1 / 19

Rami Vainio Dept of Physical Sciences, University of Helsinki, Finland

Rami Vainio Dept of Physical Sciences, University of Helsinki, Finland Timo Laitinen Dept of Physics, University of Turku, Finland. Monte-Carlo simulations of shock acceleration of solar energetic particles in self-generated turbulence. COST Action 724 is thanked for financial support.

hamish
Download Presentation

Rami Vainio Dept of Physical Sciences, University of Helsinki, Finland

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Rami Vainio Dept of Physical Sciences, University of Helsinki, Finland Timo LaitinenDept of Physics, University of Turku, Finland Monte-Carlo simulations of shock acceleration of solar energetic particles in self-generated turbulence COST Action 724 is thanked for financial support

  2. Large Solar Particle Events Reames & Ng 1998

  3. GOES Proton flux 1986-1997 Hourly fluence (protons/cm2 sr) 104 105 106 107 108 104 105 106 107 104 105 106 10 1 N ~ F -0.41 0.1 Fraction of time (%) 0.01 0.001 Most of the IP proton fluence comes from large events Reames (2003)

  4. v = velocity in solar-wind frame v dv/dt < 0 → wave growth dv/dt > 0 → wave damping v' = const. v v|| VA Streaming instability and proton transport Outward propagating AWs amplified by outward streaming SEPs → stronger scattering

  5. W2 Vsh v = particle velocity in the ambient AW frame downstream →upstream Vsh v upstream → downstream W1 = u1+vA1 dv/dt > 0 → particle acceleration v' = const. v2 > v1 v1 v|| ΔW = W2 - W1 Particle acceleration at shocks Particles crossing the shockmany times (because of strongscattering) get accelerated

  6. Self-generated Alfvén waves • Alfvén-wave growth rateΓ= ½π ωcp · pr Sp(r,pr,t)/nvA pr= m ωcp/|k| Sp= 4π p2 ∫dμ vμ f(r,p, μ,t) = proton streaming per unit momentum • Efficient wave growth (at fixed r,k) during the SEP event requires1 << ∫dt Γ(t) = ½π (ωcp/nvA) pr∫dt Sp(r,pr,t) = ½π (ωcp/nAvA) pr dN/dpr→ p dN/dp >> (2/π) nAvA/ωcp = 1033 sr-1 (vA/vA) (n/2·108cm-3)½where A = cross-sectional area of the flux tube dN/dp = momentum distr. of protons injected to the flux tube sr Vainio (2003)

  7. p dN/dp [sr-1] Vainio (2003) solar-wind model with a maximum of vA in outer corona 1034 most efficient wave growth 1033 1 10 100 r [Rsun] Self-generated waves (cont'd) • Threshold spectrum for wave-growth p dN/dp|thr =1033 sr-1 (n/2·108cm-3)½ (vA/vA(r))lowestin corona • Apply a simple IP transport model: radial diffusion → @ 1 AU, dJ/dE|max =15·(MeV/E)½/cm2·sr·s·MeVfor p dN/dp =1033 sr-1. • Thus, wave-growth unimportant • for small SEP events • at relativistic energies • Only threshold spectrum released “impulsively”, waves trap the rest → streaming limited intensities

  8. Coupled evolution of particles and waves Protons Alfvén waves t = t1 p dNp/dr weak scattering (Λ > LB) weak scattering log P(r) Γ(r) p Sp(r) r r t = t2 > t1 p dNp/dr weak scattering weak scattering log P(r) impulsive release of escaping protons turbulent trapping with gradual leakage p Sp(r) Γ(r) r r

  9. Numerical modeling of coronal DSA • Large events exceeding the threshold for wave-growth require self-consistent modeling • particles affect their own scattering conditions • Monte Carlo simulations with wave growth • SW: radial field, W = u + vA = 400 km/s • parallel shock with constant speed Vs and sc-compression ratio rsc • WKB Alfvén waves modified by wave growth • Suprathermal (~ 10 keV) particles injected to the considered flux tube at the shock at a constant rate • waves P(r,f,t) and particles f(r,p,μ,t) traced simultaneouslyΓ= π2 fcp · pr Sp(r,pr,t)/nvA <(Δθ)2>/Δt = π2 fcp · fr P(r,fr,t)/B2pr = fcp mpV/f fr = fcp mpV/p Vs B u

  10. Examples of simulation results • Shock launched at R = 1.5 Rsun at speed Vs = 1500 km/s in all examples. • Varied parameters: • Ambient scattering mean free path @ r = 1.5 Rsun and E =100 keVΛ0 = 1, 5, 30 Rsun • Injection rate q = Ninj/tmax << qswwhere qsw = ∫ n(r)A(r) dr /tmax = 2.2·1037 s-1 • Scattering center compression ratio of the shock, rsc = 2, 4

  11. rsc = 2, q ~ 4.7·1032 s-1, Λ0 = 1 Rsun - Proton acceleration up to 1 MeV in 10 min - Hard escaping proton spectrum (~ p–1 ) - Very soft (~ p–4) spectrum at the shock - Wave power spectrum increased by 2 orders of magnitude at the shock at resonant frequencies

  12. rsc = 4, q ~ 4.7·1032 s-1, Λ0 = 1 Rsun - Proton acceleration up to ~20 MeV in 10 min - Hard escaping proton spectrum (~ p–1) - Softer (~ p–2) spectrum at the shock - Wave power spectrum increased by > 3 orders of magnitude at the shock at resonant frequencies

  13. rsc = 4, q ~ 1.9·1033 s-1, Λ0 = 5 Rsun - Proton acceleration up to ~20 MeV in < 3 min - Hard escaping proton spectrum (~ p–1) - Softer (~ p–2) spectrum at the shock - Wave power spectrum increased by ~ 4 orders of magnitude at the shock at resonant frequencies

  14. rsc = 4, q ~ 3.9·1032 s-1, Λ0 = 30 Rsun - Proton acceleration up to ~100 MeV - Hard escaping proton spectrum (~ p–1) - Softer (~ p–2) spectrum at the shock - Wave power spectrum increased by > 5 orders of magnitude at the shock at resonant frequencies

  15. Comparison with the theory of Bell (1978) Qualitative agreement at the shock below cut-off Good agreement upstream behind escaping particles

  16. Escaping particles (Λ0 = 1 Rsun) threshold for wave-growth NOTE: Observational streaming- limited spectrum somewhat softer than the simulated one (~ E-1/2).

  17. Cut-off energy log f @shock • Simulations consistent with analytical modeling: • proton spectrum at the shock a power law consistent with Bell (1978) • escaping particle spectrum a hard power law consistent with Vainio (2003):pdN/dp|esc ~ 4·1033 sr–1 • Power-laws cut off at an energy, which depends strongly on the injection rate q = Ninj/tmax Ec ~ qa with a ~ 0.5 – 2 • High injection rate leads to very turbulent environment → challenge for modeling ! Bell (1978) Bell/10 Ec log E 102 101 Ec [MeV] 100 10–1 1034 1035 1036 Ninj [sr–1] simulation time = 640 s

  18. Summary and outlook • Large SEP events excite large amounts of Alfvén waves • need for self-consistent transport and acceleration modeling • quantitatively correct results require numerical simulations • Monte Carlo simulation modeling of SEP events: • qualitative agreement with analytical models of particle acceleration (Bell 1978) and escape (Vainio 2003) • modest injection strength (q < 10-4 qsw) can result in > 100 MeV protons and non-linear Alfvén-wave amplitudes • streaming-limited intensities;spectrum of escaping protons still too hard in simulations • The present model needs improvements in near future: • more realistic model of the SW and shock evolution • implementation of the full wave-particle resonance condition

  19. Vs = 2200 km/s, rsc = 4, t = 640 s,q ~ 4.7·1032 s-1, Λ0 = 1 Rsun protons waves

More Related