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NASA NTRS1984

The adiabatic energy change of plasma electrons and the frame dependence of the cross-shock potential at collisionless magnetosonic shock waves

The adiabatic energy gain of electrons in the stationary electric and magnetic field structure of collisionless shock waves was examined analytically in reference to conditions of the earth's bow shock. The study was performed to characterize the behavior of electrons interacting with the cross-shock potential. A normal incidence frame (NIF) was adopted in order to calculate the reversible energy change across a time stationary shock, and comparisons were made with predictions made by the de Hoffman-Teller (HT) model (1950). The electron energy gain, about 20-50 eV, is demonstrated to be consistent with a 200-500 eV potential jump in the bow shock quasi-perpendicular geometry. The electrons lose energy working against the solar wind motional electric field. The reversible energy process is close to that modeled by HT, which predicts that the motional electric field vanishes and the electron energy gain from the electric potential is equated to the ion energy loss to the potential.

Goodrich, C. C.↗
NASA NTRS1980

Interstellar shock waves

The structure of interstellar shocks driven by supernova remnants and by expanding H II regions around early-type stars is discussed. Jump conditions are examined, along with shock fronts, post-shock relaxation layers, collisional shocks, collisionless shocks, nonradiative shocks, radiative atomic shocks, and shock models of observed nebulae. Effects of shock waves on interstellar molecules are examined, with reference to the chemistry behind shock fronts, infrared and vibrational-rotational cooling by molecules, and observations of shocked molecules. Some current problems and applications of the study of interstellar shocks are summarized, including the initiation of star formation by radiative shock waves, interstellar masers, the stability of shocks, particle acceleration in shocks, and shocks in galactic nuclei.

Mckee, C. F.↗
NASA NTRS2023

Relativistic Electron Beams Accelerated By an Interplanetary Shock

Context: Collisionless shock waves have long been considered to be among the most prolific particle accelerators in the universe. Shocks alter the plasma they propagate through, and often exhibit complex evolution across multiple scales. Interplanetary (IP) traveling shocks have been recorded in situ for over half a century and act as a natural laboratory for experimentally verifying various aspects of large-scale collisionless shocks. A fundamentally interesting problem in both heliophysics and astrophysics is the acceleration of electrons to relativistic energies (> 300 keV) by traveling shocks. Aims: The reason for an incomplete understanding of electron acceleration at IP shocks is due to scale-related challenges and a lack of instrumental capabilities. This Letter presents the first observations of field-aligned beams of relativistic electrons upstream of an IP shock, observed thanks to the instrumental capabilities of Solar Orbiter. This study presents the characteristics of the electron beams close to the source and contributes to the understanding of their acceleration mechanism. Methods: On 25 July 2022, Solar Orbiter encountered an IP shock at 0.98 AU. The shock was associated with an energetic storm particle event, which also featured upstream field-aligned relativistic electron beams observed 14 min prior to the actual shock crossing. The distance of the beam’s origin was investigated using a velocity dispersion analysis (VDA). Peak-intensity energy spectra were analyzed and compared with those obtained from a semi-analytical fast-Fermi acceleration model. Results: By leveraging Solar Orbiter’s high temporal resolution Energetic Particle Detector (EPD), we successfully showcase an IP shock’s ability to accelerate relativistic electron beams. Our proposed acceleration mechanism offers an explanation for the observed electron beam and its characteristics, while we also explore the potential contributions of more complex mechanisms.

acceleration of particles↗
NASA NTRS1987

The interaction of quasiperpendicular shock waves in a collisionless plasma

The interaction between collisionless shocks is examined from a kinetic viewpoint using computer simulations of shock collisions spanning the range of ambient plasma and shock parameters typical of the interplanetary medium. It is found that the interaction between two subcritical, perpendicular shocks is largely fluidlike with no evidence for accelerated particles. The electromagnetic fields associated with each shock, but not the plasmas, pass through each other during the collision. This interaction is due to self-consistently generated electric fields which adjust to the value needed to bring to rest the two incoming streams. The interaction between two supercritical perpendicular collisionless shocks is similar to the subcritical case, in that the electromagnetic fields associated with each shock are transmitted whereas particles are not. However, the interaction is also highly dynamic with substantial acceleration of ions. Increasing the Mach number gives rise to an increasing number of energetic particles.

Cargill, P. J.↗
NASA NTRS2012

Coronal Magnetic Field Measurement Using CME-Driven Shock Observations

Collisionless shocks form ahead of coronal mass ejections (CMEs) when the CME speed exceeds the Alfven speed of the ambient plasma in the corona and interplanetary medium. The shock stands at a distance from the CME flux rope that depends on the shock Mach number, the geometry of the driver, and the adiabatic index. While the shock ahead of the CME has been observed for a long time in the in situ data, it has been identified recently near the Sun in the coronagraphic and EUV images. Unlike in situ observations, the imaging observations are two dimensional, so one can better discern the CME-shock relationship near the Sun. Gopalswamy and Yashiro demonstrated that the coronal magnetic field can be derived from the shock standoff distance measured in coronagraphic images. The method involves measuring the standoff distance, the radius of curvature of the flux rope, and assuming the value of the adiabatic index and deriving the Alfvenic Mach number. The next step is to derive the Alfvenic Mach number from the measured shock speed and an estimate of the local solar wind speed. The final step involves deriving the magnetic field from the Alfven speed by measuring the local plasma density either from coronagraphic (polarized brightness) images or from the band-splitting of type II radio bursts. In this paper, we derive the combined magnetic field profile from near the Sun to the edge of the LASCO field of view (1.5 to 30 solar radii) and compare it with the current model profiles.

Gopalswarmy, Nat↗
NASA NTRS2024

Electrostatic Waves and Electron Holes in Simulations of Low-Mach Quasi-Perpendicular Shocks

Collisionless low Mach number shocks are abundant in astrophysical and space plasma environments, exhibiting complex wave activity and wave-particle interactions. In this paper, we present 2D Particle in-Cell (PIC) simulations of quasi-perpendicular nonrelativistic (vsh ≈ (5500−22000) km/s) low Mach number shocks, with a specific focus on studying electrostatic waves in the shock ramp and the precursor regions. In these shocks, an ion-scale oblique whistler wave creates a configuration with two hot counter streaming electron beams, which drive unstable electron acoustic waves (EAWs) that can turn into electrostatic solitary waves (ESWs) at the late stage of their evolution. By conducting simulations with periodic boundaries, we show that EAW properties agree with linear dispersion analysis. The characteristics of ESWs in shock simulations, including their wavelength and amplitude, depend on the shock velocity. When extrapolated to shocks with realistic velocities (vsh ≈ 300 km/s), the ESW wavelength is reduced to one tenth of the electron skin depth and the ESW amplitude is anticipated to surpass that of the quasi-static electric field by more than a factor of 100. These theoretical predictions may explain a discrepancy, between PIC and satellite measurements, in the relative amplitude of high and low-frequency electric field fluctuations.

Plasma astrophysics↗
NASA NTRS1993

Collisionless parallel shocks

Consideration is given to a collisionless parallel shock based on solitary-type solutions of the modified derivative nonlinear Schroedinger equation (MDNLS) for parallel Alfven waves. The standard derivative nonlinear Schroedinger equation is generalized in order to include the possible anisotropy of the plasma distribution and higher-order Korteweg-de Vies-type dispersion. Stationary solutions of MDNLS are discussed. The anisotropic nature of 'adiabatic' reflections leads to the asymmetric particle distribution in the upstream as well as in the downstream regions of the shock. As a result, nonzero heat flux appears near the front of the shock. It is shown that this causes the stochastic behavior of the nonlinear waves, which can significantly contribute to the shock thermalization.

Khabibrakhmanov, I. KH.↗
NASA NTRS1994

Magnetic field waves at Uranus

The research efforts funded by the Uranus Data Analysis Program (UDAP) grant to the Bartol Research Institute (BRI) involved the study of magnetic field waves associated with the Uranian bow shock. Upstream wave studies are motivated as a study of the physics of collisionless shocks. Collisionless shocks in plasmas are capable of 'reflecting' a fraction of the incoming thermal particle distribution and directing the resulting energetic particle motion back into the upstream region. Once within the upstream region, the backward streaming energetic particles convey information of the approaching shock to the supersonic flow. This particle population is responsible for the generation of upstream magnetic and electrostatic fluctuations known as 'upstream waves', for slowing the incoming wind prior to the formation of the shock ramp, and for heating of the upstream plasma. The waves produced at Uranus not only differed in several regards from the observations at other planetary bow shocks, but also gave new information regarding the nature of the reflected particle populations which were largely unmeasurable by the particle instruments. Four distinct magnetic field wave types were observed upstream of the Uranian bow shock: low-frequency Alfven or fast magnetosonic waves excited by energetic protons originating at or behind the bow shock; whistler wave bursts driven by gyrating ion distributions within the shock ramp; and two whistler wave types simultaneously observed upstream of the flanks of the shock and argued to arise from resonance with energetic electrons. In addition, observations of energetic particle distributions by the LECP experiment, thermal particle populations observed by the PLS experiment, and electron plasma oscillations recorded by the PWS experiment proved instrumental to this study and are included to some degree in the papers and presentations supported by this grant.

Smith, Charles W.↗
NASA NTRS2009

Particle Acceleration and Associated Emission from Relativistic Shocks

Five talks consist of a research program consisting of numerical simulations and theoretical development designed to provide an understanding of the emission from accelerated particles in relativistic shocks. The goal of this lecture is to discuss the particle acceleration, magnetic field generation, and radiation along with the microphysics of the shock process in a self-consistent manner. The discussion involves the collisionless shocks that produce emission from gamma-ray bursts and their afterglows, and producing emission from supernova remnants and AGN relativistic jets. Recent particle-in-cell simulation studies have shown that the Weibel (mixed mode two-stream filamentation) instability is responsible for particle (electron, positron, and ion) acceleration and magnetic field generation in relativistic collisionless shocks. 3-D RPIC code parallelized with MPI has been used to investigate the dynamics of collisionless shocks in electron-ion and electron-positron plasmas with and without initial ambient magnetic fields. In this lecture we will present brief tutorials of RPIC simulations and RMHD simulations, a brief summary of recent RPIC simulations, mechanisms of particle acceleration in relativistic shocks, and calculation of synchrotron radiation by tracing particles. We will discuss on emission from the collisionless shocks, which will be calculated during the simulation by tracing particle acceleration self-consistently in the inhomogeneous magnetic fields generated in the shocks. In particular, we will discuss the differences between standard synchrotron radiation and the jitter radiation that arises in turbulent magnetic fields.

Nishkawa, Ken-Ichi↗
NASA NTRS1988

Theory and simulation of collisionless parallel shocks

This paper presents a self-consistent theoretical model for collisionless parallel shock structure, based on the hypothesis that shock dissipation and heating can be provided by electromagnetic ion beam-driven instabilities. It is shown that shock formation and plasma heating can result from parallel propagating electromagnetic ion beam-driven instabilities for a wide range of Mach numbers and upstream plasma conditions. The theoretical predictions are compared with recently published observations of quasi-parallel interplanetary shocks. It was found that low Mach number interplanetary shock observations were consistent with the explanation that group-standing waves are providing the dissipation; two high Mach number observations confirmed the theoretically predicted rapid thermalization across the shock.

Quest, K. B.↗
NASA NTRS1982

Particle acceleration at planetary bow shock waves

One property of the collisionless shocks that may be studied through a comparison of their behavior in a variety of plasma conditions at several different planets is the occurrence of MHD waves, associated with particle beams accelerated at these shocks and flowing backward to the sun. Mercury, Venus, earth and Jupiter observations of one of these wave classes show that (1) the empirical relationship between interplanetary field strength and wave frequency in the observer's rest frame is approximately true at all the planets considered, and (2) the observed frequencies are consistent with resonance with beams of ions of the same energy at each of the planets. This is, in turn, in keeping with the Sonnerup (1969) geometrical model of ion reflection at collisionless shocks. It is suggested that this ion acceleration mechanism may occur in astrophysical systems similar to the solar system, providing a source of acceleration for cosmic rays.

Hoppe, M. M.↗
NASA NTRS1983

Structure of perpendicular shocks in collisionless plasma

The macrostructure of perpendicular shocks in the supercritical regime is investigated theoretically. The coupling between the shock precursor (foot region) associated with reflected ions and the magnetic ramp associated with electron ohmic heating is analyzed using a model in which the ions are treated as a multifluid and the electrons as a massless fluid. The results are found to be in good agreement with a number of features exhibited by recent numerical simulations of perpendicular shocks, including the morphology of the reflected-gyrating ion stream, the presence of potential and magnetic field overshoots, and the Mach number dependence of the shock structure.

Leroy, M. M.↗
NASA NTRS2014

Quantified Energy Dissipation Rates in the Terrestrial Bow Shock: Analysis Techniques and Methodology - 1.

We present a detailed outline and discussion of the analysis techniques used to compare the relevance of different energy dissipation mechanisms at collisionless shock waves. We show that the low-frequency, quasi-static fields contribute less to ohmic energy dissipation, (−j ⋅ E ) (minus current density times measured electric field), than their high-frequency counterparts. In fact, we found that high-frequency, large-amplitude (greater than 100 millivolts per meter and/or greater than 1 nanotesla) waves are ubiquitous in the transition region of collisionless shocks. We quantitatively show that their fields, through wave-particle interactions, cause enough energy dissipation to regulate the global structure of collisionless shocks. The purpose of this paper, part one of two, is to outline and describe in detail the background, analysis techniques, and theoretical motivation for our new results presented in the companion paper. The companion paper presents the results of our quantitative energy dissipation rate estimates and discusses the implications. Together, the two manuscripts present the first study quantifying the contribution that high-frequency waves provide, through wave-particle interactions, to the total energy dissipation budget of collisionless shock waves.

Terrestrial bow↗