1 july 14, 20052005 shine workshopkeauhou, hawaii, usa chanruangrith channok, 1 david ruffolo, 1...

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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

2


… 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).

6


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)

7


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.

8


We solve the PDE …

… discretized as a system of ODEs

Initial & inflow conditions correspond to the observed ambient seed spectrum

9


(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)

10


We use the FTSA model to fit 3 ESP events from the sample of

Desai et al. (2004):

11


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

12


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

13


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

14


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

15


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

16


… 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]

17


Pitch-angle transport equation [DR, ApJ ’95]

18


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]

19


Magnetic Configurations

20


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]

21


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]

22


“halo” of low SEP density over wide lateral region

“core” of SEP with dropouts

[DR, Matthaeus, & Chuychai 2003]

23


Thank you for your attention

ขอบคุ�ณคุรับ

24


25


… 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!

26


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

32


3. Particle acceleration in space:Shock acceleration

33


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

34


)()( 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

35


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)

36


(related to log p)

37


(related to log p)

38


(related to log p)

39


(related to log p)

40


(related to log p)

41


(related to log p)

42


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

43


r, varying - ODE model

Analytic solution:

),(),(),( tnAtnEtnP +=

),(/),(

),()(),1(/),( 1

tnAdttndE

tnArtnArdttndA

n

nnn

=+−−= −

0)0,(,0)0,1(,1)0,0( ==≥= nEnAA

44


More model parameters ...

… after Drury (1983)

45


Numerical Results

t / tacc =

46


Four Lines of Work:

1. Particle Acceleration

2. Magnetic Turbulence & Effects on Particle Transport

3. Detection/ Data Analysis4. Earth

Effects

CME

1 july 14, 20052005 shine workshopkeauhou, hawaii, usa chanruangrith channok, 1 david ruffolo, 1...

Documents

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