Artem Bohdan

Collisionless shocks are common in astrophysical systems and stand as sites of particle acceleration. While particles at perpendicular shocks may not return to the upstream region, at oblique shocks a fraction of energetic electrons manage to escape the shock and travel upstream. An extended region known as the electron foreshock is formed, where these reflected particles drive various instabilities that may promote electron acceleration. Here we present the first 2D3V particle-in-cell (PIC) simulations of electron–ion nonrelativistic oblique shocks that explore the interaction of the foreshock with preexisting compressive turbulence with a relative amplitude of 15% based on estimates of the interstellar medium. We find that preexisting turbulence influences the emergence and behavior of the whistler-wave instability, as it enhances the amplitudes of the magnetic field fluctuations and leads to larger nonlinear structures. This impacts the dynamics of the reflected electrons, resulting in a shorter and hotter electron foreshock. At the end of our simulations, with preexisting upstream turbulence we observe nonthermal electrons that are more numerous, reach higher energies, and carry a larger portion of the total energy.

Collisionless low Mach number shocks are abundant in astrophysical and space plasma environments, exhibiting complex wave activity and wave-particle interactions. In this paper, we present 2D Particle-in-Cell (PIC) simulations of quasi-perpendicular nonrelativistic low Mach number shocks, with a specific focus on studying electrostatic waves in the shock ramp and the precursor regions. In these shocks, an ion-scale oblique whistler wave creates a configuration with two hot counter-streaming electron beams, which drive unstable electron acoustic waves (EAWs) that can turn into electrostatic solitary waves (ESWs) at the late stage of their evolution. By conducting simulations with periodic boundaries, we show that EAW properties agree with linear dispersion analysis. The characteristics of ESWs in shock simulations, including their wavelength and amplitude, depend on the shock velocity. When extrapolated to shocks with realistic velocities, the ESW wavelength is reduced to one tenth of the electron skin depth and the ESW amplitude is anticipated to surpass that of the quasi-static electric field by more than a factor of 100. These theoretical predictions may explain a discrepancy, between PIC and satellite measurements, in the relative amplitude of high- and low-frequency electric field fluctuations.

Collisionless shocks play a key role in space and astrophysical plasmas, enabling the conversion of large-scale kinetic energy into heat and non-thermal particle populations without relying on binary Coulomb collisions. Instead, these shocks are sustained by collective effects such as wave-particle interactions that are inherently kinetic and often nonlinear. Despite significant observational and theoretical efforts, the precise mechanisms and spatial localization of energy dissipation in collisionless shocks remain debated. While it is widely accepted that dissipation occurs within the shock ramp, simulations and observations have shown that energy conversion may also extend upstream and downstream, involving shock structures such as the foot and overshoot. Observational studies using Magnetospheric Multiscale (MMS) have further highlighted that ion heating are often concentrated in the ramp and foot, while electron heating may remain nearly constant or increase only under specific conditions such as enhanced wave activity in the transition region.We analyze high-resolution measurements from the MMS mission across multiple quasi-perpendicular bow shock crossings. We quantify energy contribution of different particle species within a vicinity of the shock ramp to analyze energy transfer among electrons, ions and electromagnetic fields within collisionless shocks. By correcting the measured ion and electron distribution functions for instrumental effects, we isolate the energy contributions of each species and examine how they vary throughout the shock structure. We calculate the theoretically expected values for thermal energy from mass conservation principles and Rankine-Hugoniot conditions to analyze the observed deviation from adiabatic behavior in collisionless shocks. Finally, we discuss how energy transfer between species depends on various shock parameters.

Context. Jetted active galactic nuclei aligned with our line of sight known as blazars are promising high-energy neutrino source candidates. However, leptohadronic models face challenges in describing neutrino emission within a viable energy budget and their predictive power are limited by the commonly used single-zone approximation and reliance on phenomenological parameters. Aims. We tested the scenario where energetic protons are continuously accelerated up to ultra-high energies in inner blazar jets, while accounting for the source energetics and jet dynamics. Methods. We present a new leptohadronic model, where a sub-Eddington jet evolves from being magnetically to kinetically dominated. A constant fraction of 10 ⁻⁶ –10 ⁻⁸ of the electrons and protons picked up by the jet are continuously accelerated to a power-law spectrum. We can estimate their normalization and maximum energies based on the local magnetic field strength, turbulence, and medium density, for which we assumed power-law profiles. The model parameters are thus directly tied to the jet physics and are comparable in number to a single-zone model. We then calculate the emission along the jet, including neutrinos and electromagnetic cascades. Results. Applying the model to IceCube candidate TXS 0506+056, we find that protons accelerated in the inner jet produce a neutrino flux up to ∼100 PeV that is consistent with the public IceCube ten-year point-source data. Proton emission at 0.1 pc describes the X-ray and γ -ray data, while electron emission at the parsec scale describes the optical data. Protons carry a power of about 1% of the Eddington luminosity. The particle spectra follow E ^−1.8 , with diffusion scaling as E ^0.3 , ruling out Bohm-like diffusion. Additional particle injection near the broad line region can reproduce the 2017 flare associated to a high-energy neutrino. We also applied the model to the blazar PKS 0605-085, which could be associated with a recent neutrino detected by KM3NeT above 100 PeV. Conclusions. Magnetic acceleration in blazar jets can describe multimessenger observations with viable energetics. Our model constrains jet properties such as the energy-dependent particle diffusion and predicts the spatial distribution of the multiwavelength and neutrino emission along the jet. The results suggest that blazars are efficient neutrino emitters at ultra-high energies, making them prime candidates for future experiments targeting this challenging energy range.

Aims. Plasma shock waves stand out as one of the most promising sites of efficient particle acceleration in extragalactic jets. In electron-ion plasma shocks, electrons can be heated up to large Lorentz factors, making them an attractive scenario to explain the high minimum electron Lorentz factors regularly needed to describe the emission of BL Lac type objects. Still, the (relativistic) thermal electron component is commonly neglected when modelling the observations, although it holds key information on the shock properties. Methods. Considering a shock acceleration scenario, we modelled the broadband emission of the archetypal high synchrotron peaked blazar Markarian 421; we employed particle distributions that included a thermal (relativistic) Maxwellian component at low energies followed by a non-thermal power law, as motivated by particle-in-cell simulations. The observations, in particular in the optical/UV and MeV-GeV bands, efficiently restricted the non-thermal emission from the Maxwellian electrons, which we used to derive constraints on the basic properties, such as the fraction ϵ _e of the total shock energy stored in the non-thermal electrons. Results. The best-fit model yields a non-thermal electron power law with an index of ∼2.4, close to predictions from shock acceleration. Successful fits are obtained when the ratio between the Lorentz factor at which the non-thermal distribution begins ( γ _nth ) and the dimensionless electron temperature ( θ ) satisfies γ _nth / θ ≲ 8. Since γ _nth / θ controls ϵ _e , the latter limit implies that at least ϵ _e ≈ 10% of the shock energy is transferred to the non-thermal electrons. These results are almost insensitive to the shock velocity γ _sh , but radio observations indicate γ _sh ≳ 5 since for lower shock velocities the fluxes in the millimetre band are overproduced by the Maxwellian electrons. Therefore, if shocks drive the particle energisation, our findings indicate that they operate in the mildly to fully relativistic regime with efficient electron acceleration. This paper lays the ground for future works, in which we will use plasma simulations to investigate if, and under which conditions, the findings presented here can be reproduced.

Planetary bow shocks provide an excellent laboratory for studying shock physics. Over the past six decades, they have been extensively investigated in situ by various satellite missions aiming to study particle behavior and fields at both macro and micro scales. Despite significant progress, in situ measurements are limited to the spacecraft’s trajectory, providing only a partial description of the shock’s 3D structure. To address this problem, we can combine these measurements with kinetic plasma simulations, which can significantly enhance our understanding of shock physics. Fully kinetic methods, such as Particle-in-Cell (PIC) simulations, have the capability to describe the evolution of shocks at ion scales while also resolving the dynamics of electrons. However, to cover the necessary spatial and temporal scales, PIC simulations often require the use of unrealistic numerical parameters, such as artificially high shock velocities and reduced ion-to-electron mass ratios. These approximations introduce additional challenges because various aspects of shock microphysics—such as parameters of driven instabilities, heating mechanisms, and particle acceleration—exhibit distinct dependencies on these numerical parameters. This discrepancy complicates direct comparisons between PIC simulations and in situ measurements. To mitigate these issues, rescaling procedures tailored to specific phenomena are necessary. Here, we address the problems of magnetic field amplification, electron heating, and electrostatic waves, each requiring its own distinct set of rescaling procedures.

Cosmic-ray acceleration processes in astrophysical plasmas are often investigated with fully kinetic or hybrid kinetic numerical simulations, which enable us to describe a detailed microphysics of particle energization mechanisms. Tracing of individual particles in such simulations is especially useful in this regard. However, visually inspecting particle trajectories introduces a significant amount of bias and uncertainty, making it challenging to pinpoint specific acceleration mechanisms. Here, we present a novel approach utilizing neural networks to assist in the analysis of individual particle data. We demonstrate the effectiveness of this approach using the dataset from our recent particle-in-cell (PIC) simulations of non-relativistic perpendicular shocks, which consists of 252 000 electrons, each characterized by their position, momentum, and electromagnetic field at particle’s position, recorded in a time series of 1200 time steps. These electrons cross a region affected by the electrostatic Buneman instability, and a small percentage of them attain high energies. We perform classification, regression, and anomaly detection algorithms on the dataset by using a convolutional neural network, a multi-layer perceptron, and an autoencoder. Despite the noisy and imbalanced dataset, all methods demonstrate the capability to differentiate between thermal and accelerated electrons with remarkable accuracy. The proposed methodology may considerably simplify particle classification in large-scale PIC and hybrid simulations.

Collisionless low-Mach-number shocks are abundant in astrophysical and space plasma environments, exhibiting complex wave activity and wave–particle interactions. In this paper, we present 2D Particle-in-Cell (PIC) simulations of quasi-perpendicular nonrelativistic (v _sh ≈ (5500–22000) km s⁻¹) low-Mach-number shocks, with a specific focus on studying electrostatic waves in the shock ramp and precursor regions. In these shocks, an ion-scale oblique whistler wave creates a configuration with two hot counterstreaming electron beams, which drive unstable electron acoustic waves (EAWs) that can turn into electrostatic solitary waves (ESWs) at the late stage of their evolution. By conducting simulations with periodic boundaries, we show that the EAW properties agree with linear dispersion analysis. The characteristics of ESWs in shock simulations, including their wavelength and amplitude, depend on the shock velocity. When extrapolated to shocks with realistic velocities (v _sh ≈ 300 km s⁻¹), the ESW wavelength is reduced to one-tenth of the electron skin depth and the ESW amplitude is anticipated to surpass that of the quasi-static electric field by more than a factor of 100. These theoretical predictions may explain a discrepancy, between PIC and satellite measurements, in the relative amplitude of high- and low-frequency electric field fluctuations.

Strong nonrelativistic shocks are known to accelerate particles up to relativistic energies. However, for diffusive shock acceleration, electrons must have a highly suprathermal energy, implying the need for very efficient preacceleration. Most published studies consider shocks propagating through homogeneous plasma, which is an unrealistic assumption for astrophysical environments. Using 2D3V particle-in-cell simulations, we investigate electron acceleration and heating processes at nonrelativistic high-Mach-number shocks in electron-ion plasma with a turbulent upstream medium. For this purpose, slabs of plasma with compressive turbulence are simulated separately and then inserted into shock simulations, which require matching of the plasma slabs at the interface. Using a novel procedure of matching electromagnetic fields and currents, we perform simulations of perpendicular shocks setting different intensities of density fluctuations (≲10%) in the upstream region. The new simulation technique provides a framework for studying shocks propagating in turbulent media. We explore the impact of the fluctuations on electron heating, the dynamics of upstream electrons, and the driving of plasma instabilities. Our results indicate that while the presence of turbulence enhances variations in the upstream magnetic field, their levels remain too low to significantly influence the behavior of electrons at perpendicular shocks.