A multi-island mechanism for particle acceleration during magnetic reconnection in solar flares

1. A multi-island mechanism for particle acceleration during magnetic reconnection in solar flares J. F. Drake and M. Swisdak University of Maryland

2. Some energetic particle observations in impulsive flares • In solar flares energetic electrons up to MeVs and ions up to GeVs are measured • A significant fraction of the released magnetic energy appears in the form of energetic electrons and ions (Lin and Hudson ‘76, Emslie et al ‘05) • Must explain such extraordinary efficiency and link particle energy gain to magnetic energy release • The energetic electron beta can approach unity in over-the-limb observations (Krucker et al 2010) • Correlation between > 300keV energetic electrons and > 30 MeV ions (Shih et al 2009) • Common acceleration mechanism? • In impulsive flares see enhancements of high M/Q ions (e.g., Mason ‘07)

3. Impulsive flare timescales • Hard x-ray and radio fluxes • 2002 July 23 X-class flare • Onset of 10’s of seconds • Duration of 100’s of seconds. • Bursts of 100keV x-rays occur on time scales as short as 100ms (Vilmer et al 1996) RHESSI and NoRH Data (White et al., 2003)

4. RHESSI observations • July 23 γ-ray flare • Holman, et al., 2003 • Double power-law fit with spectral indices: 1.5 (34-126 keV) 2.5 (126-300 keV) • Typically see soft-hard-soft spectral evolution

5. Energetic electron and ion correlation • > 300keV x-ray fluence (electrons) correlated with 2.23 MeV neutron capture line (> 30 MeV protons) • Acceleration mechanisms of electrons and protons linked? Shih et al 2008

6. RHESSI occulted flare observations 30-50keV 17GHz • Observations of a December 31, 2007, flare • All electrons in the flaring region are part of the energetic component (10keV to several MeV) • The pressure of the energetic electrons approaches that of the magnetic field. • Remarkable! Krucker et al 2010

7. Impulsive flare energetic ion abundance enhancement • During impulsive flares see heavy ion abundances enhanced over coronal values • Enhancement linked to Q/M Mason, 2007

8. Main Points • A single x-line model of flares can not explain the observations • Parallel electric fields are too localized around the x-line to explain the large numbers of energetic electrons (Drake et al 2005, Egedal et al 2009) • Magnetic energy release does not take place at the x-line but downstream as the magnetic field line relaxes its tension • Instead magnetic energy release takes place in regions with volume filling magnetic islands (Tajima and Shibata 1997, Onofri et al 2006, Drake et al 2006) • Electron acceleration is dominated by first order Fermi acceleration in contracting islands (Kliem 1994, Drake et al 2006) • Electron energy gain is linked to magnetic energy release

9. Main Points (cont.) • Ion acceleration takes place in two steps • Ions entering reconnection exhausts act like “pickup” particles and gain a thermal velocity equal to the Alfven speed • Abundance enhancements of high M/Q ions occur because during guide-field reconnection (typical for the sun) they more easily behave like “pickup” particles than protons (Drake et al 2009) • Super-Alfvenic ions, like electrons, gain energy through Fermi reflection in contracting islands (Drake et al 2010) • Links acceleration mechanism of electrons and ions • Both ions and electrons gain energy through island contraction (increasing the parallel energy) until reaching the marginal firehose condition • At the marginal firehose limit reconnection is throttled • The energetic particle beta approaches unity (e.g., Krucker et al 2010) • Balance of Fermi drive and convective loss leads to powerlaw distributions with spectral indices with a lower limit of 1.5 in a low-beta system

10. E|| Electron acceleration by the parallel reconnection electric field • Parallel electric fields during reconnection are typically highly localized near the x-line and along separatrices • A single x-line model can not explain the large numbers of electrons seen in flares • Parallel electric fields are too spatially localized to be a significant source of large numbers of energetic electrons • The electron flux would produce currents that exceed the coronal fields by orders of magnitude • Finally, the x-line is not where magnetic energy is released.

11. A multi-island acceleration model • Narrow current layers spawn multiple magnetic islands in reconnection with a guide field • Must abandon the classical single x-line picture!!

13. uin CAx CAx Multi-island reconnection • Give up single x-line model • How are electrons and ions accelerated in a multi-island environment? • Fermi reflection in contracting magnetic islands increase the parallel particle energy • Rate of energy gain independent of particle mass  Thermal protons are not fast enough to bounce since are sub-Alfvenic -- need seed heating mechanism

14. Seeding super-Alfvenic ions through pickup in reconnection exhausts • Ions moving from upstream cross a narrow boundary layer into the Alfvenic reconnection exhaust • The ion can then act like a classic “pick-up” particle, where it gains an effective thermal velocity equal to the Alfvenic outflowTi ~ micA2 ~ 10-100keV/nucleon. • Energy proportional to mass (Fujimoto and Nakamura, 1994; Drake et al 2009)

15. What about the numbers problem? • To explain the large numbers of accelerated electrons in flares the contracting island region must be macroscopic Island region

16. Parker’s equation and Fermi acceleration in contracting islands w ⇒ • Area of the island Lw is preserved ⇒ incompressible dynamics • Magnetic field line length L decreases • Parker’s transport equation • Only compression drives energy gain. Why? • Parker equation assumes strong scattering ⇒ isotropic plasma

17. Fermi acceleration in contracting islands w ⇒ • Area of the island Lw is preserved • Magnetic flux Bw is preserved • Particle conservation laws • Magnetic moment • Parallel action V|| L • Energy gain for initially isotropic plasma • No energy gain for infinitesimal change in L ⇒ consistent with Parker • Significant energy gain for finite contraction • Parker equation is missing some important physical processes

18. Linking magnetic energy release to particle energy gain • A key flare observation is that energetic particle energy gain is linked to the released magnetic energy. Why? • Island contraction continues until the firehose marginal stability condition is reached. At this point • The rate of particle energy gain equals the rate of release of magnetic energy • This establishes the key linkage between particle and magnetic energy seen in flares • Magnetic energy released depends on β0 • Low β0 • High β0

19. Particle acceleration in a periodic magnetic field • Simulations of particle acceleration in a realistic sheared magnetic field is intrinsically 3-D -- Not feasible in PIC model • Treat a system with periodic reversals as a test bed • Can study for the first time particle acceleration in a true multi-island environment with a PIC model • Low initial beta with a strong guide field to mimic the corona Jez Jez

20. Development of pressure anisotropy • The parallel pressure increases • faster the perpendicular pressure • consistent with the Fermi • mechanism. • System approaches the marginal • firehose condition at late time • Shuts off reconnection since magnetic • fields have no tension at the firehose • marginal limit • e.g., Alfven wave

21. Jez Firehose condition • Within islands and along separatrices bump against the firehose condition • Not as clear as in anti-parallel case (Drake et al 2010) • This condition limits island contraction • Controls particle spectra • Self-consistency is crucial in exploring particle acceleration

22. Electron and ion energy spectra • Both ions and electrons gain energy • Electrons gain energy first and then saturate. Why? • A key feature is that the rate of energy gain of particles increases with energy • first order Fermi • Ongoing study of acceleration mechanisms ions f(E) electrons E

23. 1-D Model equations • Rate of energy gain: first order Fermi • Model equation for the omni-directional distribution function • Above the source energy this is an equidimensional equation • powerlaw solutions

24. Distributions and spectral indices • Exact steady state solutions for F(v) • Spectral index • Since the island sizes are much smaller than the system size, • spectral index controlled by marginal firehose condition

25. Magnetic islands release energetic electrons in bursts • Secondary magnetic island merging with a large-scale field releases energetic electrons in narrow filaments • Source of millisecond bursts of energetic electrons? • Can analysis of the time structure of energetic electrons reveal information about the size distribution of magnetic islands? Te

26. Conclusions • The single x-line model can not explain the large number of energetic electrons seen in flares • Magnetic reconnection with a guide field as in the corona naturally leads to a multi-x-line configuration • High energy particle production during magnetic reconnection involves the interaction with many magnetic islands • Electron acceleration is dominated by a Fermi-like reflection in contracting magnetic islands • Ion interaction with the reconnection exhaust seeds them to super-Alfvenic velocities. • Ions that act as pickup particles as they enter reconnection exhausts gain most energy • M/Q threshold for pickup behavior • Yields abundance enhancement of high M/Q ions

27. Conclusions (cont.) • Efficient heating of super-Alfvenic ions through magnetic island contraction • Balance of contraction drive and convective loss yields powerlaw solutions for all species • Spectral indices are controlled by the approach to firehose stability • M/Q threshold for pickup behavior is a possible explanatation of impulsive flare heavy ion abundance enhancements • This hypothesis can be tested with PIC simulations

28. Mirror and firehose conditions • Within islands bump against the firehose condition • This condition limits island contraction • Controls particle spectra • In current layers and along separatrices bump against mirror mode limit • Self-consistency is crucial in exploring particle acceleration firehose mirror

29. Ey μi Bz0 = 5.0 t Pickup threshold: guide field • Protons and alpha particles remain adiabatic (μ is conserved) • Only particles that behave like pickup particles gain significant energy  threshold for pickup behavior mi=16mp βpx