X-ray lines; Strong Radio
1-D CR-hydro model couples eff. DSA to SNR hydrodynamics
Kepler’s SNR Radio obs.XMM X-ray obs. of SN 1006
Rothenflug et al. (2004)
Chandra observations of Tycho’s SNR
(Warren et al. 2005)DeLaney et al., 2002
Use semi-analytic model for nonlinear DSA from P. Blasi and co-workers combined in VH-1 hydro code (J. Blondin)
SNR
Escaping particles
CRs in SNR
Total
Total
Escaping particles dominate energy budget. Most SN explosion energy ends up in escaping particles !
Escaping particles don’t suffer adiabatic losses. Cosmic Rays that remain in SNR do suffer losses escaping particles will dominate energy budget if DSA is efficient.
Work in progress
Very efficient DSA
CRs in SNR
Escaping particles
Look at acceleration efficiency in SNR over 104 yr. Energy is divided between CRs that stay in the remnant and those that escape
SN
CRs
E
E
Acce
l. Effi
cien
cy (f
rac.
)En
ergy
/ E
SN
Don Ellison, Cracow Oct 2008
Escaping particles
CRs in SNR
Total
Total
Escaping particles don’t suffer adiabatic losses. CRs that remain in SNR do suffer losses Here, CRs in SNR dominate energy budget
Work in progress
Less efficient DSA
Escaping particles
CRs in SNR
Note: work in progress means I’m not sure I’m right
Don Ellison, Cracow Oct 2008
Effect of escaping particles on nearby mass distributions: One-dimension SNR model in a 3-D box with arbitrary mass distribution (Lee, Kamae & Ellison 2008)
Protons escaping from forward shock impact nearby molecular cloud
Don Ellison, Cracow Oct 2008
3-D simulation box
Protons just behind the blast wave shock
Escaping protons 9 pc away from center of SNR
Just before impacting molecular cloud
Lee et al 2008
Don Ellison, Cracow Oct 2008
Simulation of SNR in 3-D box with arbitrary mass distribution
Highest energy CRs leave the outer shock and propagate to nearby material, e.g. a dense molecular cloud
Lee, Kamae & Ellison 2008
Line-of-sight projections
GeV
TeVHESS: SNR Vela Jr.
Conclusions:
1)Magnetic field amplification (MFA) is intrinsically nonlinear must be calculated self-consistently with shock structure
2)Until exact analytic descriptions of strong turbulence become available, must use approximate methods to study MFA
a) Monte Carlo simulationsb) Semi-analytic methods
3)In principle, can solve problem completely with PIC simulations. a) However, difficult for non-relativistic shocksb) Critical problems – thermal injection, initial creation of B-fields, etc.,
can be addressed with current PIC simulations
4)If shock acceleration is efficient, escaping particles will be important. a) These will strongly influence wave generation and must be considered in
models for CR production, TeV emission
5)If MFA is important in SNRs, it should be important in other systems with strong shocks (GRBs, radio jets, shocks in galaxy clusters)
Conclusions:
1)Magnetic field amplification (MFA) is intrinsically nonlinear must be calculated self-consistently with shock structure
2)Until exact analytic descriptions of strong turbulence become available, must use approximate methods to study MFA
a) Monte Carlo simulationsb) Semi-analytic methods
3)In principle, can solve problem completely with PIC simulations. a) However, difficult for non-relativistic shocksb) Critical problems – thermal injection, initial creation of B-fields, etc.,
can be addressed with current PIC simulations
4)If shock acceleration is efficient, escaping particles will be important. a) These will strongly influence wave generation and must be considered in
models for CR production, TeV emission
5)If MFA is important in SNRs, it should be important in other systems with strong shocks (GRBs, radio jets, shocks in galaxy clusters)
Don Ellison (NCSU) Talk at Cracow meeting, Oct 2008
Don Ellison (NCSU) Talk at Cracow meeting, Oct 2008
Supplementary slides follow
Green line is contact discontinuity (CD)
CD lies close to outer blast wave determined from 4-6 keV (non-thermal) X-rays
Chandra observations of Tycho’s SNR (Warren et al. 2005)
2-D Hydro simulation Blondin & Ellison 2001
No acceleration
Efficient DSA acceleration
FS
Morphology: Strong evidence for Efficient production of cosmic ray ions at outer shock with compression ratio > 4
FSRS CD
Don Ellison, NCSU
Berezhko & Voelk (2006) model of SNR J1713
radio
X-ray
-ray
Broad-band continuum emission from SNRs
curvature in synchrotron emission HESS data
fit with pion-decay from protons.
Assumes large B-field
Monte Carlo simulation (Baring, Ellison & Jones 1994)PIC simulation (Spitkovsky 2008)
upstream
downstream
upstreamDS
Thermal Leakage Injection
Assumption: If thermal leakage is the primary injection process, this can be meaningfully described with Monte Carlo methods
Note: This is only presented as a illustration. The shocks considered here (Spitkovsky simulation and Monte Carlo results) have extremely different parameters and I’m not trying to compare them directly.
Individual particle trajectories
speed
Antoni et al. (KASCADE) AstroPart Phys. 2005
2.7E
knee
A power law can be drawn through CR data BUT, is there room for structure below the knee ??
Do individual SNRs, noticeably, contribute to all particle spectrum?? The presence of TeV electrons in CRs shows there must be a source within 100 pc
2005
KASCADE is ground-based
Uncertainties in data well below the knee as well:Cosmic ray data below the knee (<1015 eV) are from balloons. These measurements are difficult !!
Antoni et al. (KASCADE) AstroPart Phys. 2005
2.7E
knee2005
SNR 1SNR 2
Cartoon of what might see from nearby sources.
Will structure appear in CR spectra with more sensitive observations ?
Bottom line: Need more observations at all energies, including balloon-based below the knee
What does a heliospheric shock look like?
Earth bow shock observed by AMPTE spacecraft
(Ellison, Moebius & Paschmann 1990)
Spacecraft give great deal of information at one point. Little or no global information
shock crosses spacecraft
time of day
Ellison, Mobius & Paschmann 90
Earth Bow Shock
AMPTE observations of diffuse ions at Q-parallel Earth bow shock
H+, He2+, & CNO6+
Observed during time when solar wind magnetic field was nearly radial.
Critical range for injection
Observe injection of thermal solar wind ions at Quasi-parallel bow shock
Real shocks inject and accelerate thermal ions:
DS UpS DS
Modeling suggests nonlinear effects important
Ellison, Mobius & Paschmann 90
Observed acceleration efficiency is quite high:
Dividing energy 4 keV gives 2.5% of proton density in superthermal particles, and
>25% of energy flux crossing the shock put into superthermal protons
Maxwellian
Note: Acceleration of thermal electrons much less likely in heliospheric shocks
Superthermal electrons routinely seen accelerated by heliospheric shocks, but
In general, heliosphere shocks are seen NOT to accelerate thermal electrons
Baring etal 1997
ULYSSES (SWICS) observations of solar wind THERMAL ions injected and accelerated at a highly oblique Interplanetary shock
Interplanetary shock
Real shocks, even oblique ones, inject thermal ions:
θBn=77o
Bn
Baring etal 1997
ULYSSES (SWICS) observations of solar wind THERMAL ions injected and accelerated at a highly oblique Interplanetary shock
Monte Carlo modeling implies strong scattering ~3.7 rg
Simultaneous H+ and He2+ data and modeling supports assumption that particle interactions with background magnetic field are nearly elastic
Essential assumption in DSA
Interplanetary shock
Critical range for injection Smooth injection of thermal solar wind ions but much less efficient than Bow shock
Real shocks, even oblique ones, inject thermal ions:
θBn=77o
Don Ellison, Cracow, Oct 2008
Baring et al ApJ 1997
Self-generated turbulence at weak IPS
Interplanetary Shock Obs. With GEOTAIL, 21 Feb 1994
Shimada, Terasawa, etal 1999
Protons
Electrons
0.09 keV
38 keV
One of the very few examples where thermal electrons were observed to be injected and accelerated at heliospheric shocks
Most observations of heliospheric shocks do not show the acceleration of thermal electrons
Another heliospheric shock: