Motion Of Relativistic Electrons Research Articles

LAW OF LARGE NUMBERS OF PROBABILITY THEORY AND FORMATION OF THE ENERGY SPECTRUM OF SYNCHROTRON RADIATION OF RELATIVISTIC ELECTRON IN THE STORAGE RING

The fluctuations of synchrotron radiation (SR) energy losses during the motion of relativistic electrons in the uniform magnetic field in a storage ring are considered. The influence on the formation of the energy spectrum of the SR photon flux of the duration of registration of SR relativistic electrons is analyzed. It has been established that with the increase in the duration of temporal registration, the energy spectrum of the SR photon flux is regularly transformed into the asymptotically normal density in accordance with the law of large numbers of probability theory. It is determined that the main mechanism in the formation of the energy spectrum is successive convolutions of the current spectra.

Light-to-Plasma Momentum Transfer

The momentum of light in a plasma and the momentum transfer from light to plasma is calculated for a uniform plane of light incident into a uniform plasma. At low irradiance, the Minkowski and Abraham expressions for photon momentum are shown to be equivalent. We evaluate relativistic electron motion at a high irradiance for a plasma and show that most light momentum is transferred to the electrons associated with motion parallel to the light propagation at an irradiance corresponding to the reduced vector potential ao≈3.7 (reduced irradiance Iλ2≈2×1019 W cm−2 μm2). Our results show that to ensure the maximum momentum transfer from photons to electrons in motion parallel to the k-direction for fixed laser pulse energy, the laser focusing should be adjusted to achieve ao≈3.7, even if tighter focusing, and thus higher ao values, are possible.

Topological charge-entropy scaling in kagome Chern magnet TbMn6Sn6

In ordinary materials, electrons conduct both electricity and heat, where their charge-entropy relations observe the Mott formula and the Wiedemann-Franz law. In topological quantum materials, the transverse motion of relativistic electrons can be strongly affected by the quantum field arising around the topological fermions, where a simple model description of their charge-entropy relations remains elusive. Here we report the topological charge-entropy scaling in the kagome Chern magnet TbMn6Sn6, featuring pristine Mn kagome lattices with strong out-of-plane magnetization. Through both electric and thermoelectric transports, we observe quantum oscillations with a nontrivial Berry phase, a large Fermi velocity and two-dimensionality, supporting the existence of Dirac fermions in the magnetic kagome lattice. This quantum magnet further exhibits large anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects, all of which persist to above room temperature. Remarkably, we show that the charge-entropy scaling relations of these anomalous transverse transports can be ubiquitously described by the Berry curvature field effects in a Chern-gapped Dirac model. Our work points to a model kagome Chern magnet for the proof-of-principle elaboration of the topological charge-entropy scaling.

Real-time ultrafast oscilloscope with a relativistic electron bunch train

The deflection of charged particles is an intuitive way to visualize an electromagnetic oscillation of coherent light. Here, we present a real-time ultrafast oscilloscope for time-frozen visualization of a terahertz (THz) optical wave by probing light-driven motion of relativistic electrons. We found the unique condition of subwavelength metal slit waveguide for preserving the distortion-free optical waveform during its propagation. Momentary stamping of the wave, transversely travelling inside a metal slit, on an ultrashort wide electron bunch enables the single-shot recording of an ultrafast optical waveform. As a proof-of-concept experiment, we successfully demonstrated to capture the entire field oscillation of a THz pulse with a sampling rate of 75.7 TS/s. Owing to the use of transversely-wide and longitudinally-short electron bunch and transversely travelling wave, the proposed “single-shot oscilloscope” will open up new avenue for developing the real-time petahertz (PHz) metrology.

Nonlinear Cone Model for Investigation of Runaway Electron Synchrotron Radiation Spot Shape

The runaway electron event is the fundamental physical phenomenon and tokamak is the most advanced conception of the plasma magnetic confinement. The energy of disruption generated runaway electrons can reach as high as tens of mega-electron-volt and they can cause a catastrophic damage of plasma-facing-component surfaces in large tokamaks and International Thermonuclear Experimental Reactor (ITER). Due to its importance, this phenomenon is being actively studied both theoretically and experimentally in leading thermonuclear fusion centers. Thus, effective monitoring of the runaway electrons is an important task. The synchrotron radiation diagnostic allows direct observation of such runaway electrons and an analysis of their parameters and promotes the safety operation of present-day large tokamaks and future ITER. In 1990 such diagnostic had demonstrated its effectiveness on the TEXTOR (Tokamak Experiment for Technology Oriented Research, Germany) tokamak for investigation of runaway electrons beam size, position, number, and maximum energy. Now this diagnostic is installed practically on all the present-day’s tokamaks. The parameter v┴/|v||| strongly influences on the runaway electron synchrotron radiation behavior (v|| is the longitudinal velocity, v┴ is the transverse velocity with respect to the magnetic field B). The paper is devoted to the theoretical investigation of runaway electron synchrotron radiation spot shape when this parameter is not small that corresponds to present-day tokamak experiments. The features of the relativistic electron motion in a tokamak are taken into account. The influence of the detector position on runaway electron synchrotron radiation data is discussed. Analysis carried out in the frame of the nonlinear cone model. In this model, the ultrarelativistic electrons emit radiation in the direction of their velocity v→ and the velocity vector runs along the surface of a cone whose axis is parallel to the magnetic field B. The case of the small parameter v┴/|v||| (v┴/|v|||<<1, linear cone model) was considered in the paper: Plasma Phys. Rep. 22, 535 (1996) and these theoretical results are used for experimental data analysis.

Statistical Properties of the Transverse-Motion Energy Levels for Channeling Electrons in a Silicon Crystal under Dynamical Chaos Conditions

The classical motion of particles in external fields is frequently chaotic although deterministic within the classical limit. Studying the quantum mechanical behavior of such systems amounts to the problematics of quantum chaos. Quantum chaos manifests itself primarily in the statistical properties of the energy-level arrays of such systems. However, the typical objects under consideration are systems of the type billiards with rigid walls. This paper studies the calculated energy levels of the transverse motion of relativistic electrons in the axial-channeling regime along the [100] direction of the silicon crystal which is described as motion in the smooth potential well. The nearest-level spacing distributions as well as the spectral rigidity are studied for the range of parameters where electron motion is chaotic within the classical limit. Both these characteristics demonstrate agreement with quantum-chaos-theory predictions.

Generation of Terawatt Attosecond Pulses from Relativistic Transition Radiation.

When a femtosecond duration and hundreds of kiloampere peak current electron beam traverses the vacuum and high-density plasma interface, a new process, that we call relativistic transition radiation (RTR), generates an intense ∼100 as pulse containing ∼1 terawatt power of coherent vacuum ultraviolet (VUV) radiation accompanied by several smaller femtosecond duration satellite pulses. This pulse inherits the radial polarization of the incident beam field and has a ring intensity distribution. This RTR is emitted when the beam density is comparable to the plasma density and the spot size much larger than the plasma skin depth. Physically, it arises from the return current or backward relativistic motion of electrons starting just inside the plasma that Doppler up shifts the emitted photons. The number of RTR pulses is determined by the number of groups of plasma electrons that originate at different depths within the first plasma wake period and emit coherently before phase mixing.

Theoretical research on the annular intensive relativistic electron motion focused by coaxial cusped periodic permanent magnetic field

This paper theoretically investigates the motion characteristics of an annular intensive relativistic electron beam (IREB) in a coaxial, smooth waveguide under a cusped periodic permanent magnetic (CPPM) field. The motion of the electron beam clearly exhibits a periodic oscillation in a CPPM. For the effective transmission of an IREB, the structural parameters of the CPPM must be chosen carefully. Based on theoretical analysis, stability conditions are suggested. The influence of the magnetic field phase, strength, and period on the oscillation amplitude of the beam envelope is analyzed, and the criteria for minimal oscillation amplitude are proposed accordingly. Notably, the theoretical formula, used to predict the oscillation period of the beam envelope, is proposed and verified by single-particle and particle-in-cell simulation results.

Ultra-intense laser pulse characterization using ponderomotive electron scattering

We present a new analytical solution for the equation of motion of relativistic electrons in the focus of a high-intensity laser pulse. We approximate the electron’s transverse dynamics in the averaged field of a long laser pulse focused to a Gaussian transverse profile. The resultant ponderomotive scattering is found to feature an upper boundary of the electrons’ scattering angles, depending on the laser parameters and the electrons’ initial state of motion. In particular, we demonstrate the angles into which the electrons are scattered by the laser scale as a simple relation of their initial energy to the laser’s amplitude. We find two regimes to be distinguished in which either the laser’s focusing or peak power are the main drivers of ponderomotive scattering. Based on this result, we demonstrate how the intensity of a laser pulse can be determined from a ring-shaped pattern in the spatial distribution of a high-energy electron beam scattered from the laser. We confirm our analysis by means of detailed relativistic test particle simulations of the electrons’ averaged ponderomotive dynamics in the full electromagnetic fields of the focused laser pulse.

Relativistic Self-Focusing of Hermite-cosh-Gaussian Laser Beam in Magnetoplasma with Exponential Plasma Density Ramp

In the present manuscript, we analyse the effect of exponential plasma density ramp for relativistic self-focusing of Hermite-cosh-Gaussian laser pulse in magnetoplasma. The exponential plasma density ramp is found to be more prominent in achieving the stronger self-focusing of Hermite-cosh-Gaussian laser beam in comparison to the tangential plasma density ramp. We propose a theoretical model for propagation of Hermite-cosh-Gaussian laser pulse in magnetoplasma with exponential density ramp. The nonlinearity in the medium arises because of the relativistic motion of electrons, being responsible for relativistic self-focusing. Equation of the beam width parameter is set up by taking the expression for the dielectric function and following Wentzel-Kramers-Brillouin (WKB) with paraxial ray approximations for mode indices m = 0, 1 and 2. Effect of decentered parameter is also analysed, which results in stronger self-focusing of the Hermite-cosh-Gaussian laser beam. Stronger self-focusing of laser beam is more pronounced in high density plasma with higher magnetic field.

Stronger self-focusing of cosh-Gaussian laser beam under exponential density ramp in plasma with linear absorption

A theoretical model is purposed which explains propagation of the cosh-Gaussian laser beam in the plasma with exponential density transition. Also the influence of linear absorption on self-focusing of the beam is taken into account and it may be helpful in achieving enhanced self-focusing of laser beam. The nonlinearity arises because of the relativistic motion of electrons, is considered for the penetration of laser in plasma. By considering the expression of dielectric function, we have set up differential equation for the beam width parameter. Further, the effect of decentred parameter is studied which results in stronger self-focusing of cosh-Gaussian laser beam. Stronger self-focusing of laser beam is also noticed on account of the increased plasma frequency.

Positron Annihilation Spectroscopy of Active Galactic Nuclei

This paper focuses on the interpretation of radiation fluxes from active galactic nuclei. The advantage of positron annihilation spectroscopy over other methods of spectral diagnostics of active galactic nuclei (therefore AGN) is demonstrated. A relationship between regular and random components in both bolometric and spectral composition of fluxes of quanta and particles generated in AGN is found. We consider their diffuse component separately and also detect radiative feedback after the passage of high-velocity cosmic rays and hard quanta through gas-and-dust aggregates surrounding massive black holes in AGN. The motion of relativistic positrons and electrons in such complex systems produces secondary radiation throughout the whole investigated region of active galactic nuclei in form of cylinder with radius R= 400-1000 pc and height H=200-400 pc, thus causing their visible luminescence across all spectral bands. We obtain radiation and electron energy distribution functions depending on the spatial distribution of the investigated bulk of matter in AGN. Radiation luminescence of the noncentral part of AGN is a response to the effects of particles and quanta falling from its center created by atoms, molecules and dust of its diffuse component. The cross-sections for the single-photon annihilation of positrons of different energies with atoms in these active galactic nuclei are determined. For the first time we use the data on the change in chemical composition due to spallation reactions induced by high-energy particles. We establish or define more accurately how the energies of the incident positron, emitted γ-quantum and recoiling nucleus correlate with the atomic number and weight of the target nucleus. For light elements, we provide detailed tables of all indicated parameters. A new criterion is proposed, based on the use of the ratio of the fluxes of γ-quanta formed in one- and two-photon annihilation of positrons in a diffuse medium. It is concluded that, as is the case in young supernova remnants, the two-photon annihilation tends to occur in solid-state grains as a result of active loss of kinetic energy of positrons due to ionisation down to thermal energy of free electrons. The singlephoton annihilation of positrons manifests itself in the gas component of active galactic nuclei. Such annihilation occurs as interaction between positrons and K-shell electrons; hence, it is suitable for identification of the chemical state of substances comprising the gas component of the investigated media. Specific physical media producing high fluxes of positrons are discussed; it allowed a significant reduction in the number of reaction channels generating positrons. We estimate the brightness distribution in the γ-ray spectra of the gas-and-dust media through which positron fluxes travel with the energy range similar to that recorded by the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) research module. Based on the results of our calculations, we analyse the reasons for such a high power of positrons to penetrate through gas-and-dust aggregates. The energy loss of positrons by ionisation is compared to the production of secondary positrons by high-energy cosmic rays in order to determine the depth of their penetration into gas-and-dust aggregations clustered in active galactic nuclei. The relationship between the energy of γ-quanta emitted upon the single-photon annihilation and the energy of incident electrons is established. The obtained cross sections for positron interactions with bound electrons of the diffuse component of the non-central, peripheral AGN regions allowed us to obtain new spectroscopic characteristics of the atoms involved in singlephoton annihilation.

QED Phenomena in an Ultrastrong Magnetic Field. I. Electron–Photon Scattering, Pair Creation, and Annihilation

We evaluate several basic electrodynamic processes as modified by the presence of a very strong magnetic field, exceeding $B_{\rm Q} \equiv m^2/e = 4.4\times 10^{13}$ G. These results are needed to build models of dissipative phenomena outside magnetars and some other neutron stars. Differential and total cross sections and rates are presented for electron-photon scattering, the annihilation of an electron-positron pair into two photons, the inverse process of two-photon pair creation, and single-photon pair creation into the lowest Landau state. The relative importance of these interactions changes as the background magnetic field grows in strength. The particle phase space relevant for a given process may be restricted by single-photon pair creation, which also opens up efficient channels for pair multiplication, e.g. in combination with scattering. Our results are presented in the form of compact formulae that allow for relativistic electron (positron) motion, in the regime where Landau excitations can be neglected (corresponding to $10^3B_{\rm Q} \gg B \gg B_{\rm Q}$ for moderately relativistic motion along the magnetic field). Where a direct comparison is possible, our results are tested against earlier calculations, and a brief astrophysical context is provided. A companion paper considers electron-positron scattering, scattering of electrons and positrons by ions, and relativistic electron-ion bremsstrahlung.

Identifying the quantum radiation reaction by using colliding ultraintense lasers in gases

A scheme for identifying the quantum radiation reaction effect on relativistic electron motion in strong electromagnetic fields is proposed, where two ultraintense lasers are used to collide with each other in a tenuous gas. Different from the previous method by collision of an ultraintense laser with a high-energy electron beam, in which the radiation reaction effect is evidenced by the energy loss in the electron energy spectrum, here the transition between the classical and quantum radiation reaction regimes is distinguished from the angular distribution of the total electron radiations. With no need of additional relativistic electron beams, the scheme is more robust and easily achievable in experiments. Both theory and two-dimensional particle-in-cell simulations show that the classical radiation dominates in the transverse direction perpendicular to laser axis, forming a dipolelike pattern, while that in the quantum regime dominates at four diagonal directions, constituting a butterflylike structure.

Nonlinear Landau damping in a relativistic electron-ion plasma–non-local nonlinear Schrödinger-equation and Krylov Bogoliubov Mitropolsky method

A nonlinear theory of amplitude modulation of electrostatic envelopes in an electron-ion plasma is developed taking care of relativistic effect, using the Vlasov-Poisson equation. By using the multiple scale reductive perturbation, it is shown that such evolution is characterized by the non-local, nonlinear Schrödinger equation. This non-local term is known to take care of the resonant particles having group velocity = ∂ω/∂k on a finite amplitude plasma wave. On the other hand it is well-known that waves in plasmas can undergo collision-less damping when they resonantly interact with trapped/free particles. Such collision-less damping was termed Landau damping. Our intention in this analysis is to analyze the effect of relativistic electron motion on such collision-less damping in detail. But since the corresponding effect of phase velocity resonance in this classical case is not so prominent, we have not attempted to treat it here and, as assumed, the amplitude is not very large. This gives rise to some new estimates of the frequency shift and energy transfer rate, in both relativistic and non-relativistic cases. In the next phase, we have analyzed the condition of a modulational instability in the non-local, nonlinear Schrödinger equation. Then, the Bogoliubov-Mitropolsky approach is used to study the change in the solitary wave profile due to the presence of non-local nonlinearity in the equation, which is being treated as a perturbation. Last but not the least, the magnitude of the Landau damping is also computed. In the concluding remarks we have compared the kinetic and the usual reductive perturbation approach to the nonlinear Schrödinger equation.

Electron Motion in the Three-Dimensional Field of Undulator

In this paper we consider the motion of relativistic electrons in an ideal three-dimensional magnetic field of an undulator. The ideality of the magnetic field means that, on the undulator axis, the field is directed strictly vertically upward and has a strictly sinusoidal shape. In the overwhelming majority of cases, only this leading component of the field is taken into account in calculating the electron trajectory. In this paper, in the equations of motion of an electron in the magnetic field of an undulator, all three components of the field are taken into account, so that the undulator field under consideration satisfies the stationary Maxwell equations. In this case, the differential equations of motion of the electron are solved analytically with the help of perturbation theory, and not by the method of averaging over fast oscillations of the electron, as was done in a number of previous papers. These analytic expressions for trajectories describe the behavior of particles in the focusing magnetic field of an undulator much more completely. An analysis of these expressions shows that the behavior of electrons in such a three-dimensional field of the undulator is much more complicated than what follows from the equations obtained by the averaging method. In particular, there is a cross effect when changes in the initial vertical parameters of the electron trajectory cause changes in the horizontal component of its trajectory and vice versa. A comparison of the solutions obtained analytically with the results of numerical calculations of electron trajectories using the Runge–Kutta method demonstrates their high accuracy.

Analytical Description of Electron Motion in a Three-Dimensional Undulator Field

The motion of relativistic electrons in an ideal three-dimensional magnetic undulator field satisfying the stationary Maxwell equation is considered. The system of nonlinear differential equations of the electron motion is solved analytically using perturbation theory rather than the method for averaging fast oscillations of the electron trajectory (the focusing approximation), as was done in a series of previous studies. The obtained analytical expressions for the trajectories describe the behavior of particles in a three-dimensional magnetic undulator field much more accurately than the formulas obtained within the framework of the focusing approximation. The analysis of these expressions shows that the behavior of electrons in a three-dimensional undulator field is much more complicated than that described by equations obtained using the averaging method. In particular, it turns out that the electron trajectories in the undulator have a cross dependence; in this case, variations in the initial trajectory parameters in the vertical plane cause changes in the horizontal trajectory components, and vice versa. The results of calculations of the trajectories carried out using analytical expressions are close to those of numerical calculations using the Runge-Kutta method.

Trapped-ion Lissajous trajectories by engineering Rashba- and Dresselhaus-type spin-orbit interactions in a Paul trap

Here we present a protocol for generating Lissajous curves with a trapped ion by engineering Rashba- and the Dresselhaus-type spin-orbit (SO) interactions in a Paul trap. The unique anisotropic Rashba , and Dresselhaus , couplings afforded by our setup also enable us to obtain an “unusual” Zitterbewegung, i.e., the semiconductor analog of the relativistic trembling motion of electrons, with cycloidal trajectories in the absence of magnetic fields. We have also introduced bounded SO interactions, confined to an upper-bound vibrational subspace of the Fock states, as an additional mechanism to manipulate the Lissajous motion of the trapped ion. We have also accounted for dissipative effects on the vibrational degrees of freedom of the ion and find that the Lissajous trajectories are still robust and well defined for realistic parameters.

Quasicharacteristic radiation of relativistic electrons at orientation motion in lithium halides crystals along charged planes and axes

The paper deals with the investigation of the orientation motion of relativistic electrons in charged (111) planes and charged [110] axes of lithium halides ionic crystals of LiF, LiCl, LiBr and LiI. On the basis of these investigations the spectra of quasicharacteristic radiation for the electron beams with various Lorentz-factors both in planar and axial cases have been calculated numerically.

Impact of quantum effects on relativistic electron motion in a chaotic regime.

The impact of quantum effects on electron dynamics in a plane linearly polarized standing wave with relativistic amplitudes is considered. Using spectral analysis of Lyapunov characteristic exponents with and without radiation losses we show that the contraction effect of phase space due to the radiation reaction force in the classical form does not occur in the quantum case when the discreteness of photon emission is taken into account. It is also demonstrated that electron bunch kinetics has a diffusion solution rather than the d'Alambert type solution as in the classical description. For this case, we applied the Markov chain formalism and showed that this method gives exact characteristics of electron bunch evolution, such as motion of the center of mass and electron bunch dimensions.