Electron Heating in 2D Particle-in-cell Simulations of Quasi-perpendicular Low-beta Shocks

Tran, Aaron; Sironi, Lorenzo

doi:10.3847/1538-4357/ad1f69

Title: Electron Heating in 2D Particle-in-cell Simulations of Quasi-perpendicular Low-beta Shocks

Abstract

Abstract We measure the thermal electron energization in 1D and 2D particle-in-cell simulations of quasi-perpendicular, low-beta ( β _p = 0.25) collisionless ion–electron shocks with mass ratio m _i / m _e = 200, fast Mach number $M_{ms} = 1$ –4, and upstream magnetic field angle θ _Bn = 55°–85° from the shock normal $\hat{n}$ . It is known that shock electron heating is described by an ambipolar, B -parallel electric potential jump, Δ ϕ _∥ , that scales roughly linearly with the electron temperature jump. Our simulations have $Δ ϕ_{∥} / (0.5 m_{i} {u_{sh}}^{2}) \sim 0.1$ –0.2 in units of the pre-shock ions’ bulk kinetic energy, in agreement with prior measurements and simulations. Different ways to measure ϕ _∥ , including the use of de Hoffmann–Teller frame fields, agree to tens-of-percent accuracy. Neglecting off-diagonal electron pressure tensor terms can lead to a systematic underestimate of ϕ _∥ in our low- β _p shocks. We further focus on two θ _Bn = 65° shocks: a $M_{s} = 4$ ( $M_{A} = 1.8$ ) case with a long, 30 d _i precursor of whistler waves along $\hat{n}$ , and a $M_{s} = 7$ ( $M_{A} = 3.2$ ) case with a shorter, 5 d _i precursor of whistlers oblique to both $\hat{n}$ and B ; d _i is the ion skin depth. Within the precursors, ϕ _∥ has a secular rise toward the shock along multiple whistler wavelengths and also has localized spikes within magnetic troughs. In a 1D simulation of the $M_{s} = 4$ , θ _Bn = 65° case, ϕ _∥ shows a weak dependence on the electron plasma-to-cyclotron frequency ratio ω _pe /Ω _ce , and ϕ _∥ decreases by a factor of 2 as m _i / m _e is raised to the true proton–electron value of 1836.

Authors:

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Publication Date:: Tue Apr 02 00:00:00 EDT 2024

Sponsoring Org.:: USDOE

OSTI Identifier:: 2332919

Grant/Contract Number:: SC0023015

Resource Type:: Published Article

Journal Name:: The Astrophysical Journal

Additional Journal Information:: Journal Name: The Astrophysical Journal Journal Volume: 965 Journal Issue: 1; Journal ID: ISSN 0004-637X

Publisher:: American Astronomical Society

Country of Publication:: United States

Language:: English

Citation Formats


                    Tran, Aaron, and Sironi, Lorenzo. Electron Heating in 2D Particle-in-cell Simulations of Quasi-perpendicular Low-beta Shocks.  United States: N. p., 2024. 
Web.  doi:10.3847/1538-4357/ad1f69.

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                    Tran, Aaron, & Sironi, Lorenzo. Electron Heating in 2D Particle-in-cell Simulations of Quasi-perpendicular Low-beta Shocks.  United States.  https://doi.org/10.3847/1538-4357/ad1f69

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                    Tran, Aaron, and Sironi, Lorenzo. Tue .  
"Electron Heating in 2D Particle-in-cell Simulations of Quasi-perpendicular Low-beta Shocks".  United States.  https://doi.org/10.3847/1538-4357/ad1f69.

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@article{osti_2332919,

  title        = {Electron Heating in 2D Particle-in-cell Simulations of Quasi-perpendicular Low-beta Shocks},

  author       = {Tran, Aaron and Sironi, Lorenzo},

  abstractNote = {Abstract We measure the thermal electron energization in 1D and 2D particle-in-cell simulations of quasi-perpendicular, low-beta ( β p = 0.25) collisionless ion–electron shocks with mass ratio m i / m e = 200, fast Mach number M ms = 1 –4, and upstream magnetic field angle θ Bn = 55°–85° from the shock normal n ˆ . It is known that shock electron heating is described by an ambipolar, B -parallel electric potential jump, Δ ϕ ∥ , that scales roughly linearly with the electron temperature jump. Our simulations have Δ ϕ ∥ / ( 0.5 m i u sh 2 ) ∼ 0.1 –0.2 in units of the pre-shock ions’ bulk kinetic energy, in agreement with prior measurements and simulations. Different ways to measure ϕ ∥ , including the use of de Hoffmann–Teller frame fields, agree to tens-of-percent accuracy. Neglecting off-diagonal electron pressure tensor terms can lead to a systematic underestimate of ϕ ∥ in our low- β p shocks. We further focus on two θ Bn = 65° shocks: a M s = 4 ( M A = 1.8 ) case with a long, 30 d i precursor of whistler waves along n ˆ , and a M s = 7 ( M A = 3.2 ) case with a shorter, 5 d i precursor of whistlers oblique to both n ˆ and B ; d i is the ion skin depth. Within the precursors, ϕ ∥ has a secular rise toward the shock along multiple whistler wavelengths and also has localized spikes within magnetic troughs. In a 1D simulation of the M s = 4 , θ Bn = 65° case, ϕ ∥ shows a weak dependence on the electron plasma-to-cyclotron frequency ratio ω pe /Ω ce , and ϕ ∥ decreases by a factor of 2 as m i / m e is raised to the true proton–electron value of 1836.},

  doi          = {10.3847/1538-4357/ad1f69},

  journal      = {The Astrophysical Journal},

  number       = 1,

  volume       = 965,

  place        = {United States},

  year         = {Tue Apr 02 00:00:00 EDT 2024},

  month        = {Tue Apr 02 00:00:00 EDT 2024}

}

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Title: Electron Heating in 2D Particle-in-cell Simulations of Quasi-perpendicular Low-beta Shocks

Abstract

Citation Formats

Ion heating in oblique low-Mach number shocks journal, October 1997

The structure of perpendicular bow shocks journal, July 1982

Quasi-adiabatic and Stochastic Heating and Particle Acceleration at Quasi-perpendicular Shocks journal, November 2020

Electron dynamics in two‐ and one‐dimensional oblique supercritical collisionless magnetosonic shocks journal, April 1994

A review of the physics of electron heating at collisionless shocks journal, January 1995

Low-Frequency Instabilities in Magnetic Pulses journal, November 1971

Low Frequency Waves at and Upstream of Collisionless Shocks book, February 2016

Simulations of high Mach number perpendicular shocks with resistive electrons journal, August 1986

Electron velocity distributions near the Earth's bow shock journal, January 1983

Electron heating and phase space signatures at strong and weak quasi-perpendicular shocks journal, February 1998

Mach number dependence of electron heating in high Mach number quasiperpendicular shocks journal, April 2010

Generation of High-frequency Whistler Waves in the Earth’s Quasi-perpendicular Bow Shock journal, September 2021

Microinstabilities associated with a high Mach number, perpendicular bow shock journal, January 1984

Numerical simulation of electron distributions upstream and downstream of high Mach number quasi‐perpendicular collisionless shocks journal, August 2008

The structure of oblique subcritical bow shocks: ISEE 1 and 2 observations journal, January 1984

Steepening of kinetic magnetosonic waves into shocklets: Simulations and consequences for planetary shocks and comets journal, January 1990

Quasi-perpendicular shocks: Length scale of the cross-shock potential, shock reformation, and implication for shock surfing journal, January 2003

Relativistic Electrons Produced by Foreshock Disturbances Observed Upstream of Earth’s Bow Shock journal, November 2016

Electron dynamics and cross-shock potential at the quasi-perpendicular Earth's bow shock: ELECTRON DYNAMICS AND SHOCK POTENTIAL journal, September 2007

Spacecraft Observations and Theoretical Understanding of Slow Electron Holes journal, October 2021

The resolved layer of a collisionless, high β, supercritical, quasi-perpendicular shock wave: 3. Vlasov electrodynamics journal, January 1986

Adaptation of the de Hoffmann–Teller frame for quasi-perpendicular collisionless shocks journal, March 2015

Magnetic reconnection and kinetic waves generated in the Earth's quasi-parallel bow shock journal, September 2020

The structure of magneto-hydrodynamic shock waves journal, December 1955

Electron cross talk and asymmetric electron distributions near the Earth's bowshock journal, March 2012

Observational Evidence for Stochastic Shock Drift Acceleration of Electrons at the Earth’s Bow Shock journal, February 2020

Preacceleration in the Electron Foreshock. I. Electron Acoustic Waves journal, June 2022

Cross‐Shock Electrostatic Potentials at Mars Inferred From MAVEN Measurements journal, March 2021

Electron dynamics and whistler waves at quasi‐perpendicular shocks journal, August 1995

Electron‐Scale Reconnection in Three‐Dimensional Shock Turbulence journal, August 2022

Dispersive Nature of High Mach Number Collisionless Plasma Shocks: Poynting Flux of Oblique Whistler Waves journal, January 2012

The Discrepancy Between Simulation and Observation of Electric Fields in Collisionless Shocks journal, January 2021

Electron Bulk Acceleration and Thermalization at Earth’s Quasiperpendicular Bow Shock journal, May 2018

Solitary Waves Across Supercritical Quasi‐Perpendicular Shocks journal, June 2018

The field‐aligned flow approximation for electrons within layers possessing a normal mass flux: A corollary to the deHoffmann‐Teller Theorem journal, December 1987

MMS Observations of Electrostatic Waves in an Oblique Shock Crossing journal, November 2018

ARTEMIS Observations of Plasma Waves in Laminar and Perturbed Interplanetary Shocks journal, June 2021

Electron Scattering by High-frequency Whistler Waves at Earth’s Bow Shock journal, June 2017

Electron temperature and de Hoffmann-Teller potential change across the Earth's bow shock: New results from ISEE 1 journal, September 2000

Subcritcal dispersive shock waves upstream of planetary bow shocks and at comet Giacobini‐Zinner journal, October 1988

A parametric survey of the first critical Mach number for a fast MHD shock journal, December 1984

Whistler critical Mach number and electron acceleration at the bow shock: Geotail observation journal, December 2006

Magnetic structure of the low beta, quasi‐perpendicular shock journal, September 1993

Electron acceleration at quasi-perpendicular shocks in sub- and supercritical regimes: 2D and 3D simulations journal, October 2018

Structure of the quasi-perpendicular laminar bow shock journal, February 1975

Electron Resonant Interaction With Whistler Waves Around Foreshock Transients and the Bow Shock Behind the Terminator journal, February 2022

An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas journal, August 1983

Transition scale at quasiperpendicular collisionless shocks: Full particle electromagnetic simulations journal, June 2006

Realistic Electron Diffusion Rates and Lifetimes Due to Scattering by Electron Holes journal, August 2021

Upstream whistlers generated by protons reflected from a quasi‐perpendicular shock journal, May 1997

Electron Heating in Perpendicular Low-beta Shocks journal, September 2020

Electron ‐ whistler interaction at the Earth's bow shock: 2. Electron pitch angle diffusion journal, August 1993

The plasma physics of shock acceleration journal, December 1991

On the noncoplanarity of the magnetic field within a fast collisionless shock journal, March 1987

Electron acceleration and heating influenced by whistler wave packets at quasi‐parallel shock waves journal, July 2002

Particle acceleration at oblique shock fronts journal, August 1989

Nonstationarity of strong collisionless quasiperpendicular shocks: Theory and full particle numerical simulations journal, April 2002

Electron heating in quasi‐perpendicular shocks: A Monte Carlo Simulation journal, September 1990

Strong reconnection electric fields in shock-driven turbulence journal, April 2022

Whistler waves associated with weak interplanetary shocks journal, November 2012

Standing waves at low Mach number laminar bow shocks journal, February 1975

Model for the partition of temperature between electrons and ions across collisionless, fast mode shocks journal, December 2000

Electron velocity distributions near interplantary shocks journal, January 1983

Electron heating and the potential jump across fast mode shocks journal, January 1988

Discontinuous Galerkin algorithms for fully kinetic plasmas journal, January 2018

Evaluating the deHoffmann‐Teller Cross‐Shock Potential at Real Collisionless Shocks journal, August 2021

Observations of Energized Electrons in the Martian Magnetosheath journal, April 2021

Non-adiabatic electron behaviour due to short-scale electric field structures at collisionless shock waves journal, January 2013

Microturbulence in the electron cyclotron frequency range at perpendicular supercritical shocks: ELECTRON CYCLOTRON DRIFT INSTABILITY journal, May 2013

Heating and acceleration of electrons through the whistler precursor in 1-D and 2-D oblique shocks journal, January 1995

Plasma heating through a supercritical oblique collisionless shock journal, April 1987

Effect of strong thermalization on shock dynamical behavior journal, January 2005

Numerical studies of electron dynamics in oblique quasi‐perpendicular collisionless shock waves journal, June 1991

Intense Whistler-mode Waves at Foreshock Transients: Characteristics and Regimes of Wave−Particle Resonant Interaction journal, February 2023

Modified two-stream instability at perpendicular collisionless shocks: Full particle simulations journal, March 2012

Electron ‐ whistler interaction at the Earth's bow shock: 1. Whistler instability journal, August 1993

Direct evidence of nonstationary collisionless shocks in space plasmas journal, February 2019

Ion heating in oblique low-Mach number shocks
journal, October 1997

The structure of perpendicular bow shocks
journal, July 1982

Quasi-adiabatic and Stochastic Heating and Particle Acceleration at Quasi-perpendicular Shocks
journal, November 2020

Electron dynamics in two‐ and one‐dimensional oblique supercritical collisionless magnetosonic shocks
journal, April 1994

A review of the physics of electron heating at collisionless shocks
journal, January 1995

Low-Frequency Instabilities in Magnetic Pulses
journal, November 1971

Low Frequency Waves at and Upstream of Collisionless Shocks
book, February 2016

Simulations of high Mach number perpendicular shocks with resistive electrons
journal, August 1986

Electron velocity distributions near the Earth's bow shock
journal, January 1983

Electron heating and phase space signatures at strong and weak quasi-perpendicular shocks
journal, February 1998

Mach number dependence of electron heating in high Mach number quasiperpendicular shocks
journal, April 2010

Generation of High-frequency Whistler Waves in the Earth’s Quasi-perpendicular Bow Shock
journal, September 2021

Microinstabilities associated with a high Mach number, perpendicular bow shock
journal, January 1984

Numerical simulation of electron distributions upstream and downstream of high Mach number quasi‐perpendicular collisionless shocks
journal, August 2008

The structure of oblique subcritical bow shocks: ISEE 1 and 2 observations
journal, January 1984

Steepening of kinetic magnetosonic waves into shocklets: Simulations and consequences for planetary shocks and comets
journal, January 1990

Quasi-perpendicular shocks: Length scale of the cross-shock potential, shock reformation, and implication for shock surfing
journal, January 2003

Relativistic Electrons Produced by Foreshock Disturbances Observed Upstream of Earth’s Bow Shock
journal, November 2016

Electron dynamics and cross-shock potential at the quasi-perpendicular Earth's bow shock: ELECTRON DYNAMICS AND SHOCK POTENTIAL
journal, September 2007

Spacecraft Observations and Theoretical Understanding of Slow Electron Holes
journal, October 2021

The resolved layer of a collisionless, high β, supercritical, quasi-perpendicular shock wave: 3. Vlasov electrodynamics
journal, January 1986

Adaptation of the de Hoffmann–Teller frame for quasi-perpendicular collisionless shocks
journal, March 2015

Magnetic reconnection and kinetic waves generated in the Earth's quasi-parallel bow shock
journal, September 2020

The structure of magneto-hydrodynamic shock waves
journal, December 1955

Electron cross talk and asymmetric electron distributions near the Earth's bowshock
journal, March 2012

Observational Evidence for Stochastic Shock Drift Acceleration of Electrons at the Earth’s Bow Shock
journal, February 2020

Preacceleration in the Electron Foreshock. I. Electron Acoustic Waves
journal, June 2022

Cross‐Shock Electrostatic Potentials at Mars Inferred From MAVEN Measurements
journal, March 2021

Electron dynamics and whistler waves at quasi‐perpendicular shocks
journal, August 1995

Electron‐Scale Reconnection in Three‐Dimensional Shock Turbulence
journal, August 2022

Dispersive Nature of High Mach Number Collisionless Plasma Shocks: Poynting Flux of Oblique Whistler Waves
journal, January 2012

The Discrepancy Between Simulation and Observation of Electric Fields in Collisionless Shocks
journal, January 2021

Electron Bulk Acceleration and Thermalization at Earth’s Quasiperpendicular Bow Shock
journal, May 2018

Solitary Waves Across Supercritical Quasi‐Perpendicular Shocks
journal, June 2018

The field‐aligned flow approximation for electrons within layers possessing a normal mass flux: A corollary to the deHoffmann‐Teller Theorem
journal, December 1987

MMS Observations of Electrostatic Waves in an Oblique Shock Crossing
journal, November 2018

ARTEMIS Observations of Plasma Waves in Laminar and Perturbed Interplanetary Shocks
journal, June 2021

Electron Scattering by High-frequency Whistler Waves at Earth’s Bow Shock
journal, June 2017

Electron temperature and de Hoffmann-Teller potential change across the Earth's bow shock: New results from ISEE 1
journal, September 2000

Subcritcal dispersive shock waves upstream of planetary bow shocks and at comet Giacobini‐Zinner
journal, October 1988

A parametric survey of the first critical Mach number for a fast MHD shock
journal, December 1984

Whistler critical Mach number and electron acceleration at the bow shock: Geotail observation
journal, December 2006

Magnetic structure of the low beta, quasi‐perpendicular shock
journal, September 1993

Electron acceleration at quasi-perpendicular shocks in sub- and supercritical regimes: 2D and 3D simulations
journal, October 2018

Structure of the quasi-perpendicular laminar bow shock
journal, February 1975

Electron Resonant Interaction With Whistler Waves Around Foreshock Transients and the Bow Shock Behind the Terminator
journal, February 2022

An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas
journal, August 1983

Transition scale at quasiperpendicular collisionless shocks: Full particle electromagnetic simulations
journal, June 2006

Realistic Electron Diffusion Rates and Lifetimes Due to Scattering by Electron Holes
journal, August 2021

Upstream whistlers generated by protons reflected from a quasi‐perpendicular shock
journal, May 1997

Electron Heating in Perpendicular Low-beta Shocks
journal, September 2020

Electron ‐ whistler interaction at the Earth's bow shock: 2. Electron pitch angle diffusion
journal, August 1993

The plasma physics of shock acceleration
journal, December 1991

On the noncoplanarity of the magnetic field within a fast collisionless shock
journal, March 1987

Electron acceleration and heating influenced by whistler wave packets at quasi‐parallel shock waves
journal, July 2002

Particle acceleration at oblique shock fronts
journal, August 1989

Nonstationarity of strong collisionless quasiperpendicular shocks: Theory and full particle numerical simulations
journal, April 2002

Electron heating in quasi‐perpendicular shocks: A Monte Carlo Simulation
journal, September 1990

Strong reconnection electric fields in shock-driven turbulence
journal, April 2022

Whistler waves associated with weak interplanetary shocks
journal, November 2012

Standing waves at low Mach number laminar bow shocks
journal, February 1975

Model for the partition of temperature between electrons and ions across collisionless, fast mode shocks
journal, December 2000

Electron velocity distributions near interplantary shocks
journal, January 1983

Electron heating and the potential jump across fast mode shocks
journal, January 1988

Discontinuous Galerkin algorithms for fully kinetic plasmas
journal, January 2018

Evaluating the deHoffmann‐Teller Cross‐Shock Potential at Real Collisionless Shocks
journal, August 2021

Observations of Energized Electrons in the Martian Magnetosheath
journal, April 2021

Non-adiabatic electron behaviour due to short-scale electric field structures at collisionless shock waves
journal, January 2013

Microturbulence in the electron cyclotron frequency range at perpendicular supercritical shocks: ELECTRON CYCLOTRON DRIFT INSTABILITY
journal, May 2013

Heating and acceleration of electrons through the whistler precursor in 1-D and 2-D oblique shocks
journal, January 1995

Plasma heating through a supercritical oblique collisionless shock
journal, April 1987

Effect of strong thermalization on shock dynamical behavior
journal, January 2005

Numerical studies of electron dynamics in oblique quasi‐perpendicular collisionless shock waves
journal, June 1991

Intense Whistler-mode Waves at Foreshock Transients: Characteristics and Regimes of Wave−Particle Resonant Interaction
journal, February 2023

Modified two-stream instability at perpendicular collisionless shocks: Full particle simulations
journal, March 2012

Electron ‐ whistler interaction at the Earth's bow shock: 1. Whistler instability
journal, August 1993

Direct evidence of nonstationary collisionless shocks in space plasmas
journal, February 2019

Whistler Waves in the Foot of Quasi‐Perpendicular Supercritical Shocks
journal, May 2022

The electron foreshock at high-Mach-number non-relativistic oblique shocks
journal, May 2022

Electron Injection by Whistler Waves in Non-Relativistic Shocks
journal, May 2011