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NASA NTRS2021

Evaluating the De Hoffmann-Teller Cross-Shock 2 Potential at Real Collisionless Shocks

Shock waves are common in the heliosphere and beyond. The collisionless nature of most astrophysical plasmas allows for the energy processed by shocks to be partitioned amongst particle sub-populations and electromagnetic fields via physical mechanisms that are not well understood. The electrostatic potential across such shocks is frame dependent. In a frame where the incident bulk velocity is parallel to the magnetic field, the deHoffmann-Teller frame, the potential is linked directly to the ambipolar electric field established by the electron pressure gradient. Thus measuring and understanding this potential solves the electron partition problem, and gives insight into other competing shock processes. Integrating measured electric fields in space is problematic since the measurements can have offsets that change with plasma conditions. The offsets, once integrated, can be as large or larger than the shock potential. Here we exploit the high-quality field and plasma measurements from NASA’s Magnetospheric Multiscale mission to attempt this calculation. We investigate recent adaptations of the deHoffmann-Teller frame transformation to include time variability, and conclude that in practice these face difficulties inherent in the 3D time-dependent nature of real shocks by comparison to 1D simulations. Potential estimates based on electron fluid and kinetic analyses provide the most robust measures of the deHoffmann-Teller potential, but with some care direct integration of the electric fields can be made to agree. These results suggest that it will be difficult to independently assess the role of other processes, such as scattering by shock turbulence, in accounting for the electron heating.

Steven J Schwartz↗

NASA NTRS1991

Physics in strong magnetic fields near neutron stars

Electromagnetic phenomena occurring in the strong magnetic fields of neutron stars are currently of great interest in high-energy astrophysics. Observations of rotation rate changes and cyclotron lines in pulsars and gamma-ray bursts indicate that surface magnetic fields of neutron stars often exceed a trillion gauss. In fields this strong, where electrons behave much as if they were in bound atomic states, familiar processes undergo profound changes, and exotic processes become important. Strong magnetic fields affect the physics in several fundamental ways: energies perpendicular to the field are quantized, transverse momentum is not conserved, and electron-positron spin is important. Neutron stars therefore provide a unique laboratory for the study of physics in extremely high fields that cannot be generated on earth.

Harding, Alice K.↗

NASA NTRS2005

Particle acceleration, magnetic field generation, and emission in relativistic pair jets

Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas. Recent simulations show that the Weibel instability created by relativistic pair jets is responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet propagating through an ambient plasma with and without initial magnetic fields. The growth rates of the Weibel instability depends on the distribution of pair jets. The Weibel instability created in the collisionless shock accelerates particles perpendicular and parallel to the jet propagation direction. This instability is also responsible for generating and amplifying highly nonuniform, small-scale magnetic fields, which contribute to the electron s transverse deflection behind the jet head. The jitter radiation from deflected electrons has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.

Nishikawa, K.-I.↗

NASA NTRS1981

The telecommunications and data acquisition report

Deep Space Network operations, engineering, and implementation are reported. Developments in Earth-based radiotechnology as applied to other research programs in the fields of Geodynamics, Astrophysics, and programs related to radio searchers (instrumentation and methods) in extraterrestrial areas in the microwave region of the electromagnetic spectrum are also presented.

Renzetti, N. A.↗

NASA NTRS1995

Sensitivity analysis in multipole-accelerated panel methods for potential flow

In the design of an airframe, the effect of changing the geometry on resulting computations is necessary for design optimization. The geometry is defined in terms of a series of design variables, including design variables to define the wing planform, tail, canard, pylon, and nacelle. Design optimization in this research is based on how these design variable affect the potential flow. The potential flow is computed as a function of the geometry and location of a series of panels describing the airframe, which are in turn a function of the design variables. Multipole accelerated panel methods improve the computational complexity of the problem and thus are an attractive approach. To utilize the methods in design optimization, it was necessary to define the appropriate sensitivity derivatives. The overhead incurred from finding the sensitivity derivatives in conjunction with the original computation should be small. This research developed the background for multipole-accelerated panel methods and the framework for finding sensitivity derivatives in the methods. Potential flow panel codes are commonly used for powered-lift aerodynamic predictions for three dimensional geometries. Given an airframe which has been discretized into a series of panels to define the airframe geometry, potential is computed as a function of the influence of all panels on all other panels. This is a computationally intensive problem for which efficient solutions are desired to improve the computational time and to allow greater resolution by use of more panels. One such solution is the use of hierarchical multipole methods which entail approximations of the effects of far-field terms. Hierarchical multipole methods have become prevalent in molecular dynamics and gravitational physics, and have been introduced into the fields of capacitance calculations, computational fluid dynamics, and electromagnetics. The methods utilize multipole expansions to describe the effect of bodies (i.e. particles, astrophysical bodies, panels, etc.) within a sphere on points distant from the sphere, where the influence diminishes as a function of distance. The expansions are exact with infinite series, however, for practical computations, the series are truncated and accuracy is selected based on the number of terms retained in the expansions. A hierarchical tree structure groups bodies together based on proximity to allow definition of multipole expansions for each group. The multipole expansions are then used to compute the effect of the bodies in a group on distant bodies.

Leathrum, James F., Jr.↗

DOE OSTI2022

Modeling the Dynamics of Energetic Protons in Earth's Inner Magnetosphere

Recently, Van Allen Probes data have revealed the interesting energy-dependent dynamics of energetic protons in Earth's inner magnetosphere. To quantify the role of radial diffusion and charge exchange to the observed energy-dependent dynamics of ring current protons, a 1D radial diffusion model with charge exchange loss is implemented. The observed proton flux over the long-term period of November 2012 to September 2013 is first converted to phase space densities, which are then simulated by our model driven by an outer boundary condition at L* = 5.5 derived from the data. The simulation results show that our model generally captures the transport and acceleration of energetic protons at μ = 30, 50, and 80 MeV/G and K = 0.11 G 1/2 R E , suggesting that radial diffusion is the dominant source mechanism for >75 keV protons at L* = 3.5–5.5. Additionally, the observed fast decay of protons at lower μ and slow decay at higher μ are well captured by the model, demonstrating the dominant role of charge exchange in explaining the observed energy-dependent proton decay. For higher μ protons, prompt losses of protons on the time scale of hours are observed over a wide range of L*, which is too fast to be explained by charge exchange. Some of the prompt losses at high L* regions are reproduced by the model with outward radial diffusion to the outer boundary. However, many prompt losses observed at lower L* regions are not captured by the model, which could be due to other loss mechanisms including electromagnetic ion cyclotron wave scattering and field line curvature scattering.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1992

Intrinsically asymmetric astrophysical jets

Previous work on the origin of self-collimated electromagnetic jets is extended to the general case where there is no reflection symmetry of the magnetic field about the equatorial plane of the disk. The axisymmetric field structure inside the disk is obtained by solving for the magnetic flux function, and the toroidal magnetic field, from the generalized thin-disk induction equation, which is derived. The asymptotic (large-z) magnetic field structure outside the disk is obtained by solving the force-free Grad-Shafranov equation semianalytically. Jet solutions are found in which the power flow is carried mainly by the Poynting flux of the electromagnetic field and the angular momentum outflow from the disk is carried by the magnetic field. The ratio of jet luminosities (top/bottom) depends directly on the degree of asymmetry of the field and can easily be much greater than unity. It is argued that the degree of field asymmetry in the disk is determined by the asymmetry of the weak galactic field fed into the disk at large distances over long periods of time.

Wang, J. C. L.↗

NASA NTRS1995

Fast Multipole Methods for Three-Dimensional N-body Problems

We are developing computational tools for the simulations of three-dimensional flows past bodies undergoing arbitrary motions. High resolution viscous vortex methods have been developed that allow for extended simulations of two-dimensional configurations such as vortex generators. Our objective is to extend this methodology to three dimensions and develop a robust computational scheme for the simulation of such flows. A fundamental issue in the use of vortex methods is the ability of employing efficiently large numbers of computational elements to resolve the large range of scales that exist in complex flows. The traditional cost of the method scales as Omicron (N(sup 2)) as the N computational elements/particles induce velocities at each other, making the method unacceptable for simulations involving more than a few tens of thousands of particles. In the last decade fast methods have been developed that have operation counts of Omicron (N log N) or Omicron (N) (referred to as BH and GR respectively) depending on the details of the algorithm. These methods are based on the observation that the effect of a cluster of particles at a certain distance may be approximated by a finite series expansion. In order to exploit this observation we need to decompose the element population spatially into clusters of particles and build a hierarchy of clusters (a tree data structure) - smaller neighboring clusters combine to form a cluster of the next size up in the hierarchy and so on. This hierarchy of clusters allows one to determine efficiently when the approximation is valid. This algorithm is an N-body solver that appears in many fields of engineering and science. Some examples of its diverse use are in astrophysics, molecular dynamics, micro-magnetics, boundary element simulations of electromagnetic problems, and computer animation. More recently these N-body solvers have been implemented and applied in simulations involving vortex methods. Koumoutsakos and Leonard (1995) implemented the GR scheme in two dimensions for vector computer architectures allowing for simulations of bluff body flows using millions of particles. Winckelmans presented three-dimensional, viscous simulations of interacting vortex rings, using vortons and an implementation of a BH scheme for parallel computer architectures. Bhatt presented a vortex filament method to perform inviscid vortex ring interactions, with an alternative implementation of a BH scheme for a Connection Machine parallel computer architecture.

Koumoutsakos, P.↗

NASA NTRS2011

Simulation of Relativistic Shocks and Associated Radiation from Turbulent Magnetic Fields

Using our new 3-D relativistic particle-in-cell (PIC) code, we investigated long-term particle acceleration associated with a relativistic electron-positron jet propagating in an unmagnetized ambient electron-positron plasma. The simulations were performed using a much longer simulation system than our previous simulations in order to investigate the full nonlinear stage of the Weibel instability and its particle acceleration mechanism. Cold jet electrons are thermalized and ambient electrons are accelerated in the resulting shocks. Acceleration of ambient electrons leads to a maximum ambient electron density three times larger than the original value as predicted by hydrodynamic compression. Behind the bow shock, in the jet shock, strong electromagnetic fields are generated. These fields may lead to time dependent afterglow emission. In order to go beyond the standard synchrotron model used in astrophysical objects we have used PIC simulations and calculated radiation based on first principles. We calculated radiation from electrons propagating in a uniform parallel magnetic field to verify the technique. We also used the technique to calculate emission from electrons based on simulations with a small system. We obtain spectra which are consistent with those generated from electrons propagating in turbulent magnetic fields. This turbulent magnetic field is similar to the magnetic field generated at an early nonlinear stage of the Weibel instability. A fully developed shock within a larger system may generate a jitter/synchrotron spectrum.

Nishikawa, K.-I.↗

NASA NTRS2004

Particle Acceleration and Magnetic Field Generation in Electron-Positron Relativistic Shocks

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic electron-positron jet front propagating into an ambient electron-positron plasma with and without initial magnetic fields. We find small differences in the results for no ambient and modest ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The non-linear fluctuation amplitudes of densities, currents, electric, and magnetic fields in the electron-positron shock are larger than those found in the electron-ion shock studied in a previous paper. This comes from the fact that both electrons and positrons contribute to generation of the Weibel instability. Additionally, we have performed simulations with different electron skin depths. We find that growth times scale inversely with the plasma frequency, and the sizes of structures created by the Weibel instability scale proportional to the electron skin depth. This is the expected result and indicates that the simulations have sufficient grid resolution. While some Fermi acceleration may occur at the jet front, the majority of electron and positron acceleration takes place behind the jet front and cannot be characterized as Fermi acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying nonuniform, small-scale magnetic fields which contribute to the electron's (positron's) transverse deflection behind the jet head. This small scale magnetic field structure is appropriate to the generation of "jitter" radiation from deflected electrons (positrons) as opposed to synchrotron radiation. The jitter radiation has different properties than synchrotron radiation calculated assuming a a uniform magnetic field. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks.

Nishikawa, K.-I.↗

NASA NTRS2004

Particle Acceleration and Magnetic Field Generation in Electron-Positron Relativistic Shocks

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic electron-positron jet front propagating into an ambient electron-positron plasma with and without initial magnetic fields. We find small differences in the results for no ambient and modest ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The non-linear fluctuation amplitudes of densities, currents, electric, and magnetic fields in the electron-positron shock are larger than those found in the electron-ion shock studied in a previous paper at the comparable simulation time. This comes from the fact that both electrons and positrons contribute to generation of the Weibel instability. Additionally, we have performed simulations with different electron skin depths. We find that growth times scale inversely with the plasma frequency, and the sizes of structures created by the Weibel instability scale proportional to the electron skin depth. This is the expected result and indicates that the simulations have sufficient grid resolution. While some Fermi acceleration may occur at the jet front, the majority of electron and positron acceleration takes place behind the jet front and cannot be characterized as Fermi acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying nonuniform: small-scale magnetic fields which contribute to the electron's (positron's) transverse deflection behind the jet head. This small scale magnetic field structure is appropriate to the generation of jitter radiation from deflected electrons (positrons) as opposed to synchrotron radiation. The jitter radiation has different properties than synchrotron radiation calculated assuming a a uniform magnetic field. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks.

Nishikawa, K.-L.↗

NASA NTRS2019

Enabling Real-time Multi-messenger Astrophysics Discoveries with Deep Learning

Multi-messenger astrophysics is a fast-growing, interdisciplinary field that combines data, which vary in volume and speed of data processing, from many different instruments that probe the Universe using different cosmic messengers: electromagnetic waves, cosmic rays, gravitational waves and neutrinos. In this Expert Recommendation, we review the key challenges of real-time observations of gravitational wave sources and their electromagnetic and astroparticle counterparts, and make a number of recommendations to maximize their potential for scientific discovery. These recommendations refer to the design of scalable and computationally efficient machine learning algorithms; the cyber-infrastructure to numerically simulate astrophysical sources, and to process and interpret multi-messenger astrophysics data; the management of gravitational wave detections to trigger real-time alerts for electromagnetic and astroparticle follow-ups; a vision to harness future developments of machine learning and cyber-infrastructure resources to cope with the big-data requirements; and the need to build a community of experts to realize the goals of multi-messenger astrophysics.

E A Huerta↗

DOE OSTI2020

On numerical errors to the fields surrounding a relativistically moving particle in PIC codes

The particle-in-cell (PIC) method is widely used to model the self-consistent interaction between discrete particles and electromagnetic fields. It has been successfully applied to problems across plasma physics including plasma based acceleration, inertial confinement fusion, magnetically confined fusion, space physics, astrophysics, high energy density plasmas. In many cases the physics involves how relativistic particles (those with high relativistic γ factors) are generated and interact with plasmas. However, when relativistic particles stream across the grid, both in “vacuum” and in plasma, many numerical issues may arise which can lead to unphysical results. We present a detailed analysis of how discretized Maxwell solvers used in PIC codes can lead to numerical errors to the fields that surround particles that move at relativistic speeds across the grid. Expressions for the axial electric field as integrals in k space are presented that reveal two types of errors. The first arises from errors to the numerator of the integrand and leads to unphysical fields that are antisymmetric about the particle. Furthermore, the second arises from errors to the denominator of the integrand and lead to Cherenkov like radiation in “vacuum”. These fields are not anti-symmetric, extend behind the particle, and cause the particle to accelerate or decelerate depending on the solver and parameters. The unphysical fields are studied in detail for two representative solvers - the Yee solver and the FFT based solver. Although the Cherenkov fields are absent, the space charge fields are still present in the fundamental Brillouin zone for the FFT based solvers. In addition, the Cherenkov fields are present in higher order zones for the FFT based solvers. Comparison between the analytical solutions and PIC simulation results are presented. A solution for eliminating these unphysical fields by modifying the k operator in the axial direction is also presented. Using a customized finite difference solver, this solution was successfully implemented into OSIRIS [1]. Results from the customized solver are also presented. Additionally, this solution will be useful for a beam of particles that all move in one direction with a small angular divergence.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2005

Particle Acceleration and Magnetic Field Generation in Electron-Positron Relativistic Shocks

Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel, and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a three-dimensional relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic electron-positron jet front propagating into an ambient electron-positron plasma with and without initial magnetic fields. We find small differences in the results for no ambient and modest ambient magnetic fields. New simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. Furthermore, the nonlinear fluctuation amplitudes of densities, currents, and electric and magnetic fields in the electron-positron shock are larger than those found in the electron-ion shock studied in a previous paper at a comparable simulation time. This comes from the fact that both electrons and positrons contribute to generation of the Weibel instability. In addition, we have performed simulations with different electron skin depths. We find that growth times scale inversely with the plasma frequency, and the sizes of structures created by tine Weibel instability scale proportionally to the electron skin depth. This is the expected result and indicates that the simulations have sufficient grid resolution. While some Fermi acceleration may occur at the jet front, the majority of electron and positron acceleration takes place behind the jet front and cannot be characterized as Fermi acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying nonuniform, small-scale magnetic fields, which contribute to the electron s (positron s) transverse deflection behind the jet head. This small- scale magnetic field structure is appropriate to the generation of "jitter" radiation from deflected electrons (positrons) as opposed to synchrotron radiation. The jitter radiation has different properties than synchrotron radiation calculated assuming a uniform magnetic field. The jitter radiation resulting from small-scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks.

Nishikawa, K.-I.↗

DOE OSTI2022

Long-term general relativistic magnetohydrodynamics simulations of magnetic field in isolated neutron stars

ABSTRACT Strong magnetic fields play an important role in powering the emission of neutron stars. Nevertheless, a full understanding of the interior configuration of the field remains elusive. In this work, we present general relativistic magnetohydrodynamics (MHD) simulations of the magnetic field evolution in neutron stars lasting ${\sim } {880}\,$ms (∼6.5 Alfvén crossing periods) and up to resolutions of $0.1155\,$km using Athena++. We explore two different initial conditions, one with purely poloidal magnetic field and the other with a dominant toroidal component, and study the poloidal and toroidal field energies, the growth times of the various instability-driven oscillation modes, and turbulence. We find that the purely poloidal setup generates a toroidal field, which later decays exponentially reaching $1{{\ \rm per\ cent}}$ of the total magnetic energy, showing no evidence of reaching equilibrium. The initially stronger toroidal field setup, on the other hand, loses up to 20 per cent of toroidal energy and maintains this state till the end of our simulation. We also explore the hypothesis, drawn from previous MHD simulations, that turbulence plays an important role in the quasi-equilibrium state. An analysis of the spectra in our higher resolution setups reveals, however, that in most cases we are not observing turbulence at small scales, but rather a noisy velocity field inside the star. We also observe that the majority of the magnetic energy gets dissipated as heat increasing the internal energy of the star, while a small fraction gets radiated away as electromagnetic radiation.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2004

Particle Acceleration, Magnetic Field Generation, and Emission in Relativistic Pair Jets

Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating into an ambient plasma. We find that the growth times depend on the Lorenz factors of jets. The jets with larger Lorenz factors grow slower. Simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The small scale magnetic field structure generated by the Weibel instability is appropriate to the generation of "jitter" radiation from deflected electrons (positrons) as opposed to synchrotron radiation. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks.

Nishikawa, K. I.↗

NASA NTRS2005

Particle Acceleration, Magnetic Field Generation in Relativistic Shocks

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating through an ambient plasma with and without initial magnetic fields. We find only small differences in the results between no ambient and weak ambient parallel magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates particles perpendicular and parallel to the jet propagation direction. New simulations with an ambient perpendicular magnetic field show the strong interaction between the relativistic jet and the magnetic fields. The magnetic fields are piled up by the jet and the jet electrons are bent, which creates currents and displacement currents. At the nonlinear stage, the magnetic fields are reversed by the current and the reconnection may take place. Due to these dynamics the jet and ambient electron are strongly accelerated in both parallel and perpendicular directions.

Nishikawa, Ken-Ichi↗

NASA NTRS2003

Particle Acceleration and Radiation associated with Magnetic Field Generation from Relativistic Collisionless Shocks

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating through an ambient plasma with and without initial magnetic fields. We find only small differences in the results between no ambient and weak ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates particles perpendicular and parallel to the jet propagation direction. While some Fermi acceleration may occur at the jet front, the majority of electron acceleration takes place behind the jet front and cannot be characterized as Fermi acceleration. The simulation results show that this instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields, which contribute to the electron s transverse deflection behind the jet head. The "jitter" radiation from deflected electrons has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.

Nishikawa, K.↗