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Title: Ion-acoustic shocks with self-regulated ion reflection and acceleration

Abstract

Here, an analytic solution describing an ion-acoustic collisionless shock, self-consistently with the evolution of shock-reflected ions, is obtained. The solution extends the classic soliton solution beyond a critical Mach number, where the soliton ceases to exist because of the upstream ion reflection. The reflection transforms the soliton into a shock with a trailing wave and a foot populated by the reflected ions. The solution relates parameters of the entire shock structure, such as the maximum and minimum of the potential in the trailing wave, the height of the foot, as well as the shock Mach number, to the number of reflected ions. This relation is resolvable for any given distribution of the upstream ions. In this paper, we have resolved it for a simple “box” distribution. Two separate models of electron interaction with the shock are considered. The first model corresponds to the standard Boltzmannian electron distribution in which case the critical shock Mach number only insignificantly increases from M ≈ 1:6 (no ion reflection) to M ≈ 1:8 (substantial reflection). The second model corresponds to adiabatically trapped electrons. They produce a stronger increase, from M ≈ 3:1 to M ≈ 4:5. The shock foot that is supported by themore » reflected ions also accelerates them somewhat further. A self-similar foot expansion into the upstream medium is described analytically.« less

Authors:
ORCiD logo [1];  [2];  [3];  [4];  [1]; ORCiD logo [2];  [2]; ORCiD logo [2]
  1. Univ. of California, San Diego, CA (United States). Center for Astrophysics and Space Sciences (CASS) and Dept. of Physics
  2. Univ. of Maryland, College Park, MD (United States)
  3. Univ. of Maryland, College Park, MD (United States); Russian Academy of Sciences (RAS), Novosibirsk (Russian Federation). Inst. of Computational Technologies
  4. Russian Academy of Sciences (RAS), Novosibirsk (Russian Federation). Inst. of Computational Technologies; Univ. of Rostock (Germany). Dept. of Physics
Publication Date:
Research Org.:
Univ. of California, San Diego, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24); National Aeronautic and Space Administration (NASA)
Contributing Org.:
John von Neumann Inst. for Computing (NIC), Julich (Germany)
OSTI Identifier:
1470316
Alternate Identifier(s):
OSTI ID: 1247065
Grant/Contract Number:  
FG02-04ER54738; NNX14AH36G; HRO03
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 23; Journal Issue: 4; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 97 MATHEMATICS AND COMPUTING

Citation Formats

Malkov, M. A., Sagdeev, R. Z., Dudnikova, G. I., Liseykina, T. V., Diamond, P. H., Papadopoulos, K., Liu, C. -S., and Su, J. J. Ion-acoustic shocks with self-regulated ion reflection and acceleration. United States: N. p., 2016. Web. doi:10.1063/1.4945649.
Malkov, M. A., Sagdeev, R. Z., Dudnikova, G. I., Liseykina, T. V., Diamond, P. H., Papadopoulos, K., Liu, C. -S., & Su, J. J. Ion-acoustic shocks with self-regulated ion reflection and acceleration. United States. doi:10.1063/1.4945649.
Malkov, M. A., Sagdeev, R. Z., Dudnikova, G. I., Liseykina, T. V., Diamond, P. H., Papadopoulos, K., Liu, C. -S., and Su, J. J. Tue . "Ion-acoustic shocks with self-regulated ion reflection and acceleration". United States. doi:10.1063/1.4945649. https://www.osti.gov/servlets/purl/1470316.
@article{osti_1470316,
title = {Ion-acoustic shocks with self-regulated ion reflection and acceleration},
author = {Malkov, M. A. and Sagdeev, R. Z. and Dudnikova, G. I. and Liseykina, T. V. and Diamond, P. H. and Papadopoulos, K. and Liu, C. -S. and Su, J. J.},
abstractNote = {Here, an analytic solution describing an ion-acoustic collisionless shock, self-consistently with the evolution of shock-reflected ions, is obtained. The solution extends the classic soliton solution beyond a critical Mach number, where the soliton ceases to exist because of the upstream ion reflection. The reflection transforms the soliton into a shock with a trailing wave and a foot populated by the reflected ions. The solution relates parameters of the entire shock structure, such as the maximum and minimum of the potential in the trailing wave, the height of the foot, as well as the shock Mach number, to the number of reflected ions. This relation is resolvable for any given distribution of the upstream ions. In this paper, we have resolved it for a simple “box” distribution. Two separate models of electron interaction with the shock are considered. The first model corresponds to the standard Boltzmannian electron distribution in which case the critical shock Mach number only insignificantly increases from M ≈ 1:6 (no ion reflection) to M ≈ 1:8 (substantial reflection). The second model corresponds to adiabatically trapped electrons. They produce a stronger increase, from M ≈ 3:1 to M ≈ 4:5. The shock foot that is supported by the reflected ions also accelerates them somewhat further. A self-similar foot expansion into the upstream medium is described analytically.},
doi = {10.1063/1.4945649},
journal = {Physics of Plasmas},
number = 4,
volume = 23,
place = {United States},
year = {2016},
month = {4}
}

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    Works referencing / citing this record:

    Low Mach-number collisionless electrostatic shocks and associated ion acceleration
    journal, January 2018

    • Pusztai, I.; TenBarge, J. M.; Csapó, A. N.
    • Plasma Physics and Controlled Fusion, Vol. 60, Issue 3
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