1
July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Chanruangrith Channok,1 David Ruffolo,1
Mihir Desai,2 and Glenn Mason2
1THAILAND 2USA
Finite-Time Shock Accelerationand Fits to ESP Ion Spectra
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
… and in the spirit End-to-End Modeling of CMEs and SEPs,
a few words on
• Modeling SEP transport to infer injection and transport parameters
• Interplanetary turbulence and perpendicular transport
22 23 24 25 26 27
2001 November (UT)
10-710-6
10-5
10-4
10-3
10-2
10-1
100
101
102103
0.14
0.27
0.55
1.09
2.19
4.37
8.55
14.35
25.20
51.35
ACE ULEIS + SISOxygen Intensities
MeV n-1
S
S15W34
Oxygen Intensities for November 24 Oxygen Intensities for November 24 2001 IP shock 2001 IP shock
(Desai et al. 2003)(Desai et al. 2003)
ESP
SEP
(Desai et al. 2004)
10-4
10-3
10-2
10-1
100
101
102
103
10-2
10-1
100
101
22 23 24 25 26 27 28 29
1999 June (UT)
10-1
100
101
ACE/ULEIS C, O, Fe Intensities
ACE/ULEIS C/O ratio
ACE/ULEIS Fe/O ratio
S2
0.16-0.23 MeV n-1 (x10)
0.91-1.28 MeV n-1
OCFe
0.2 MeV n-1
1.0 MeV n-1
0.2 MeV n-1
1.0 MeV n-1
Ambient
(a)
(b)
(c)
Shock
Fe/O at IP shocks Fe/O at IP shocks
is depleted is depleted
relative to relative to
ambient values ambient values
Larger decrease Larger decrease
at higher energy at higher energy
Spectra and abundances Spectra and abundances for Nov. 24 2001 IP shockfor Nov. 24 2001 IP shock
10-1 100 101 102
Kinetic Energy (MeV n-1)
10-3
10-1
101
103
105
107
109
10-2
10-1
100
101
10-1 100 101 102
Kinetic Energy (MeV n-1)
C/OFe/O
COFe
(a) (b)
(Desai et al. 2004, ApJ).(Desai et al. 2004, ApJ).
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Possible mechanisms suggested by Ellison & Ramaty (1985)
shock thickness ~ κ/u energy is too low
drift over shock width rollover at ~ 100 MeV/Q
finite time for shock acceleration considered here
(see also: Klecker et al. 1981; Lee 1983)
Why do ESP spectra roll overat ~ 0.1 - 10 MeV/n?
(data - see also: Gosling et al. 1981; van Nes et al. 1985)
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Finite-Time Shock Acceleration Probability approach (like Bell 1978, Drury 1983) Acceleration rate, r = 1/Δt Escape rate, Time at present (age of shock), t
Simulation parameters: λ = λ0 (P/ MV)α so vary λ0 and α (shorter λ0 is
equivalent to longer time duration) Time t fixed by observations, v0 = 200 km/s in
wind frame, shock angles & speeds as observed.
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
We solve the PDE …
… discretized as a system of ODEs
Initial & inflow conditions correspond to the observed ambient seed spectrum
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
(well above injection energy)
λ = const. Ec /A ∞ t2, independent of Q/A
λ ∞ Pα
Ec /A ∞ t2/(α+1) (Q/A)2α/(α+1)
Rollover energy (Ec /A)
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
We use the FTSA model to fit 3 ESP events from the sample of
Desai et al. (2004):
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Event #3: λ0 = 0.24 AU, α = 0.18
• λ is consistent with typical IP values• FTSA rollover is at lower E, minor accel. of seed population
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Event #2: λ0 = 0.042 AU, α = 0.10
• λ is smaller but not inconsistent with IP values• FTSA rollover is at lower E, moderate accel. of seed population
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Event #1: λ0 = 4.0x10-3 AU, α = 0.07
• λ at shock is much lower than typical IP values …• … as expected for proton-amplified waves [Ng et al. 1999]
• model rollover is sharper than observed, probably due to use of spatially const. λ
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Fe/O ratios
• Fe/O lower at shock, due to higher λ for Fe• model does not match observed trend for Event 2• expect trend vs. E like seed population above the rollover
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Conclusions on ESP spectra …
1. Finite-time shock acceleration model• power law spectrum at low energy• faster dropoff at high energy
2. Expect Ec /A ∞ t2/(α+1) (Q/A)2α/(α+1)
3. For 3 events, able to simultaneously fit measurements
of C, O, and Fe ions
4. Fits to weak events: Infer λ as typical IP values
5. Fit to strong event: Infer much lower λ, consistent with
expectations for proton-amplified waves
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
… but wait – there’s more!Key processes of interplanetary transport
• Scattering• Focusing (a.k.a. mirroring)• Solar wind effects
- Convection- Adiabatic deceleration
Note: mean free path is ~ 0.1 to 3 AU
Aim to quantitatively explain profiles of intensity & anisotropy vs. time
[Jokipii 1966]
[Roelof 1969]
[DR 1995]
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Pitch-angle transport equation [DR, ApJ ’95]
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Fitting SEP data- Simultaneous fit to intensity vs. time anisotropy vs. time- Optimal piecewise linear injection (least squares)- Optimal scattering mean free path, λ [Ruffolo et al. 1998]
- Optimal magnetic configuration [Bieber et al. 2002]
Simulation of interplanetary transport- Specify magnetic field configuration- Solve PDE- Runs in a few minutes [Nutaro et al. 2001]
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Magnetic Configurations
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Results of fitting GLE data(relativistic solar protons)
Bastille Day: July 14, 2000 - magnetic bottleneck [Bieber et al. 2002]
Easter: April 15, 2001 - full Spaceship Earth network, 1-minute timing of injection [Bieber et al. 2004]
October 22, 1989 - injection along both legs of a closed interplanetary loop [poster, this meeting]
October 28, 2003 … well, we don’t claim to understand everything … [Bieber et al. 2005]
January 20, 2005 - possible effect of self-generated waves: nonlinear transport! [poster, this meeting]
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Comparison with EM timing
All times are “Solar Time” or UT minus 8 min. for EM emissions
EMISSION APR. 15, 2001 OCT. 28, 2003
START PEAK END START PEAK END
Relativistic Protons 13:42 13:48 11:03 11:41
Soft X-rays 13:11 13:42 13:47 10:52** 11:02 11:16
H-alpha 13:28 13:41 15:27 09:53 11:57 14:12
Type III radio burst 13:36 13:38 - -
CME liftoff* 13:24-31 10:53-58
Type II radio burst 13:40 13:47 10:54 11:03
Type IV radio burst 13:44 14:57 10:25 15:23
* Linear - quadratic fits ** Sudden onset of intense emission
[Bieber et al. 2004] [Bieber et al. 2005]
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
“halo” of low SEP density over wide lateral region
“core” of SEP with dropouts
[DR, Matthaeus, & Chuychai 2003]
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Thank you for your attention
ขอบคุ�ณคุรับ
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
… and also in the spirit End-to-End Modeling of CMEs and SEPs:
See some posters!
87 DR et al. – Turbulence, dropouts, and suppression of the field line random walk
96 Bieber et al. – Record-setting Ground Level Enhancement: January 20, 2005
107 DR et al. – Relativistic Solar Protons on 1989October 22: Injection along Both Legs of a Loop
… and also someone else’s poster …
105 Mulligan et al. – validates our results for July 14, 2000!
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Early observations [Bryant et al. 1962]
Spectral Properties of Heavy Spectral Properties of Heavy Ions Accelerated by Ions Accelerated by
Interplanetary Shocks Near 1 AUInterplanetary Shocks Near 1 AU
M. I. Desai M. I. Desai University of Maryland, College Park, MD 20742, USAUniversity of Maryland, College Park, MD 20742, USA
Co-Authors: Co-Authors: G. M. Mason, C. M. S. Cohen, R. A. Mewaldt, M. E. G. M. Mason, C. M. S. Cohen, R. A. Mewaldt, M. E.
Wiedenbeck, J. E. Mazur, J. R. Dwyer, A. C. Cummings, E. Wiedenbeck, J. E. Mazur, J. R. Dwyer, A. C. Cummings, E. C. Stone, R. A. Leske, R.E. Gold, E. R. Christian, S. M. C. Stone, R. A. Leske, R.E. Gold, E. R. Christian, S. M. Krimigis, C.W. Smith, Q. Hu, R. M. Skoug, and T. T. von Krimigis, C.W. Smith, Q. Hu, R. M. Skoug, and T. T. von
RosenvingeRosenvinge
Spectral Properties of Heavy Spectral Properties of Heavy Ions Accelerated by Ions Accelerated by
Interplanetary Shocks Near 1 AUInterplanetary Shocks Near 1 AU
M. I. Desai M. I. Desai University of Maryland, College Park, MD 20742, USAUniversity of Maryland, College Park, MD 20742, USA
Co-Authors: Co-Authors: G. M. Mason, C. M. S. Cohen, R. A. Mewaldt, M. E. G. M. Mason, C. M. S. Cohen, R. A. Mewaldt, M. E.
Wiedenbeck, J. E. Mazur, J. R. Dwyer, A. C. Cummings, E. Wiedenbeck, J. E. Mazur, J. R. Dwyer, A. C. Cummings, E. C. Stone, R. A. Leske, R.E. Gold, E. R. Christian, S. M. C. Stone, R. A. Leske, R.E. Gold, E. R. Christian, S. M. Krimigis, C.W. Smith, Q. Hu, R. M. Skoug, and T. T. von Krimigis, C.W. Smith, Q. Hu, R. M. Skoug, and T. T. von
RosenvingeRosenvinge
Upstream & IP shock Upstream & IP shock abundancesabundances
Solar wind & IP Solar wind & IP shock abundances shock abundances
0
1
2
3
4
1 2 3 4 5 6Mass/Charge (AMU e-1)
m = 1.22 ± 0.23
c = 0.40 ± 0.22
cu
2 =3.34; =1.45 10P x-3
= 0.43; =0.13r p
4He C
Mg
Ne
N
O
Si
S
Fe
GI = + *[c m MIQO/MOQI]
0.2
0.4
0.6
0.8
2.0
1.0
1 2 3 4 5 6Mass/Charge (AMU e-1)
m = -0.64 ± 0.05
c = 0.63 ± 0.04
=4.39;P=2.56x10-5
r = -0.92; p=7.8x10-5
cu
2
(logGI) = + *[c m MIQO/MOQI]
4He N
CO
Ne
MgSi
S
Ca Fe
(Desai et al. 2003 ApJ 558, (Desai et al. 2003 ApJ 558, 1149).1149).
Upstream and SEP Abundances Upstream and SEP Abundances
(Desai et al. 2003 ApJ 558, 1149).(Desai et al. 2003 ApJ 558, 1149). Upstream and SEP Abundances Upstream and SEP Abundances
(Desai et al. 2003 ApJ 558, 1149).(Desai et al. 2003 ApJ 558, 1149).
Upstream Upstream
material material
comprises comprises
~30% ~30%
contribution contribution
from impulsive from impulsive
flares, and flares, and
~70% from ~70% from
large gradual large gradual
SEPsSEPs
Gradual SEPs
Impulsive SEPs
Upstream Material
10-2
10-1
100
C N O Ne MgSi S Ca Fe
12 1416 20 24 2832 40 56
Mass (AMU)
Spectral Variability in IP shocks Spectral Variability in IP shocks
(Desai et al. 2003 to be (Desai et al. 2003 to be submitted to ApJ).submitted to ApJ).
Fe/O Ratio at shock versus Fe/O ratio Fe/O Ratio at shock versus Fe/O ratio upstream upstream (Desai et al. 2003 ApJ vol. 558, (Desai et al. 2003 ApJ vol. 558,
1149)1149)
Fe/O Ratio at shock versus Fe/O ratio Fe/O Ratio at shock versus Fe/O ratio upstream upstream (Desai et al. 2003 ApJ vol. 558, (Desai et al. 2003 ApJ vol. 558,
1149)1149)
10-2
10-1
100
Fe/O (Upstream)10-2 10-1 100
log(Fe/OShock) = c + m*log(Fe/OUpstream)
cu2 =0.53; =1.0P
=62; =0.51; =1.0 10N r p x -5
= 0.40 m ± 0.02 = 0.26 c ± 0.05
#29event
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
3. Particle acceleration in space:Shock acceleration
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
0)(2 >−=Δ du uuv duv 2−=Δ duv 2−=Δ duv 2−=Δ
Fundamental mechanism of shock acceleration
Following collision with a scattering center: lose energy
Head-on collision with a scattering center: gain energy
Since u1 > u2 there is a net gain in energy
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
)()( tTeeTP tT −+= −− δ
Poisson distribution for n acceleration events with accel. rate r
Distribution of residence time T for particles with escape rate
Overall probability of n acceleration events after time t
t is time at present T
T = t
!/)(),( nerTTnP rTn −=
∫=t
dTTPTnPtnP0
)(),(),(
tT ≤P(T)
r, constant w/ energy - combinatorial model
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
trn
nk
ktr
n
en
rt
k
tre
r
r
rtnP )(
1
)(
!
)(
!
])[(),(
+−
∞
+=
+− ++
⎟⎠
⎞⎜⎝
⎛++
= ∑
Using r=0.9 & =0.1 ...
n
r
r
rtnP ⎟
⎠
⎞⎜⎝
⎛++
≈
),(
T < t (temporary residents)T = t
(permanent residents)
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
(related to log p)
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
(related to log p)
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
(related to log p)
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
(related to log p)
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
(related to log p)
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
(related to log p)
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Application to an interplanetary shock:
What if r vary with time? Physical characteristics of a shock change greatly as it
moves out from the Sun Observations: high energy particles are accelerated only
when shock is near the Sun Near Sun: tacc (=1/r) was low, t /tacc was high, spectrum
does not roll over until high energy (rollover mechanism not clear)
Interplanetary space: tacc greatly increased Effectively decouple SEP, ESP acceleration
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
r, varying - ODE model
Analytic solution:
),(),(),( tnAtnEtnP +=
),(/),(
),()(),1(/),( 1
tnAdttndE
tnArtnArdttndA
n
nnn
=+−−= −
0)0,(,0)0,1(,1)0,0( ==≥= nEnAA
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
More model parameters ...
… after Drury (1983)
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Numerical Results
t / tacc =
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July 14, 2005 2005 SHINE Workshop Keauhou, Hawaii, USA
Four Lines of Work:
1. Particle Acceleration
2. Magnetic Turbulence & Effects on Particle Transport
3. Detection/ Data Analysis4. Earth
Effects
CME
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