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Extreme SEP Events and the Streaming Limit

Extreme SEP Events and the Streaming Limit. Don Reames IPST, Univ. of Maryland, College Park, MD Chee Ng George Mason University, Fairfax, VA 2014 June 9-11. The Streaming Limit.

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Extreme SEP Events and the Streaming Limit

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  1. Extreme SEP Events andthe Streaming Limit Don Reames IPST, Univ. of Maryland, College Park, MD Chee Ng George Mason University, Fairfax, VA 2014 June 9-11 Reames & Ng – Extreme SEP Events

  2. The Streaming Limit In large SEP events, intensities of protons of a few MeV never seemed to exceed ~200 protons/(cm2 sr s MeV) early in the events. Reames, 1990, ApJ 358, L63 Reames & Ng – Extreme SEP Events

  3. Streaming Particles Generate or Amplify Waves • Stix, T. H.: 1962, 1992 Waves in Plasmas • Melrose, D. B.: 1980, Plasma Astrophysics, Vol. 1 Ions streaming along B generate or amplify Alfvén waves of wave number k ≈ B/Pμ, where P = pc/Qe is the magnetic rigidity of a particle of momentum p and μ is the cosine of its pitch angle with respect to the field, B. The wave growth rate in the wave frame is: Reames & Ng – Extreme SEP Events

  4. Self-amplified waves throttle SEP transport More injected particles  more self-amplified waves  lower peak intensity than without wave growth Ng & Reames (1994 ApJ 424, 1032) Reames & Ng – Extreme SEP Events

  5. Energy DependenceReames & Ng (1998, ApJ 504, 1002) Reames & Ng – Extreme SEP Events

  6. x Duration: The streaming limit can bound SEP intensities for about half a day until the shock approaches Effectively, the streaming limit traps SEPs near the shock, increasing acceleration and making the shock peaks higher. You pay for the limit with a larger increase later. Reames & Ng – Extreme SEP Events

  7. H and O Spectra of 5 largest GLEson the Plateau Resonance condition: The wave number k ≈ B/Pμ, High-energy protons arrive first, amplify resonant waves, and scatter into small μ where theyamplify waves that scatter low-energy ions just emerging with μ~1 Reames & Ng (2010 ApJ 723, 1286) Reames & Ng – Extreme SEP Events

  8. Theoretical Fit Time-dependent transport of particles and Alfvén waves from a shock. 1) Streaming protons control the wave growth and 2) Waves control the particle scattering Ng, Reames, & Tylka 2012 AIP Conf. Proc.1436, 212 Reames & Ng – Extreme SEP Events

  9. 98 May 2 Proton SpectrumWhen the ~10MeV protons are absent, the ~1 MeV intensities can rise.k ≈ B/Pμ Reames & Ng 2010, ApJ 723, 1286 Ng, Reames, & Tylka 2012 AIP Conf. Proc.1436, 212 Reames & Ng – Extreme SEP Events

  10. Radial Dependence Intensities begin to rise above the streaming limit plateau as the shock approaches. Reames & Ng – Extreme SEP Events

  11. Space-Time Variation of Alfvén WavesNg et al. 2003 ApJ 591 461 Wave Intensity vs. k/B=1/Pμ λ vs. Rigidity Scattering varies greatly with both space and time! Reames & Ng – Extreme SEP Events

  12. SEP observation: 2005 Jan 20 Event Interplanetary transport model with input of escape proton flux Mewaldt et al. 2007, AIP CP 932, 277-282 Enough protons must flow to generate waves to establish the streaming limit, which is an equilibrium process. Reames & Ng – Extreme SEP Events

  13. Streaming Limit - Theory • Lee (1983, 2005) – equilibrium streaming-limited spectrum ~ 1/E • Vainio (2003) - equilibrium streaming-limited spectrum ~ 1/p • Giacalone (2004) – hybrid shock simulation • Ng et al. (1994, 2003, 2012) - includes time dependence and pitch angle. Quasi-perp. shock theories typically assume constant scattering (No wave generation – no streaming limit) Other shock simulations assume high-energy particles are test particles (No wave generation – no streaming limit) Yet, it does not matter how particles were accelerated. The streaming limit is a transport phenomenon, a wave-particle equilibrium. Reames & Ng – Extreme SEP Events

  14. Evolution of SEPs at a Shock Ng & Reames 2008, ApJ, L123 Proton intensity shock spectrum 12.3 proton intensity spatial profile Reames & Ng – Extreme SEP Events

  15. Spectral Knees Control Radiation Risk Proton spectral knees matter - Sept 1989: 40 mSv/h dose behind 10 g/cm2 What determines proton knee energies? Lee (2005) Sandroos & Vainio (2009) Battarbee et al. (2011) Reames & Ng – Extreme SEP Events

  16. Conclusions • Early SEP intensities are streaming limited by proton-amplified waves that can couple ions of different energies to produce intensity maxima in the ion spectra. • Energies of spectral knees are determined by growth of particle energy (& resonant waves) at a shock that persists until the shock begins to weaken. • Knowledge of intensity limits and knee energies might help in forecasting or mitigatingradiation hazards. Reames & Ng – Extreme SEP Events

  17. Thank you! Reames & Ng – Extreme SEP Events

  18. Coupled wave-particle evolution at shock • Particle transport equation • Wave kinetic equation • Pitch-angle diffusion coefficient from wave intensities • Wave growth rate from particle momentum gradient • Wave transmission at shock (Vainio & Schlickeiser 1999). Ng & Reames 2008, ApJ, L123 Reames & Ng – Extreme SEP Events

  19. Evolution of SEPs and Alfvén waves Upstream IR+ Alfvén wave spectrum Downstream IR+ Alfvén wave spectrum k/B=1/PμNg& Reames (2008) Reames & Ng – Extreme SEP Events

  20. Evolution of pitch-angle diffusion coefficient Upstream D Downstream D Ng & Reames 2008, ApJ, L123 Reames & Ng – Extreme SEP Events

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