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

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

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Electron and Proton Energization in 3D Reconnecting Current Sheets in Semirelativistic Plasma with Guide Magnetic Field

Abstract Using 3D particle-in-cell simulation, we characterize energy conversion, as a function of guide magnetic field, in a thin current sheet in semirelativistic plasma, with relativistic electrons and subrelativistic protons. There, magnetic reconnection, the drift-kink instability (DKI), and the flux-rope kink instability all compete and interact in their nonlinear stages to convert magnetic energy to plasma energy. We compare fully 3D simulations with 2D in two different planes to isolate reconnection and DKI effects. In zero guide field, these processes yield distinct energy conversion signatures: ions gain more energy than electrons in 2Dxy(reconnection), while the opposite is true in 2Dyz(DKI), and the 3D result falls in between. The flux-rope instability, which occurs only in 3D, allows more magnetic energy to be released than in 2D, but the rate of energy conversion in 3D tends to be lower. Increasing the guide magnetic field strongly suppresses DKI, and in all cases slows and reduces the overall amount of energy conversion; it also favors electron energization through a process by which energy is first stored in the motional electric field of flux ropes before energizing particles. Understanding the evolution of the energy partition thus provides insight into the role of various plasma processes, and is important for modeling radiation from astrophysical sources such as accreting black holes and their jets.

Astronomy & Astrophysics↗

Reconnection and particle acceleration in three-dimensional current sheet evolution in moderately magnetized astrophysical pair plasma

Magnetic reconnection, a plasma process converting magnetic energy to particle kinetic energy, is often invoked to explain magnetic energy releases powering high-energy flares in astrophysical sources including pulsar wind nebulae and black hole jets. Reconnection is usually seen as the (essentially two-dimensional) nonlinear evolution of the tearing instability disrupting a thin current sheet. To test how this process operates in three dimensions, we conduct a comprehensive particle-in-cell simulation study comparing two- and three-dimensional evolution of long, thin current sheets in moderately magnetized, collisionless, relativistically hot electron–positron plasma, and find dramatic differences. We first systematically characterize this process in two dimensions, where classic, hierarchical plasmoid-chain reconnection determines energy release, and explore a wide range of initial configurations, guide magnetic field strengths and system sizes. We then show that three-dimensional (3-D) simulations of similar configurations exhibit a diversity of behaviours, including some where energy release is determined by the nonlinear relativistic drift-kink instability. Thus, 3-D current sheet evolution is not always fundamentally classical reconnection with perturbing 3-D effects but, rather, a complex interplay of multiple linear and nonlinear instabilities whose relative importance depends sensitively on the ambient plasma, minor configuration details and even stochastic events. It often yields slower but longer-lasting and ultimately greater magnetic energy release than in two dimensions. Intriguingly, non-thermal particle acceleration is astonishingly robust, depending on the upstream magnetization and guide field, but otherwise yielding similar particle energy spectra in two and three dimensions. Although the variety of underlying current sheet behaviours is interesting, the similarities in overall energy release and particle spectra may be more remarkable.

Physics↗

Kinetic Simulations of the Kruskal–Schwarzschild Instability in Accelerating Striped Outflows: Dynamics and Energy Dissipation

Astrophysical relativistic outflows are launched as Poynting-flux dominated, yet the mechanism governing efficient magnetic dissipation, which powers the observed emission, is still poorly understood. We study magnetic energy dissipation in relativistic "striped" jets, which host current sheets separating magnetically dominated regions with opposite field polarity. The effective gravity force g in the rest frame of accelerating jets drives the Kruskal–Schwarzschild instability (KSI), a magnetic analog of the Rayleigh–Taylor instability. By means of 2D and 3D particle-in-cell simulations, we study the linear and nonlinear evolution of the KSI. The linear stage is well described by linear stability analysis. The nonlinear stages of the KSI generate thin (skin-depth-thick) current layers, with length comparable to the dominant KSI wavelength. There, the relativistic drift-kink mode and the tearing mode drive efficient magnetic dissipation. The dissipation rate can be cast as an increase in the effective width Δ eff of the dissipative region, which follows dΔ eff /dt ≃ 0.05 $\sqrt{Δ_{eff} g}$. Our results have important implications for the location of the dissipation region in gamma-ray burst and active galactic nuclei jets.

79 ASTRONOMY AND ASTROPHYSICS↗

Toroidal modeling of Alfvén eigenmodes excited by runaway electrons in DIII-D and ITER

The non-perturbative MHD-kinetic hybrid code MARS-K (Liu et al 2014 Phys. Plasmas 21 056105) is updated to include relativistic effects for kinetic fast particles, enabling the code to model excitation of Alfvén eigenmodes (AEs) by runaway electrons (REs) in post-disruption tokamak plasmas. Applying the updated code to RE beams in both DIII-D and ITER, a zoo of AE modes triggered by trapped REs due to precessional drift-kinetic resonances is computed while scanning the RE energy. At fixed RE energy, multiple unstable roots are also excited. These AE modes possess radially different eigenmode structures, ranging from global modes to core-localized ones. The computed mode frequency is in the Alfvén frequency range, increasing with the assumed RE energy in a staircase fashion and quantitatively matching the experimental measurement (in DIII-D). At the (more relevant) high-frequency range (above 1 MHz), the modeled eigenmodes are identified as compressional AEs (CAEs) in DIII-D and a mixture of CAE and shear Alfvén waves in ITER.

Alfvén eigenmodes↗

A Particle-in-cell Method for Plasmas with A Generalized Momentum Formulation, Part III: A family of Gauge Conserving Methods

In this paper, we introduce a new family of spatially co-located field solvers for particle-in-cell applications which evolve the potential formulation of Maxwell’s equations under the Lorenz gauge. Our recent work [2] introduced the concept of time-consistency, which connects charge conservation to the preservation of the gauge at the semi-discrete level. It will be shown that there exists a large family of time discretizations which satisfy this property. Additionally, it will be further shown that for large classes of time marching methods, the satisfaction of the gauge condition automatically implies the satisfaction of Gauss’s law for electricity, with the potential formulation ensuring that that Gauss’s law for magnetism is satisfied by definition. We focus on popular time marching methods including centered differences, backward differences, and diagonally-implicit Runge-Kutta methods, which are coupled to a spectral discretization in space. We demonstrate the theory by testing the methods on a relativistic Weibel instability and a drifting cloud of electrons.

97 MATHEMATICS AND COMPUTING↗

Conditional guided generative diffusion for particle accelerator beam diagnostics

Abstract Advanced accelerator-based light sources such as free electron lasers (FEL) accelerate highly relativistic electron beams to generate incredibly short (10s of femtoseconds) coherent flashes of light for dynamic imaging, whose brightness exceeds that of traditional synchrotron-based light sources by orders of magnitude. FEL operation requires precise control of the shape and energy of the extremely short electron bunches whose characteristics directly translate into the properties of the produced light. Control of short intense beams is difficult due to beam characteristics drifting with time and complex collective effects such as space charge and coherent synchrotron radiation. Detailed diagnostics of beam properties are therefore essential for precise beam control. Such measurements typically rely on a destructive approach based on a combination of a transverse deflecting resonant cavity followed by a dipole magnet in order to measure a beam’s 2D time vs energy longitudinal phase-space distribution. In this paper, we develop a non-invasive virtual diagnostic of an electron beam’s longitudinal phase space at megapixel resolution (1024 × 1024) based on a generative conditional diffusion model. We demonstrate the model’s generative ability on experimental data from the European X-ray FEL.

43 PARTICLE ACCELERATORS↗

Particle Acceleration in Relativistic Alfvénic Turbulence

Abstract Strong magnetically dominated Alfvénic turbulence is an efficient engine of nonthermal particle acceleration in a relativistic collisionless plasma. We argue that in the limit of strong magnetization, the type of energy distribution attained by accelerated particles depends on the relative strengths of turbulent fluctuations δ B 0 and the guide field B 0 . If δ B 0 ≪ B 0 , the particle magnetic moments are conserved, and the acceleration is provided by magnetic curvature drifts. Curvature acceleration energizes particles in the direction parallel to the magnetic field lines, resulting in log-normal tails of particle energy distribution functions. Conversely, if δ B 0 ≳ B 0 , interactions of energetic particles with intense turbulent structures can scatter particles, creating a population with large pitch angles. In this case, magnetic mirror effects become important, and turbulent acceleration leads to power-law tails of the energy distribution functions.

79 ASTRONOMY AND ASTROPHYSICS↗

The role of plasma instabilities in relativistic radiation-mediated shocks: stability analysis and particle-in-cell simulations

ABSTRACT Relativistic radiation-mediated shocks are likely formed in prodigious cosmic explosions. The structure and emission of such shocks are regulated by copious production of electron–positron pairs inside the shock-transition layer. It has been pointed out recently that substantial abundance of positrons inside the shock leads to a velocity separation of the different plasma constituents, which is expected to induce a rapid growth of plasma instabilities. In this paper, we study the hierarchy of plasma microinstabilities growing in an electron-ion plasma loaded with pairs and subject to a radiation force. Linear stability analysis indicates that such a system is unstable to the growth of various plasma modes which ultimately become dominated by a current filamentation instability driven by the relative drift between the ions and the pairs. These results are validated by particle-in-cell simulations that further probe the non-linear regime of the instabilities, and the pair-ion coupling in the microturbulent electromagnetic field. Based on this analysis, we derive a reduced-transport equation for the particles via pitch-angle scattering in the microturbulence and demonstrate that it can couple the different species and lead to non-adiabatic compression via a Joule-like heating. The heating of the pairs and, conceivably, the formation of non-thermal distributions, arising from the microturbulence, can affect the observed shock-breakout signal in ways unaccounted for by current single-fluid models.

79 ASTRONOMY AND ASTROPHYSICS↗

Daily modulations and broadband strategy in axion searches: An application with the CAST-CAPP detector

It has been previously advocated that the presence of the daily and annual modulations of the axion flux on the Earth’s surface may dramatically change the strategy of the axion searches. The arguments were based on the so-called Axion Quark Nugget (AQN) dark matter model which was originally put forward to explain the similarity of the dark and visible cosmological matter densities Ω dark ∼ Ω visible . In this framework, the population of galactic axions with mass 10 − 6 eV ≲ m a ≲ 10 − 3 eV and velocity ⟨ v a ⟩ ∼ 10 − 3 c will be accompanied by axions with typical velocities ⟨ v a ⟩ ∼ 0.6 c emitted by AQNs. Furthermore, in this framework, it has also been argued that the AQN-induced axion daily modulation (in contrast with the conventional weakly interactive massive particle paradigm) could be as large as (10–20)%, representing the main motivation for the present investigation. We argue that the daily modulations along with the broadband detection strategy can be very useful tools for the discovery of such relativistic axions. The data from the CAST-CAPP detector have been used following such arguments. Unfortunately, due to the dependence of the amplifier chain on temperature-dependent gain drifts and other factors, we could not conclusively show the presence or absence of a dark sector-originated daily modulation. However, this proof of principle analysis procedure can serve as a reference for future studies. Published by the American Physical Society 2025

Caspers, F.↗

Electromagnetic Fireworks: Fast Radio Bursts from Rapid Reconnection in the Compressed Magnetar Wind

One scenario for the generation of fast radio bursts (FRBs) is magnetic reconnection in a current sheet of the magnetar wind. Compressed by a strong magnetic pulse induced by a magnetar flare, the current sheet fragments into a self-similar chain of magnetic islands. Time-dependent plasma currents at their interfaces produce coherent radiation during their hierarchical coalescence. We investigate this scenario using 2D radiative relativistic particle-in-cell simulations to compute the efficiency of the coherent emission and to obtain frequency scalings. Consistent with expectations, a fraction of the reconnected magnetic field energy, f ~ 0.002, is converted to packets of high-frequency fast magnetosonic waves, which can escape from the magnetar wind as radio emission. In agreement with analytical estimates, we find that magnetic pulses of 10 47 erg s –1 can trigger relatively narrowband GHz emission with luminosities of approximately 10 42 erg s –1 , sufficient to explain bright extragalactic FRBs. The mechanism provides a natural explanation for a downward frequency drift of burst signals, as well as the ~100 ns substructure recently detected in FRB 20200120E.

79 ASTRONOMY AND ASTROPHYSICS↗

Observations and Simulations of Dropout Events and Flux Decays in October 2013: Comparing MEO Equatorial With LEO Polar Orbit

We compare ESA PROBA-V observations of electron flux at LEO with those from the NASA Van Allen Probes mostly at MEO for October 2013. Dropouts are visible at all energy during four storms from both satellites. Equatorially trapped electron fluxes are higher than at LEO by 10 2 (<1 MeV) to 10 5 (>2.5 MeV). We observe a quite isotropic structure of the outer belt during quiet times, contrary to the inner belt, and pitch angle dependence of high energy injection. We find a very good overlap of the outer belt at MEO and LEO at ~0.5 MeV. We use test-particle simulations of the energetic electrons trapped in the terrestrial magnetic field to study the outer radiation belt electron flux changes during geomagnetic storms. We show that the Dst (Disturbance storm time) effect during the main phase of a geomagnetic storm results in a betatron mechanism causing outward radial drift and a deceleration of the electrons. This outward drift motion is energy independent, pitch angle-dependent, and represents a significant distance (~1 L-shell at L = 5 for moderate storms). At fixed L-shell, this causes a decay of the LEO precipitating flux (adiabatic outward motion), followed by a return to the normal state (adiabatic inward motion) during main and recovery phases. Dst effect, associated with magnetopause shadowing and radial diffusion can explain the main characteristics of outer radiation belt electron dropouts in October 2013. We also use Fokker-Planck simulations with event-driven diffusion coefficients at high temporal resolution, to distinguish instantaneous loss from the gradual scattering that depopulates the slot region and the outer belt after storms. Simulations reproduce the slot formation and the gradual loss in the outer belt. The typical energy dependence of these losses leads to the absence of scattering for relativistic and ultra-relativistic electrons in the outer belt, oppositely to dropouts.

79 ASTRONOMY AND ASTROPHYSICS↗

Contributions to Loss Across the Magnetopause During an Electron Dropout Event

Abstract Dropout events are dramatic decreases in radiation belt electron populations that can occur in as little as 30 minutes. Loss to magnetopause due to a combination of magnetopause shadowing and outward radial transport plays a significant role in these events. We examine the dropout of relativistic electron populations during the October 2012 geomagnetic storm using simulated electron phase space density, evaluating the contribution of different processes to losses across the magnetopause. We compare loss contribution from outward transport calculated using a standard empirical radial diffusion model that assumes a dipolar geomagnetic field to an event‐specific radial diffusion model evaluated with a non‐dipolar geomagnetic field. We additionally evaluate the contribution of Shabansky type 1 particles, which bounce along magnetic field lines with local equatorial maxima, to the loss calculated during this event. We find that the empirical radial diffusion model with a dipolar background field underestimates the contribution of radial diffusion to this dropout event by up to 10% when compared to the event‐specific, non‐dipolar radial diffusion model. We additionally find that including Shabansky type 1 particles in the initial electron phase space density, that is, allowing some magnetic field lines distorted from the typical single‐minima configuration in drift shell construction, increases the calculated loss by an average of 0.75%. This shows that the treatment of the geomagnetic field significantly impacts the calculation of electron losses to the magnetopause during dropout events, with the non‐dipolar treatment of radial diffusion being essential to accurately quantify the loss of outer radiation belt populations.

79 ASTRONOMY AND ASTROPHYSICS↗

Generation of ultrafast electron bunch trains via trapping into multiple periods of plasma wakefields

We demonstrate a novel approach to the generation of femtosecond electron bunch trains via laser-driven wakefield acceleration. We use two independent high-intensity laser pulses, a drive, and an injector, each creating their own plasma wakes. The interaction of the laser pulses and their wakes results in a periodic injection of free electrons in the drive plasma wake via several mechanisms, including ponderomotive drift, wake-wake interference, and pre-acceleration of electrons directly by strong laser fields. Electron trains were generated with up to four quasi-monoenergetic bunches, each separated in time by a plasma period. In conclusion, the time profile of the generated trains is deduced from an analysis of beam loading and confirmed using 2D particle-in-cell simulations

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Towards modelling AR Sco: calibration – reproducing high-energy pulsar emission and testing convergence to Aristotelian electrodynamics

In recent years, kinetic simulations have been crucial to further our understanding of pulsar electrodynamics. Yet, due to the large-scale separation between the gyro-period and the stellar rotation period, resolving the particle gyration has been computationally unfeasible for realistic pulsar parameters. The main aim of this work is comparing our gyro-phase-resolved model with a gyro-centric pulsar model, where our model solves the general equations of motion with included radiation reaction using a higher order numerical solver with adaptive time-steps. Specifically, we aim to (i) reproduce a pulsar’s high-energy emission maps, namely one with 10 per cent of the surface B-field strength of Vela, and the spectra produced by an independent gyro-centric pulsar emission model; and (ii) test convergence of these results to the radiation-reaction limit of Aristotelian electrodynamics. (iii) Additionally, we identify the effect that a large $E_{\parallel }$-field has on the trajectories and radiation calculations. We find that we can reproduce the curvature radiation emission maps and spectra well, using 10 per cent field strengths of the Vela pulsar and injecting our particles at a higher altitude in the magnetosphere. Using sufficiently large $E_{\parallel }$-fields, our numeric results converge to the analytic radiation-reaction limit trajectories. Additionally, we illustrate the importance of accounting for the $\mathbf {E}\times \mathbf {B}$-drift in the particle trajectories and radiation calculations, validating the Harding and collaborators’ model approach. Lastly, we found that our model deals very well with the high-radiation-reaction and high-field regimes present in pulsars.

79 ASTRONOMY AND ASTROPHYSICS↗

Commissioning of Extended Electron Beam Ion Source at Brookhaven National Laboratory

Here, the Extended Electron Beam Ion Source (EEBIS) has been installed and commissioned at Brookhaven National Laboratory (BNL) hadron accelerator complex in the spring of 2023. EEBIS has replaced its predecessor, RhicEBIS, which provided ions for BNL hadron facilities for over a decade since 2009. The motivations for the source upgrade are to provide higher intensities of the Au 32+ ion beam for the Relativistic Heavy Ion Collider (RHIC) and to provide of an intense source of polarized 3 He 2+ ions for the future Electron Ion Collider (EIC) at BNL. EEBIS is and will continue to be the primary source for a variety of different ion species for the NASA Space Radiation Laboratory (NSRL) at BNL. EEBIS utilizes two identical, two-meter-long unshielded 5T warm bore superconducting solenoids, and it is operated with electron beam current up to 10 A, providing a high-capacity ion traps to fulfill the requirement for high intensity ion beams. The upstream solenoid contains a “short ion trap” with a length of 95 cm, while the “long ion trap” with a length of 178 cm is located inside the downstream solenoid bore. The main features of EEBIS are: * A Gas injection and ionization cell equipped with a Lorenz pulse valve * High-capacity ZAO non-evaporable getter (NEG) custom linear pumping units * In situ apparatus for pumping speed measurements to monitor NEG activation and saturation * “External drift tube” construction with differential pumping stages to provide space for Lorentz pulse valve and 3 He high-field polarization cell * A Ba oxide electron gun cathode. The design of EEBIS as well as the results of its commissioning and first-year operation are presented and discussed.

43 PARTICLE ACCELERATORS↗