Shock wave

About: Shock wave is a research topic. Over the lifetime, 36184 publications have been published within this topic receiving 635848 citations. The topic is also known as: Shock waves & shockwave.

A Simple Model of Nonlinear Diffusive Shock Acceleration

Abstract: We present a simple model of nonlinear diffusive shock acceleration (also called first-order Fermi shock acceleration) that determines the shock modification, spectrum, and efficiency of the process in the plane-wave, steady state approximation as a function of an arbitrary injection parameter, η. The model, which uses a three-power-law form for the accelerated particle spectrum and contains only simple algebraic equations, includes the essential elements of the full nonlinear model and has been tested against Monte Carlo and numerical kinetic shock models. We include both adiabatic and Alfven wave heating of the upstream precursor. The simplicity and ease of calculation make this model useful for studying the basic properties of nonlinear shock acceleration, as well as providing results accurate enough for many astrophysical applications. It is shown that the shock properties depend upon the shock speed u0 with respect to a critical value u ηp, which is a function of the injection rate η and maximum accelerated particle momentum pmax. For u0 MA0, or by rtot ≈ 1.5M in the opposite case (MS0 is the sonic Mach number and MA0 is the Alfven Mach number). If u0 > u, the shock, although still strong, becomes almost unmodified and accelerated particle production decreases inversely proportional to u0.

Simulations of Ion Acceleration at Non-relativistic Shocks. I. Acceleration Efficiency

Abstract: We use two-dimensional and three-dimensional hybrid (kinetic ions-fluid electrons) simulations to investigate particle acceleration and magnetic field amplification at non-relativistic astrophysical shocks. We show that diffusive shock acceleration operates for quasi-parallel configurations (i.e., when the background magnetic field is almost aligned with the shock normal) and, for large sonic and Alfvenic Mach numbers, produces universal power-law spectra ∝p –4, where p is the particle momentum. The maximum energy of accelerated ions increases with time, and it is only limited by finite box size and run time. Acceleration is mainly efficient for parallel and quasi-parallel strong shocks, where 10%-20% of the bulk kinetic energy can be converted to energetic particles and becomes ineffective for quasi-perpendicular shocks. Also, the generation of magnetic turbulence correlates with efficient ion acceleration and vanishes for quasi-perpendicular configurations. At very oblique shocks, ions can be accelerated via shock drift acceleration, but they only gain a factor of a few in momentum and their maximum energy does not increase with time. These findings are consistent with the degree of polarization and the morphology of the radio and X-ray synchrotron emission observed, for instance, in the remnant of SN 1006. We also discuss the transition from thermal to non-thermal particles in the ion spectrum (supra-thermal region) and we identify two dynamical signatures peculiar of efficient particle acceleration, namely, the formation of an upstream precursor and the alteration of standard shock jump conditions.

The gap lemma and geometric criteria for instability of viscous shock profiles

Abstract: An obstacle in the use of Evans function theory for stability analysis of traveling waves occurs when the spectrum of the linearized operator about the wave accumulates at the imaginary axis, since the Evans function has in general been constructed only away from the essential spectrum. A notable case in which this difficulty occurs is in the stability analysis of viscous shock profiles. Here we prove a general theorem, the “gap lemma,” concerning the analytic continuation of the Evans function associated with the point spectrum of a traveling wave into the essential spectrum of the wave. This allows geometric stability theory to be applied in many cases where it could not be applied previously. We demonstrate the power of this method by analyzing the stability of certain undercompressive viscous shock waves. A necessary geometric condition for stability is determined in terms of the sign of a certain Melnikov integral of the associated viscous profile. This sign can easily be evaluated numerically. We also compute it analytically for solutions of several important classes of systems. In particular, we show for a wide class of systems that homoclinic (solitary) waves are linearly unstable, confirming these as the first known examples of unstable viscous shock waves. We also show that (strong) heteroclinic undercompressive waves are sometimes unstable. Similar stability conditions are also derived for Lax and overcompressive shocks and for nn

S/WAVES: The radio and plasma wave investigation on the STEREO Mission

Abstract: This paper introduces and describes the radio and plasma wave investigation on the STEREO Mission: STEREO/WAVES or S/WAVES. The S/WAVES instrument includes a suite of state-of-the-art experiments that provide comprehensive measurements of the three components of the fluctuating electric field from a fraction of a hertz up to 16 MHz, plus a single frequency channel near 30 MHz. The instrument has a direction finding or goniopolarimetry capability to perform 3D localization and tracking of radio emissions associated with streams of energetic electrons and shock waves associated with Coronal Mass Ejections (CMEs). The scientific objectives include: (i) remote observation and measurement of radio waves excited by energetic particles throughout the 3D heliosphere that are associated with the CMEs and with solar flare phenomena, and (ii) in-situ measurement of the properties of CMEs and interplanetary shocks, such as their electron density and temperature and the associated plasma waves near 1 Astronomical Unit (AU). Two companion papers provide details on specific aspects of the S/WAVES instrument, namely the electric antenna system (Bale et al., Space Sci. Rev., 2007) and the direction finding technique (Cecconi et al., Space Sci. Rev., 2007).