1. Coupled ion acceleration and
Alfven wave excitation at an expanding coronal shock
E. Berezhko and S. Taneev
Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy
Yakutsk, Russia
Main question:
What is a role of selfexcited Alfven waves in
Solar Energetic Particles (SEP) production by CME driven shock?
Remark:
Solar Energetic Particles = Solar Cosmic Rays (SCRs)
SH :30-19:30

2. SEP event characteristics
Miroshnichenko & Perez-Peraza, 2008

3. Diffusive shock acceleration of CRs
Krymsky 1977
Bell 1978
log nCR
p- Δp
log p
Cutoff due to
finite shock size or
due to restricted
system age
scattering centers
 = ( + 2)/( -1)
shock compression ratio

4. Coronal Mass Ejection driven shockw
Shock
Earth Vp Vs
Sun
CME Rs
Solar wind
escaping particles
SCRs, g > 0.1
freshly accelerated
particles, g < 0.1
Modulation parameter: I
flare
ε1 > ε2 > ε3 ε3
Berezhko, Krymsky (1987)
Intensity of energetic particles,
measured by distinct observer ε2 ε1
shock t

5. SCRs

6. At which distances from the Sun SCRs are produced?
Zank, Rice, Wu (2000): Solar wind (RS > 20RSun),”onion-shell” plane wave approach,
assumed efficient Alfven wave excitation leading to Bohm limit diffusion.
εmax ~ 100 MeV
Rice, Zank, Li (2003): Solar wind (RS > 20RSun),”onion-shell” plane wave approach,
upstream Alfven wave intensity according to quasilinear model (Gordon et al.1999)
εmax ~ (1- 10) MeV ( too small !)
Ng, Reames, Tylka (2003): Solar wind (RS > 10RSun ), focused upstream transport
of SCRs with their ad hoc source term,
Alfven wave excitation by SCRs in upstream region
Lee (2005): Solar wind (RS > 10RSun), plane wave steady state approach,
upstream Alfven wave intensity according to quasilinear model (Gordon et al.1999)
However according to observations SCR onset usually occur at ~ 0.2 – 1 hr after
flare at height of (2-4)RSun above photosphere (Kahler 1994; Krucker, Lin 2000)

7. Physical factors relevant for acceleration efficiency
NCR
CR energy spectrum
ninj
NCR = A ε−γexp(−ε/εmax)
ε - γ
vinj ~ VS− w
speed of injected ions
εinj
εmax ε
CR diffusion coefficient
κ(εmax) ≈ 0.1 RS(VS – w – cA)
maximal CR energy
A ~ RS3ρ(RS)(VS – w)3/(σeff -1)
total number of accelerated CRs
γ = 0.5 (σeff +2)/(σeff - 1)
power law index
σeff = σ(1 – cA/VS)
effective compression ratio

8. Solar corona parameters
Alfven speed
solar wind
speed
Solar wind
number density
r/RSun

9. γ SCR acceleration efficiency within the region r < 1 AU 1500
Vs, km/s
1000
500 1
inefficient
10-3
A, AU
efficient
10-6
100
εmax, MeV 10 4 3 γ 2 1 1 10
100

10. Alfven waves in solar corona
Fw = 106 erg/(cm2 s)
Alfven wave energy flux at r = RSun
P(ν)=dEw /dν~ r -δ ν -λ
Alfven wave energy spectrum νP
δ ≈ 4.3
λ = 1 at < ν < 5×10-2 Hz
λ = 3/2 at ν > 5×10-2 Hz
Relevant
for SCRs
r = 1 AU
(e.g. Suzuki, Inusuka 2006)
(e.g. Tu, Marsh 1995)
B = B0(r0/r)2
ν, Hz
10-3
10-2
10-1

11. Alfven wave excitation by shock accelerated CRs
CR anisotropy → wave excitation
f = f0 + f1 cosθ p VS θ
f1 ~ - df0/dx ~ f0VS/v
Bell (1978)
Lee(1982)
Gordon et al.(1999) x
shock
front
∂Ew/∂t = Γ Ew + …
wave energy
Γ ~ f1
wave growth rate
∂f/∂t = ∂(κ∂f/∂x)/∂x + …
κ ~ 1/Ew
particle diffusion coefficient
τacc ~ κ/VS2
acceleration time

12. Quasilinear model of SCRs acceleration
CR transport equations
(Krymsky, 1964)
source (injection) term
diffusion coefficient
Alfven wave transport equation
growth (damping) rate
(Gordon et al., 1999)
System of equations is solved numerically within the distance range of
efficient shock acceleration RS < R* = (2-5) RSun
At r > R* accelerated SCRs are assumed to propagate purely diffusively

13. Compared with the previous considerations the model includes:
SCR acceleration within corona (r < 5 RSun)
Selfexcited Alfven waves
The influence of Alfven speed on the effective compression
ratio, which determines SCR spectrum
Consistent determination of SCR maximal energy
Compared with our previous study (Berezhko&Taneev 2003) the model incledes
selfexcited Alfven waves

14. Overall energy spectra of SCRs,
produced by CME driven shock in solar corona
linear
approach
quasilinear
approach
Selfexcited Alfven waves reduce the number of SCRs
( due to decrease of effective shock compression ratio)
and do not affect SCR maximal energy/

15. Proton energy spectrum at 1 AU in the event 1977 November 22
VS = 1000 km/s
η = 10-3
linear
quasilinear

16. Conclusions Efficient SCR production by CME driven shock takes
place within the region r < 2-5 RSun
Selfexcited Alfven waves reduce the number of SCRs
due to the decrease of effective shock compression
Alfven wave generation insignificantly influence SCR maximal energy
due to steep energy spectrum of accelerated SCRs
Calculated spectra of shock accelerated SCRs in satisfactory way
agree with SCR spectra measured in gradual events

17. Alfven wave spectra near the shock front
VS = 1500 km/s

18. CR diffusion coefficient
VS = 1500 km/s
κL ≈ κQL
linear
approach
qusilinear
approach
Bohm limit

19. Solar Cosmic Ray spectrum at the Earth’s orbit
Berezhko, Taneev (2003)
VS = 2000 km/s

20. Solar corona/wind parameters
Vs = 1500 km/s
Vs = 600 km/s

21. Overall particle energy spectrum in/near acceleration region
injection rate
Expected injection rate
η ~ 10-3
η > → efficient CR production