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Courtesy of John Kirk

Particle Acceleration. Courtesy of John Kirk. Basic particle motion. No current. Dreicer DC electric fields (focusing on electrons). [Dreicer, 1959, 1960]. Electric force vs. drag force. Reaching maximum at the thermal speed. E D for typical flares is ~ 10 -4 V cm -1.

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Courtesy of John Kirk

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  1. Particle Acceleration Courtesy of John Kirk

  2. Basic particle motion No current

  3. Dreicer DC electric fields (focusing on electrons) [Dreicer, 1959, 1960] Electric force vs. drag force Reaching maximum at the thermal speed ED for typical flares is ~ 10-4 V cm-1. Coulomb logarithm < qE above v=vc, electrons will run-away E > ED: super-Dreicer E < ED: sub-Dreicer qE vs.

  4. Holman [1985] work: E ~ 10-7 V cm-1, spatial scales of L ~ 30 Mm (the size of a typical flare loop), yielding electron energies of W ~ 100 keV for an temperature of T ~ 107 K, a collision frequency of 2x103 s-1, a length scale of 10 Mm. In principle, the sub-Dreicer DC electron field mode can explain the thermal-plus-nonthermal distributions as observed in hard X-ray spectra. However, there are a number of open issues: 1) Require a large extent along the current sheet that is unstable. 2) Contradicts to the observed time-of-flight delays [Aschwanden 1996] 3) Electron beam current require counter-streaming return currents that can limit the acceleration efficiency severely. [Brown & Melrose 1977; Brown & Bingham 1984; LaRosa & Emslie 1989; Litvinenko & Somov 1991]

  5. Litvinenko [1996] work: B ~ 100 G, E ~ 10 V cm-1, d ~ 100 m the width of the current sheet, yielding electron energies of W ~ 100 keV, an acceleration length of 100 m.

  6. Stochastic Acceleration Is broadly defined as any process in which a particle can either gain or lose energy in a short interval of time, but where the particles systematically gain energy over longer times. wave-particle interaction It’s more important for particle acceleration in flares. How? Gain energy: , escape rate: b, and the escape probability of a particle with moment > p: P

  7. Melrose, Plasma Astrophysics I & II, Gordon & Breach Publishers, 1980; Benz, Plasma Astrophysics (2nd edition), 2003. Growth and damping rate Neglect the evolution of wave spectrum In an isolated homogeneous volume Second order of 1/vi Doppler resonance condition

  8. For typical coronal conditions:

  9. Consider an interaction of ions with very low-frequency waves, for example, Alfven waves The dispersion relation is To be accelerated, an ion needs to have a threshold energy. For typical coronal Alfven speeds, 2000 km s-1, the threshold should be > ½*mpvA2~20 keV. A problem is how to accelerate ions from their thermal energy (~1 keV) to the threshold energy.

  10. Resonance with a single small-amplitude wave: the gain energy oscillate with frequency of ω, the maximum energy gain is small and zero on average. E t ω4 ω3 ω2 ω1 A broadband spectrum of waves is thus typically required to accelerate particles to high energies.

  11. explain the enhanced ion abundances with the stochastic acceleration. In the scenario of turbulent MHD cascades: long-wavelength Alfven waves cascade to shorter wavelengths, gyroresonant interactions are first enabled for the lowest Ω, such as iron, and proceed then to higher Ω.

  12. Shock drift acceleration • A drift at shock front like drift • A convective electric field in the (opposite) direction • So particles gain energy when crossing shocks.

  13. Diffusive shock acceleration [Jones & Ellison, 1991] One crossing N crossesings

  14. From the downstream to the upstream From the upstream to the downstream Probability of return (two crossings) ud upstream downstream In downstream frame

  15. Assuming u << vi, only the first order of 1/vi is kept. so

  16. spectral index > 1

  17. Problems and limitations v >> uu, ud => the second order and more of u/v could be neglected. Velocity distribution should be isotropic in all relevant frames. Shock thickness should be much smaller than mean free path of particles.

  18. Acceleration time scale With a given time, Eperp > Epar [Jokipii et al.1995; Giacalone and Jokipii 1999; Zank et al. 2004; Bieber et al. 2004] For a particle energyE = 1 MeV electron (rg ~ 108 cm , v ~ 1010 cm/s) tacc ~ 102 s proton (rg ~ 1011 cm , v ~ 109 cm/s) tacc ~ 104 s~ 0.1 day E = 1 GeVrg ~ 1012 cm , v ~ 1010 cm/s tacc ~ 106 s ~ 0.1 AU ~ 1 month E = 1 PeV(= 1015 eV) rg ~ 1018 cm , v ~ 1010 cm/s tacc ~ 1012 s ~ 1 pc ~ 105 yr E= 1 EeV(=1018 eV) rg ~ 1021 cm , v ~ 1010 cm/s tacc ~ 1015 s ~ 1 kpc ~ 108 yr

  19. ESP (Energetic Storm Particle) events [Reams, 1999] [courtesy of Ho et al., 2004]

  20. [courtesy of Ho et al., 2004]

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