Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Cosmic Ray Acceleration: the need and ways of
doing it faster
M.A. Malkov
University of California, San Diego
Ackn: R.Z. Sagdeev, P.H. Diamond
Supported by NASA and US DoE
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Outline
1
2
3
Why need faster acceleration?
Benchmarks are challenging for acceleration mechanisms
(DSA)
DSA sluggishness
Selection of astrophysical settings
SNR and other large scale shocks
NL shock modication
Shock Rippling
Proton Zevatrons in DM laments
Accretion ows and CR Acceleration in Cosmic Web
Betatron inductive acceleration
Evading photo-disentegration in accelerator and exit fees
institution-logo-./UCS
2 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Knee, Ankle and GZK cuto
DSA sluggishness
Selection of astrophysical settings
Benchmarks CR spectrum: knee, ankle, GZK
Possible interpretations of the breaks
need single acceleration mechanism up to the knee for protons
may argue then that the spectrum extends to the ankle
because
heavier nuclei
superposition of sources, exceptional SNRs, pre-supernova
dense wind (Völk & Biermann 1988)
change in acceleration regime (M & Diamond 2006)
diusive shock acceleration -DSA operating in SNRs embodies
above ingredients thus appearing plausible, BUT...
institution-logo-./UCS
3 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Knee, Ankle and GZK cuto
DSA sluggishness
Selection of astrophysical settings
Maximum energy: knee
predictions for maximum energy/knee for DSA in SNR are model
dependent
major problem: CR scattering environment: dominant turbulence
mode and saturation level
under optimistic assummptions might reach PeV ;
-Bohm diusion of CR-κB ∼ rg c on resonant Alfven waves (e.g.
Berezhko et al 90s);
-spreading of short non-resonant waves to resonance at krg ∼ 1 -Bell
04; Bykov et all 11,13; Diamond & M 2007; Simulations largely
supportive: Zirakashvili & Ptuskin, Spitkovsky+, Caprioli...
pessimistic estimates: DSA falls short by one-two orders of
magnitude (Laggage & Cesarsky 1983, partially also Bell 2014
recapitulates concerns)
institution-logo-./UCS
bottom line: DSA needs an order of magnitude boost to reach
the
knee during SNR active life
4 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Knee, Ankle and GZK cuto
DSA sluggishness
Selection of astrophysical settings
DSA: operation and potential for improvement
Linear (TP) phase of acceleration
Downstream
NL, with CR back-reaction
Upstream
U(x)
shock
Downstream
Upstream
U(x)
x
x
Sub-shock
Scattering
Centers, frozen
Into flow
NL-modified flow
In both cases momentum gain is small ∆p /p ∼ U /c can be
deduced from adiabatic invariant
I
pk dl
= const
institution-logo-./UCS
5 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Knee, Ankle and GZK cuto
DSA sluggishness
Selection of astrophysical settings
DSA: why slow?
long waiting time upstream and downstream: number of
scattering
N
∼ c /U 1
needed before momentum is increased upon shock crossing by
∆p /p ∼ U /c
acceleration time grows with momentum, as both the collision
time ( in the linear case ωc−1 ∝ p ) and precursor crossing time
[κ (pmax ) /U 2 =τacc in NL regime] increase
institution-logo-./UCS
6 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Knee, Ankle and GZK cuto
DSA sluggishness
Selection of astrophysical settings
DSA characteristic times cont'd
τacc '
κ (p )
U2
∼ λ c /U 2 ∼ τcol c 2 /U 2 = τcol N 2
λ -particle mean free path (m.f.p.)
τcol -collision time (ωc−1 at least)
DSA time hierarchy
τacc : τcycl : τcol ∼
c
2
U
2
:
c
U
:1
improvement strategy: decouple one of these ratios (or
both) from the small parameter
U /c
institution-logo-./UCS
7 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Knee, Ankle and GZK cuto
DSA sluggishness
Selection of astrophysical settings
Case studies for enhanced acceleration
1
DSA in large scale shocks such as SNR
working hypothesis of CR origin
DSA is robust and well established acceleration mechanism
plethora of new SNR observations
2
Accretion ow on DM lament suitable site for UHECR
acceleration
weak magnetic and photon elds in accelerator surroundings
synchrotron-Compton losses negligible
pair production losses insignicant
photo-pion losses are signicant but beatable
institution-logo-./UCS
8 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
NL shock modication
Shock Rippling
Possible ways to accelerate DSA
grows linearly (slow) both in unmodied and modied
shocks but for dierent reasons
p (t )
ṗ /p
∝ 1/τacc ∝ 1/p
in modied shocks due to precursor ination Lp ∝ pmax , as
τacc = precursor crossing time
→ attempt to prevent precursor from growing
nonlinear shock modication with xed
ṗ /p
precursor scale
∝ U /Lp (pfixed ) = const
-exponential growth of momentum
shock corrugation resulting in partially quasi-perpendicular
acceleration regime without particle loss downstream
institution-logo-./UCS
- reduction in acceleration time by making τcycle short
9 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
NL shock modication
Shock Rippling
Acceleration in CR shock precursor
acceleration rate in CR modied shocks
ṗ = 1 ∂ U ∼ U /L (p )
NL ∗
p 3 ∂z
is the same as in ordinary shocks except LNL ∼ κ (p∗ ) /U instead of
Lp ∼ κ (p ) /U
p∗ is where CR partial pressure is at maximum
if the spectrum is harder than p −2
p∗
' pmax
If p∗ is xed, p∗ pmax then p (t ) grows exponentially rather
than linearly in the range
p∗
< p < pmax
institution-logo-./UCS
10 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
NL shock modication
Shock Rippling
Enhanced Acceleration Scenario
1
Initial linear growth
2
NL shock modication, Drury instability on ∇PCR (Drury &
Falle 1986)
3
formation of multiple shocks in precursor and CR losses for
p > p∗ → steeper spectrum for p > p∗
4
change of CR connement regime to super-diusive for
to make a steeper spectrum
5
precursor does not grow as max PCR (p ) is xed at PCR (p∗ )
particle momentum grows exponentially for p & p∗
6
p
∝ t up to
p
= p∗ (M & Diamond 2006)
p
> p∗
Limitation: rg (p ) κ (p∗ ) /U ∼ rg (p∗ ) c /U
institution-logo-./UCS
11 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
NL shock modication
Shock Rippling
Switch to quasi-perpendicular geometry
-No idling but short
acceleration, Jokipii 1987+
V
Field lines
Quasi-parallel
shock
v
Quasi-perpendicular
shock
B
upstream
E
Stream lines
shock
rarefaction
downstream
-rippled shock surface may
result in protracted particle
interaction with shock
compression
but ordinary shocks are stable
with respect to corrugations
institution-logo-./UCS
(LL, Mond and Drury'98 +CRs)
12 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Combined
⊥/k
NL shock modication
Shock Rippling
acceleration scenario
CRs destabilize shock surface
particle return to shock
since CR mirror force depends
through quasi-parallel parts of
on shock normal angle
its surface
perpendicular (fast) phase has
no idling time
Field lines
v
Quasi-parallel
shock
parallel (slow) phase has
p-independent duration
Quasi-perpendicular
shock
τacc . κ/U 2
with fast
acceleration spikes in
⊥-regime
set ripples in motion
horizontally
acceleration cycle comprises
two phases: perpendicular and
parallel
bottom line: a factor of a few
gain in acc'n rate
institution-logo-./UCS
13 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
NL shock modication
Shock Rippling
Stronger acceleration speed-up by particle trapping
shock
Magnetic field
Trapped
particle
- CR trapped between rapidly
converging mirrors
- trapping suggests
I
pk dl
= const
- promotes corrugations
energy gain up to factor c /U in
one trapping event (lmin ∼ rg ,
lmax ∼ rg c /U )
lmax may be longer if ripple
dynamics results in their
coalescence, akin 1D shock
dynamics (bad for the previous
⊥ / k scenario)
loss cone particles downstream
have chances to reappear
upstream on k shock region
institution-logo-./UCS
14 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
NL shock modication
Shock Rippling
Evidence of shock rippling?
Chandra SNR 1006
-may be interpreted as shock
corrugation or projected radial
shocks
Tycho (Eriksen et al 2011)
straiates appear to be more
consistent with surface
institution-logo-./UCS
phenomenon
15 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Accretion ows and CR Acceleration in Cosmic Web
Betatron inductive acceleration
Evading photo-disentegration in accelerator and exit fees
Why new UHECR acceleration mechanism?
Proton Zevatrons in DM laments
GRB origin of UHECR is likely ruled out: neutrino upper limit
factor ~3.7 below predictions (Abbasi et al, IceCube, 2012)
AGN scenario encounters problems with IC/synchrotron losses,
photo-pion losses; powerful accelerators generate strong
photon- and magnetic elds (Norman et al 95)
large-scale structure shocks accelerate particles too slow to
overcome losses (Norman et al 95, Jones 04) → BUT: seed
population 1019.5 eV for the mechanism suggested here:
operates inside accretion ow onto a lament between two
nodes (M, Sagdeev & Diamond 2011)
institution-logo-./UCS
16 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Accretion ows and CR Acceleration in Cosmic Web
Betatron inductive acceleration
Evading photo-disentegration in accelerator and exit fees
Large-scale structure simulation
DM web: laments and nodes
accretion ow onto laments
Schaal & Springel 2014
from voids
institution-logo-./UCS
17 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Accretion ows and CR Acceleration in Cosmic Web
Betatron inductive acceleration
Evading photo-disentegration in accelerator and exit fees
Acceleration mechanism
Compare and Contrast with SDA
starts similarly to shock-drift
acceleration (SDA)
in SDA part of the orbit is
decelerating
V
change of orbit topology
from drift to circumscribing
the lament -betatron
regime
pure energy gain, no
deceleration phase
B
E
Seed ~10^19 eV
B
E=-VxB
F
V
Exit > 10^20 eV
institution-logo-./UCS
18 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Accretion ows and CR Acceleration in Cosmic Web
Betatron inductive acceleration
Evading photo-disentegration in accelerator and exit fees
Accelerator setup
ow pattern (solid lines)
magnetic eld (dashed
lines)
magnetic eld increases
towards lament
−3/2
Bz ∝ r
two nodes connected by a
lament provide magnetic
trap as the eld increases
toward nodes
initial drift acceleration
2
regime: p⊥
/Bz = const
-slow phase
change to betatron
regime: explosive institution-logo-./UCS
acceleration
19 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Accretion ows and CR Acceleration in Cosmic Web
Betatron inductive acceleration
Evading photo-disentegration in accelerator and exit fees
Particle Dynamics
6
betatron regime
Particle Potential Energy
5
%
Escape
4
400
3
350
300
2
250
t 200
1
150
re
Start
0
-3
-2
rs
-1
rd -Particle Guiding Center
0
1
Distance from Axis
ln r
100
50
0
6
4
2
0
acceleration control parameter
v = − rur B
RB cB∞
RB - Bondi radius
-2
2
3
slow energy gain
p⊥2 /Bz = const
0
1
drift motion toward lament,
r
-4
4
5
qr
-6
explosive acceleration
p (t ) = (P0 − vt )−1
P0
-canonical momentum
institution-logo-./UCS
20 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Accretion ows and CR Acceleration in Cosmic Web
Betatron inductive acceleration
Evading photo-disentegration in accelerator and exit fees
Why short explosive acceleration is critical?
Overjumping the photopion wall
12
p(t)
p ad invar
Betatron
acceleration
10
3
p(t) ~ 1/(t0 - t)
6
r pr
rg / R B
2
8
1
separatrix
0
-1
-2
4
-3
0.5
1.0
1.5
2.0
2.5
3.0
r / RB
2
0
0
ts
5
10
15 tc/R
B
20
25
the photo-pion wall can be
overjumped
likely need tunneling with m.f.p
γπ
wall at
E
' 1019.5 eV
(Berezinsky et al 2006)
BUT! betatron energy growth is
explosive!
lπ ∼ 10Mpc
upon crossing separatrix particles
institution-logo-./UCS
escape immediately, thus
evading
high magnetic and photon elds
21 / 22
Why need faster acceleration?
SNR and other large scale shocks
Proton Zevatrons in DM laments
Summary
Summary
Galactic CR, SNR, DSA
NL shock modication speeds up acceleration in the smooth
part of the upstream ow
sizable fraction of Ushock /c 1 factor can be used to increase
acceleration rate
shock surface is shown to be corrugationally unstable due to
CR shock reection
acceleration at CR-corrugated shocks is signicantly enhanced
UHECR
betatron acceleration in DM laments suggested
acceleration end-thrust overcomes losses, fatal for other
mechanisms (e.g., DSA)
mechanism is capable of proton reacceleration to the
maximum energy & 1020 eV
seed particles with energies ∼ 1019 eV are required institution-logo-./UCS
22 / 22