1. Propagation and acceleration of High Energy CRs
Jungyeon Cho (CNU, Korea)

2. “Interaction of CRs with MHD Turbulence”
Q1. Do we need to consider MHD turbulence
for ultra high energy CRs?
* UHECRs come from Extra-Galactic sources

3. Local universe (~GZK radius)
30Mpc

4. Local universe (a bit smaller than the GZK radius)
3Mpc

5. Possible sources: radio galaxys, AGNs, shocks,…
(Jones’ and Ryu’s talks)
cluster:
shock
surfaces
From T. Jones

6. The Universe is magnetized!
cluster
Photons have zero charge fi
travel in geodesics
(straightest lines)
point back to source
Extra-galactic B
-Clusters: 1-10 mG
& lc ~ 10kpc?
-Filaments:~0.1 mG
-Voids: <~10-3 mG
deflected by Magnetic Fields
a few Mpc

7. Magnetic field can deflect charged particles!B dv
----- = (v x B) (e/gmc) dt
v2/r = evB/gmc
rL=E/eB

8. Turbulent B field (B0 ~ b)
Figure by S. Das

9. Low energy particles stay longer in clusters
a few Mpc
Photons have zero charge fi
travel in geodesics
(straightest lines)
point back to source
High E ( E > eV)
Low E
deflected by Magnetic Fields
B~1-10 mG &
lc ~ 10kpc
rL ~ 1 kpc (E/1018eV)(B/1mG)-1

10. So, UHECRs with E > 1019 eV can escape the ICM without
showing significant deflections
=>Turbulence may not be very important for these particles
* But, magnetic lensing can be still important.
CRs with E < 1019 eV spend a lot of time in clusters.
=> They interact with ICM turbulence
=> They can be accelerated by turbulence!

11. Outside clusters, magnetic fields are weaker
Deflection of particle is smaller (Dolag’s talk)
* Magnetic lensing can be still important
source
E> eV
Galaxy

12. Q2. OK. MHD turbulence may be important in the ICM
even for UHECRs.
Then, is it also important in our Galaxy?
Yes. It’s also important for Galactic CRs, solar CRs,…

13. Galactic B Our Galaxy -mol. clouds: > 10 mG -disk: 5-8 mG
-halo: ~1 mG ?
Our Galaxy

14. Galactic sources : supernova remnants, winds, …
(Biermann’s talk)

15. rL ~ 1 kpc (E/1018eV)(B/1mG)-1
B in disk ~ a few mG
B in halo < ~ 1 mG
(lc < ~100pc)
MHD turbulence is important for Galactic CRs with
E < eV

16. MHD turbulence and CRs
MHD turbulence can accelerate and/or scatter CRs.
*Acceleration by MHD turbulence:
- large-scale compressible motion
- pitch-angle scattering
*Note: astrophysical acceleration mechanisms:
- Shock acceleration
- Turbulence (2nd order Fermi acceleration)
- Direct acceleration by electric field
- …

17. Q3. Then, how can MHD turbulence accelerate CRs?
assumption: rL < lc

18. 2nd order Fermi acceleration
wall
Vptl
Dp/p ~ +V/Vptl V
Vptl
Dp/p ~ -V/Vptl V
After many collisions, Dp/p ~ V/Vptl (No. of collisions)1/2

19. Example: acceleration by MHD turbulenceVA
Dv per back-scattering ~ vA (=Alfven speed)
Dp/p ~ VA/Vptl

20. Dp ~ (Dp)2/Dt Dt Dp p t
p shows a random walk-like behavior
diffusion in momentum space
Dp ~ ???
In spatial diffusion case:
diffusion coefficient ~ Vptl lmfp ~ lmfp2/t

21. What makes p change? VA 1. Pitch-angle scattering:
Dp/ p ~ (VA/Vptl), Dt ~ 1/n
=> Dp ~ p2(VA/Vptl)2n
scattering freq.
2. Large scale compressible motions:
Dp =? , Dt = ?

22. Large scale compressible motions
Fact1: Compression in perpendicular direction increases momentum B
Fact2: Compression in parallel direction increases momentum
Conclusion: V matters!
*Earlier studies in this direction:
Ptuskin (1998); Chandran (2003)

23. Large scale compressible motions
- (Dp/Dt) / p ~ V
- Dt =?
fast diffusion
Dt ~ l||2/D||
slow diffusion
Dt ~twave
Dp~(Dp)2/Dt ~ p2(V )2 Dt ~ p2(V )2 twave
We need to know V .

24. B There are two compressible modes in magnetized fluids:
slow and fast modes
* Alfven modes are not compressible B

25. Slow & fast waves
Cho, Lazarian, & Vishniac (2003)

26. Structure of MHD turbulence
Alfven
-Alfven and slow modes
are elongated along B
-Slow modes are passive
(Slow modes follow
Alfvenic time scales)
-Fast modes are NOT
elongated
fast
Lithwick & Goldreich (01); Cho & Lazarian (02; 03)

27. Acceleration by fast modes
*Small scales contribute more
Vl ~ Vl,fast / l
When diffusion is slow,
Dt ~ l/Cf (wave period)
Dp  p2(Vl )2 (l/Cf)
~ p2Vl,fast2 /(l Cf)
~ (p2VA / l)(Vl,fast /Cf)2(Cf/VA)
* Cf=speed of fast wave
In general, fast modes are more efficient than slow modes .

28. Acceleration by fast modesDp
Larger than 1 for slow diffusion case
b=Pgas/PB
slow diffusion

29. Acceleration by slow modes
*All scales contribute equally
When diffusion is slow:Dt ~ L||/VA
Dp  p2(V )2 (L|| / VA )
~ p2VL,slow2 / (L|| VA)
~ (p2VA/L) (VL,slow / VA) 2

30. Acceleration by slow modes: resultsDp
slow diffusion
Note: QTD=1, if particles are tied to B
=ln(LVA/D), if particles can move to
different B lines
See Chandran (2003)

31. Acceleration by pitch-angle scattering
What is pitch-angle scattering? l
E field

32. Acceleration by pitch-angle scatteringVA
Dv per back-scattering ~ vA (=Alfven speed)
Dp / p ~ (VA/Vptl), Dt ~ 1/n
scattering freq.
Dp ~(Dp)2/Dt ~ p2(VA/Vptl)2n
~ p2(VA/Vptl)2 (Vptl/lmfp)
~ (p2VA/L)(LVA/Vptllmfp) ~(p2VA/L)(tL,diff/ tL,wave)

33. Acceleration by pitch-angle scattering
More efficient than slow or fast modes when diffusion is slow

34. 4.What happens when B is weak?

35. Deflection of CRs by weak Blc
Dq~ lc /rL r lc rL
Random walk => (r/ lc)1/2 Dq ~(rlc )1/2/ rL

36. Effects of weak B field Deflection
If Blc1/2 < G Mpc1/2, small deflection,
If Blc1/2 > G Mpc1/2, diffusion,
Time delay ( <=CRs arrive later than light)
*Similar to the typical lifetime of AGNs ?
Formulae from Lemoine (05)

37. Magnetic lensing initially uniformly distributed
Figure by H.K. Kim
initially uniformly distributed
Initially particles are located in the yellow plane.
We marked the position of the particles when they cross this plane B

38. Summary Dpfast ~ (p2VA/L)(LVA/lmpfVptl)a when diffusion is slow
MHD turbulence can accelerate charged particles
Fast modes are more efficient than slow modes
Pitch-angle scattering is more efficient than fast or slow
modes when diffusion is slow
Magnetic lensing may be important for small scale
anisotropy
Dpfast ~ (p2VA/L)(LVA/lmpfVptl)a when diffusion is slow