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Diffusive shock acceleration & magnetic field amplification Tony Bell University of Oxford

Diffusive shock acceleration & magnetic field amplification Tony Bell University of Oxford Rutherford Appleton Laboratory. SN1006: A supernova remnant 7,000 light years from Earth

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Diffusive shock acceleration & magnetic field amplification Tony Bell University of Oxford

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  1. Diffusive shock acceleration & magnetic field amplification Tony Bell University of Oxford Rutherford Appleton Laboratory SN1006: A supernova remnant 7,000 light years from Earth X-ray (blue): NASA/CXC/Rutgers/G.Cassam-Chenai, J.Hughes et al; Radio (red): NRAO/AUI/GBT/VLA/Dyer, Maddalena & Cornwell; Optical (yellow/orange): Middlebury College/F.Winkler. NOAO/AURA/NSF/CTIO Schmidt & DSS

  2. Diffusive shock acceleration and magnetic field amplification magnetic field amplification1) Basic theory2) Observational indicators

  3. DIFFUSIVE SHOCK ACCELERATIONCosmic ray wanders around shock-scattered by magnetic field B1 B2 Low velocity plasma High velocity plasma CR track Due to scattering, CR recrosses shock many times Gains energy on each crossing

  4. Idealised shock acceleration: diffusion, no magnetic field shock velocity: u Upstream Downstream fluid velocity = u/4 fluid velocity = u Uniform density nCR } Rate CR cross shock = nCRc/4 Probability of escape = u/c Rate CR escape downstream = nCRu/4

  5. Idealised shock acceleration: diffusion, no magnetic field shock velocity: u Upstream Downstream fluid velocity = u/4 fluid velocity = u Uniform density nCR } Rate CR cross shock = nCRc/4 Probability of escape = u/c Rate CR escape downstream = nCRu/4 On each crossing Fractional CR loss DN/N = -u/c } DN/DE = -N/E Nf E-1 Fractional energy gain on each crossing DE/E=u/c EdN/N = - EdE/E differential spectrum n(E) dEfE -2 dE

  6. L R CR pre-cursor shock Maximum CR energy Shock (velocity u) Exponential distn Balance between advection and diffusion upstream downstream L mfp Precursor scaleheight: shock vel Acceleration time: (Lagage & Cesarsky) Shock expansion time:

  7. L R CR pre-cursor shock Maximum CR energy Shock (velocity u) Exponential distn Balance between advection and diffusion upstream downstream L mfp Precursor scaleheight: shock vel Acceleration time: Shock expansion time: Emax < 6x1013 eV u = 5000 kms-1, R = 1017 m, B = 3 mG

  8. How to increase CR energy 1) Bohm diffusion: mean free path l ~ rg CR path Disordered magnetic field: dB/B~ 1 rg 2) Magnetic field amplification Need B ~ 100 mG to reach few x 1015eV

  9. Streaming instability driven by cosmic rays Lucek & Bell 2000 CR Cavity forms inside spirals dB/B>>1 scatters energetic particles

  10. Linear instability Model Thermal plasma as MHD fluid CR as fixed uniform current jCR B z Bx, vx B0, jCR By, vy MHD equation of motion Flux freezing Purely growing, circularly polarised transverse mode:

  11. Non-linear growth – expanding loops Slices through |B| - time sequence (fixed CR current) Cavities and walls in |B| & r

  12. Instability must be strongly driven (large CR electric current) Condition for unstable growth: tension in magnetic field line driving force Back-of-envelope: scalelength Growth only if scalelength L shorter than CR Larmor radius: (otherwise CR tied to field lines)

  13. Saturation magnetic field Growth condition CR electric current: CR energy flux in precursor: CR efficiency h: Allowing for compression of B (~times 2) at shock

  14. ObservationsShock thickness & synchrotron lossesGood evidence for field amplification(Vink & Laming, Voelk et al)

  15. Tycho 1572AD Kepler 1604AD SN1006 Cas A 1680AD Historical shell supernova remnants Chandra observations NASA/CXC/Rutgers/ J.Hughes et al. NASA/CXC/Rutgers/ J.Warren & J.Hughes et al. NASA/CXC/NCSU/ S.Reynolds et al. NASA/CXC/MIT/UMass Amherst/ M.D.Stage et al.

  16. ObservationsScale length of turbulenceCan we observe structure of magnetic field?

  17. Estimate shock structure scale dL h R jcr shock CR precursor vshock jcrxB moves upstream plasma a distance Using scaling arguments for jCR, B, r & t ~0.01 1 1

  18. SNR in historical order (CHANDRA) Chandra observations SN1006 Tycho 1572AD Kepler 1604AD Cas A 1680AD NASA/CXC/Rutgers/ J.Hughes et al. NASA/CXC/Rutgers/ J.Warren & J.Hughes et al. NASA/CXC/NCSU/ S.Reynolds et al. NASA/CXC/MIT/UMass Amherst/ M.D.Stage et al. High speed shrapnel? Clumpy ambient medium? CR-driven instability? Cas A radio (VLA) Shock structure maps out pre-shock features (B, r…) Cas A, CHANDRA (Patnaude et al 2008)

  19. RX J1713.7-3946 (SN of 393AD) HESS, Aharonian et al 2007 HESS Cerenkov telescope (0.3-100TeV) Direct evidence for 100TeV CR CHANDRA (0.1-10keV) Changes in ~1 year imply mG magnetic field Uchiyama et al 2007

  20. Conclusions • Magnetic field amplification an important part of shock acceleration • Opportunity to bring theory & observation closer together • Potential diagnostics of physical environment & CR origin • Magnetic field (from shock thickness) gives ru3 • Time-dependent shock structure maps out ambient medium

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