Scatttering of High-Energy Particles at a Collisionless Shock Front: Dependence on the Shock Angle

2016

JGR Space Physics

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The dependence of ion dynamics on the cross‐shock potential and upstream βi in low‐Mach number marginally critical shocks is studied using advanced test particle analysis,. The directly transmitted ions provide the main contribution to the downstream ion pressure. The fraction of reflected ions increases with the increase of the cross‐shock potential and βi. This fraction is small and their contribution to the downstream ion pressure is negligible in marginally critical shocks. A population of quasi‐reflected ions is identified. These ions make a loop inside the ramp and do not appear upstream. They acquire energies comparable to the energies of the true reflected ions, are observed as a halo in the downstream ion distribution, and contribute significantly to the downstream pressure. Thus, the transmitted and quasi‐reflected ions shape the downstream magnetic profile. At higher cross‐shock potentials and βi the reflected ions cause formation of a magnetic dip just ahead of the ramp. A small fraction of ions are multiply reflected at the shock front. All these ions escape into the upstream region and all escaping ions are mutliply reflected.

Section: Discussionmentioning

confidence: 99%

b_{z} = \frac{B_{z}}{B_{u} \sin θ} = \frac{1}{2} ([], (R + 1) + (R - 1) G ((), \frac{x}{D}))

b_{y} = \frac{B_{y}}{B_{u}} = C_{By} ((), \frac{\cos θ}{M^{2}}) \frac{d B_{z}}{d x}

E_{y} = \frac{V_{u} B_{u} \sin θ}{c} = const, E_{z} = 0

E_{x} = - \frac{d ϕ}{d x}, ϕ = s ((), \frac{m_{i} V_{u}^{2}}{2}) ((), \frac{b_{z} - 1}{R - 1})

G (u) = 1 + \tanh (3 u)

Section: Numerical Analysismentioning

confidence: 99%

See 1 more Smart Citation

Transmitted, reflected, quasi‐reflected, and multiply reflected ions in low‐Mach number shocks

2016

JGR Space Physics

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“…By adjusting the shock parameters, we make the far downstream‐derived field consistent with the initial model profile. The following fields will be used as a model of a low‐Mach number shock [see, e.g., Gedalin et al , ]:

b_{z} = \frac{\sin θ}{2} ([], (R + 1) + (R - 1) Ψ ((), \frac{X}{MD}))

b_{y} = C_{By} ((), \frac{\cos θ}{M^{2}}) \frac{normald b_{z}}{normald X}

e_{x} = - \frac{normald ϕ}{normald X}, ϕ = s ((), \frac{b_{z} - 1}{R - 1})

where

Ψ (u) = 1 + \tanh (3 u)

. The motional electric field

e_{y} = \sin θ

(where θ is the angle between the shock normal and the upstream magnetic field) is constant throughout the shock, while e z =0.…”

Section: Numerical Analysismentioning

confidence: 99%

“…By adjusting the shock parameters, we make the far downstream-derived field consistent with the initial model profile. The following fields will be used as a model of a low-Mach number shock [see, e.g., Gedalin et al, 2015b]:…”

Section: Numerical Analysismentioning

confidence: 99%

Effect of alpha particles on the shock structure

2017

JGR Space Physics

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The magnetic profile of a collisionless shock is shaped by ions. Dynamics of the ions is governed by the fields in the shock front. Species with different charge‐to‐mass ratio have different gyroradii; thus, their distributions upon crossing the shock became substantially different. Accordingly, the dependencies of the density and temperature on the coordinate along the shock normal should differ. In a stable one‐dimensional stationary shock the total pressure must remain constant throughout. Therefore, the magnetic pressure should anticorrelate with the particle pressure. Since the particle pressure is not uniform, downstream spatial magnetic oscillations should arise. Each of the species results in its own dependence of the pressure on the coordinate along the shock normal; therefore, the oscillations are not spatially periodic. The magnetic compression in the shocks with alpha particles is higher than the magnetic compression in purely proton shocks, while the amplitude of the downstream magnetic oscillations is lower.

Collisionless relaxation of non-gyrotropic downstream ion distributions: dependence on shock parameters

2015

J. Plasma Phys.

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Upon crossing the shock front, ions begin to gyrate. The ion distribution just behind the ramp is manifestly non-gyrotropic. The gyration of the ion distribution as a whole results in spatially periodic oscillations of the ion pressure. The magnetic pressure must oscillate in the opposite phase to ensure the maintenance of the pressure balance throughout the shock front. The ion non-gyrotropy and the pressure oscillations gradually damp due to the collisionless gyrophase mixing. The rate of this relaxation depends on the basic shock parameters. The most influential are the angle between the shock normal and the magnetic field, the upstream ion temperature and the magnetic compression.