Interaction between cosmic rays and background plasmas

on multiple scales 

Tony BellUniversity of Oxford

Rutherford Appleton Laboratory

Instabilities driven by streaming energetic particles

Kepler 1604ADTycho 1572AD

SN1006 Cas A  1680AD

Magnetic field  due toCR/MHD interaction

Chandra observations

Instability on Larmor scale

thermal Larmor radius   <   scalelength   <   CR Larmor radius

dB/B>>1 scatters energetic particles

Cavity forms inside spirals

Streaming instability driven by cosmic raysLucek & Bell 2000

CR

j x Bj x B

Essence of instability:  expanding loops of B

jxB  expands loops      decreases mass attached to field line element

increases jxB/r  acceleration      Loops expand more rapidly

Positive feedback - instability

B

CR current

CR/MHD calculation

|B|

Conditions for instability

1) loop radius R < CR Larmor radius

2) Mag tension < jxB

RcBCR

BjBB 0

1

3vsCRj r

cBR

jB CR

0

2

0

2

vvs

s

cB r

Saturation mag field

Estimate saturated magnetic field

Consistent with obs. (Vink, Völk, et al)

CR efficiency

CR energy (eV)

jBRB

0

2

ie

Growth requires cjB CR

0

2

Self-organisation on intermediate  scale

Filamentation & self-focussing

proton beam  jvelocity vbeam

Bimposed

Time sequence: magnitude of |B| - across beam

Same results – sections through beam

Filamentation & self-focussing

proton beam  jvelocity vbeam

E drives turbulence    slows beam

B

R

Magnetic field growth tU

jRtB turb

1~

E=0

E=0

jEtU turb

RE

tB ~

Energy conservation

Maxwell equation

Always focuses CR onto axis

Saturation power carried by filament/beam

0

2c

I eVAlfven

Power in beam  eVAlfvenAlfven IP

=1015eV AlfvenP 1.7x1028 W  = 3x10-12 Moc2yr-1 =1021eV AlfvenP 1.7x1040 W  = 3 Moc2yr-1

Apply saturation conditions1) Beam radius = CR Larmor radius2) Magnetic tension = jxB

    Beam carries Alfven current

CR energy

Structures on scale of shock radius

scalelength > CR Larmor radius

CR behaviour: diffusive rather than ballistic

SN in dense wind with Parker spiral magnetic field

SN in dense wind with Parker spiral magnetic field

Perpendicular shock

CR drift at perpendicular shock

shock

CR distribution f0 in a circumstellar wind

,,1

max20 tu

rpp

Ft

fs

Self-similar solution in (r,q)

Radius normalised to shock radius ust

Allows for density ~ r-2latitude

000

00 ...

31. fDfD

pf

pftf

huu

h

h0=1 h0=3 h0=10

10-2

100

log CR pressure for different collisionalities h0=()max

Self-similar solution for CR distribution

shock

Spiral field deflects diffusive CR flux towards axis

Small B on axis allows escape

10-6 0 /2 /2 /2q q q

101

h0=1 h0=3 h0=100 0

102

10-2

100.2 100.8

10-210-2

ppmax

CR spectrum (p-4f) at the shockfor different collisionalities h0=()max

pole equator

CR

mom

entu

m

Dominated by highest energy CR at pole

latitude

CR pressure in Parker spiral

12 rBrr

v.;1v 1 rrr

tP

t cr

Self-similar linear hydrodynamics

Density perturbation near pole

Large CR pressure                polar cavity in B r

crPshock

CR escape along axis

latitude

pole

equator

radius

rshock

1.3xrshock

non-linear density increase at shock

shockPlasma pushed away from axis

Cavity due to high CR pressure on axis

Density structure in front of shock, h0=10

Unperturbed upstreamplasma, r1=0

10-50% CR efficiencyfull cavity on axis

Shock around cavity

CR-driven relativistic expansion into low density

Magneticspiral expansion instabilityCR flow into cavity

PCR>rus2

shock

CR acceleration/drift begins at shock breakout• Shock steepens – non-radiation-dominated• Coulomb collisions• Inverse Compton losses• Pair-production• Proton-proton losses

May produce non-thermal effectsanisotropy on SN shock breakouteg x-ray flashes (XRF)

Summary

Similar effects on many scales

jxB focuses CR flux towards centre of spiral magnetic field

Reactive force:  expands spiral  increases magnetic energy  creates cavity on axis