ミクロなプラズマ素過程に基づく衝撃波粒⼦加速機構
Shock Acceleration Mechanisms Based on
Microscopic Plasma Physical Processes
天野孝伸 (東京⼤学)
Takanobu Amano (U-Tokyo)
Collaborators

T. Katou, M. Hoshino (U-Tokyo), Y. Matsumoto (Chiba U), M. Oka (UCB), S. Matsukiyo(Kyusyu U) O. Kobzar (Jagiellonian U), J. Niemiec (INP/PAS), A. Bohdan M. Pohl (DESY)Non-thermal Particles
Highly energetic charged particles with energies much larger than the thermal energy are ubiquitous inmany astrophysical phenomena. The energy density of the non-thermal populations can be comparable tothe thermal component.
Earth bow shock
solar flare

Lin+2003
Amano+2020
magnetotail

Cosmic Rays
Blasi (2013), Amato (2014)Øieroset+2002

Fundamental Question: Energy Partition
Upstream Flow
Kinetic Energy

ThermalNonthermal

Thermalelectrons

Nonthermal
electrons

Wave(EM-field)

Thermalions

Crab nebula

SN1006CME

Nonthermal
ions

Tsurutani+1981

Schaeffer+2017

Standard Shock Acceleration Theory• Diffusive Shock Acceleration (DSA)– A simple yet powerful model that predicts a nearly universal power-law; N(E) ∝ E-2[e.g., Bell 1978, Blandford & Ostriker 1978]

X-ray image by
Chandra[Bamba+2003]

M. Scholer

In-situ obs. by Geotail[Shimada+1999]

Balogh and Treumannreflected (field-aligned) ionsdiffuse ions

Acceleration rate relative to the parallel shock• While the spectral index does not change, quasiperpendicular shocks can be much more efficientthan quasi-parallel shocks in terms accelerationtime.
• The diffusion approximation will breakdown when
the shock is very close to purely perpendicularshock.
[cf., Kirk & Schneider 1987, Takamoto & Kirk 2015]

The Electron Injection
electrons with < 0.1-1 MeV cannot be scattered by MHD waves !
SN1006

kvk = ⌦/

theoretical gap

Ref: Levinson 1992, Amano & Hoshino 2010, Shimada+1999, Lario+2003, Dresing+2016

ü Sub-relativistic electrons
cannot be accelerated by
the standard first-order
Fermi mechanism.
ü Substantial energy gain isneeded from thermal torelativistic energies by someother mechanisms.
ü Sub-relativistic
suprathermal electrons are“invisible” with typicalastrophysical observations,while they are observablewith in-situ spacecraft
measurement.

Acceleration Time and Injection Problem

Quasi-linear estimate:The gyroradii of low-energy electrons are very small and will be well below
the dissipation range of MHD turbulence.
→ no electron acceleration should be expected?
• MHD waves cannot resonantly scatter subrelativistic electrons.
• Intense high-frequency (whistler) waves toscatter low-energy electrons?
• Any other mechanisms to energize low-energyelectrons to mildly relativistic energies?

MHD regime(Alfven waves)

Amano & Hoshino (2010)

Electron Injection Scenario
DSA (diffusion length >> shock thickness)l Diffusive and slow particle acceleration wellbeyond the shock thickness.
l The canonical power-law: f(p) ∝ p-4
l It may operate only when SSDA provides
sufficiently energetic electrons.

SSDA (diffusion length ~ shock thickness)l Diffusive and fast particle acceleration within theshock transition layer.
l It results in a steeper power-law for energyindependent diffusion (consistent withobservations at the bow shock.)l Higher-energy electrons will eventually escape
toward upstream because of diffusion lengths
longer than the shock thickness.
Amano+(2020, PRL), Katou & Amano (2019, ApJ), Kobzar+(2021, ApJ), Matsumoto+(2017, PRL)

Amano & Hoshino (in prep)

Particle Acceleration at Oblique Shock of Finite Thickness
Solutions of the diffusion-convection equation at a shock of finite thickness Ls

Amano & Hoshino (in prep)

Unifying SSDA and DSA

Both SSDA and DSA may be described by the diffusion-convection equation:energy gain = flow divergence

diffusion along B
Both SDA (∇B) and first-order Fermi (∇V) contributes tothe energy gain but ∇B is dominant at quasi-perp shocks

The steady-state spectrum may be estimated aswithdiffusion length >> shock thickness→ standard DSA (q=4)

steeper SSDA

canonical DSA

injectiondiffusion length ~ shock thickness→ SSDAratio between diffusion length and shock thickness→ predicted spectrum is steeper than DSA (q>6),
but the acceleration time is much shorter

downstream spectrum

Energy spectrum for MA = 10

Amano & Hoshino (in prep)Ø A steep spectrum at low energy and the harder DSA spectrum
at high energy may be connected smoothly, if parameterschosen appropriately.
Ø This indicates that the electron injection and further
acceleration to ultra-relativistic energy may be described by asingle model.
Ø The question is what is the condition for injection.

observation

modelDSA

Earth’s Bow Shock: Laboratory for Electron Injection

Gosling+1989

Oka+2006

Amano+2020• Non-thermal electrons with a clear power-law spectrum have been observed
occasionally at the bow shock.
• The typical energy range of non-thermal electrons measured at the bow
shock is the most important energy range for the injection.

Stochastic SDA (SSDA)
negligible at Qperp shock(major term for DSA)

mirror force

Katou & Amano (2019)

SSDA Signatures
B field
particle flux
downstream

upstreamOka+2017 (MMS obs.)
Stochastic Shock Drift Acceleration
mirror reflection + scattering

Kobzar+ (ApJ, 2021)
2D high-beta and low Mach no. shock

Matsumoto+2017
3D Weibel-dominated shock

Katou & Amano 2019transition layer

Bow Shock Crossing on 2016 Dec 9• Vsw ~ 600 km/s
• θBn ~ 85 (quasi-perp.)• MA ~ 8.9 (high Mach num.)

Substantial flux enhancements
for high energy (>1 keV) electrons.
FEEPS also detected electrons up
to ~100 keV.
Unusual for bow shock crossings.

Exponential increase ofparticle intensity

Nearly isotropic pitch-angle
distribution

Enhanced wave power (inparticular, high-frequency
whistlers)Smoking-Gun Evidence ?
• Simultaneous appearance of energetic electron profiles, weakanisotropy, enhanced wave power are all consistent with thetheory. However, the agreement is only qualitative.
• The observed power-law index is roughly consistent with thetheory. But it does not necessarily identify the mechanism.
• The theory predicts that the high-energy cutoff of the spectrum isdetermined by the single parameter D𝜇𝜇power-lawresonanceenergy 0.1-1 keV

Dµµ > thresholdwhistlers(f/fce = 0.1-0.5)

threshold based on QLTAmano+(2020, PRL)

ここまでのまとめ• 電⼦の輸送⽅程式が拡散で書けるのであれば，上⼿くパラメータ（拡散係数）を選べば⾮相対論的エネルギーから相対論的エネルギーまでの電⼦加速が記述でき，スペクトルも求まる．宇宙線電⼦の絶対量も原理的には決まる．
• 問題：拡散係数はどのように決定されるのか？
運動量pの電⼦を加速できる条件

DSAへの電⼦の注⼊条件：観測(Oka+2006)や理論(Amano & Hoshino 2010, Levinson 1992-1996)で何故かよく出てくるパラメータSuper-critical ShockIon Reflection at Super-critical Shocks

Energization of reflected ions by the
motional E-field provides the effective"viscous" heating in the sense that thedownstream pressure is dominated by
the reflected ions.

Johlander+2016, PRLParallel and Perpendicular Shocks

Electron Acceleration Diagramhigh MA

Saturn’s bow shock [e.g., Masters+2013, 2016]
shock surfing (Buneman) + Weibel/Reconnection?
[e.g., Hoshino & Shimada 2002, Matsumoto+2015, 2017, Bohdan+2019]

Earth’s bow shock[e.g., Oka+2006, Amano+2020]
intercluster shocks?

low MA
Q-paraQ-perpc.f., Amano & Hoshino 2010

Kobzar+2021

Multi-scale Plasma Waves at High-β Shock•••

MA = 6.1, MS = 3, mi/me = 100, βi = βe = 2.5
Rippling (AIC/Mirror), whistlers, firehose, ES (ion acoustic or Langmuir) waves…
A clear power-law tail is identified for the downstream spectrum.

Kobzar+2021

SSDA and multiple-SDA

Guo+2014

Ha+2021, arXiv:2102.03042

Amano & Hoshino 2007

Injection into SDA/SSDA

SDAには初期にある程度⼤きなエネルギーを持った電⼦が必要→ 別のメカニズムでの加熱・加速

1012 particles in8800 x 768 x 768 cells(55di x 4.8di x 4.8di)

3D PIC on the K computer (Matsumoto+2017, PRL)

• mi/me=64,• MA=20,• θBn=74

Weibel turbulence

B u nem an w avesc.f., McClements+2001, Hoshino & Shimada 2002

Shock Surfing Acceleration in 3D
downstream

upstream

Buneman-generated electrostatic
waves in fully 3D(mi/me = 64, theta = 74, Ma=20)
3D PIC on the K computer (Matsumoto+2017, PRL)

3D PIC on the K computer (Matsumoto+2017, PRL)

Shock Drift Acceleration
drift

surfing

Theoretical energy gain via SDA:

3D PIC on the K computer (Matsumoto+2017, PRL)

Scattering by Weibel Turbulence

The strong Weibel turbulence play
the role for the pitch-angle
scattering.
More effective confinement of theparticles in the acceleration region
becomes possible.

Spontaneous Magnetic Reconnection of Weibel-Generated
Magnetic field

Upstream Flow Energy↓
Generation of B-field↓
Magnetic Reconnection↓Particle Acceleration
Ma=45, mi/me=225
Matsutmoto+(Science, 2015), Bohdan+(2020)

Nishigai & Amano 2021

Transition from Classical to Weibel-dominated shock
Weibel-likesound Mach number

AIC-like

Alfven Mach number••••

Alfven Mach number

The instability property transitions continuously from AIC (γ/Ωi < 1) at lower Mach numbers to Weibel (γ/Ωi » 1)
regimes at higher Mach numbers.
Typical bow shock parameters correspond to AIC-like (or rippling) instability, while young SNR shocks will likely bedominated by more violent Weibel-like instability.
The Weibel-like instability might become dominant under exceptional solar wind conditions with very small
magnetic fields and low temperatures. [c.f., Sundberg+2017, Madanian+2020]
Efficiency and roles of magnetic reconnection are still uncertain. [Bohdan+2020]

Electron Acceleration Diagramhigh MA

Saturn’s bow shock [e.g., Masters+2013, 2016]
shock surfing (Buneman) + Weibel/Reconnection?
[e.g., Hoshino & Shimada 2002, Matsumoto+2015, 2017, Bohdan+2019]

Earth’s bow shock[e.g., Oka+2006, Amano+2020]
intercluster shocks?

low MA
Q-paraQ-perpc.f., Amano & Hoshino 2010

結論
• 衝撃波電⼦加速問題の解決への道筋が（おぼろげながら）⾒えてきた．
• 拡散係数（散乱効率）が最も重要な量であると同時に最も⼤きな不定性でもある．
ただし直接観測や数値シミュレーションで詰めていくことは可能．
• 別のアプローチ（レーザー実験・天⽂観測）も相補的に使える可能性あり．
Fiuza+2020 (Laser Experiments @ NIF)

Tanaka+2018 (NuSTAR obs for W49B)