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The Fermi-LAT collaboration, A. A. Abdo Et Al., the Magic Collaboration, J. Aleksić et Al., the VERITAS Collaboration, V. A. Acciari Et Al., the GASP-WEBT consortium, Multi-Wavelength Partners
Published: 24 November 2010
Abstract:
We report on the gamma-ray activity of the blazar Mrk 501 during the first 480 days of Fermi operation. We find that the average LAT gamma-ray spectrum of Mrk 501 can be well described by a single power-law function with a photon index of 1.78 +/- 0.03. While we observe relatively mild flux variations with the Fermi-LAT (within less than a factor of 2), we detect remarkable spectral variability where the hardest observed spectral index within the LAT energy range is 1.52 +/- 0.14, and the softest one is 2.51 +/- 0.20. These unexpected spectral changes do not correlate with the measured flux variations above 0.3GeV. In this paper, we also present the first results from the 4.5-month-long multifrequency campaign (2009 March 15 - August 1) on Mrk 501, which included the VLBA, Swift, RXTE, MAGIC and VERITAS, the F-GAMMA, GASP-WEBT, and other collaborations and instruments which provided excellent temporal and energy coverage of the source throughout the entire campaign. The average spectral energy distribution of Mrk 501 is well described by the standard one-zone synchrotron self-Compton model. In the framework of this model, we find that the dominant emission region is characterized by a size <~ 0.1 pc (comparable within a factor of few to the size of the partially-resolved VLBA core at 15-43 GHz), and that the total jet power (~10^{44} erg s^{-1}) constitutes only a small fraction (~10^{-3}) of the Eddington luminosity. The energy distribution of the freshly-accelerated radiating electrons required to fit the time-averaged data has a broken power-law form in the energy range 0.3GeV-10TeV, with spectral indices 2.2 and 2.7 below and above the break energy of 20GeV. We argue that such a form is consistent with a scenario in which the bulk of the energy dissipation within the dominant emission zone of Mrk 501 is due to relativistic, proton-mediated shocks.
Espen Gaarder Haug
European Journal of Applied Physics, Volume 4, pp 24-27; https://doi.org/10.24018/ejphysics.2022.4.4.190

Abstract:
In 1923, Arthur Holly Compton introduced what today is known as the Compton wavelength. Even if the Compton scattering derivation by Compton is relativistic in the sense that it takes into account the momentum of photons traveling at the speed of light, the original Compton derivation indirectly assumes that the electron is stationary at the moment it is scattered by electrons, but not after it has been hit by photons. Here, we extend this to derive Compton scattering for the case when the electron is initially moving at a velocity v.
Published: 6 September 2021
Abstract:
In this paper, we show how one can find the Compton scattering formula and thereby also the Compton wavelength based on new concepts from collision-space time. This gives us the standard Compton wavelength, but we go one step forward and show how to find the relativistic Compton wavelength from Compton scattering as well. (That is, when the electron is also moving initially.) The original Compton formula only gives the electron's rest-mass Compton wavelength, or we could call it the standing electron's Compton wave.
Preprint
Open Access
Izak van der Westhuizen, Brian van Soelen, Markus Böttcher, Pieter Meintjes
Proceedings of 36th International Cosmic Ray Conference — PoS(ICRC2019), Volume 358; https://doi.org/10.22323/1.358.0811

Abstract:
Relativistic jets associated with active galactic nuclei (AGN) produce radiation over a large range of the electromagnetic spectrum. While relativistic magneto-hydrodynamic (RMHD) simulations have become a powerful tool to model the physical structure of jets, in order to correlate them to observations, estimates of the radiation must also be determined. We present the initial results from a study to calculate the multi-wavelength radiation by applying Monte-Carlo methods, using the parameters provided by the RMHD simulations. We present our initial implementation of a Monte Carlo code that interfaces with the RMHD simulation of a steady state axis-symmetric jet created using the PLUTO code. Properties such as the number density, energy density, magnetic field and bulk Lorentz factor are obtained from the RMHD simulations and used to generate a synchrotron photon distribution in each cell. These photons are tracked as they move through the simulation environment and undergoes inverse Compton scattering. Each photon is recorded when it exits the simulation domain and is used to construct multi-wavelength SEDs and light curves. This will provide a time-dependent, multi-zone Synchrotron Self-Compton (SSC) emission model for RMHD simulations.
Journal of Modern Physics, Volume 11, pp 528-534; https://doi.org/10.4236/jmp.2020.114035

Abstract:
K. Suto has recently pointed out an interesting relativistic extension of Rydberg’s formula. Here we also discuss Rydberg’s formula, and offer additional evidence on how one can easily see that it is non-relativistic and therefore a good approximation, at best, when . We also extend the Suto formula to hold for any atom and examine the formula in detail.
Antony J. Bourdillon
Journal of Modern Physics, Volume 09, pp 2295-2307; https://doi.org/10.4236/jmp.2018.913145

Abstract:
Because magnetic moment is spatial in classical magnetostatics, we progress beyond the axiomatic concept of the point particle electron in physics. Orbital magnetic moment is well grounded in spherical harmonics in a central field. There, quantum numbers are integral. The half-integral spinor moment appears to be due to cylindrical motion in an external applied magnetic field; when this is zero , the spin states are degenerate. Consider lifting the degeneracy by diamagnetism in the cylindrical magnetic field: a uniquely derived electronic magnetic radius shares the identical value to the Compton wavelength.
I.V Pogorelsky
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Volume 411, pp 172-187; https://doi.org/10.1016/s0168-9002(98)00259-9

The publisher has not yet granted permission to display this abstract.
Physical Review D, Volume 86; https://doi.org/10.1103/physrevd.86.025029

Abstract:
Building on our previous work [Phys. Rev. D 82, 085016 (2010)], we show in this paper how a Brownian motion on a short scale can originate a relativistic motion on scales that are larger than particle’s Compton wavelength. This can be described in terms of polycrystalline vacuum. Viewed in this way, special relativity is not a primitive concept, but rather it statistically emerges when a coarse-graining average over distances of order, or longer than the Compton wavelength is taken. By analyzing the robustness of such a special relativity under small variations in the polycrystalline grain-size distribution we naturally arrive at the notion of doubly-special relativistic dynamics. In this way, a previously unsuspected, common statistical origin of the two frameworks is brought to light. Salient issues such as the rôle of gauge fixing in emergent relativity, generalized commutation relations, Hausdorff dimensions of representative path-integral trajectories and a connection with Feynman chessboard model are also discussed. DOI: http://dx.doi.org/10.1103/PhysRevD.86.025029 © 2012 American Physical Society
Elliott H. Lieb, Robert Seiringer
Published: 5 November 2009
Abstract:
In this second chapter we will review the basic mathematical and physical facts about quantum mechanics and establish physical units and notation. Those readers already familiar with the subject can safely jump to the next chapter. An attempt has been made to make the presentation in this chapter as elementary as possible, and yet present the basic facts that will be needed later. There are many beautiful and important topics which will not be touched upon such as self-adjointness of Schrödinger operators, the general mathematical structure of quantum mechanics and the like. These topics are well described in other works, e.g.. Much of the following can be done in a Euclidean space of arbitrary dimension, but in this chapter the dimension of the Euclidean space is taken to be three-which is the physical case-unless otherwise stated. We do this to avoid confusion and, occasionally, complications that arise in the computation of mathematical constants. The interested reader can easily generalize what is done here to the R d, d >3 case. Likewise, in the next chapters we mostly consider N particles, with spatial coordinates in R3, so that the total spatial dimension is 3N. A Brief Review of the Connection Between Classical and Quantum Mechanics Considering the range of validity of quantum mechanics, it is not surprising that its formulation is more complicated and abstract than classical mechanics. Nevertheless, classical mechanics is a basic ingredient for quantum mechanics. One still talks about position, momentum and energy which are notions from Newtonian mechanics.
Published: 6 September 2021
Abstract:
In this paper, we show how one can find the Compton scattering formula and thereby also the Compton wavelength based on new concepts from collision-space time. This gives us the standard Compton wavelength, but we go one step forward and show how to find the relativistic Compton wavelength from Compton scattering as well. (That is, when the electron is also moving initially.) The original Compton formula only gives the electron's rest-mass Compton wavelength, or we could call it the standing electron's Compton wave.
Espen Gaarder Haug
Journal of Modern Physics, Volume 11, pp 1938-1949; https://doi.org/10.4236/jmp.2020.1112122

Abstract:
In a recent paper, we [1] discussed that Suto [2] has pointed out an interesting relativistic extension of Rydberg’s formula. In that paper, we had slightly misunderstood Suto’s approach, something we will comment on further here. The relativistic Suto formula is actually derived from a theory where the standard relativistic momentum relation is changed. The relativistic Rydberg formula we presented and mistakenly thought was the same as Suto’s formula is, on the other hand, derived to be fully consistent with the standard relativistic momentum relation. Here we will point out the differences between the formulas and correct some errors in our previous paper. The paper should give deeper and better intuition about the Rydberg formula and what it represents.
Franz Schwabl
Published: 1 January 1999
The publisher has not yet granted permission to display this abstract.
Zhirong Huang
Radiative Cooling of Relativistic Electron Beams; https://doi.org/10.2172/663283

Abstract:
Modern high-energy particle accelerators and synchrotron light sources demand smaller and smaller beam emittances in order to achieve higher luminosity or better brightness. For light particles such as electrons and positrons, radiation damping is a natural and effective way to obtain low emittance beams. However, the quantum aspect of radiation introduces random noise into the damped beams, yielding equilibrium emittances which depend upon the design of a specific machine. In this dissertation, the author attempts to make a complete analysis of the process of radiation damping and quantum excitation in various accelerator systems, such as bending magnets, focusing channels and laser fields. Because radiation is formed over a finite time and emitted in quanta of discrete energies, he invokes the quantum mechanical approach whenever the quasiclassical picture of radiation is insufficient. He shows that radiation damping in a focusing system is fundamentally different from that in a bending system. Quantum excitation to the transverse dimensions is absent in a straight, continuous focusing channel, and is exponentially suppressed in a focusing-dominated ring. Thus, the transverse normalized emittances in such systems can in principle be damped to the Compton wavelength of the electron, limited only by the Heisenberg uncertainty principle. In addition,more » he investigates methods of rapid damping such as radiative laser cooling. He proposes a laser-electron storage ring (LESR) where the electron beam in a compact storage ring repetitively interacts with an intense laser pulse stored in an optical resonator. The laser-electron interaction gives rise to rapid cooling of electron beams and can be used to overcome the space charge effects encountered in a medium energy circular machine. Applications to the designs of low emittance damping rings and compact x-ray sources are also explored.« less
Allan H. Sørensen
Physical Review A, Volume 64; https://doi.org/10.1103/physreva.64.012703

Abstract:
The resolution in space of processes involving high-energy photons incident on atoms or bare atomic nuclei is investigated. A simple analysis, based on momentum transfer, gives first indications of the length scale being defined by the Compton wavelength of the electron for both the photoeffect and electron-positron pair creation with the electron bound to the atomic nucleus. Since the simple method of converting a momentum transfer q to a distance of ħ/q has potential pitfalls, we continue with a detailed wave-packet study. This study, which is undertaken for the case of the photoeffect, involves the incidence of a photon localized in space and time on a hydrogenlike atom. The wave-packet approach confirms the Compton wavelength, and not the extent of the atomic state, to be the decisive measure for photon energies in excess of the electron rest energy mc2. In addition, it provides a direct and detailed picture of the impact-parameter dependence of the process. As an introduction to the wave-packet study, we compare calculations based on a plane-wave representation of the unbound lepton to lowest-order perturbative calculations.
G.A. Horton-Smith
A study of high field quantum electrodynamics in the collision of high energy electrons with a terawatt laser; https://doi.org/10.2172/663331

Abstract:
An experiment is described which studied quantum electrodynamic interactions under conditions of extremely high fields, along with a review of the relevant theory. The high fields were created by an intense, tightly-focused pulse of laser light at green or infrared wavelengths, into which was sent an ultra-relativistic electron beam of 46.6-GeV energy. The relevant theory is that of an electron in an electromagnetic wave so intense that the electron's mass is effectively shifted by the transverse momentum imparted to it by the wave, and the electron encounters field strengths comparable to the Schwinger critical field strength of 511 kV per Compton wavelength. An electron in the intense wave may radiate a photon and balance 4-momentum by absorbing multiple photons from the laser, which can lead to real photons with energies above the kinematic limit for conventional Compton scattering. All particles have significant probability of scattering multiple times while in the focus of the laser, including the photons radiated by the electrons, which may convert into electron-positron pairs, again with absorption of multiple photons from the laser. This experiment was able to measure the rates and spectra of positrons, electrons, and photons emerging from the interaction region. Results from both experimentmore » and theoretical simulations are presented and compared. The results from the electron and positron measurements are compatible with the accepted theory, within experimental uncertainties due mainly to the laser intensity measurement. The photon spectrum shows the correct shape, but the ratio of rates in the linear and two-absorbed-photon portions of the spectrum does not vary as expected with the laser intensity, suggesting a disagreement with the accepted theory, with a significance of roughly two standard deviations. A follow-up experiment would be in order.« less
Paolo Christillin,
Physical Review A, Volume 76; https://doi.org/10.1103/physreva.76.042104

Abstract:
The transmission of fermions of mass m and energy E through an electrostatic potential barrier of rectangular shape (i.e., supporting an infinite electric field), of height U>E+mc2—due to the many-body nature of the Dirac equation evidentiated by the Klein paradox—has been widely studied. Here we exploit the analytical solution, given by Sauter for the linearly rising potential step, to show that the tunneling rate through a more realistic trapezoidal barrier is exponentially depressed, as soon as the length of the regions supporting a finite electric field exceeds the Compton wavelength of the particle—the latter circumstance being hardly escapable in most realistic cases.
Published: 1 July 2013
Physics of Plasmas, Volume 20; https://doi.org/10.1063/1.4811475

Abstract:
Using a quantum fluid model, the linear dispersion relation for FEL pumped by a short wavelength laser wiggler is deduced. Subsequently, a new quantum corrected resonance condition is obtained. It is shown that, in the limit of low energy electron beam and low frequency pump, the quantum recoil effect can be neglected, recovering the classical FEL resonance condition, ks=4kwγ2 . On the other hand, for short wavelength and high energy electron beam, the quantum recoil effect becomes strong and the resonance condition turns into ks=2kw/ƛcγ3/2 , with ƛc being the reduced Compton wavelength. As a result, a set of nonlinear coupled equations, which describes the quantum FEL dynamics as a three-wave interaction, is obtained. Neglecting wave propagation effects, this set of equations is solved numerically and results are presented.
Published: 14 January 2019
by MDPI
Abstract:
We suggest that momentum should be redened in order to help make physics more consistent and more logical. In this paper, we propose that there is a rest-mass momentum, a kinetic momentum, and a total momentum. This leads directly to a simpler relativistic energy momentum relation. As we point out, it is the Compton wavelength that is the true wavelength for matter; the de Broglie wavelength is mostly a mathematical artifact. This observation also leads us to a new relativistic wave equation and a new and likely better QM. Better in terms of being much more consistent and simpler to understand from a logical perspective.
F. E. Leys, N. H. March, ,
Physical Review B, Volume 67; https://doi.org/10.1103/physrevb.67.113105

Abstract:
The displaced charge in an initially homogeneous electron gas due to a weak perturbing potential as calculated by March and Murray was generalized to include relativistic effects by Baltin and March. This latter result is here used to study the relativistic corrections to the static Lindhard dielectric function. An analytic generalization of the Lindhard function to the second order in the Compton wavelength is presented.
A. M. Rasulova
Odessa Astronomical Publications, Volume 28, pp 147-149; https://doi.org/10.18524/1810-4215.2015.28.70609

Abstract:
The expression for the tidal forces of the two relativistic protons at a distance of the order of the Compton wavelength near a rotating black hole is found. The analysis shows that the tidal forces are dependent on the plane of incidence and sharply increase with increasing Lorentz factor.
A.V. Tulupov
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Volume 331, pp 437-439; https://doi.org/10.1016/0168-9002(93)90086-w

The publisher has not yet granted permission to display this abstract.
P. Krekora, Q. Su,
Physical Review Letters, Volume 93; https://doi.org/10.1103/physrevlett.93.043004

Abstract:
Using space-time resolved solutions to relativistic quantum field theory we analyze the electron-positron pair creation process from vacuum. For early times the entangled electron-positron wave function can be obtained analytically. We show that there are, in principle, no limitations to the localization length of an electron and demonstrate that its spatial probability density can be much narrower than the Compton wavelength. We also find that quantum field theory prohibits the occurrence of Zitterbewegung for an electron.
Jan C. A. Boeyens
Published: 13 August 2016
The publisher has not yet granted permission to display this abstract.
A. O. Barut, H. Kleinert, S. Malin
Published: 1 December 1968
Il Nuovo Cimento A Series 10, Volume 58, pp 835-847; https://doi.org/10.1007/bf02825374

The publisher has not yet granted permission to display this abstract.
Journal of Physics A: Mathematical and General, Volume 32, pp 5367-5382; https://doi.org/10.1088/0305-4470/32/28/314

Abstract:
The dynamics of wavepackets in a relativistic Dirac oscillator (DO) is compared with that of the Jaynes-Cummings model. The strong spin-orbit coupling of the DO produces the entanglement of the spin with the orbital motion similar to that observed in the model of quantum optics. The resulting collapses and revivals of the spin extend to a relativistic theory our previous findings on a nonrelativistic oscillator where they were known as spin-orbit pendulum. The Foldy-Wouthuysen transformation can be performed exactly for the DO. It produces the well known smoothing effect over the Compton wavelength. Thus, after this transformation, zitterbewegung disappears just as the components of the WP associated to negative energy states.
Applied Physics Express, Volume 1; https://doi.org/10.1143/apex.1.087003

Abstract:
We propose a new terahertz-wave spectrophotometry by Compton backscattering using relativistic electron bunches and coherent radiations generated by them. The terahertz-wave spectrophotometry can be realized simultaneously with Compton backscattering, where the characteristics in the terahertz-wave region are converted to those in the visible and ultraviolet regions. The number of Compton backscattered photons is estimated to be more than 100 counts per second with a wavelength divergence of 5% in the visible and ultraviolet regions using the compact S-band linac at National Institute of Advanced Industrial Science and Technology. This spectrophotometry becomes significant in energy recovery linacs.
S. V. Kuzikov, A. V. Savilov,
Published: 21 July 2014
Applied Physics Letters, Volume 105; https://doi.org/10.1063/1.4890586

Abstract:
A concept for the room-temperature rf undulator, designed to produce coherent X-ray radiation by means of a relatively low-energy electron beam and pulsed mm-wavelength radiation, is proposed. The “flying” undulator is a high-power short rf pulse co-propagating together with a relativistic electron bunch in a helically corrugated waveguide. The electrons wiggle in the rf field of the −1st spatial harmonic with the phase velocity directed in the opposite direction in respect to the bunch velocity, so that particles can irradiate high-frequency Compton's photons. A high group velocity (close to the speed of light) ensures long cooperative motion of the particles and the co-propagating rf pulse.
Th. W. Ruijgrok
Published: 30 December 1998
Few-Body Systems, Volume 25, pp 5-27; https://doi.org/10.1007/s006010050091

The publisher has not yet granted permission to display this abstract.
, Zdenka Kuncic, Kinwah Wu
Published: 11 June 2009
Abstract:
We investigate the polarization of Compton scattered X-rays from relativistic jets in active galactic nuclei using Monte Carlo simulations. We consider three scenarios: scattering of photons from an accretion disk, scattering of cosmic microwave background (CMB) photons, and synchrotron self-Comptonization (SSC) within the jet. For Comptonization of thermal disk photons or CMB photons the maximum linear polarization attained is slightly over 20% at viewing angles close to 90 degrees. The value decreases with the viewing inclination. For SSC, the maximum value may exceed 80%. The angle dependence is complicated, and it varies with the photon injection sites. Our study demonstrates that X-ray polarization, in addition to multi-wavelength spectra, can distinguish certain models for emission and particle acceleration in relativistic jets.
Adam D. Helfer
Published: 10 September 2018
Abstract:
It has been suggested that dark matter is a superfluid of particles whose masses are on the rough order of $10^{-22}$ eV. Since the occupation numbers are huge, the state is coherent, and the speeds typical of orbital velocities in halos, it has generally been assumed that a classical effective non-relativistic treatment is adequate. However, the Compton wavelength would be $\sim 1\, {\rm pc}$, and around the Compton scale concerns about some aspects of quantum measurement theory, known in principle but not quantitatively significant in previous cases, become pronounced. I estimate here the stress--energy operator, averaged over a few Compton wavelengths; a rough but useful approximation has a remarkably simple form. Conventional quantum measurement theory gives physically unacceptable results: a thought-experiment to measure the stress--energy is described which would involve only a modest apparatus but would excite particles in the observation volume to relativistic energies; these particles would escape the Galaxy, and there would be a substantial violation of energy conservation. Related foundational questions come up: the meaning of measurements of observables with continuous spectra, and the problem of predicting when measurements occur. The effective classical theory of fuzzy dark matter is not affected; however, the underlying quantum theory cannot be regarded as satisfactory without resolving these issues. But we may interpret the results more broadly. The macroscopic Compton scale amplifies inadequacies of measurement theory which have not previously seemed pressing.
Omar Jamil, Markus Boettcher
Published: 12 September 2012
Abstract:
We report on the development of a numerical code to calculate the angle-dependent synchrotron + synchrotron self-Compton radiation from relativistic jet sources with partially ordered magnetic fields and anisotropic particle distributions. Using a multi-zone radiation transfer approach, we can simulate magnetic-field configurations ranging from perfectly ordered (unidirectional) to randomly oriented (tangled). We demonstrate that synchrotron self-Compton model fits to the spectral energy distributions (SEDs) of extragalactic jet sources may be possible with a wide range of magnetic-field values, depending on their orientation with respect to the jet axis and the observer. This is illustrated with the example of a spectral fit to the SED of Mrk~421 from multi-wavelength observations in 2006, where acceptable fits are possible with magnetic-field values varying within a range of an order of magnitude for different degrees of B-field alignment and orientation.
P. Krekora, Q. Su
Published: 20 January 2005
Journal of Modern Optics, Volume 52, pp 489-504; https://doi.org/10.1080/09500340412331303243

Abstract:
We analyse the degree of two-particle entanglement between an electron and a positron that are created in vacuum in the presence of a supercritical field. This degree of entanglement is determined from the spatially and temporally resolved two-particle wave function calculated from relativistic quantum field theory. Some spin components of the two particles are fully correlated with respect to a simultaneous measurement. However, the positions where the two particles are created by the field can be apart from each other by as much as the Compton wavelength for an extended supercritical field. We calculate the K parameter from the two-particle wave function as a quantitative measure for the degree of entanglement.
Martin Rivas
Journal of Mathematical Physics, Volume 35, pp 3380-3399; https://doi.org/10.1063/1.530474

Abstract:
Quantization of generalized Lagrangian systems suggests that wave functions for elementary particles must be defined on the kinematical space rather than on configuration space. For spinning particles the center of mass and center of charge are different points. Their separation is of the order of the Compton wavelength. Spin‐1/2 particles arise if the classical model rotates but no half integer spins are obtained for systems with spin of orbital nature. Dirac’s equation is obtained when quantizing the classical relativistic spinning particles whose center of charge is circling around its center of mass at the speed c. Internal orientation of the electron completely characterizes its Dirac’s algebra.
Gunjan Tomar, Nayantara Gupta, Raj Prince
Published: 17 July 2021
Abstract:
Low luminosity active galactic nuclei are more abundant and closer to us than the luminous ones but harder to explore as they are faint. We have selected the four sources NGC 315, NGC 4261, NGC 1275, and NGC 4486, which have been detected in gamma rays byFermi-LAT. We have compiled their long-term radio, optical, X-ray data from different telescopes, analysed XMM-Newton data for NGC 4486, XMM-Newton and Swift data for NGC 315. We have analysed the Fermi-LAT data collected over the period of 2008 to 2020 for all of them. Electrons are assumed to be accelerated to relativistic energies in sub-parsec scale jets, which radiate by synchrotron and synchrotron self-Compton emission covering radio to gamma-ray energies. This model can fit most of the multi-wavelength data points of the four sources. However, the gamma-ray data points from NGC 315 and NGC 4261 can be well fitted only up to 1.6 GeV and 0.6 GeV, respectively in this model. This motivates us to find out the origin of the higher energy {\gamma}-rays detected from these sources. Kilo-parsec scale jets have been observed previously from these sources in radio and X-ray frequencies. If we assume {\gamma}-rays are also produced in kilo-parsec scale jets of these sources from inverse Compton scattering of starlight photons by ultra-relativistic electrons, then it is possible to fit the gamma-ray data at higher energies. Our result also suggests that strong host galaxy emission is required to produce GeV radiation from kilo-parsec scale jets.
Published: 25 May 2004
Abstract:
In this paper, we use the theory of fractional powers of linear operators to construct a general (analytic) representation theory for the square-root energy operator of relativistic quantum theory, which is valid for all values of the spin. We focus on the spin 1/2 case, considering a few simple yet solvable and physically interesting cases, in order to understand how to interpret the operator. Our general representation is uniquely determined by the Green's function for the corresponding Schrodinger equation. We find that, in general, the operator has a representation as a nonlocal composite of (at least) three singularities. In the standard interpretation, the particle component has two negative parts and one (hard core) positive part, while the antiparticle component has two positive parts and one (hard core) negative part. This effect is confined within a Compton wavelength such that, at the point of singularity, they cancel each other providing a finite result. Furthermore, the operator looks like the identity outside a few Compton wavelengths (cutoff). To our knowledge, this is the first example of a physically relevant operator with these properties.
J. Rayford Nix
Published: 25 February 1994
Abstract:
We discuss future directions in the development of classical hadrodynamics for extended nucleons, corresponding to nucleons of finite size interacting with massive meson fields. This new theory provides a natural covariant microscopic approach to relativistic nucleus-nucleus collisions that includes automatically spacetime nonlocality and retardation, nonequilibrium phenomena, interactions among all nucleons, and particle production. The present version of our theory includes only the neutral scalar ($\sigma$) and neutral vector ($\omega$) meson fields. In the future, additional isovector pseudoscalar ($\pi^+$,~$\pi^-$,~$\pi^0$), isovector vector ($\rho^+$,~$\rho^-$,~$\rho^0$), and neutral pseudoscalar ($\eta$) meson fields should be incorporated. Quantum size effects should be included in the equations of motion by use of the spreading function of Moniz and Sharp, which generates an effective nucleon mass density smeared out over a Compton wavelength. However, unlike the situation in electrodynamics, the Compton wavelength of the nucleon is small compared to its radius, so that effects due to the intrinsic size of the nucleon dominate.
I.V. Pogorelsky
High-intensity laser synchrotron x-ray source; https://doi.org/10.2172/197223

Abstract:
A laser interacting with a relativistic electron beam behaves like a virtual wiggler of an extremely short period equal to half of the laser wavelength. This approach opens a route to relatively compact, high-brightness x-ray sources alternative or complementary to conventional synchrotron light sources. Although not new, the Laser Synchrotron Light Source (LSLS) concept is still waiting for a convincing demonstration. Available at the BNL`s Accelerator Test Facility (ATF), a high-brightness electron beam and the high-power C0{sub 2} laser may be used as prototype LSLS brick stones. In a feasible demonstration experiment, 10-GW, 100-ps C0{sub 2} laser beam will be brought to a head-on collision with a 10-ps, 0.5-nC, 70 MeV electron bunch. Flashes of well-collimated, up to 9.36-keV ({approximately}{Angstrom}) x-rays of 10-ps pulse duration, with a flux of {approximately}10{sup 19} photons/sec will be produced via linear Compton backscattering. The x-ray spectrum is tunable proportionally to a variable e-beam energy. A natural short-term extension of the proposed experiment would be further enhancement of the x-ray flux to a 10{sup 21}{minus}10{sup 22} photons/sec level, after the ongoing ATF CO{sub 2} laser upgrade to 1 TW peak power and electron bunch shortening to 3 ps. The ATF LSLS x-ray beamline, exceeding bymore » orders of magnitude the peak fluxes attained at the National Synchrotron Light Source (NSLS) x-ray storage ring, may become attractive for certain users, e.g., for biological x-ray microscopy. In addition, a terawatt CO{sub 2} laser will enable harmonic multiplication of the x-ray spectrum via nonlinear Compton scattering. « less
J Manners
Published: 8 October 2018
Abstract:
Chapter I The origins of quantum physics I The Compton effect — a strange dichotomy in the nature of electromagnetic radiation In a series of experiments conducted between 1919 and 1923, Arthur Holly Compton (Figure 1.1) investigated the scattering of monochromatic (single-wavelength) X-rays from graphite targets. He found that the radiation scattered at an angle 0 to the incident beam contained, in addition to radiation of the same wavelength as the incident radiation, a second component with a considerably longer wavelength. The existence of this second component in the scattered radiation could not be explained by the well-established theory of the scattering of electromagnetic waves by electrons. Compton considered instead the process illustrated in Figure 1.2, in which a particle of electromagnetic radiation, collides with a slow moving electron, which then recoils absorbing some of the X-ray particle’s energy. Treating the process as a collision between particles, and using only the (relativistic) conservation laws of energy and momentum, Compton was able to account for the effect completely. However, at the same time, in the same experiment, Compton was using interference effects, depending wholly on the wave model, in order to determine the wavelength of the scattered radiation. So here was an experiment which apparently required the simultaneous use of both the wave and particle models of electromagnetic radiation for the interpretation of the results! The existence of this strange dichotomy in the nature of electromagnetic radiation was just one indication of the need for a radical revision of views regarding the physical world.
Published: 27 September 2018
Physical Review D, Volume 98; https://doi.org/10.1103/physrevd.98.065015

Abstract:
It has been suggested that dark matter is a superfluid of particles whose masses are on the rough order of 1022eV. Since the occupation numbers are huge, the state is coherent, and the speeds typical of orbital velocities in halos, it has generally been assumed that a classical effective nonrelativistic treatment is adequate. However, the Compton wavelength would be 1pc, and around the Compton scale concerns about some aspects of quantum measurement theory, known in principle but not quantitatively significant in previous cases, become pronounced. I estimate here the stress-energy operator, averaged over a few Compton wavelengths; a rough but useful approximation has a remarkably simple form. Conventional quantum measurement theory gives physically unacceptable results: a thought-experiment to measure the stress-energy is described which would involve only a modest apparatus but would excite particles in the observation volume to relativistic energies; these particles would escape the Galaxy, and there would be a substantial violation of energy conservation. Related foundational questions come up: the meaning of measurements of observables with continuous spectra, and the problem of predicting when measurements occur. The effective classical theory of fuzzy dark matter is not affected; however, the underlying quantum theory cannot be regarded as satisfactory without resolving these issues. But we may interpret the results more broadly. The macroscopic Compton scale amplifies inadequacies of measurement theory which have not previously seemed pressing.
A. A. Broyles
International Journal of Quantum Chemistry, Volume 17, pp 47-74; https://doi.org/10.1002/qua.560170106

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, , Yasuyuki T. Tanaka, , Koji S. Kawabata, , Kenji Kawaguchi, Yuka Kanda
Published: 10 February 2015
Abstract:
Blazars are thought to possess a relativistic jet that is pointing toward the direction of the Earth and the elect of relativistic beaming enhances its apparent brightness. They radiate in all wavebands from the radio to the gamma-ray bands via the synchrotron and the inverse Compton scattering process. Numerous observations are performed but the mechanism of variability, creation and composition of jets are still controversial. We performed multi-wavelength monitoring with optical polarization for 3C 66A, Mrk 421, CTA 102 and PMN J0948+0022 to investigate the mechanisms of variability and research the emission region in the relativistic jets. Consequently, an emergence of new emission component in flaring state is suggested in each object. The most significant aspect of these results is its wide range of sizes of emission regions from $10^{14}-10^{16}$ cm, which implies the model with a number of independent emission regions with variety sizes and randomly orientation. The "shock-in-jet" scenario can explain high PD and direction of PA in each objects. It might reflect the common mechanism of flares in the relativistic jets.
Luigi Costamante
Proceedings of High Energy Phenomena in Relativistic Outflows VII — PoS(HEPRO VII), Volume 354; https://doi.org/10.22323/1.354.0020

Abstract:
Relativistic jets from Active Galactic Nuclei (AGN) are powerful sources of radiation at every wavelength, but particularly in gamma-rays. Multi-wavelength observations in the last decade, driven by the new generation of large-area GeV and TeV telescopes, have revealed several new aspects of their structure and emission properties. This paper summarizes some recent progress in our understanding of relativistic jets, focusing in particular on the following results: a) evidence against the Broad Line Region (BLR) as origin of seed photons for the inverse Compton (IC) mechanism; b) spectral variability in gamma-rays that defies the usual SED classification, c) discovery of extreme-TeV sources, which challenge standard acceleration and emission scenarios, d) evidence of relativistic motion at the VLBI scale also in high-energy peaked BL Lacs. Other fundamental topics such as ultra-fast variability, neutrino emission and M87 images at event horizon scale are briefly mentioned, as discussed in other contributions at these proceedings.
L. Vega-García, A. P. Lobanov, M. Perucho, G. Bruni, , J. M. Anderson, I. Agudo, R. Davis, J. L. Gómez, Y. Y. Kovalev, et al.
Published: 4 September 2020
Astronomy & Astrophysics, Volume 641; https://doi.org/10.1051/0004-6361/201935168

Abstract:
Context. Detailed studies of relativistic jets in active galactic nuclei (AGN) require high-fidelity imaging at the highest possible resolution. This can be achieved using very long baseline interferometry (VLBI) at radio frequencies, combining worldwide (global) VLBI arrays of radio telescopes with a space-borne antenna on board a satellite. Aims. We present multiwavelength images made of the radio emission in the powerful quasar S5 0836+710, obtained using a global VLBI array and the antenna Spektr-R of the RadioAstron mission of the Russian Space Agency, with the goal of studying the internal structure and physics of the relativistic jet in this object. Methods. The RadioAstron observations at wavelengths of 18 cm, 6 cm, and 1.3 cm are part of the Key Science Program for imaging radio emission in strong AGN. The internal structure of the jet is studied by analyzing transverse intensity profiles and modeling the structural patterns developing in the flow. Results. The RadioAstron images reveal a wealth of structural detail in the jet of S5 0836+710 on angular scales ranging from 0.02 mas to 200 mas. Brightness temperatures in excess of 1013 K are measured in the jet, requiring Doppler factors of ≥100 for reconciling them with the inverse Compton limit. Several oscillatory patterns are identified in the ridge line of the jet and can be explained in terms of the Kelvin–Helmholtz (KH) instability. The oscillatory patterns are interpreted as the surface and body wavelengths of the helical mode of the KH instability. The interpretation provides estimates of the jet Mach number and of the ratio of the jet to the ambient density, which are found to be Mj ≈ 12 and η ≈ 0.33. The ratio of the jet to the ambient density should be conservatively considered an upper limit because its estimate relies on approximations.
Dheeraj Pasham, Matteo Lucchini, Tanmoy Laskar, Benjamin Gompertz, Shubham Srivas, Matt Nicholl, , , , Rob Fender, et al.
Published: 10 June 2022
Abstract:
The tidal forces of a black hole can rip apart a star that passes too close to it, resulting in a stellar Tidal Disruption Event (TDE, (1)). In some such encounters, the black hole can launch a powerful relativistic jet (2-6). If this jet fortuitously aligns with our line of sight, the overall brightness is Doppler boosted by several orders of magnitude. Consequently, such on-axis relativistic TDEs have the potential to unveil cosmological (redshift z>1) quiescent black holes and are ideal test beds to understand the radiative mechanisms operating in super-Eddington jets. Here, we present multi-wavelength (X-ray, UV, optical, and radio) observations of the optically discovered transient AT 2022cmc at z=1.193 (7). Its unusual X-ray properties, including a peak observed luminosity of >1048 erg s-1, systematic variability on timescales as short as 1000 seconds, and overall duration lasting more than 30 days in the rest-frame are traits associated with relativistic TDEs. This makes AT 2022cmc only the fourth member of this rare class and the first one identified in the optical and with well-sampled optical data. The X-ray to radio spectral energy distributions spanning 5-50 days after discovery can be explained as synchrotron emission from a relativistic jet (radio), synchrotron self-Compton (X-rays), and thermal emission similar to that seen in low-redshift TDEs (UV/optical). Our modeling implies a beamed, highly relativistic jet akin to blazars (e.g., (8,9)) but requires extreme matter-domination, i.e, high ratio of electron-to-magnetic field energy densities in the jet, and challenges our theoretical understanding of jets. This work provides one of the best multi-wavelength datasets of a newborn relativistic jet to date and will be invaluable for testing more sophisticated jet models, and for identifying more such events in transient surveys.
O. Halpern, M. H. Johnson
Physical Review, Volume 59, pp 896-901; https://doi.org/10.1103/physrev.59.896

Abstract:
The paper discusses the question how far observables in quantum theory permit accurate measurement if no assumptions are made about the values of conjugate variables. The physical connection between the uncertainty principle and the commutation relations is briefly discussed. A treatment of the γray microscope makes it appear that even with small-angle diffraction no great improvement beyond the Compton wave-length can be obtained. An analysis of an ideal arrangement to measure electric field strengths leads to the result that, admitting the existence of arbitrarily constituted test bodies, the accuracy of the measurement still cannot exceed certain limits which are mainly defined by the wave-length of the field and the spatial and temporal domain of measurement. These restrictions are due to the properties of the "vacuum," which are changed as a consequence of the possibility of pair production.
M. A. Piestrup
Conference on Lasers and Electro-Optics; https://doi.org/10.1364/cleo.1982.thh5

Abstract:
The two-stream instability problem has been studied in plasma physics for over 30 years and has been used to generate microwaves of centimeter wavelengths. The device, independently devised and constructed by Haeff1 and Pierce,2 was called an electron wave tube or two-stream amplifier and consists of two low-energy electron streams interacting to give an increasing space-charge wave without field supporting structure. The latter fact is clearly an advantage for submillimeter and shorter wavelength sources, since conventional microwave devices require circuit elements whose dimensions are of the order of the generated wavelength.
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