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 »
- Authors:
-
[1];
[2];
[2]
- Univ. of California, San Diego, CA (United States). Center for Astrophysics and Space Sciences (CASS) and Dept. of Physics
- Univ. of Maryland, College Park, MD (United States)
- Univ. of Maryland, College Park, MD (United States); Russian Academy of Sciences (RAS), Novosibirsk (Russian Federation). Inst. of Computational Technologies
- 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); National Aeronautics 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. https://doi.org/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. https://doi.org/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 = {Tue Apr 12 00:00:00 EDT 2016},
month = {Tue Apr 12 00:00:00 EDT 2016}
}
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Works referenced in this record:
Escape of heated ions upstream of quasi-parallel shocks
journal, May 1982
- Edmiston, J. P.; Kennel, C. F.; Eichler, David
- Geophysical Research Letters, Vol. 9, Issue 5
Interstellar pickup ions and quasi-perpendicular shocks: Implications for the termination shock and interplanetary shocks
journal, January 1996
- Zank, G. P.; Pauls, H. L.; Cairns, I. H.
- Journal of Geophysical Research: Space Physics, Vol. 101, Issue A1
Pickup ion energization by shock surfing
journal, March 1996
- Lee, Martin A.; Shapiro, Vitali D.; Sagdeev, Roald Z.
- Journal of Geophysical Research: Space Physics, Vol. 101, Issue A3
Origin of diffuse superthermal ions at quasi-parallel supercritical collisionless shocks
journal, January 1991
- Kucharek, H.; Scholer, M.
- Journal of Geophysical Research, Vol. 96, Issue A12
The “injection problem” for quasiparallel shocks
journal, October 2001
- Zank, G. P.; Rice, W. K. M.; le Roux, J. A.
- Physics of Plasmas, Vol. 8, Issue 10
PAMELA Measurements of Cosmic-Ray Proton and Helium Spectra
journal, March 2011
- Adriani, O.; Barbarino, G. C.; Bazilevskaya, G. A.
- Science, Vol. 332, Issue 6025
Ion acceleration by superintense laser-plasma interaction
journal, May 2013
- Macchi, Andrea; Borghesi, Marco; Passoni, Matteo
- Reviews of Modern Physics, Vol. 85, Issue 2
Optics in the relativistic regime
journal, April 2006
- Mourou, Gerard A.; Tajima, Toshiki; Bulanov, Sergei V.
- Reviews of Modern Physics, Vol. 78, Issue 2
On ion injection at quasiparallel shocks
journal, October 2002
- Scholer, M.; Kucharek, H.; Kato, C.
- Physics of Plasmas, Vol. 9, Issue 10
Cosmic Ray Origins: An Introduction
journal, November 2014
- Blandford, Roger; Simeon, Paul; Yuan, Yajie
- Nuclear Physics B - Proceedings Supplements, Vol. 256-257
Proton-Helium Spectral Anomaly as a Signature of Cosmic Ray Accelerator
journal, February 2012
- Malkov, M. A.; Diamond, P. H.; Sagdeev, R. Z.
- Physical Review Letters, Vol. 108, Issue 8
Monoenergetic Proton Beams Accelerated by a Radiation Pressure Driven Shock
journal, January 2011
- Palmer, Charlotte A. J.; Dover, N. P.; Pogorelsky, I.
- Physical Review Letters, Vol. 106, Issue 1
Oncological hadrontherapy with laser ion accelerators
journal, July 2002
- Bulanov, S. V.; Esirkepov, T. Zh; Khoroshkov, V. S.
- Physics Letters A, Vol. 299, Issue 2-3
Nonlinear theory of diffusive acceleration of particles by shock waves
journal, March 2001
- Malkov, M. A.; Drury, L. O'C
- Reports on Progress in Physics, Vol. 64, Issue 4
High Statistics Measurement of the Positron Fraction in Primary Cosmic Rays of 0.5–500 GeV with the Alpha Magnetic Spectrometer on the International Space Station
journal, September 2014
- Accardo, L.; Aguilar, M.; Aisa, D.
- Physical Review Letters, Vol. 113, Issue 12
Distribution of escaping ions produced by non-specular reflection at the stationary quasi-perpendicular shock front: ESCAPING IONS
journal, May 2008
- Gedalin, M.; Liverts, M.; Balikhin, M. A.
- Journal of Geophysical Research: Space Physics, Vol. 113, Issue A5
Particle Acceleration by Shocks in Supernova Remnants
journal, May 2014
- Bell, Anthony Raymond
- Brazilian Journal of Physics, Vol. 44, Issue 5
Ion Acceleration at the Earth’s Bow Shock
journal, June 2012
- Burgess, D.; Möbius, E.; Scholer, M.
- Space Science Reviews, Vol. 173, Issue 1-4
Simulations and Theory of ion Injection at Non-Relativistic Collisionless Shocks
journal, December 2014
- Caprioli, Damiano; Pop, Ana-Roxana; Spitkovsky, Anatoly
- The Astrophysical Journal, Vol. 798, Issue 2
Non-linear dynamics of a rarefied ionized gas
journal, January 1975
- Gurevich, A. V.; Pitaevsky, L. P.
- Progress in Aerospace Sciences, Vol. 16, Issue 3
Ion-acoustic shocks with reflected ions: modelling and particle-in-cell simulations
journal, July 2015
- Liseykina, T. V.; Dudnikova, G. I.; Vshivkov, V. A.
- Journal of Plasma Physics, Vol. 81, Issue 5
Collisionless shock waves in a plasma in a weak magnetic field
journal, January 1963
- Moiseev, S. S.; Sagdeev, R. Z.
- Journal of Nuclear Energy. Part C, Plasma Physics, Accelerators, Thermonuclear Research, Vol. 5, Issue 1
Imaging particle beams for cancer treatment
journal, October 2015
- Polf, Jerimy C.; Parodi, Katia
- Physics Today, Vol. 68, Issue 10
Cosmic ray energy spectrum from measurements of air showers
journal, April 2013
- Gaisser, T. K.; Stanev, T.; Tilav, S.
- Frontiers of Physics, Vol. 8, Issue 6
Ion acceleration from laser-driven electrostatic shocks
journal, May 2013
- Fiuza, F.; Stockem, A.; Boella, E.
- Physics of Plasmas, Vol. 20, Issue 5
Particle acceleration at astrophysical shocks: A theory of cosmic ray origin
journal, October 1987
- Blandford, Roger; Eichler, David
- Physics Reports, Vol. 154, Issue 1
Ion-acoustic soliton in a plasma with finite-temperature ions
journal, January 2009
- Medvedev, Yu. V.
- Plasma Physics Reports, Vol. 35, Issue 1
The Acceleration of Thermal Protons at Parallel Collisionless Shocks: Three-Dimensional Hybrid Simulations
journal, August 2013
- Guo, Fan; Giacalone, Joe
- The Astrophysical Journal, Vol. 773, Issue 2
On double-structured, perpendicular, magneto-plasma shock waves
journal, January 1971
- Woods, L. C.
- Plasma Physics, Vol. 13, Issue 4
Can diffusive shock acceleration in supernova remnants account for high-energy galactic cosmic rays?
journal, April 2005
- Hillas, A. M.
- Journal of Physics G: Nuclear and Particle Physics, Vol. 31, Issue 5
Collisionless shocks in laser-produced plasma generate monoenergetic high-energy proton beams
journal, November 2011
- Haberberger, Dan; Tochitsky, Sergei; Fiuza, Frederico
- Nature Physics, Vol. 8, Issue 1
Ion leakage from quasiparallel collisionless shocks: Implications for injection and shock dissipation
journal, October 1998
- Malkov, M. A.
- Physical Review E, Vol. 58, Issue 4
Advanced strategies for ion acceleration using high-power lasers
journal, November 2013
- Macchi, A.; Sgattoni, A.; Sinigardi, S.
- Plasma Physics and Controlled Fusion, Vol. 55, Issue 12
A Quarter Century of Collisionless Shock Research
book, March 2013
- Kennel, C. F.; Edmiston, J. P.; Hada, T.
- Collisionless Shocks in the Heliosphere: A Tutorial Review, Vol. 34
Microinstabilities and Anomalous Transport
book, March 2013
- Papadopoulos, K.
- Collisionless Shocks in the Heliosphere: A Tutorial Review
Monoenergetic proton beams accelerated by a radiation pressure driven shock
text, January 2010
- Palmer, C. A. J.; Dover, N. P.; Pogorelsky, I.
- arXiv
Proton-Helium Spectral Anomaly as a Signature of Cosmic Ray Accelerator
text, January 2011
- Malkov, M. A.; Diamond, P. H.; Sagdeev, R. Z.
- arXiv
Ion acceleration from laser-driven electrostatic shocks
text, January 2013
- Fiuza, F.; Stockem, A.; Boella, E.
- arXiv
Ion acceleration by superintense laser-plasma interaction
text, January 2013
- Macchi, Andrea; Borghesi, Marco; Passoni, Matteo
- arXiv
Advanced strategies for ion acceleration using high power lasers
text, January 2013
- Macchi, A.; Sgattoni, A.; Sinigardi, S.
- arXiv
Simulations and Theory of Ion Injection at Non-relativistic Collisionless Shocks
text, January 2014
- Caprioli, Damiano; Pop, Ana-Roxana; Spitkovsky, Anatoly
- arXiv
Works referencing / citing this record:
Structure of a collisionless pair jet in a magnetized electron–proton plasma: flow-aligned magnetic field
journal, January 2019
- Dieckmann, M. E.; Folini, D.; Hotz, I.
- Astronomy & Astrophysics, Vol. 621
Lower-hybrid drift instability and macroscopic flow of colliding magnetized plasmas
journal, October 2018
- Malkov, M. A.; Sotnikov, V. I.
- Physics of Plasmas, Vol. 25, Issue 10
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
Shocks and phase space vortices driven by a density jump between two clouds of electrons and protons
journal, December 2019
- Moreno, Q.; Dieckmann, M. E.; Folini, D.
- Plasma Physics and Controlled Fusion, Vol. 62, Issue 2
Acceleration of Cosmic Rays in Supernova Shocks: Elemental Selectivity of the Injection Mechanism
journal, February 2019
- Hanusch, Adrian; Liseykina, Tatyana V.; Malkov, Mikhail
- The Astrophysical Journal, Vol. 872, Issue 1
Low Mach-number collisionless electrostatic shocks and associated ion acceleration
text, January 2017
- Pusztai, Istvan; TenBarge, Jason M.; Csapó, Aletta N.
- arXiv
Lower-Hybrid Drift Instability and Macroscopic Flow of Colliding Magnetized Plasmas
text, January 2018
- Malkov, Mikhail; Sotnikov, Vladimir
- arXiv
Structure of a collisionless pair jet in a magnetized electron-proton plasma: flow-aligned magnetic field
text, January 2018
- Dieckmann, M. E.; Folini, D.; Hotz, I.
- arXiv
Lower-Hybrid Drift Instability and Macroscopic Flow of Colliding Magnetized Plasmas
text, January 2018
- Malkov, Mikhail; Sotnikov, Vladimir
- arXiv