Relativistic Charged Particles Research Articles

Gravitational lensing in dispersive media and deflection angle of charged massive particles in terms of curvature scalars and energy-momentum tensor

In this work we extend the approach used in [Emanuel Gallo and Osvaldo M. Moreschi, Phys. Rev. D 83, 12 083007 (2011)] to the study of weak gravitational lensing in a plasma medium. First, we present expressions for the deflection angle and optical scalars in terms of the components of the energy-momentum tensor for spherically symmetric lenses surrounded by a cold non-magnetized plasma. Second, we show that the same expressions can be deduced using the Gauss-Bonnet theorem. Finally, we establish a correspondence between the spatial orbits of photons in a non-homogeneous plasma and the non-geodesic curves followed by test massive particles whose dynamics also depend on an external central field. As an application, we use the Gauss-Bonnet theorem to compute the deflection angle of the non-geodesic trajectories followed by relativistic test massive charged particles in a Reissner-Nordstr\"om spacetime.

Orbital angular momentum of Liénard–Wiechert fields

Abstract We derive a general expression for the electromagnetic field radiated by a relativistic charged particle with arbitrary periodic orbit, in the form of multi-pole expansion of the Liénard–Wiechert potential, which explicitly includes the charged particle motion. Using this expression, we discuss the orbital angular momentum radiated from a relativistic charged particle. It has recently been indicated that the radiation emitted by circularly orbiting charged particles carries well-defined orbital angular momentum. We show that, even for the general cases of arbitrary periodic orbits, the radiation field possesses well-defined orbital angular momentum.

Study of relativistic charged particles production in 84Kr36 emulsion interactions ∼1GeV per nucleon with wounded nucleon model

The experimental results on the multiplicity and probability distribution of the emitted charged pions [Formula: see text] in the interactions of [Formula: see text]Kr[Formula: see text] projectile at around 1[Formula: see text]GeV per nucleon with nuclear emulsion targets are reported. In this work, we have employed a wounded nucleon model (WNM) to calculate the total number of wounded nucleons [Formula: see text] and the total number of interactions [Formula: see text]. The dependence of average multiplicities of produced relativistic charged particles on the calculated wounded nucleons and total interactions are investigated. The obtained results revealed that the average multiplicity of [Formula: see text] is dependent on the projectile and target mass number. The calculated values of the total number of wounded nucleons and the total numbers of interactions show a strong dependence on the mass of the colliding nuclei. The emission rate of the mean multiplicity of [Formula: see text] and [Formula: see text] linearly increases with increasing the total number of wounded nucleons and interactions.

Exact solution of the relativistic finite-difference equation for the Coulomb plus a ring-shaped-like potential

In this paper, a three-dimensional problem of the motion of a charged relativistic particle in a noncentral Coulomb plus ring-shaped potential is studied. Our investigation is based on a finite-difference version of relativistic quantum mechanics. The energy eigenvalues and the corresponding wave functions are obtained analytically. It is shown that radial part and the angular part of the wave functions are expressed through the Meixner–Pollaczek polynomials and Jacobi polynomials, respectively. All relativistic expressions, for example, radial wave functions and energy spectrum, have the correct nonrelativistic limit. We also build a dynamical symmetry group for the radial part of the equation of motion, which allows us to find the energy spectrum purely algebraically.

Angular momentum of radiation from a charge in circular and spiral motion

We study theoretically the vortex radiation of a relativistic charged particle. General expressions for the spectral and angular distributions of angular momentum of radiation are derived for an arbitrary moving charge. Special attention is given to calculation of the angular momentum of synchrotron radiation. We obtain the spectrum and the angular distribution of angular momentum carried by synchrotron radiation. Similar expressions for the angular momentum of radiation of a charge moving on a spiral trajectory are derived by use of Lorentz transformations. It is shown that the main part of angular momentum in this case is emitted at a small angle to the vortex axis. Relativistic charged particles at spiral motion are effective source of the vortex photon beams at wave lengths ranging from radio waves to gamma rays. The obtained equations can be used for calculations of the angular momentum emitted by charged particles in the helical undulators and at axial channeling in solid crystal.

A charge reconstruction algorithm for DAMPE silicon microstrip detectors

The DArk Matter Particle Explorer (DAMPE) can detect electrons and photons from 5 GeV to 10 TeV and charged nuclei from a few tens of GeV to 100 TeV. The silicon–tungstentracker (STK), which is composed of 768 singled-sided silicon microstrip detectors, is one of four subdetectors in DAMPE providing photon conversion, track reconstruction, and charge identification for relativistic charged particles. This paper focuses on the charge identification performance of the STK detector. The charge response depends mainly on the incident angle and the impact position of the incoming particle. To improve the charge resolution, a reconstruction algorithm to correct for these parameters was tested during a test beam campaign conducted with a high-intensity ion beam at CERN. This algorithm was successfully applied to the ion test beam and the ion charge of Z=4∼10 and was successfully reconstructed for both normal and 9°incident beams.

Relativistic Charged-Particle Beam Space-Charge Limited Current in Finite Length Coaxial Drift Tube

In the strong axial (guide) magnetic field and uniform beam density approximations, we calculate scalar potential distribution induced by axisymmetric annular relativistic charged-particle beam in a finite-length coaxial drift tube. This scalar potential distribution allows us to find an approximate radial position at which the extremum of the scalar potential is attained in the coaxial drift tube inside the annular relativistic charged-particle beam. By knowing the approximate extremal radial position, we obtain the analytical estimate for the space-charge limited (SCL) current of axisymmetric annular (finite thickness) relativistic charged-particle beam propagating in strong axial magnetic field in a finite length coaxial drift tube and establish a simple correspondence of this result to that in a long coaxial drift tube. A comparison of numerical nonlinear calculations and the analytical estimate for the SCL current in the finite-length coaxial drift tube is also given.

Statistics of relativistic electrons radiating in periodic fields

We developed a general method for assessing the evolution of the energy spectrum of relativistic charged particles that have undergone small quantum losses, such as the ionization losses when the electrons pass through matter and the radiation losses in the periodic fields. These processes are characterized by a small magnitude of the recoil quantum as compared with the particle's initial energy. We convey the statistical consideration of the radiating electrons. We demonstrate that in the initial stage, the electron's spectrum can be described as a composition of consecutive convolutions of the recoil spectrum with itself, taken with the Poisson mass. In this stage, at the relatively small average number of the recoils, the electron spectrum reveals some individual characteristics of the recoil spectrum. Furthermore, the spectrum loses individuality and allows for proximate description in the terms of statistical parameters. The results of this consideration reveal that the width of the electron spectrum is increasing with the number of recoils according to the power law, with the power index being inverse to the stability parameter, which gradually increases with the number of recoils from one to two. Increase of the spectrum width limits the ability of the beam to generate coherent radiation in hard x-ray and gamma-ray region.

Explicit high-order gauge-independent symplectic algorithms for relativistic charged particle dynamics

Symplectic schemes are powerful methods for numerically integrating Hamiltonian systems, and their long-term accuracy and fidelity have been proved both theoretically and numerically. However direct applications of standard symplectic schemes to relativistic charged particle dynamics result in implicit and electromagnetic gauge-dependent algorithms. In the present study, we develop explicit high-order gauge-independent noncanonical symplectic algorithms for relativistic charged particle dynamics using a Hamiltonian splitting method in the 8D phase space. It is also shown that the developed algorithms can be derived as variational integrators by appropriately discretizing the action of the dynamics. Numerical examples are presented to verify the excellent long-term behavior of the algorithms.

On the uniform motion of a relativistic charged particle in a homogeneous electromagnetic field in Minkowski space

We discuss the geometric characterization of the trajectory of a moving charged particle, for the case of a homogeneous electromagnetic field, in Minkowski space when the motion is governed by the Lorentz equation. We employ a totally relativistic approach during the discussion. It is based on a systematic use of the Faraday antisymmetric tensor properties of the electromagnetic field and of the four‐dimensional Frenet‐Serret formula, which is adapted to the Minkowski 4‐space with index two to determine the worldline geometry of the electromagnetic field acting on the particle. Finally, we present the necessary and sufficient conditions to obtain uniform motion of the relativistic charged particle in a homogeneous electromagnetic field in

Event-by-event fluctuations clusterization and entropy production in AA collisions at AGS and SPS energies

Event-by-event (ebe) fluctuations in mean pseudorapidity values of relativistic charged particles in full phase space are studied by analyzing experimental data on [Formula: see text] collisions at 14.5A, 60A and 200A GeV/c and [Formula: see text] collisions at 200A GeV/c. The findings are compared with the prediction of A Multi-Phase Transport (AMPT) model and those obtained from the analysis of correlation free Monte-Carlo events. Fluctuations in mean pseudorapidity distributions are noted to be in excess to that expected from the statistically independent particle emission. The observed dependence of the fluctuation strength measure parameter, [Formula: see text] on the beam energy and number of participating target nucleons indicate that nucleus–nucleus collisions cannot be treated as simple superposition of multiple nucleon–nucleon interactions. Presence of clusters or jet-like phenomena in multihadron final states are searched for on ebe basis by using the concept of Jaynes Shannon entropy. The findings indicate the presence of cluster-like objects in the experimental data with their size and frequency increasing with increasing beam energy. These observations in turn suggest that the clustering or jet-like algorithm adopted in the present study may be used as a tool for triggering different classes of events.

Duality Occurrences: Physical Origin of Wave Functions

The quantum mystery began with the probabilistic interpretation of the wave function. However, this usefulness is definitive in Quantum Mechanics while the suspense continues. The present paper aims to investigate the origin of such a mystery. Hence, considering a relativistic charged particle in quantum vacuum, it appeared that: (i) from a classical association, this electromagnetismself-consistent derives from the usual wave function, which corresponds to the scalar nature in addition to the vector one. (ii) Such duplicity is only justifiable when the related gauge fields describe fermions, in accordance with the previous theory of duality field-matter. This occurrence then corresponds to the appearance of bosons at cell intersections in vacuum lattice, whatever is the field. (iii) From the related gauge couplings, the scalar function must have an unknown vector companion. Both appear as originating the related conservation laws on one side. On the other side, specific variations of the field front would explain their physical origin. (iv) Moreover, both define an original gauge field to which that of law conservation is sensible. (v) Due to definition validity in any reference system, their possible quantization should lead to that of scalar and vector fields of stationary states. At last, the results highlight the connection between waves and fields associable to any object, emphasizing the field unification framework.

A distributed beam loss monitor for the Australian Synchrotron

A distributed beam loss monitoring system, named the optical fibre Beam Loss Monitor, has been installed at the Australian Synchrotron. Relativistic charged particles produced in beam loss events generate photons via the Cherenkov mechanism in four silica fibres that run parallel to the beam pipe and cover the majority of the accelerator’s length. These photons are then guided by the fibres to detectors located outside of the accelerator tunnel. By measuring the time of flight of these photons, the locations of beam losses can be reconstructed. Based on this method a calibration was produced, mapping the time of flight to a position along the accelerator. This calibration was applied to loss signals collected on the first pass of the beam through the accelerator and the locations of prominent losses were determined. Using this system it was possible to investigate the effect, on the location and intensity of losses, in response to changes in the lattice parameters on a shot-by-shot basis. This system is now used in routine operations and has resulted in a 40 % increase in the capture efficiency of the booster ring.

Superintegrable relativistic systems in scalar background fields

We consider a relativistic charged particle in a background scalar field depending on both space and time. Poincaré, dilation and special conformal symmetries of the field generate conserved quantities in the charge motion, and we exploit this to generate examples of superintegrable relativistic systems. We also show that the corresponding single-particle wavefunctions needed for the quantum scattering problem can be found exactly, by solving the Klein–Gordon equation.

Characterisation of the fused silica surface quality with a [formula omitted]-source

A method to characterise the quality of a fused silica surface using a β-source is presented. Two fused silica bars (5×10×400mm3) were fabricated for the Cherenkov detector for proton Flux Measurement installed at vacuum chamber of the Super Proton Synchrotron at CERN. The resolution of such device is defined by the collection efficiency of the Cherenkov light, which is produced by relativistic charged particles in the fused silica. Thus, the surface quality of the radiator should be as good as possible to avoid light losses. The method is based on the scanning of the radiator surface with a 90Sr radioactive source and measurements of the Cherenkov light rate, detected by a PMT attached to the quartz bars. The data have been compared with a Monte-Carlo simulation, providing an estimation of the radiator’s probability of the total internal reflection and inefficient area at the edges of the bars.

Spin Flip of a Channeling Particle in a Thin Crystal

On the basis of an exact solution of the Bargmann–Michel–Telegdi equation, we have investigated spin flip of relativistic charged particles passing through a thin crystal in the planar channeling regime.

Peculiarities of electromagnetic field oscillations of a charged particle rotating about a conductive ball

Abstract. The paper investigates some characteristic features of the electromagnetic field of a relativistic charged particle that uniformly rotates about a conductive ball in its equatorial plane. It is assumed that the braking of the particle due to radiation is compensated by an external influence (e.g. the electric force) that compels the particle to turn uniformly in a circle. The magnetic permittivity of the ball is assumed to be one. The work is based on the corresponding exact analytic solutions of Maxwell’s equations. The generalized Drude-Lorentz-Sommerfeld formula for the dielectric function of the conductive ball is used in numerical calculations. It is shown that localized oscillations of a high-amplitude electromagnetic field can be generated at a given harmonic inside the ball at a certain (resonant) particle rotation frequency at a small distance from the surface of the ball. Herewith, at large distances from the trajectory of the particle, these localized oscillations are accompanied by intense radiation at the same harmonic, which is many times more intense than the analogous radiation in the case when the ball is absent. The possibilities of using this phenomenon to develop sources of quasi-monochromatic electromagnetic radiation in the range from giga- to terra hertz frequencies are discussed.

Peculiarities of electromagnetic field oscillations of a charged particle rotating about a conductive ball

Abstract. The paper investigates some characteristic features of the electromagnetic field of a relativistic charged particle that uniformly rotates about a conductive ball in its equatorial plane. It is assumed that the braking of the particle due to radiation is compensated by an external influence (e.g. the electric force) that compels the particle to turn uniformly in a circle. The magnetic permittivity of the ball is assumed to be one. The work is based on the corresponding exact analytic solutions of Maxwell’s equations. The generalized Drude-Lorentz-Sommerfeld formula for the dielectric function of the conductive ball is used in numerical calculations. It is shown that localized oscillations of a high-amplitude electromagnetic field can be generated at a given harmonic inside the ball at a certain (resonant) particle rotation frequency at a small distance from the surface of the ball. Herewith, at large distances from the trajectory of the particle, these localized oscillations are accompanied by intense radiation at the same harmonic, which is many times more intense than the analogous radiation in the case when the ball is absent. The possibilities of using this phenomenon to develop sources of quasi-monochromatic electromagnetic radiation in the range from giga- to terra hertz frequencies are discussed.

Interfacing Geant4, Garfield++ and Degrad for the simulation of gaseous detectors

For several years, attempts have been made to interface Geant4 and other software packages with the aim of simulating the complete response of a gaseous particle detector. In such a simulation, Geant4 is always responsible for the primary particle generation and the interactions that occur in the non-gaseous detector material. Garfield++ on the other hand always deals with the drift of ions and electrons, amplification via electron avalanches and finally signal generation. For the ionizing interaction of particles with the gas, different options and physics models exist. The present paper focuses on how to use Geant4, Garfield++ (including its Heed and SRIM interfaces) and Degrad to create the ionization electron-ion pairs in the gas. Software-wise, the proposed idea is to use the Geant4 physics parameterization feature, and to implement a Garfield++ or Degrad based detector simulation as an external model. With a Degrad model, detailed simulations of the X-ray interaction in gaseous detectors, including shell absorption by photoelectric effect, subsequent Auger cascade, shake-off and fluorescence emission, become possible. A simple Garfield++ model can be used for photons (Heed), heavy ions (SRIM) and relativistic charged particles or MIPs (Heed). For non-relativistic charged particles, more effort is required, and a combined Geant4/Garfield++ model must be used. This model, the Geant4/Heed PAI model interface, uses the Geant4 PAI model in conjunction with the Heed PAI model. Parameters, such as the lower production cut of the Geant4 PAI model and the lowest electron energy limit have to be set correctly. The paper demonstrates how to determine these parameters for certain values of the W parameter and Fano factor of the gas mixture. The simulation results of this Geant4/Heed PAI model interface are then verified against the results obtained with the stand-alone software packages.

Response of narrow cylindrical plasmas to dense charged particle beams

By combining the linear theory and numerical simulations, we study the response of a radially bounded axisymmetric plasma to relativistic charged particle beams in a wide range of plasma densities. We present analytical expressions for the magnetic field generated in the dense plasma, demonstrate vanishing of the wakefield potential beyond the trajectory of the outermost plasma electron, and follow the wakefield potential change as the plasma density decreases. At high plasma densities, wavefronts of electron density and radial electric field are distorted due to beam charge and current neutralization, while wavefronts of wakefield potential and longitudinal electric field are not. At plasma densities lower than or of the order of the beam density, multiple electron flows develop in and outside the plasma, resulting in a nonzero wakefield potential around the plasma column.