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

Yuan, Xingqiu; Cairns, Iver H.; Robinson, P. A.

doi:10.1029/2008ja013268

Cited by 9 publications

(8 citation statements)

References 48 publications

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“…Simulated electron velocity distribution in the shock normal frame upstream of a shock with θ bn = 85°, Alfvén Mach number M A = 7.7, and sonic Mach number M s = 5.0, taken from Yuan et al [2008]. Dash‐dotted and dotted lines show the loss cones defined by the shock's magnetic mirror with and without, respectively, the cross‐shock potential.…”

Section: Reflection Resultsmentioning

confidence: 99%

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Type II radio bursts: 1. New entirely analytic formalism for the electron beams, Langmuir waves, and radio emission

Schmidt

Cairns

2012

J. Geophys. Res.

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[1] Type II radio bursts drift in frequency as shock waves and coronal mass ejections (CMEs) move through the Sun's corona and the solar wind. This paper extends the theoretical models for type II radio bursts of Knock et al. (2001Knock et al. ( , 2003, Knock and Cairns (2005), Cairns and Knock (2006) and Schmidt and Gopalswamy (2008). The theory treats the acceleration of electrons at the shock, formation of electron beams, growth of Langmuir waves, and conversion of Langmuir energy into radiation. An entirely analytical and more general formalism is developed, which includes kappa electron velocity distribution functions for the plasma electrons and the shock-reflected electron beam. The radiation model also includes the plateauing of the electron beam, which releases energy for the Langmuir waves. This paper has two parts. First, the new entirely analytical formalism is presented. Second, first numerical results for synthetic radio images and synthetic dynamic spectra are discussed, gained by applying our radiation model to MHD simulations of a shock driven by a CME. The results are compared with earlier analytic approaches. This work is also applicable to other shock-related emissions in space and astrophysical plasmas.Citation: Schmidt, J. M., and I. H. Cairns (2012), Type II radio bursts: 1. New entirely analytic formalism for the electron beams, Langmuir waves, and radio emission,

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Section: Reflection Resultsmentioning

confidence: 99%

“…Simulated electron velocity distribution in the shock normal frame upstream of a shock with q bn = 85 , Alfvén Mach number M A = 7.7, and sonic Mach number M s = 5.0, taken fromYuan et al [2008]…”

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confidence: 99%

Type II radio bursts: 1. New entirely analytic formalism for the electron beams, Langmuir waves, and radio emission

Schmidt

Cairns

2012

J. Geophys. Res.

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“…(corresponding to reflected speeds v k,2^0 ) in the shock reference frame can be reflected into the foreshock region, giving rise to a modified loss cone distribution [Wu, 1984;Fitzenreiter et al, 1990;Yuan et al, 2008]. Here the subscripts u and d denote upstream and downstream from the bow shock, respectively, in the shock normal frame, while 1 and 2 refer to the incident and reflected electrons in the upstream.…”

Section: Generation Of Unstable Electron Beamsmentioning

confidence: 99%

“…Upon reaching the bow shock, some solar wind electrons are magnetically reflected. Conservation of energy and magnetic moment imply that only those electrons (incident on the bow shock) whose initial perpendicular and parallel speeds satisfy (corresponding to reflected speeds , 2 ≳ 0) in the shock reference frame can be reflected into the foreshock region, giving rise to a modified loss cone distribution [ Wu , 1984; Fitzenreiter et al , 1990; Yuan et al , 2008]. Here the subscripts u and d denote upstream and downstream from the bow shock, respectively, in the shock normal frame, while 1 and 2 refer to the incident and reflected electrons in the upstream.…”

Section: Introductionmentioning

confidence: 99%

Terrestrial foreshock Langmuir waves: STEREO observations, theoretical modeling, and quasi‐linear simulations

Malaspina

Cairns

et al. 2009

J. Geophys. Res.

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[1] Langmuir waves in the terrestrial electron foreshock are investigated using observations from the STEREO spacecraft, theoretical modeling, and quasi-linear simulations. Emphases are placed on spatial variations of Langmuir field strength with distance between the spacecraft and the tangent point and on the effects of ambient density fluctuations on these variations. The STEREO mission provides new observations of foreshock Langmuir waves at distances more than twice as far from Earth as previously observed. Based on established geometric properties of the foreshock region, two methods are developed for separating Langmuir waves of foreshock origin from those of solar and/or heliospheric origins. The observed maximum foreshock Langmuir field strength falls with distance via a power law with an exponent À1.01 ± 0.12. The theory and simulations predict field strengths and power law spatial variations in field strengths that are consistent with the observations when scattering of Langmuir waves by density fluctuations is included. The power law exponents predicted by both theory and simulations fall within the uncertainty of the observations for the typical solar wind conditions observed but differ by a factor of %1.5 from simulations that assume density homogeneity. This indicates that density fluctuations play an important role in the beamLangmuir wave dynamics in the foreshock.

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“…Analytical theories and numerical simulations have shown that at quasi-perpendicular shocks, electrons can be accelerated through shock-drift acceleration (Wu 1984;Krauss-Varban et al 1989;Yuan et al 2008;Park et al 2012). In this mechanism, charged particles drift because of the gradient in the magnetic field at the shock front.…”

Section: Introductionmentioning

confidence: 99%

The Acceleration of Electrons at Collisionless Shocks Moving Through a Turbulent Magnetic Field

Guo

Giacalone

2015

ApJ

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We perform a numerical-simulation study of the acceleration of electrons at shocks that propagate through a prespecified, kinematically defined turbulent magnetic field. The turbulence consists of broadband magnetic fluctuations that are embedded in the plasma and cover a range of wavelengths, the smallest of which is larger than the gyroradii of electrons that are initially injected into the system. We find that when the variance of the turbulent component of the upstream magnetic field is sufficiently large-s 2 ∼ 10 B 0 2 , where B 0 is the strength of the background magnetic field-electrons can be efficiently accelerated at a collisionless shock regardless of the orientation of the mean upstream magnetic field relative to the shock-normal direction. Since the local angle between the incident magnetic-field vector and the shock-normal vector can be quite large, electrons can be accelerated through shock-drift acceleration at the shock front. In the upstream region, electrons are mirrored back to the shock front leading to multiple shock encounters. Eventuallythe accelerated electrons are energetic enough that their gyroradii are of the same order as the wavelength of waves that are included in our description of the turbulent magnetic field. Our results are consistent with recent in situ observations at Saturn's bow shock. Thisstudy may help us to understand the acceleration of electrons at shocks in space and astrophysical systems.

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

Cited by 9 publications

References 48 publications

Type II radio bursts: 1. New entirely analytic formalism for the electron beams, Langmuir waves, and radio emission

Type II radio bursts: 1. New entirely analytic formalism for the electron beams, Langmuir waves, and radio emission

Terrestrial foreshock Langmuir waves: STEREO observations, theoretical modeling, and quasi‐linear simulations

The Acceleration of Electrons at Collisionless Shocks Moving Through a Turbulent Magnetic Field

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