Diffusive shock acceleration & magnetic field amplification Tony Bell University of Oxford
Theory of Shock Acceleration of Hot Ion Populations
description
Transcript of Theory of Shock Acceleration of Hot Ion Populations
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Theory of Shock Acceleration of Hot Ion Populations
Marty Lee
Durham, New Hampshire
USA
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Current Issues & Challenges• Theory of Planar Stationary Diffusive Shock Acceleration
• Injection Rates and Injection Thresholds
• “Hot” and “Cold” Seed Particle Populations
• Quasilinear Wave Excitation
• Ion Fractionation Upstream of the Shock
• Power-law Index: Observations Versus Theory
• Varying Magnetic Obliquity Within an Event
• Geometry: Earth’s Bow Shock & Solar Wind Termination Shock
• Nonlinear Waves & SLAMS
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Planar Stationary DSA - I
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f(z>0,v)=f0−(f0−f∞)(1−e−ζ)(1−e−ζ∞)−1
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f0≡β d′ v′ v0
v∫ f∞( ′ v)(1−e−′ ζ ∞)−1v′ v ⎛ ⎝ ⎜ ⎞ ⎠ ⎟-βexp−β d′ ′ v
′ ′ ve−′ ′ ζ ∞(1−e−′ ′ ζ ∞)−1′ vv∫ ⎡ ⎣ ⎢ ⎤
⎦ ⎥
€
Vz∂fi∂z−∂∂z(Ki,zz
∂fi∂z)−13dVzdzv
∂fi∂v=Qi
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ζ(z)= [V/Kzz(z')]dz'0z∫
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Planar Stationary DSA - II
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−Kzz∂f∂zz→∞
=V(f0−f∞)e−ζ∞(1−e−ζ∞)−1
€
fp,∞= np(4πvp,02 )−1δ(v−vp,0)+ Cv−γS(v− vp,0)
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Planar Stationary DSA - III
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log f
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log f
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log v
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Ani
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f∞ (v)∝δ (v − v0)
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Kzz = K0 (v /v0)2
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β =5
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Z = Vz /K0
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Z
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Z
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Z = 0
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Z = 8
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v /v0 = 1
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v /v0 = 5
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v /v0 = 1€
v /v0 = 5
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Planar Stationary DSA - IV
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log f
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log f
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log v
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Ani
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f∞ (v)∝δ (v − v0)
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Kzz = K0 (v /v0)2
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β =5€
Z = Vz /K0
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Z
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Z
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Vzesc /K0 = 10
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Z = 0
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Z = 8
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v /v0 = 1
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v /v0 = 1€
v /v0 = 5
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v /v0 = 5
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Planar Stationary DSA - V
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log f
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log f
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log v
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Ani
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Kzz = K0 (v /v0)2
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f∞ = (v /v0)−8
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β =5
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Z = Vz /K0
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Z = 0
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Z = 20
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Z
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Z
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v /v0 = 1.5
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v /v0 = 1.5
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v /v0 = 5
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v /v0 = 5
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Planar Stationary DSA - VI
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log f
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log f
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log v
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Ani
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Kzz = K0 (v /v0)2
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f∞ = (v /v0)−4.2
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β =5
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Z = Vz /K0
€
Z
€
Z
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Z = 0
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Z = 20
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v /v0 = 1.01
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v /v0 = 1.01
€
v /v0 = 5
€
v /v0 = 5
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Current Issues & Challenges• Theory of Planar Stationary Diffusive Shock Acceleration
• Injection Rates and Injection Thresholds
• “Hot” and “Cold” Seed Particle Populations
• Quasilinear Wave Excitation
• Ion Fractionation Upstream of the Shock
• Power-law Index: Observations Versus Theory
• Varying Magnetic Obliquity Within an Event
• Geometry: Earth’s Bow Shock & Solar Wind Termination Shock
• Nonlinear Waves & SLAMS
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Tylka et al., 2005
Injection and Shock Obliquity
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Anisotropy Limitation
€
|S |
vf=
V
v1+
KA2 sin2 θ + (K|| − K⊥)2 sin2 θ cos2 θ
(K|| cos2 θ + K⊥sin2 θ)2
⎡
⎣ ⎢
⎤
⎦ ⎥
1/ 2
€
K|| >> K⊥,KA :
€
⇒|S |
vf=
V
v cosθGiacalone and Jokipii, 1999
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“Energetic Storm
Particle” Event
Complexity
Van Nes et al., 1984
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Ion Features
Van Nes et al., 1984
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ACE Shock Survey
Lario et al., 2005
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Quasi-Perpendicular
Shock Simulation
Giacalone, 1999
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Shock Energetic Particle
Correlation Lengths
Neugebauer et al., 2006
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Current Issues & Challenges• Theory of Planar Stationary Diffusive Shock Acceleration
• Injection Rates and Injection Thresholds
• “Hot” and “Cold” Seed Particle Populations
• Quasilinear Wave Excitation
• Ion Fractionation Upstream of the Shock
• Power-law Index: Observations Versus Theory
• Varying Magnetic Obliquity Within an Event
• Geometry: Earth’s Bow Shock & Solar Wind Termination Shock
• Nonlinear Waves & SLAMS
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Example Event:1999 / 47-49(Cold Seeds)
Density compression: d/ u ~ 2.9
Clear proton foreshock of appropriate scale.
Softening particle spectra on the same ESP scale.
Particle intensity index appropriate to shock strength.
Small proton anisotropy.
Wave foreshock appropriate scale.
Argued and confirmed to be cold ion seed population leading to shock acceleration.
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Example Event:1998 / 217-219
(Hot Seeds)Density compression: d/ u ~ 1.8
Very modest or questionable proton foreshock if SEP event is properly recognized.
Softening particle spectra on SEP scale.
Moderate proton anisotropy.
Nonexistent wave foreshock.
Argued and confirmed to be hot ion seed population leading to shock acceleration.
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Current Issues & Challenges• Theory of Planar Stationary Diffusive Shock Acceleration
• Injection Rates and Injection Thresholds
• “Hot” and “Cold” Seed Particle Populations
• Quasilinear Wave Excitation
• Ion Fractionation Upstream of the Shock
• Power-law Index: Observations Versus Theory
• Varying Magnetic Obliquity Within an Event
• Geometry: Earth’s Bow Shock & Solar Wind Termination Shock
• Nonlinear Waves & SLAMS
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Wave Excitation - I
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−V∂I±/∂z=2γ±I±
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I≅I+=Io+(k)+4π2k2VAV|Ωp|mpcosψ dvv3(1−Ωp2
k2v2)(fp−fp,∞)|Ωp/k|∞∫
€
fp,∞= np(4πvp,02 )−1δ(v−vp,0)+ Cv−γS(v− vp,0)
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Wave Excitation - II
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I=Io+ +4π2k2VAV|Ωp|mpcosψ dvv3(1−Ωp2
k2v2)|Ωp/k|∞∫ ⋅
€
⋅ β n4πv0,p3 (
vv0,p)
−βS(v−v0,p)− n4πv0,p2 δ(v−v0,p)
⎧ ⎨ ⎩
€
+ C v0,p−γβ−γ γ(v v0,p)−γ−β(v v0,p)
−β ⎡ ⎣ ⎢
⎤ ⎦ ⎥S(v− v0,p)
⎫ ⎬ ⎭⋅
€
⋅exp−V d′ zcos2ψv34π
B20Ωp2dμ|μ|(1−μ2)I(Ωpμ−1v−1)+sin2ψK⊥−1
1∫ ⎡ ⎣ ⎢
⎤ ⎦ ⎥−1
0z∫ ⎫ ⎬ ⎭
⎧ ⎨ ⎩
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Wave Excitation - IIIβ = 7; I0(k) 0
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Current Issues & Challenges• Theory of Planar Stationary Diffusive Shock Acceleration
• Injection Rates and Injection Thresholds
• “Hot” and “Cold” Seed Particle Populations
• Quasilinear Wave Excitation
• Ion Fractionation Upstream of the Shock
• Power-law Index: Observations Versus Theory
• Varying Magnetic Obliquity Within an Event
• Geometry: Earth’s Bow Shock & Solar Wind Termination Shock
• Nonlinear Waves & SLAMS
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Ion Fractionation
Tylka et al., 1999
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Current Issues & Challenges• Theory of Planar Stationary Diffusive Shock Acceleration
• Injection Rates and Injection Thresholds
• “Hot” and “Cold” Seed Particle Populations
• Quasilinear Wave Excitation
• Ion Fractionation Upstream of the Shock
• Power-law Index: Observations Versus Theory
• Varying Magnetic Obliquity Within an Event
• Geometry: Earth’s Bow Shock & Solar Wind Termination Shock
• Nonlinear Waves & SLAMS
![Page 28: Theory of Shock Acceleration of Hot Ion Populations](https://reader035.fdocuments.in/reader035/viewer/2022070404/56813b21550346895da3d87e/html5/thumbnails/28.jpg)
Complications within DSAWave-frame compression ratio:
Van Nes et al., 1984
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Current Issues & Challenges• Theory of Planar Stationary Diffusive Shock Acceleration
• Injection Rates and Injection Thresholds
• “Hot” and “Cold” Seed Particle Populations
• Quasilinear Wave Excitation
• Ion Fractionation Upstream of the Shock
• Power-law Index: Observations Versus Theory
• Varying Magnetic Obliquity Within an Event
• Geometry: Earth’s Bow Shock & Solar Wind Termination Shock
• Nonlinear Waves & SLAMS
![Page 30: Theory of Shock Acceleration of Hot Ion Populations](https://reader035.fdocuments.in/reader035/viewer/2022070404/56813b21550346895da3d87e/html5/thumbnails/30.jpg)
Fe/O Versus Energy
Tylka et al., 2005
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Time Evolution
€
vt ≈ V secθ
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A Simple Model for Composition
Tylka and Lee, 2006
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Fe/O Versus Energy
Tylka and Lee, 2006
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Current Issues & Challenges• Theory of Planar Stationary Diffusive Shock Acceleration
• Injection Rates and Injection Thresholds
• “Hot” and “Cold” Seed Particle Populations
• Quasilinear Wave Excitation
• Ion Fractionation Upstream of the Shock
• Power-law Index: Observations Versus Theory
• Varying Magnetic Obliquity Within an Event
• Geometry: Earth’s Bow Shock & Solar Wind Termination Shock
• Nonlinear Waves & SLAMS
![Page 35: Theory of Shock Acceleration of Hot Ion Populations](https://reader035.fdocuments.in/reader035/viewer/2022070404/56813b21550346895da3d87e/html5/thumbnails/35.jpg)
The Blunt Termination Shock
McComas and Schwadron, 2006
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Stone et al., 2008
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Bow Shock
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Kis et al., 2007
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Kis et al., 2007
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Current Issues & Challenges• Theory of Planar Stationary Diffusive Shock Acceleration
• Injection Rates and Injection Thresholds
• “Hot” and “Cold” Seed Particle Populations
• Quasilinear Wave Excitation
• Ion Fractionation Upstream of the Shock
• Power-law Index: Observations Versus Theory
• Varying Magnetic Obliquity Within an Event
• Geometry: Earth’s Bow Shock & Solar Wind Termination Shock
• Nonlinear Waves & SLAMS
![Page 41: Theory of Shock Acceleration of Hot Ion Populations](https://reader035.fdocuments.in/reader035/viewer/2022070404/56813b21550346895da3d87e/html5/thumbnails/41.jpg)
Upstream Waves
Hoppe et al., 1981
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SLAMS
Lucek et al., 2008