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Chanruangrith Channok , 1 David Ruffolo , 1 Mihir Desai, 2 and Glenn Mason 2 1 THAILAND 2 USA

Finite-Time Shock Acceleration and Fits to ESP Ion Spectra. Chanruangrith Channok , 1 David Ruffolo , 1 Mihir Desai, 2 and Glenn Mason 2 1 THAILAND 2 USA. … and in the spirit End-to-End Modeling of CMEs and SEPs, a few words on. Modeling SEP transport to infer

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Chanruangrith Channok , 1 David Ruffolo , 1 Mihir Desai, 2 and Glenn Mason 2 1 THAILAND 2 USA

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  1. Finite-Time Shock Accelerationand Fits to ESP Ion Spectra Chanruangrith Channok,1 David Ruffolo,1 Mihir Desai,2 and Glenn Mason2 1THAILAND 2USA

  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

  3. S 3 10 2 ACE ULEIS + SIS 10 Oxygen Intensities S15W34 1 -1 10 MeV n 0.14 0 10 0.27 0.55 -1 10 1.09 2.19 -2 10 4.37 -3 10 8.55 -4 10 14.35 -5 10 25.20 -6 10 51.35 -7 10 22 23 24 25 26 27 2001 November (UT) Oxygen Intensities for November 24 2001 IP shock ESP SEP (Desai et al. 2003)

  4. Fe/O at IP shocks is depleted relative to ambient values Larger decrease at higher energy (Desai et al. 2004)

  5. Spectra and abundances for Nov. 24 2001 IP shock (Desai et al. 2004, ApJ).

  6. Why doESP spectra roll overat ~ 0.1 - 10 MeV/n?(data - see also: Gosling et al. 1981; van Nes et al. 1985) 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)

  7. Finite-Time Shock Acceleration • Probability approach (like Bell 1978, Drury 1983) • Acceleration rate, r= 1/Δt Escape rate, e Time at present (age of shock),t Simulation parameters: • λ= λ0 (P/ MV)αso vary λ0and α(shorter λ0is 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. Rollover energy (Ec/A) (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)

  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. Conclusionson ESP spectra … • 1. Finite-time shock accelerationmodel • 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: Inferλ 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 [Jokipii 1966][Roelof 1969][DR 1995] Aim toquantitativelyexplain profiles ofintensity&anisotropyvs. time

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

  18. Simulation of interplanetary transport • Specify magnetic field configuration • Solve PDE • Runs in a few minutes[Nutaro et al. 2001] 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]

  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 [Bieber et al. 2004] [Bieber et al. 2005] * Linear - quadratic fits ** Sudden onset of intense emission All times are “Solar Time” or UT minus 8 min. for EM emissions

  22. “core” of SEP with dropouts “halo” of low SEP density over wide lateral region [DR, Matthaeus, & Chuychai 2003]

  23. Thank you for your attentionขอบคุณครับ

  24. … 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 1989 October 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!

  25. Early observations[Bryant et al. 1962]

  26. Spectral Properties of Heavy Ions Accelerated by Interplanetary Shocks Near 1 AUM. I. Desai University of Maryland, College Park, MD 20742, USACo-Authors: G. M. Mason, C. M. S. Cohen, R. A. Mewaldt, M. 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. Krimigis, C.W. Smith, Q. Hu, R. M. Skoug, and T. T. von Rosenvinge

  27. (Desai et al. 2003 ApJ 558, 1149). Solar wind & IP shock abundances Upstream & IP shock abundances

  28. Upstream and SEP Abundances (Desai et al. 2003 ApJ 558, 1149). Upstream material comprises ~30% contribution from impulsive flares, and ~70% from large gradual SEPs

  29. Spectral Variability in IP shocks (Desai et al. 2003 to be submitted to ApJ).

  30. Fe/O Ratio at shock versus Fe/O ratio upstream (Desai et al. 2003 ApJ vol. 558, 1149)

  31. 3. Particle acceleration in space:Shock acceleration

  32. 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

  33. r, e constant w/ energy - combinatorial model Distribution of residence timeT for particles with escape ratee P(T) T = t tis time at present T Poisson distribution for n acceleration events with accel. rater Overall probability of n acceleration events after time t

  34. T = t (permanent residents) T < t (temporary residents) Using r=0.9&e=0.1 ...

  35. (related to log p)

  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. Application to an interplanetary shock: What if e, 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

  42. r, e varying - ODE model Analytic solution:

  43. More model parameters ... … after Drury (1983)

  44. Numerical Results t / tacc =

  45. Four Lines of Work: 2. Magnetic Turbulence & Effects on Particle Transport 3. Detection/ Data Analysis 1. Particle Acceleration 4. Earth Effects CME

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