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Magnetic Field Amplification in Cosmic Ray Acceleration Mechanisms

Study on cosmic ray acceleration at shocks and the role of magnetic fields in the process, exploring the interaction between cosmic rays and plasma leading to field amplification. The research investigates the dynamics of shock-accelerated cosmic rays scattering by magnetic fields, their trajectories, and feedback mechanisms driving instability and field growth. Observations from SN1006 and Cassiopeia A are used to analyze the evolution of magnetic fields and turbulence in supernova remnants. The findings suggest that high-velocity shocks favor rapid acceleration to high energies, impacting the development of young supernova remnants.

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Magnetic Field Amplification in Cosmic Ray Acceleration Mechanisms

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  1. Magnetic fieldandaccelerated shock acceleration Tony Bell Imperial College, London Lucek & Bell, MNRAS 314, 65 (2000) Bell & Lucek, MNRAS 321, 433 (2001) Bell, MNRAS 353, 550 (2004) Bell, MNRAS 358,181 (2005)

  2. SNR suitable CR source below 1015eV x-ray image of SN1006 Radio image of SN1006 Reynolds, 1986 Long, 2003

  3. B1 B2 Low velocity plasma High velocity plasma Cosmic ray wanders around shock-scattered by magnetic field CR track Due to scattering, CR recrosses shock many times

  4. B1 B2 Low velocity plasma High velocity plasma Cosmic ray wanders around shock-scattered by magnetic field CR track Due to scattering, CR recrosses shock many times

  5. ‘Bohm diffusion’ Mean free path lcr ~ rg (proportional to 1/B) rg Requires disordered magnetic field: dB/B ~ 1

  6. R L CR pre-cursor shock Scaleheight must be less than SNR radius Need L<R Bohm diffusion: lcr = rg L= rg c /3vshock Want small rg (large B) for rapid acceleration to high energy

  7. Reducing the CR mean free pathMagnetic field amplification

  8. CR B CR/Alfven wave interaction (conventional theory) • If CR gyration length matches Alfven wavelength • CR scattered strongly by waves • Waves excited by CR

  9. For SNR conditions, instability strongly driven- changes nature of turbulence Re(w) Im(w) krg=1 k in units of rg-1 w in units of vS2/crg

  10. CR interaction with short wavelength waves CR trajectory B CR trajectories unaffected by dB Wave growth driven by jcr||xB

  11. R L CR pre-cursor shock Electric currents carried by CR and thermal plasma jcr Density of 1015eV CR: 10-3 m-3 Current density: jcr ~ 10-17 Amp m-2 CR current must be balanced by current carried by thermal plasma jthermal = - jcr jthermalxB force acts on plasma to balance jcrxB force on CR

  12. Unstable growth of magnetic field CR current Magnetic field frozen into thermal plasma j j x B j j x B Current carried by thermal plasma j x B force expands the spiral Lengthens field lines Increases magnetic field Increases j x B force POSITIVE FEEDBACK (INSTABILITY)

  13. Time sequence: four adjacent field lines a) b) d) c) No reason for non-linear saturation of a single mode

  14. Growth time of fastest growing mode Uncertain efficiency factor SNR expand rapidly for ~1000 yrs Acceleration favoured by high velocity and high density Look to very young SNR for high energy eg SN1993J in M81 (Bartel et al, 2002) After 1 year: vs =1.5x107 ms-1 ne~106cm-3 After 9 years: vs =0.9x107 ms-1 ne~104cm-3 Shock velocity drops in Sedov phase – reduces max. CR energy

  15. MHD simulations demonstratemagnetic field amplification Development of previous modelling, Lucek & Bell (2000)

  16. t=0

  17. t=6.4 t=9.5 t=12.4 t=16.8

  18. Evolution of magnetic field Magnetic field (log) time rms field grows 30x max. field grows 100x linear non-linear Estimate of saturation magnetic field

  19. Linear growth kmin= (CR Larmor radius) -1 ~ B kmax B = m0 jCR kmin kmax B increases during non-linear growth “kmin”increases, “kmax”decreases Growth saturates whenkmax = kmin= 1/CR Larmor radius

  20. Cassiopeia A (Chandra) Indicates magnetic field amplification at shock (Vink & Laming, 2003; Völk, Berezhko, Ksenofontov, 2005)

  21. Structure of turbulence

  22. Cavities in density and magnetic field Slices perpendicular to CR flux at t=6 Magnetic field Density Field lines – wandering spirals

  23. Cavities and Filaments

  24. Spiral field lines configured as a single mode Alternative configuration

  25. j x B j x B Spiral expands leaving a central cavity

  26. Expanding filament Magnetic field (theta component) Density Cavity in density and magnetic field

  27. Filamentation & self-focussing B proton beam j velocity vbeam

  28. MHD response to beam – mean |B| along line of sight t=2 t=4 x z t=8 t=6 Current, j

  29. Slices of B and r in z at t=2 Density Magnetic field B (0.71,1.32) r (0.76,1.17)

  30. Slices of B and r in z at t=4 Density Magnetic field B (0.40,2.61) r (0.54,1.59)

  31. Slices of B and r in z at t=6 Magnetic field Density B (0.11,8.53) r (0.03,4.13) Low density & low B in filament

  32. Slices of B and r in z at t=8 Density Magnetic field B (0.,8.59) r (0.,4.51)

  33. Filamentation & self-focussing B E=0 R proton beam j velocity vbeam E=-uxB E=0 Magnetic field growth Focuses CR, evacuates cavity Ideal for focussing CR into beam

  34. CR exhausts and jets1) SN in circumstellar wind, aligned rotator2) CR source at centre of accretion disk

  35. c CR pressure CR Larmor radius vsrvs2 cavity radius Supernova in Wind from star with dipole aligned with rotation axis CR flux drives cavity along axis Low energy CR escape through cavity Number of e-foldings ~ 1/2 vs = SNR shock velocity

  36. CR flux produces cavity Exhaust of low energy CR & thermal plasma Accretion disk jets Disk wind carries magnetic field Rotating disk threaded by magnetic field Central source of CR • Consequences: • Magnetic field spirals clockwise • Jets on 2 sides or none

  37. Power carried by filament/beam W =1015eV 1.7x1028 W = 3x10-12 Moc2yr-1 1.7x1038 W = 0.03 Moc2yr-1 =1020eV Natural evolution: 1) Beam radius = Larmor radius 2) Beam carries Alfven current Power in individual filament/beam

  38. Black holes: characteristic parameters (Begelman, Blandford & Rees, 1984; based on Eddington luminosity LE) CR energy e for which: 1) Larmor radius rg = R 2) Alfven current carries LE Hillas, 2005 Mass depth independent of black hole mass M (rR for p-p energy loss = 800 kg m-2)

  39. Conclusions • Magnetic field amplification increases max CR energy • Historical SNR produce CR up to knee • Very young SNR may get beyond knee • Exhaust model may connect high energy CR to jets Lucek & Bell, MNRAS 314, 65 (2000) Bell & Lucek, MNRAS 321, 433 (2001) Bell, MNRAS 353, 550 (2004) Bell, MNRAS 358,181 (2005)

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