Trajectories Of Charged Particles Research Articles

Radiating particles accelerated by a weakly charged Schwarzschild black hole

It is well known that supermassive black holes in the centers of galaxies are capable of accelerating charged particles to very high energies. In many cases, the particle acceleration by black holes occurs electromagnetically through an electric field induced by the source. In such scenarios, the accelerated particles radiate electromagnetic waves, leading to the appearance of the backreaction force, which can considerably change the dynamics, especially, if the particles are relativistic. The effect of the radiation reaction force due to accelerating electric field of the central body in curved spacetime has not been considered previously. We study the dynamics of radiating charged particles in the field of the Schwarzschild black hole in the presence of an electric field associated with a small central charge of negligible gravitational influence. We use the DeWitt-Brehme equation and discuss the effect of the self-force, also known as the tail term, within the given approach. We also study the pure effect of the self-force to calculate the radiative deceleration of radially moving charged particles. In the case of bounded orbits, we find that the radiation reaction force can stabilize and circularize the orbits of oscillating charged particles by suppressing the oscillations or causing the particles to spiral down into the black hole depending on the sign of the electrostatic interaction. In all cases, we calculate the energy losses and exact trajectories of charged particles for different values and signs of electric charge.

The derivation of Jacobian matrices for the propagation of track parameter uncertainties in the presence of magnetic fields and detector material

In high-energy physics experiments, the trajectories of charged particles are reconstructed using track reconstruction algorithms. Such algorithms need to both identify the set of measurements from a single charged particle and to fit the parameters by propagating tracks along the measurements. The propagation of the track parameter uncertainties is an important component in the track fitting to get the optimal precision in the fitted parameters. The error propagation is performed at intersections between the track and local coordinate frames defined on detector components by calculating a Jacobian matrix corresponding to the local-to-local frame transport. This paper derives the Jacobian matrix in a general manner to harmonize with numerical integration methods developed for inhomogeneous magnetic fields and materials. The Jacobian and transported covariance matrices are validated by simulating the propagation of charged particles between two frames and comparing with the results of numerical methods.

A modified Lorentz force law for point-like charged particles in classical electrodynamics

In classical electrodynamics, the well-known Lorentz force law falls short of providing a satisfactory result for the trajectory of point-like charged particles when considering that particle’s own self-force. While there have been many historical attempts, Gralla, Harte and Wald developed a new model for classical charged particles that is free from pathologies while being consistent with Maxwell’s equations and conserves stress-energy. Expanding upon this approach, we derive a relativistically correct, modified Lorentz force law in vector form, which includes radiation reaction, and spin- and magnetic moment-dependent correction terms, suitable to be included in classical electrodynamics lectures and beam dynamics simulation tools. As by-products we obtain evolution equations for mass, spin angular momentum and the radiated power. We compare the new equations to the classical ones and use the new equations to conduct numerical simulations, showing that the results are free of any nonphysical artifacts, and which might be possible to test in future experiments at particle accelerators. The new equations foster improved insight into beam dynamics.

Deep learning based event reconstruction for cyclotron radiation emission spectroscopy

The objective of the cyclotron radiation emission spectroscopy (CRES) technology is to build precise particle energy spectra. This is achieved by identifying the start frequencies of charged particle trajectories which, when exposed to an external magnetic field, leave semi-linear profiles (called tracks) in the time–frequency plane. Due to the need for excellent instrumental energy resolution in application, highly efficient and accurate track reconstruction methods are desired. Deep learning convolutional neural networks (CNNs) - particularly suited to deal with information-sparse data and which offer precise foreground localization—may be utilized to extract track properties from measured CRES signals (called events) with relative computational ease. In this work, we develop a novel machine learning based model which operates a CNN and a support vector machine in tandem to perform this reconstruction. A primary application of our method is shown on simulated CRES signals which mimic those of the Project 8 experiment—a novel effort to extract the unknown absolute neutrino mass value from a precise measurement of tritium β −-decay energy spectrum. When compared to a point-clustering based technique used as a baseline, we show a relative gain of 24.1% in event reconstruction efficiency and comparable performance in accuracy of track parameter reconstruction.

Design of the waveform distinction algorithm for the main drift chamber at the Super Tau-Charm facility

Drift chambers are essential in high-energy collider experiments for tracking the trajectory of charged particles. With the increase in peak luminosity, the detector's counting rate also rises, leading to challenges such as high beam backgrounds and an increased probability of signal pile-up in a single drift chamber channel. The Super Tau-Charm Facility (STCF) is a new electron-positron collider proposed by the Chinese particle physics community and the Main Drift Chamber (MDC) is the primary component of the STCF tracking system. The average hit rate of the innermost layer is 440 kHz with the cell size of 1 cm. This high count rate increases the pile-up probability of waveforms, making it difficult to achieve waveform discrimination even with optimized readout electronics performance. Modifying the cell size from approximately 1 cm to 5 mm is expected to decrease the innermost layer hit rate to approximately 210 kHz per channel. This paper presents a novel algorithm for waveform distinction using digital waveform data and integration curves. The algorithm is implemented on an evaluation board based on the Xilinx FPGA to achieve real-time waveform distinction. The algorithm's performance is validated through testing with the evaluation board. The test results indicate that the probability of distinction closely matches the theoretical value, the efficiency of the algorithm is about 96%, and the error probability is less than 4%. This result can serve as a reference for optimizing the MDC structure.

Reconstructing charged particle track segments with a quantum-enhanced support vector machine

Reconstructing the trajectories of charged particles from the collection of hits they leave in the detectors of collider experiments like those at the Large Hadron Collider (LHC) is a challenging combinatorics problem and computationally intensive. The tenfold increase in the delivered luminosity at the upgraded High Luminosity LHC will result in a very densely populated detector environment. The time taken by conventional techniques for reconstructing particle tracks scales worse than quadratically with track density. Accurately and efficiently assigning the collection of hits left in the tracking detector to the correct particle will be a computational bottleneck and has motivated studying possible alternative approaches. This paper presents a quantum-enhanced machine learning algorithm that uses a support vector machine (SVM) with a quantum-estimated kernel to classify a set of three hits (triplets) as either belonging to or not belonging to the same particle track. The performance of the algorithm is then compared to a fully classical SVM. The quantum algorithm shows an improvement in accuracy versus the classical algorithm. Model complexity metrics are used to hint at an explanation for favorable performance of the quantum kernel. Published by the American Physical Society 2024

Study of the Gyro and Divergence Characteristics of Relativistic Charged Particle Beam Propagation in Earth’s Magnetic Field

Relativistic charged particle beam can be used as a destructive beam weapon in space for debris removal tasks. The trajectories of charged particles are affected by both electric and magnetic forces in the Earth’s magnetic field. In this paper, we firstly analyzed the correlation parameters of the charged particle beam as a weapon when it is propagated in the geomagnetic field. Then, the models were constructed based on COMSOL Multiphysics, and the IGRF model was adopted in the simulation. The gyroradius and the related uncertainty were analyzed by simulation of the charged particle transport in the geomagnetic field at different altitudes. The charged beam spot radius divergency was also simulated. The geomagnetic field can inhibite the diffusion of the electron beam.

Квантово-механическая модель ионного двигателя малого космического аппарата

The article presents a quantum mechanical model of an ion thruster. The basic equations describing the shape of the accelerated beam are considered. Detector plates demonstrating the interference pattern in thin films are presented. A mathematical description of the relief of thin films is given using the resulting wave function. The operation of a low-power ion engine is demonstrated. The results of numerical solution of the model with different initial values are shown. Based on the results of calculations, diagrams of the trajectories of charged particles are constructed.

Towards Neural Charged Particle Tracking in Digital Tracking Calorimeters with Reinforcement Learning.

We propose a novel technique for reconstructing charged particles in digital tracking calorimeters using reinforcement learning aiming to benefit from the rapid progress and success of neural network architectures without the dependency on simulated or manually-labeled data. Here we optimize by trial-and-error a behavior policy acting as an approximation to the full combinatorial optimization problem, maximizing the physical plausibility of sampled trajectories. In modern processing pipelines used in high energy physics and related applications, tracking plays an essential role allowing to identify and follow charged particle trajectories traversing particle detectors. Due to the high multiplicity of charged particles and their physical interactions, randomly deflecting the particles, the reconstruction is a challenging undertaking, requiring fast, accurate and robust algorithms. Our approach works on graph-structured data, capturing track hypotheses through edge connections between particles in the detector layers. We demonstrate in a comprehensive study on simulated data for a particle detector used for proton computed tomography, the high potential as well as the competitiveness of our approach compared to a heuristic search algorithm and a model trained on ground truth. Finally, we point out limitations of our approach, guiding towards a robust foundation for further development of reinforcement learning based tracking.

Reconnection in a pinch

A recently published analysis of current sheets has updated the classic Harris 1D static solution by considering multiple classes of charged particle trajectories in a generalized and dynamic current sheet. It uses a 1D PIC simulation to describe dynamic pinching and bifurcation of the current sheet. These 1D results strongly suggest that properties of the inflowing plasma, including the plasma beta, have an important effect on the equilibrium thickness of the pinched current sheet. Since 1D studies cannot describe magnetic reconnection, the time appears right to carry such 1D studies over to 2D or 3D simulations to explore current sheet thickness effects on reconnection. The Magnetospheric Multiscale Mission (MMS), with its well-resolved multipoint measurements of collisionless plasma and fields, has found that collisionless reconnection is accompanied by non-adiabatic motions of electrons that only occur in magnetic structures with a narrow scale comparable to electron inertial lengths (de). The recent 1D studies suggest that a plasma pinch to such scales may only occur for inflowing magnetized plasmas with relatively low plasma beta. We conclude that a parametric exploration of simulated and observed reconnection inflow conditions, particularly plasma beta, should shed light on the enablement of reconnection in collisionless plasmas.

Monte Carlo simulations of charged particle transport in plasmas: A fast single-scattering model

When simulating a charged particle trajectory in plasmas with Monte Carlo methods, the traditional single-scattering model is accurate but computationally expensive. The traditional multiple-scattering model reduces the computation cost but assumes an exponential distribution of the scattering angle, which overestimates the cumulative scattering angle. In this paper, we develop a new Monte Carlo method for the charged particle transport simulations. The scattering angle is naturally sampled from a modified screened Rutherford scattering cross section, in which a greatly amplified minimum deflection angle is used. With this model, the simulations give the same scattering angle distribution with the single-scattering model but only take a comparable computation cost with the multiple-scattering model when the small scattering angle and Markovian approximations can be fulfilled. This model would be especially useful for the study of inertial-confinement-fusion, which is sensitive to the alpha-particle energy deposition.

Study on Power Frequency Breakdown Characteristics of Nano-TiO2 Modified Transformer Oil under Severe Cold Conditions

With 45# transformer oil as the base fluid, different concentrations of TiO2 nanomodified transformer oil were prepared via the thermal oscillation method. Nanomodified transformer oil with a concentration of 0.01 g/L was selected for evaluation via the breakdown test. Then, 0.01 g/L nanomodified transformer oil and ordinary 45# transformer oil were subjected to the variable control of different moisture contents and different temperatures, and breakdown tests under different types of electrodes were performed within the temperature range of −30 °C to 30 °C. The test results showed the following: Under severe cold conditions, the improvement effect of the breakdown voltage in different temperature ranges was different. Within the temperature range of −30 °C to −10 °C, the enhancement effect could reach 13% to 15%. Within the temperature range of −10 °C to 0 °C, the enhancement effect could reach 8% to 9%. Within the temperature range of 0 °C to 30 °C, the enhancement effect could reach 18% to 21%. Compared with the test results at high water contents, the improvement in the breakdown voltage amplitude of transformer oil by nanomaterials was more obvious at low water contents. In addition, nanomaterials could reduce the dispersion of the breakdown voltage to make the breakdown voltage more stable. Lastly, COMSOL was used to simulate the polarization process of nanoparticles under a uniform electric field and the influence of the trajectory of charged particles in the oil to further analyze the mechanism of the influence of nanoparticles in oil on the breakdown voltage of the oil gap. The simulation results showed that, when the particles were accelerated by the electric field, they moved irregularly. After adding nanoparticles, the charged particles were adsorbed by the nanoparticles when passing through the nanoparticles, which reduced the migration rate of charged particles in the oil. The breakdown voltage of the oil gap increased.

Correction of the Mathematical Method for Studying a Cathode Lens with Two Planes of Symmetry

The article is devoted to the theoretical problems of studying cathode lenses with two planes of symmetry. It is noted that the classical methods of studying conventional electron lenses are unsuitable for a detailed study of the focusing properties of cathode lenses because these methods do not take into account the specificity of the initial conditions of cathode lenses. For a cathode lens, it is inaccurate to assume that the trajectories of charged particles throughout have a small inclination to the main optical axis. In addition, in single and immersion lenses, the condition of the smallness of the spread of charged particle energies with respect to the values of the axial potential is satisfied throughout, while in the cathode lens, this condition is not satisfied in the cathode region. The method proposed in the article is based on the study of the parameters of the trajectory of an arbitrary particle in a beam of charged particles relative to the parameters of the trajectory of an axial particle with zero initial energy, the trajectory of which is chosen as a scalar motion. The results obtained in the article will expand the scope of the application of cathode lenses with two planes of symmetry.

Reconstructing charged-particle trajectories in the PANDA Straw Tube Tracker using the LOcal Track Finder (LOTF) algorithm

We present the LOcal Track Finder (lotf) algorithm, a method that performs charged-particle trajectory reconstruction using the Straw Tube Tracker, one of the central trackers of the antiProton ANnihilation at DArmstadt (PANDA) detector. The algorithm builds upon the neighboring relations of the tubes to connect individual hits and form track candidates. In addition, it uses a local fitting procedure to handle regions where several tracks overlap and utilizes a system of virtual nodes to reconstruct the z-information of the particle trajectories. We generated 30,000 events to assess the performance of our approach and compared its global track assignment efficiency with respect to two other track reconstruction methods. lotf has (1) an average of 85% of found tracks, (2) the largest number of Fully Pure tracks, (3) the lowest amount of incorrect reconstructions, and (4) is significantly faster than the other two approaches. Further, we compared the z-reconstruction performance with one of the two alternative methods and show that lotf improves the median z-error by a factor of 8.7. Finally, we tested our method using 3750 data sets composed of 4 events each, demonstrating that our approach handles cases in which events are mixed. The raw (without parallelization) average reconstruction rate is about 68,000 hits/s, which makes the present algorithm promising for online data selection and processing.

Charged particle dynamics in parabolic magnetosphere around Schwarzschild black hole

The study of charged particle dynamics in the combined gravitational and magnetic field can provide important theoretical insight into astrophysical processes around black holes. In this paper, we explore the charged particle dynamics in parabolic magnetic field configuration around Schwarzschild black hole, since the paraboloidal shapes of magnetic field lines around black holes are well motivated by the numerical simulations and supported by observations of relativistic jets. Analysing the stability of bounded orbits and using the effective potential approach, we show the possibility of existence of stable circular off-equatorial orbits around the symmetry axis. We also show the influence of radiation reaction force on the dynamics of charged particles, in particular on the chaoticity of the motion and Poincaré sections, oscillatory frequencies, and emitted electromagnetic spectrum. Applied to Keplerian accretion disks, we show that in parabolic magnetic field configuration, the thin accretion configurations can be either destroyed or transformed into a thick toroidal structure given the radiation reaction and electromagnetic-disk interactions included. Calculating the Fourier spectra for radiating charged particle trajectories, we find that the radiation reaction force does not affect the main frequency peaks, however, it lowers the higher harmonics making the spectrum more flat and diluted in high frequency range.

Новая схема интегрирования уравнений движения частиц в методе “частиц-в-ячейках” для задач физики плазмы

Представлен новый метод решения релятивистских уравнений движения заряженных частиц в электромагнитных полях, учитывающий условие постоянства их значений на каждом временном шаге. Проведено сравнение точности и эффективности вычислений при решении тестовых задач в дву- и трехмерной постановках на основе нового метода, метода Бориса и его модификаций. В каждом случае рассматривались варианты аналитически и дискретно заданных значений электрического и магнитного полей. At present, the Boris method is mostly common for the numerical solution of problems of the dynamics of charged particles in electromagnetic fields. In recent years, new modifications of the Boris method have appeared that are capable to simplify, refine, or speed up calculations. However, despite the rather large number of publications which consider algorithms for calculating the trajectories of charged particles, new, more accurate and high-performance algorithms are desired. The article presents a detailed analysis of some explicit methods for solving the problem of the motion of charged particles in electromagnetic fields, which differ in how they set the average values of velocities. A new scheme based on an analytical solution, which has not been studied before, is proposed. For the Boris, Vay, Higuera – Cary schemes and the new VD1 scheme, a comparative analysis of the accuracy, convergence and counting time for the relativistic and nonrelativistic cases is carried out. In the nonrelativistic case, the new scheme allows accurate solving of the equations for motion of charged particles, and in the relativistic case, the accuracy of the new scheme remains higher compared to other schemes. As the relativistic factor increases, the accuracy of all considered schemes for calculating the trajectory of particles in an electromagnetic field decreases. For large values of the relativistic parameter, the new scheme is more accurate than the other schemes and retains the second order. In practical calculations, when particles can have different speeds, the scheme automatically adjusts to the given speed of the particle. The presented new scheme for calculating trajectories can be important for solving a wide range of problems in astrophysics and thermonuclear fusion, where high accuracy in determining particle trajectories in inhomogeneous fields for large moments of time is required.

Experimental and Monte Carlo-based determination of magnetic field correction factors in high-energy photon fields for two ionization chambers.

The integration of magnetic resonance tomography into clinical linear accelerators provides high-contrast, real-time imaging during treatment and facilitates online-adaptive workflows in radiation therapy treatments. The associated magnetic field also bends the trajectories of charged particles via the Lorentz force, which may alter the dose distribution in a patient or a phantom and affects the dose response of dosimetry detectors. To perform an experimental and Monte Carlo-based determination of correction factors , which correct the response of ion chambers in the presence of external magnetic fields in high-energy photonfields. The response variation of two different types of ion chambers (Sun Nuclear SNC125c and SNC600c) in strong external magnetic fields was investigated experimentally and by Monte Carlo simulations. The experimental data were acquired at the German National Metrology Institute, PTB, using a clinical linear accelerator with a nominal photon energy of 6 MV and an external electromagnet capable of generating magnetic flux densities of up to 1.5 T in opposite directions. The Monte Carlo simulation geometries corresponded to the experimental setup and additionally to the reference conditions of IAEA TRS-398. For the latter, the Monte Carlo simulations were performed with two different photon spectra: the 6 MV spectrum of the linear accelerator used for the experimental data acquisition and a 7MV spectrum of a commercial MRI-linear accelerator. In each simulation geometry, three different orientations of the external magnetic field, the beam direction and the chamber orientation were investigated. Good agreement was achieved between Monte Carlo simulations and measurements with the SNC125c and SNC600c ionization chambers, with a mean deviation of 0.3% and 0.6%, respectively. The magnitude of the correction factor strongly depends on the chamber volume and on the orientation of the chamber axis relative to the external magnetic field and the beam directions. It is greater for the SNC600c chamber with a volume of 0.6cm3 than for the SNC125c chamber with a volume of 0.1 cm3 . When the magnetic field direction and the chamber axis coincide, and they are perpendicular to the beam direction, the ion chambers exhibit a calculated overresponse of less than 0.7(6)% (SNC600c) and 0.3(4)% (SNC125c) at 1.5 T and less than 0.3(0)% (SNC600c) and 0.1(3)% (SNC125c) for 0.35 T for nominal beam energies of 6 MV and 7MV. This chamber orientation should be preferred, as may increase significantly in other chamber orientations. Due to the special geometry of the guard ring, no dead-volume effects have been observed in any orientation studied. The results show an intra-type variation of 0.17% and 0.07% standard uncertainty (k=1) for the SNC125c and SNC600c, respectively. Magnetic field correction factors for two different ion chambers and for typical clinical photon beam qualities were presented and compared with the few data existing in the literature. The correction factors may be applied in clinical reference dosimetry for existing MRI-linearaccelerators.

Optimizing trigger-level track reconstruction for sensitivity to exotic signatures

Many compelling beyond the Standard Model scenarios predict signals that result in unconventional charged particle trajectories. Signatures for which unusual tracks are the most conspicuous feature of the event pose significant challenges for experiments at the Large Hadron Collider (LHC), particularly for the trigger. This article presents a study of track-based triggers for a representative set of long-lived and unconventional signatures at the upcoming High Luminosity LHC, as well as resulting recommendations for the target parameters of a hardware-based tracking system. Scenarios studied include large multiplicities of low-pT tracks produced in a soft-unclustered-energy-pattern model, displaced leptons and anomalous prompt tracks predicted in a Supersymmetry model with long-lived staus, and displaced hadrons predicted in a Higgs portal scenario with long-lived scalars.

Measurement of structure dependent radiative K+ → e+νγ decay at J-PARC

The J-PARC E36 experiment is aiming at searching for lepton universality violation by accurately measuring the ratio of branching ratio of the K + → e + ν(γ) (K e2(γ)) to K + → μ + ν(γ) (K μ2(γ)) decays. The experiment was performed at J-PARC employing a stopped K + method in conjunction with a 12-sector iron-core superconducting toroidal spectrometer. Charged particle momenta were determined by reconstructing charged particle trajectories in the spectrometer. Particle identification for e + and μ + was carried out using an aerogel Cherenkov counter and a lead-glass Cherenkov counter, as well as by measuring the time-of-flight between TOF counters. The peak structure due to K e2(γ) decay was successfully observed in the e + momentum spectrum after the e + requirement in the PID analysis. The structure dependentradiative K + → e + νγ () events were selected by imposing photon hits in the CsI(Tl) calorimeter or the GSC counter. The experimental spectra were accurately reproduced by the Monte Carlo simulation, indicating a correct understanding of the experimental conditions. The Br() value relative to Br(K e2(γ)) was determined from the and K e2(γ) yields corrected for the detector acceptances. The Br()/Br(K e2(γ)) ratio was derived to be 1.19 ± 0.07 stat ± 0.04 syst in the CsI(Tl) analysis and 1.25 ± 0.14 stat ± 0.04 syst in the GSC analysis.

A non-linear Kalman filter for track parameters estimation in high energy physics

The Kalman Filter is a widely used approach for the linear quadratic estimation of dynamical systems and is frequently employed within nuclear and particle physics experiments for the reconstruction of charged particle trajectories, known as tracks. Implementations of this formalism often make assumptions on the linearity of the underlying dynamic system and the Gaussian nature of the process noise and measurement model, which are violated in a number of track reconstruction applications. This paper introduces an implementation of a Non-Linear Kalman Filter (NLKF) within the ACTS track reconstruction toolkit. The NLKF addresses the issue of non-linearity by using a set of representative sample points during the projection of the track state to the measurement. In a typical use case, the NLKF outperforms the so-called Extended Kalman Filter in the accuracy and precision of the track parameter estimates obtained, with an increase in CPU time below a factor of two. It is therefore a promising approach for use in applications where precise estimation of track parameters is a key concern.