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. magnetic field amplification 1) Basic theory 2) Observational indicators Diffusive shock acceleration and magnetic field amplification

3. DIFFUSIVE SHOCK ACCELERATION Cosmic ray wanders around shock -scattered by magnetic field High velocity plasma Low velocity plasma B2B2 B1B1 CR track Due to scattering, CR recrosses shock many times Gains energy on each crossing

4. Idealised shock acceleration:diffusion, no magnetic field UpstreamDownstream Uniform density n CR Probability of escape = u/c shock velocity: u Rate CR cross shock = n CR c/4 fluid velocity = u fluid velocity = u/4 Rate CR escape downstream = n CR u/4 

5. Idealised shock acceleration:diffusion, no magnetic field UpstreamDownstream Uniform density n CR Probability of escape = u/c shock velocity: u Rate CR cross shock = n CR c/4 fluid velocity = u fluid velocity = u/4 Rate CR escape downstream = n CR u/4 On each crossing Fractional CR loss  N/N = -u/c Fractional energy gain on each crossing  E/E=u/c  N/  E = -N/E  E dN/N = - E dE/E  N f E -1 differential spectrum n(E) dE f E -2 dE

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

7. L Maximum CR energy Shock (velocity u) downstreamupstream Exponential dist n Balance between advection and diffusion Acceleration time: Precursor scaleheight: L R shock CR pre-cursor Shock expansion time: u = 5000 kms -1, R = 10 17 m, B = 3  G E max < 6x10 13 eV mfp shock vel

8. rgrg 1) Bohm diffusion: mean free path  ~ r g Disordered magnetic field:  B / B ~ 1 2) Magnetic field amplification Need B ~ 100  G to reach few x 10 15 eV CR path How to increase CR energy

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

10. Linear instability B 0, j CR z B x, v x B y, v y MHD equation of motion Model Thermal plasma as MHD fluid CR as fixed uniform current j CR Flux freezing Purely growing, circularly polarised transverse mode: B

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

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

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

14. Observations Shock thickness & synchrotron losses Good evidence for field amplification (Vink & Laming, Voelk et al)

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

16. Observations Scale length of turbulence Can we observe structure of magnetic field?

17. Estimate shock structure scale  L j cr xB moves upstream plasma a distance R shock CR precursor j cr v shock h ~0.01 1 1 Using scaling arguments for j CR, B,  & t

18. SNR in historical order (CHANDRA) Tycho 1572ADSN1006 Chandra observations Kepler 1604ADCas A 1680AD Cas A, CHANDRA (Patnaude et al 2008) Cas A radio (VLA) High speed shrapnel? Clumpy ambient medium? CR-driven instability? NASA/CXC/NCSU/ S.Reynolds et al. NASA/CXC/Rutgers/ J.Warren & J.Hughes et al. NASA/CXC/MIT/UMass Amherst/ M.D.Stage et al. NASA/CXC/Rutgers/ J.Hughes et al. Shock structure maps out pre-shock features ( B,  …)

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

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  u 3 Time-dependent shock structure maps out ambient medium