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

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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

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

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

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 

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

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)

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

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

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

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

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

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)

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

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

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.

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

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

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,  …)

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)

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

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