Electron heating in shocks and reconnection · Lorenzo Sironi (Columbia) with: Xinyi Guo & Michael...
Transcript of Electron heating in shocks and reconnection · Lorenzo Sironi (Columbia) with: Xinyi Guo & Michael...
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11th Plasma Kinetics Working Meeting, Vienna, July 23rd 2018 Lorenzo Sironi (Columbia)
with: Xinyi Guo & Michael Rowan (Harvard), Aaron Tran (Columbia)
Electron heating in shocks and reconnection
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! Rankine-Hugoniot relation only determines the mean post-shock temperature.! How is the shock heating distributed between electrons and protons?
! More massive protons dominate energy flux. Naively, one would expect
! Electrons will be at least heated adiabatically through shock compression
! Can collisionless processes heat electrons beyond adiabatic? What is the mechanism and how does it depend on flow conditions?
Electron Heating in ShocksThe physical motivation
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elec
tron
tem
pera
ture
(keV
)
(Markevitch 05)
adiabatic compression+Coulomb
elec
tron
tem
pera
ture
(keV
)
(Russell+12)
In some merger shocks in galaxy clusters (high beta), electrons are heated to equipartition.
elec
tron
tem
pera
ture
(keV
)
(Russell+12)
But not always!
High-beta ShocksThe observational motivation
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Simulation Setup
Particle-in-Cell Code: TRISTAN-MP (Buneman 93, Spitkovsky 05)
downstream upstreamshock
The simulation is performed in the post-shock (downstream) rest frame
x
y
u0
Te=Ti
vsh
B0
θB
2D simulations of high beta, low Mach number shocks
The electron and ion distributions are initialized as drifting Maxwellians
Magnetic obliquity θB =90 deg
[mass ratio mi/me]
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Shock Structure (protons)Reference run with Ms=3, β=16 and θB=90˚ (perp shock)
The proton temperature anisotropy drives strong long-wavelength magnetic waves (mirror and proton cyclotron modes) in the downstream.
(Guo, Sironi, Narayan 2017a)
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Shock Structure (electrons)Electron-driven waves and entropy increase
• The electron temperature anisotropy at the shock drives short-wavelength (whistler) waves.• Two preferential locations of entropy generation: (1) at the shock, and (2) where proton waves grow.
Te,? / B
Te,k / (n/B)2
Double adiabatic:
Flux freezing:
B / n
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Electron heatingTwo heat reservoirs, one transfer mechanism
dq
cold
hot
What are the two heat reservoirs?
Te,? / B
Te,k / (n/B)2
As a result of shock compression coupled with flux freezing, B increases → Te,⊥ increases.
From flux freezing, Te,|| stays the same.
What is the mediator of dq?We need a mechanism to scatter electrons in pitch angle, so that Te,|| increases at the expense of Te,⊥ (i.e., a mechanism to break adiabatic invariance). Whistler waves! (self-consistently generated due to Te,⊥>Te ||)
Model for entropy increase: Two ingredients:(a) temperature anisotropy(b) breaking of adiabatic invariance
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Whistler wavesWhistlers are present where entropy increases
[2] [1] In [1], shock compression induces electron anisotropy, that triggers whistler waves.
power spectrumspace/time plot
In [2], field amplification by proton modes induces electron anisotropy, that triggers whistlers.
power spectrumspace/time plot
whistler mode
(Guo, Sironi, Narayan 2017a)
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Model vs simulationThe heating model agrees well with PIC results
Reference run with Ms=3, β=16, θB=90˚ (perp shock) and mi/me=49
Dependence on mass ratio
The entropy increase is remarkably independent of mass ratio.
Our model correctly predicts both the location and magnitude of
electron entropy increase.
(Guo, Sironi, Narayan 2017a)
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Te2 � Te,ad
Te0' 0.044Ms (Ms � 1)
Dependence on beta and MachThe efficiency of irreversible heating is higher at larger Ms
The post-shock temperature is above the 3D adiabatic expectation by
[caveat: we expect some dependence on the field obliquity, with θB=90˚ giving a lower limit in electron entropy increase]
(Guo, Sironi, Narayan 2017b)
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Low-beta ShocksThe observational motivation
Evidence of non-adiabatic electron heating in Earth and Saturn bow shocks (beta~1).
(Vink+15)
adiabatic
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Low-beta ShocksElectron-proton temperature ratio
sonic Mach Alfvenic Mach Magnetosonic Mach
• Lower beta shocks show a larger deviation from the adiabatic expectation.
• Evidence for a “universal” electron-to-proton temperature ratio as a function of the magnetosonic Mach number.
adiabatic
adiabatic
adiabatic
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• Electron-to-proton temperature ratio is nearly independent of mass ratio.
Dimensionality and mass ratio1D not sufficient; 2D ok, independently of the mass ratio
• 1D simulations are insufficient to capture the relevant physics, as well as 2D with out-of-plane field.• 2D with in-plane background field is consistent with 3D.
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Hints on the heating physicsD
ensi
tyT e
/Tp
Bi-Maxwellian entropy
• Substantial electron heating only when the 2D simulation box is wider than ~ 1 proton Larmor radius.
• Electron heating happens in “cycles”.
Width of the simulation box
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Hints on the heating physics
Density
Shock reformation and rippling
Bi-Maxwellian entropy
• Electron heating cycles are correlated with the shock reformation and rippling.
• Evidence for electron-scale waves during heating episodes, with component of E along the background B. No ID yet.
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Electron and proton heating in trans-relativistic reconnection
(sigma~1)
� =B2
0
4⇡w� =
8⇡n0kBT
B20
As a function of beta, sigma, and the guide field strength
Bg/B0
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Dependence on betaσ=0.1 β=0.01, realistic mass ratio, ZERO guide field
Density
• Low beta: the outflow is fragmented into a number of secondary plasmoids.
(Rowan, LS & Narayan 2017)
B0
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Dependence on beta
σ=0.1 β=2, realistic mass ratio, ZERO guide field
(Rowan, LS & Narayan 2017)
Density
Density
• Low beta: the outflow is fragmented into a number of secondary plasmoids.
• High beta: smooth outflow, no secondary plasmoids.
(Rowan, LS & Narayan 2017)
σ=0.1 β=0.01, realistic mass ratio, ZERO guide field
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Characterization of heating• Blue: upstream region, starting above the current sheet.
• Red: upstream region, starting below the current sheet.
• White/yellow: mix of blue and red particles → downstream region.
Upstream Downstream
Define total electron heating as
alternatively,
and then separate adiabatic and irreversible contributions.
θ=dimensionless temperature.
υ=internal energy per unit rest mass.
(Shay et al. 2014)
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Electron heating efficiency (Bg=0)Electron-to-overall heating ratio
• Electrons are heated less then protons (for σ≪1, the ratio is ~0.2). See also Werner+18.
• Comparable heating efficiencies:- at high beta, when both species already start relativistically hot.- in ultra-relativistic (σ≫1) reconnection.
(Rowan, LS & Narayan 2017)
Qe
Qe +Qp
The curves extend up to βmax~1/(4σ)
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No dependence on the upstream Te/Ti
Adiabatic heating Irreversible heating
Ele
ctro
nsP
roto
ns
• Adiabatic heating (obviously) dependent on the temperature ratio.
• Irreversible heating nearly independent of the temperature ratio.
(Rowan, LS & Narayan 2017)
σ=0.3
MTe
,ad
MTi
,ad
MTe
,irr
MTi
,irr
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Dependence on Bg/B0
Bg/B0=0.0
Bg/B0=0.1
Bg/B0=0.3
Bg/B0=0.7
σ=0.3 β=0.003, realistic mass ratio
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Dependence on Bg/B0
Electron-to-overall heating ratio (σ=0.1)
• At low beta: electrons are heated less then protons for Bg/B0<1, but most of the dissipated energy (~90-95%) goes into electrons for Bg/B0>1.
(Rowan, LS & Narayan, in prep)
Qe
Qe +Qp
The curves extend up to βmax~1/(4σ)
Bg/B0
• In agreement with non-relativistic PIC (Tenbarge+14) and GK calculations (Numata & Loureiro 15, Kawazura+ today).
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SummaryElectron heating in high-beta low Mach number shocks:
Electron heating in trans-relativistic reconnection:
• For Bg/B0=0, electrons are heated less then protons (for σ≪1, the ratio is ~0.2).
Comparable heating efficiencies at high beta, when both species already start relativistically hot.
• At low beta: electrons are heated less then protons for Bg/B0<1, but most of the dissipated energy (~90-95%) goes into electrons for Bg/B0>1.