12,920 research outputs found
Non-planar shock waves in a magnetic field
AbstractThe method of multiple time scale is used to obtain the asymptotic solution to the spherically and cylindrically symmetric flow into a perfectly conducting gas permeated by a transverse magnetic field. The transport equations for the amplitudes of resonantly interacting high frequency waves are also found. The evolutionary behavior of non-resonant wave modes culminating into shock waves is studied
Regular shock refraction at an oblique planar density interface in magnetohydrodynamics
We consider the problem of regular refraction (where regular implies all waves meet at a single point) of a shock at an oblique planar contact discontinuity separating conducting fluids of different densities in the presence of a magnetic field aligned with the incident shock velocity. Planar ideal magnetohydrodynamic (MHD) simulations indicate that the presence of a magnetic field inhibits the deposition of vorticity on the shocked contact. We show that the shock refraction process produces a system of five to seven plane waves that may include fast, intermediate, and slow MHD shocks, slow compound waves, 180◦ rotational discontinuities, and slow-mode expansion fans that intersect at a point. In all solutions, the shocked contact is vorticity free and hence stable. These solutions are not unique, but differ in the types of waves that participate. The set of equations governing the structure of these multiple-wave solutions is obtained in which fluid property variation is allowed only in the azimuthal direction about the wave-intersection point. Corresponding solutions are referred to as either quintuple-points, sextuple-points, or septuple-points, depending on the number of participating waves. A numerical method of solution is described and examples are compared to the results of numerical simulations for moderate magnetic field strengths. The limit of vanishing magnetic field at fixed permeability and pressure is studied for two solution types. The relevant solutions correspond to the hydrodynamic triple-point with the shocked contact replaced by a singular structure consisting of a wedge, whose angle scales with the applied field magnitude, bounded by either two slow compound waves or two 180◦ rotational discontinuities, each followed by a slowmode expansion fan. These bracket the MHD contact which itself cannot support a tangential velocity jump in the presence of a non-parallel magnetic field. The magnetic field within the singular wedge is finite and the shock-induced change in tangential velocity across the wedge is supported by the expansion fans that form part of the compound waves or follow the rotational discontinuities. To verify these findings, an approximate leading-order asymptotic solution appropriate for both flow structures was computed. The full and asymptotic solutions are compared quantitatively.V. Wheatley, D. I. Pullin and R. Samtane
On the inadmissibility of non-evolutionary shocks
In recent years, numerical solutions of the equations of compressible magnetohydrodynamic (MHD) flows have been found to contain intermediate shocks for certain kinds of problems. Since these results would seem to be in conflict with the classical theory of MHD shocks, they have stimulated attempts to reexamine various aspects of this theory, in particular the role of dissipation. In this paper, we study the general relationship between the evolutionary conditions for discontinuous solutions of the dissipation-free system and the existence and uniqueness of steady dissipative shock structures for systems of quasilinear conservation laws with a concave entropy function. Our results confirm the classical theory. We also show that the appearance of intermediate shocks in numerical simulations can be understood in terms of the properties of the equations of planar MHD, for which some of these shocks turn out to be evolutionary. Finally, we discuss ways in which numerical schemes can be modified in order to avoid the appearance of intermediate shocks in simulations with such symmetry
Nonthermal radiation from relativistic electrons accelerated at spherically expanding shocks
We study the evolution of the energy spectrum of cosmic-ray electrons
accelerated at spherically expanding shocks with low Mach numbers and the
ensuing spectral signatures imprinted in radio synchrotron emission.
Time-dependent simulations of diffusive shock acceleration (DSA) of electrons
in the test-particle limit have been performed for spherical shocks with
parameters relevant for typical shocks in the intracluster medium. The electron
and radiation spectra at the shock location can be described properly by the
test-particle DSA predictions with instantaneous shock parameters. However, the
volume integrated spectra of both electrons and radiation deviate significantly
from the test-particle power-laws, because the shock compression ratio and the
flux of injected electrons at the shock gradually decrease as the shock slows
down in time.So one needs to be cautious about interpreting observed radio
spectra of evolving shocks based on simple DSA models in the test-particle
regime.Comment: corrected typos and figures, 12 pages, 7 figures, Accepted for
publication at Journal of Korean Astronomical Societ
Particle-in-cell simulation of a mildly relativistic collision of an electron-ion plasma carrying a quasi-parallel magnetic field: Electron acceleration and magnetic field amplification at supernova shocks
Plasma processes close to SNR shocks result in the amplification of magnetic
fields and in the acceleration of electrons, injecting them into the diffusive
acceleration mechanism. The acceleration of electrons and the B field
amplification by the collision of two plasma clouds, each consisting of
electrons and ions, at a speed of 0.5c is investigated. A quasi-parallel
guiding magnetic field, a cloud density ratio of 10 and a plasma temperature of
25 keV are considered. A quasi-planar shock forms at the front of the dense
plasma cloud. It is mediated by a circularly left-hand polarized
electromagnetic wave with an electric field component along the guiding
magnetic field. Its propagation direction is close to that of the guiding field
and orthogonal to the collision boundary. It has a low frequency and a
wavelength that equals several times the ion inertial length, which would be
indicative of a dispersive Alfven wave close to the ion cyclotron resonance
frequency of the left-handed mode (ion whistler), provided that the frequency
is appropriate. However, it moves with the super-alfvenic plasma collision
speed, suggesting that it is an Alfven precursor or a nonlinear MHD wave such
as a Short Large-Amplitude Magnetic Structure (SLAMS). The growth of the
magnetic amplitude of this wave to values well in excess of those of the
quasi-parallel guiding field and of the filamentation modes results in a
quasi-perpendicular shock. We present evidence for the instability of this mode
to a four wave interaction. The waves developing upstream of the dense cloud
give rise to electron acceleration ahead of the collision boundary. Energy
equipartition between the ions and the electrons is established at the shock
and the electrons are accelerated to relativistic speeds.Comment: 16 pages, 18 figures, Accepted for publication by Astron & Astrophy
Corrugation of relativistic magnetized shock waves
As a shock front interacts with turbulence, it develops corrugation which
induces outgoing wave modes in the downstream plasma. For a fast shock wave,
the incoming wave modes can either be fast magnetosonic waves originating from
downstream, outrunning the shock, or eigenmodes of the upstream plasma drifting
through the shock. Using linear perturbation theory in relativistic MHD, this
paper provides a general analysis of the corrugation of relativistic magnetized
fast shock waves resulting from their interaction with small amplitude
disturbances. Transfer functions characterizing the linear response for each of
the outgoing modes are calculated as a function of the magnetization of the
upstream medium and as a function of the nature of the incoming wave.
Interestingly, if the latter is an eigenmode of the upstream plasma, we find
that there exists a resonance at which the (linear) response of the shock
becomes large or even diverges. This result may have profound consequences on
the phenomenology of astrophysical relativistic magnetized shock waves.Comment: 14 pages, 9 figures; to appear in Ap
The evolution of a slow electrostatic shock into a plasma shock mediated by electrostatic turbulence
The collision of two plasma clouds at a speed that exceeds the ion acoustic
speed can result in the formation of shocks. This phenomenon is observed not
only in astrophysical scenarios such as the propagation of supernova remnant
(SNR) blast shells into the interstellar medium, but also in laboratory-based
laser-plasma experiments. These experiments and supporting simulations are thus
seen as an attractive platform for the small-scale reproduction and study of
astrophysical shocks in the laboratory. We model two plasma clouds, which
consist of electrons and ions, with a 2D PIC simulation. The ion temperatures
of both clouds differ by a factor of 10. Both clouds collide at a speed, which
is realistic for laboratory studies and for SNR shocks in their late evolution
phase like that of RCW86. A magnetic field, which is orthogonal to the
simulation plane, has a strength that is comparable to that at SNR shocks. A
forward shock forms between the overlap layer of both plasma clouds and the
cloud with the cooler ions. A large-amplitude ion acoustic wave is observed
between the overlap layer and the cloud with the hotter ions. It does not
steepen into a reverse shock, because its speed is below the ion acoustic
speed. A gradient of the magnetic field amplitude builds up close to the
forward shock as it compresses the magnetic field. This gradient gives rise to
an electron drift that is fast enough to trigger an instability. Electrostatic
ion acoustic wave turbulence develops ahead of the shock. It widens its
transition layer and thermalizes the ions, but the forward shock remains
intact.Comment: Accepted for publication in the New Journal of Physic
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