instabilities driven by streaming energetic particles
DESCRIPTION
Interaction between cosmic rays and background plasmas on multiple scales Tony Bell University of Oxford Rutherford Appleton Laboratory. Tycho 1572AD. Kepler 1604AD. Magnetic field due to CR/MHD interaction. SN1006. Cas A 1680AD. Instabilities driven by streaming energetic particles. - PowerPoint PPT PresentationTRANSCRIPT
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Interaction between cosmic rays and background plasmas
on multiple scales
Tony BellUniversity of Oxford
Rutherford Appleton Laboratory
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Instabilities driven by streaming energetic particles
Kepler 1604ADTycho 1572AD
SN1006 Cas A 1680AD
Magnetic field due toCR/MHD interaction
Chandra observations
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Instability on Larmor scale
thermal Larmor radius < scalelength < CR Larmor radius
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dB/B>>1 scatters energetic particles
Cavity forms inside spirals
Streaming instability driven by cosmic raysLucek & Bell 2000
CR
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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|
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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
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Self-organisation on intermediate scale
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Filamentation & self-focussing
proton beam jvelocity vbeam
Bimposed
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Time sequence: magnitude of |B| - across beam
Same results – sections through beam
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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
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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
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Structures on scale of shock radius
scalelength > CR Larmor radius
CR behaviour: diffusive rather than ballistic
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SN in dense wind with Parker spiral magnetic field
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SN in dense wind with Parker spiral magnetic field
Perpendicular shock
CR drift at perpendicular shock
shock
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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
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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
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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
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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
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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
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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)
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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