Propagation Of Energetic Particles Research Articles

Transport of energetic particles in turbulent space plasmas: pitch-angle scattering, telegraph, and diffusion equations

Introduction: In this article, we revisit the pitch-angle scattering equation describing the propagation of energetic particles through magnetized plasma. In this case, solar energetic particles and cosmic rays interact with magnetohydrodynamic turbulence and experience stochastic changes in the pitch-angle. Since this happens over an extended period of time, a pitch-angle isotropization process occurs, leading to parallel spatial diffusion. This process is described well by the pitch-angle scattering equation. However, the latter equation is difficult to solve analytically even when considering special cases for the scattering coefficient.Methods: In the past, a so-called subspace approximation was proposed, which has important applications in the theory of perpendicular diffusion. Alternatively, an approach based on the telegraph equation (also known as telegrapher’s equation) has been developed. We show that two-dimensional subspace approximation and the description based on the telegraph equation are equivalent. However, it is also shown that the obtained distribution functions contain artifacts and inaccuracies that cannot be found in the numerical solution to the problem. Therefore, an N-dimensional subspace approximation is proposed corresponding to a semi-analytical/semi-numerical approach. This is a useful alternative compared to standard numerical solvers.Results and Discussion: Depending on the application, the N-dimensional subspace approximation can be orders of magnitude faster. Furthermore, the method can easily be modified so that it can be used for any pitch-angle scattering equation.

Solar Energetic Particle and the Heliospheric Current Sheet

The effect of the heliospheric current sheet (HCS) on the propagation of solar energetic particles (SEPs) remains poorly known. In this study we address this question by surveying energetic (∼2.0–9.6 MeV nucleon–1) helium data acquired by the energetic particle acceleration, composition, and transport (EPACT) sensor on board the Wind spacecraft. A superposed epoch analysis of 319 HCS crossings made by Wind reveals a sharp drop in the SEP fluxes at the HCS for the low-energy channels and little change across the HCS for the high-energy channels. To help understand the statistical result, we studied a total of 15 SEP flux dropout (a decrease of ∼50% or more) events that coincided with the crossing of the HCS. One of the common features of these SEP events is that they were initiated in the western hemisphere but far away from the longitude of HCS crossings, suggesting that the source of SEPs was well connected initially but was cut off later after Wind moved to the opposite hemisphere (e.g., HCS crossing). Further analysis of the events suggests that the percentage of flux dropouts decreases with increasing energy. It is suggested that a strong scattering of MeV helium may have occurred as the particle gyroradius is comparable to the thickness of the current sheet. This study clearly provides solid evidence for the HCS as a barrier to suppressing SEP flux of MeV energies from the onset hemisphere to the other.

Continuous solutions of cosmic-rays and waves in astrophysical environments

The propagation of energetic charged particles and cosmic rays in magnetized thermal plasma is focused. We consider a four-fluid system that consists of thermal plasma, cosmic rays, and two opposite propagating Alfvén waves to investigate the dynamics and energy exchange mechanisms of the system. Additionally, cosmic rays diffusion within the plasma is considered along the magnetic field lines whereas neglected the cross field line diffusion effects. This study is important for understanding of pressure gradients and their impact on the feedback in astrophysical environment. Over the last few decades, this problem becomes important when we discuss the interaction of cosmic rays with plasma in space, such as interstellar clouds or interstellar medium.

Energetic particle dynamics in a simplified model of a solar wind magnetic switchback

Context.Recent spacecraft observations in the inner heliosphere have revealed the presence of local Alfvénic reversals of the magnetic field, while the field magnitude remains almost constant. These are called magnetic switchbacks (SBs) and are very common in the plasma environment close to the Sun explored by the Parker Solar Probe satellite.Aims.A simple numerical model of a magnetic field reversal with constant magnitude is used in order to explore the influence of SBs on the propagation of energetic particles within a range of energy typical of solar energetic particles.Methods.We model the reversal as a region of space of adjustable size bounded by two rotational discontinuities. By means of test particle simulations, beams of mono-energetic particles can be injected upstream of the SB with various initial pitch- and gyro-phase angles. In each simulation, the particle energy may also be changed.Results.Particle dynamics is highly affected by the ratio between the particle gyroradius and the size of the SB, with multiple pitch-angle scatterings occurring when the particle gyroradius is of the order of the SB size. Further, particle motion is extremely sensitive to the initial conditions, implying a transition to chaos; for some parameters of the system, a large share of particles is reflected backwards upstream as they interact with the SB. These results could have a profound impact on our understanding of solar energetic particle transport in the inner heliosphere, and therefore possible comparisons with in situ spacecraft data are discussed.

Energetic Particle Propagation in Three Dimensions

Energetic Particle Propagation in Three Dimensions

High resolution finite volume method for kinetic equations with Poisson brackets

Simulation of plasmas in electromagnetic fields requires numerical solution of a kinetic equation that describes the time evolution of the particle distribution function. In this paper we propose a finite volume scheme based on integral relation for Poisson brackets to solve the Liouville equation, the most fundamental kinetic equation. The proposed scheme conserves the number of particles, maintains the total-variation-diminishing (TVD) property, and provides high-quality numerical results. Other types of kinetic equations may be also formulated in terms of Poisson brackets and solved with the proposed method including the transport equations describing the acceleration and propagation of Solar Energetic Particles (SEPs), which is of practical importance, since the high energy SEPs produce radiation hazards. The proposed scheme is demonstrated to be accurate and efficient, which makes it applicable to global simulation systems analyzing space weather.

Influence of Large-scale Interplanetary Structures on the Propagation of Solar Energetic Particles: The Multispacecraft Event on 2021 October 9

An intense solar energetic particle (SEP) event was observed on 2021 October 9 by multiple spacecraft distributed near the ecliptic plane at heliocentric radial distances R ≲ 1 au and within a narrow range of heliolongitudes. A stream interaction region (SIR), sequentially observed by Parker Solar Probe (PSP) at R = 0.76 au and 48° east from Earth (ϕ = E48°), STEREO-A (at R = 0.96 au, ϕ = E39°), Solar Orbiter (SolO; at R = 0.68 au, ϕ = E15°), BepiColombo (at R = 0.33 au, ϕ = W02°), and near-Earth spacecraft, regulated the observed intensity-time profiles and the anisotropic character of the SEP event. PSP, STEREO-A, and SolO detected strong anisotropies at the onset of the SEP event, which resulted from the fact that PSP and STEREO-A were in the declining-speed region of the solar wind stream responsible for the SIR and from the passage of a steady magnetic field structure by SolO during the onset of the event. By contrast, the intensity-time profiles observed near Earth displayed a delayed onset at proton energies ≳13 MeV and an accumulation of ≲5 MeV protons between the SIR and the shock driven by the parent coronal mass ejection (CME). Even though BepiColombo, STEREO-A, and SolO were nominally connected to the same region of the Sun, the intensity-time profiles at BepiColombo resemble those observed near Earth, with the bulk of low-energy ions also confined between the SIR and the CME-driven shock. This event exemplifies the impact that intervening large-scale interplanetary structures, such as corotating SIRs, have in shaping the properties of SEP events.

Multipoint Interplanetary Coronal Mass Ejections Observed with Solar Orbiter, BepiColombo, Parker Solar Probe, Wind, and STEREO-A

Abstract We report the result of the first search for multipoint in situ and imaging observations of interplanetary coronal mass ejections (ICMEs) starting with the first Solar Orbiter (SolO) data in 2020 April–2021 April. A data exploration analysis is performed including visualizations of the magnetic-field and plasma observations made by the five spacecraft SolO, BepiColombo, Parker Solar Probe (PSP), Wind, and STEREO-A, in connection with coronagraph and heliospheric imaging observations from STEREO-A/SECCHI and SOHO/LASCO. We identify ICME events that could be unambiguously followed with the STEREO-A heliospheric imagers during their interplanetary propagation to their impact at the aforementioned spacecraft and look for events where the same ICME is seen in situ by widely separated spacecraft. We highlight two events: (1) a small streamer blowout CME on 2020 June 23 observed with a triple lineup by PSP, BepiColombo and Wind, guided by imaging with STEREO-A, and (2) the first fast CME of solar cycle 25 (≈1600 km s−1) on 2020 November 29 observed in situ by PSP and STEREO-A. These results are useful for modeling the magnetic structure of ICMEs and the interplanetary evolution and global shape of their flux ropes and shocks, and for studying the propagation of solar energetic particles. The combined data from these missions are already turning out to be a treasure trove for space-weather research and are expected to become even more valuable with an increasing number of ICME events expected during the rise and maximum of solar cycle 25.

The study of the strongest solar event on a minimum of the 24th solar cycle

The strongest solar flares of the 24th solar cycle erupted on September 6, 2017, and it was the 8th strongest solar flare recorded since 1996. This extreme solar flare occurred at the minimum of the 24th solar cycle. The active region is located in the Western Hemisphere and produced the violent explosion of class X9.3 and X2.2 on September 6, X1.3 on September 7, and X8.2 on September 10, 2017. The injection duration of the solar energetic particles of the solar event was 17 minutes. All data for this solar event was collected from the Advanced Composition Explorer and simulated for particles’ motion using the transport equation and solved by the numerical technique. We obtained the injection time of the solar energetic particle propagation by comparing fitting between the simulation results and the spacecraft data. Injection time taken by high-energy particles to travel from the Sun to the Earth was found to be in the range of 39 to 743 minutes. At the peak of this solar flare, the coronal mass ejection was detected, which increased the injection time. The Kp-index of this solar flare was 4; thus, there was no effect on the Earth. The Kp-index value increased to 8 on September 7-8, 2017, due to another solar event from the same sunspot region, indicating the effect of solar flare and CME, which resulted in the appearance of aurora.

Modelling magnetised medium particle transport in the guiding centre limit with GEANT4

Monte Carlo codes are a standard tool for studying energetic particle propagation, secondary production, and radiation in astrophysical settings. In magnetised plasmas such as those found in solar active regions, the enormous disparity between particle gyroradii and system scales proves to be a major computational obstacle. To address this problem we have written a new module in Geant4 using the guiding centre (GC) approach in which the particle motion is averaged over a gyrofrequency. We describe the formulation and implementation of this method in particular dealing with the uncertainty in gyrophase so that particle velocities are well-defined for input to the modules handling reactions. As far as feasible, we compare the propagation and slowing down of primary protons, secondary particle production, and run times in the GC limit with the Newton–Lorentz approach, finding very good agreement between the two methods and orders of magnitude improvement in run times in the GC case. Finally, we present an illustrative solar physics application involving two interacting dipoles, which is only achievable using the GC approach.

Charged-particle chaotic dynamics in rotational discontinuities.

The interplanetary plasma is characterized by a high level of complexity over a broad range of spatial scales. Spacecraft have detected a large variety of embedded structures that have been identified as discontinuities in the magnetic field vector. They can be either generated within the solar corona and advected by the plasma flow or locally generated as a result of the turbulent cascade of the solar wind turbulence. Since magnetic field fluctuations and structures influence the energetic particle propagation, here we set up a numerical model to study the interaction between charged particles and an ideal magnetohydrodynamics rotational discontinuity. This interaction is strongly influenced by the model parameters, such as the rotation angle of the discontinuity, the orientation of the mean-field direction with respect to the normal to the discontinuity direction, the initial particle pitch angle, and the initial particle gyrophase. Numerical results clearly show that the motion of particles crossing the discontinuity is extremely complex and highly sensitive to the initial conditions of the system, with transitions to a chaotic behavior. We find that particles can be temporarily trapped in rotational discontinuity and that the trapping times have a nearly power-law distribution. Also, the separatrix in the initial conditions phase space between crossing and noncrossing trajectories has a fractal structure. Implications for energetic particle propagation in space plasmas are discussed.

2D monochromatic x-ray imaging for beam monitoring of an x-ray free electron laser and a high-power femtosecond laser.

In pump-probe experiments with an X-ray Free Electron Laser (XFEL) and a high-power optical laser, spatial overlap of the two beams must be ensured to probe a pumped area with the x-ray beam. A beam monitoring diagnostic is particularly important in short-pulse laser experiments where a tightly focused beam is required to achieve a relativistic laser intensity for generation of energetic particles. Here, we report the demonstration of on-shot beam pointing measurements of an XFEL and a terawatt class femtosecond laser using 2D monochromatic Kα imaging at the Matter in Extreme Conditions end-station of the Linac Coherent Light Source. A thin solid titanium foil was irradiated by a 25-TW laser for fast electron isochoric heating, while a 7.0 keV XFEL beam was used to probe the laser-heated region. Using a spherical crystal imager (SCI), the beam overlap was examined by measuring 4.51 keV Kα x rays produced by laser-accelerated fast electrons and the x-ray beam. Measurements were made for XFEL-only at various focus lens positions, laser-only, and two-beam shots. Successful beam overlapping was observed on ∼58% of all two-beam shots for 10 μm thick samples. It is found that large spatial offsets of laser-induced Kα spots are attributed to imprecise target positioning rather than shot-to-shot laser pointing variations. By applying the Kα measurements to x-ray Thomson scattering measurements, we found an optimum x-ray beam spot size that maximizes scattering signals. Monochromatic x-ray imaging with the SCI could be used as an on-shot beam pointing monitor for XFEL-laser or multiple short-pulse laser experiments.

On fractional approximations of the Fokker–Planck equation for energetic particle transport

To determine the main effects of anomalous diffusion upon the propagation of energetic particles, the fractional modified telegraph equation is solved using the Laplace–Fourier technique and given in terms of the Fox H and M-Wright functions. Examples are used to illustrate the qualitative differences between the fractional telegraph, fractional advection–diffusion and fractional diffusion equations. The profiles of the particles densities are discussed in each case for different values of fractional orders.

Magnetic pumping model for energizing superthermal particles applied to observations of the Earth's bow shock

Energetic particle generation is an important component of a variety of astrophysical systems, from seed particle generation in shocks to the heating of the solar wind. It has been shown that magnetic pumping is an efficient mechanism for heating thermal particles, using the largest-scale magnetic fluctuations. Here we show that when magnetic pumping is extended to a spatially-varying magnetic flux tube, magnetic trapping of superthermal particles renders pumping an effective energization method for particles moving faster than the speed of the waves and naturally generates power-law distributions. We validated the theory by spacecraft observations of the strong, compressional magnetic fluctuations near the Earth’s bow shock from the Magnetospheric Multiscale mission. Given the ubiquity of magnetic fluctuations in different astrophysical systems, this mechanism has the potential to be transformative to our understanding of how the most energetic particles in the universe are generated.

Excitation and dissociation of CO2 heavily diluted in noble gas atmospheric pressure plasma

The excitation and dissociation of CO2 admixed to argon and helium atmospheric pressure radio frequency plasmas is analyzed. The absorbed plasma power is determined by voltage and current probe measurements and the excitation and dissociation of CO2 and CO by transmission mode Fourier-transform infrared spectroscopy (FTIR). It is shown, that the vibrational temperatures of CO2 and CO are significantly higher in an argon compared to a helium plasma. The rotational temperatures remain in both cases close to room temperature. The conversion efficiency, expressed as a critical plasma power to reach almost complete depletion, is four times higher in the argon case. This is explained by the lower threshold for the generation of energetic particles (electrons or metastables) in argon as the main reactive collision partner, promoting excitation and dissociation of CO2, by the less efficient quenching of vibrational excited states of CO and CO2 by argon compared to helium and by a possible contribution of more energetic electrons in an argon plasma compared to helium.

Propagation of Solar Energetic Particles in the Outer Heliosphere: Interplay between Scattering and Adiabatic Focusing

Abstract The turbulence and spatial nonuniformity of the guide magnetic field cause two competitive effects, namely, the scattering effect and the adiabatic focusing effect, respectively. In this work, we numerically solve the five-dimensional Fokker–Planck transport equation to investigate the radial evolutions of these important effects undergone by the solar energetic particles (SEPs) propagating through interplanetary space. We analyze the interplay process between the scattering and adiabatic focusing effects in the context of three-dimensional propagation, with special attention to the scenario of the outer heliosphere, in which some peculiar SEP phenomena are found and explained. We also discuss the radial dependence of the SEP peak intensities from the inner through the outer heliosphere, and conclude that it cannot be simply described by a single functional form such as R −α (R is radial distance), which is often used.

Mapping Magnetic Field Lines for an Accelerating Solar Wind

Mapping of magnetic field lines is important for studies of the solar wind and the sources and propagation of energetic particles between the Sun and observers. A recently developed mapping approach is generalised to use a more advanced solar wind model that includes the effects of solar wind acceleration, non-radial intrinsic magnetic fields and flows at the source surface/inner boundary, and conservation of angular momentum. The field lines are mapped by stepping along local magnetic field $\bm{B}$ and via a Runge-Kutta algorithm, leading to essentially identical maps. The new model's maps for Carrington rotation CR 1895 near solar minimum (19 April to 15 May 1995) and a solar rotation between CR 2145 and CR 2146 near solar maximum (14 January to 9 February 2014) are compared with the published maps for a constant solar wind model. The two maps are very similar on a large scale near both solar minimum and solar maximum, meaning that the field line orientations, winding angles, and connectivity generally agree very well. However, close inspection shows that the field lines have notable small-scale structural differences. An interpretation is that inclusion of the acceleration and intrinsic azimuthal velocity has significant effects on the local structure of the magnetic field lines. Interestingly, the field lines are more azimuthal for the accelerating solar wind model for both intervals. In addition, predictions for the pitch angle distributions (PADs) for suprathermal electrons agree at the $90$ -- $95\%$ level with observations for both solar wind models for both intervals.

Time intermittency in nondiffusive transport regimes of suprathermal ions in turbulent plasmas

Intermittent phenomena have long been studied in the context of nondiffusive transport across a variety of fields. In the TORPEX device, the cross-field spreading of an injected suprathermal ion beam by electrostatic plasma turbulence can access different nondiffusive transport regimes. A comprehensive set of suprathermal ion time series has been acquired, and time intermittency quantified by their skewness. Values distinctly above background level are found across all observed transport regimes. Intermittency tends to increase toward quasi- and superdiffusion and for longer propagation times of the suprathermal ions. The specific prevalence of intermittency is determined by the meandering motion of the instantaneous ion beam. We demonstrate the effectiveness of an analytical model developed to predict local intermittency from the time-average beam. This model might thus be of direct interest for similar systems, e.g., in beam physics, or meandering flux-rope models for solar energetic particle propagation. More generally, it illustrates the importance of identifying the system-specific sources of time-intermittent behavior when analyzing nondiffusive transport.

Stochastic Propagation of Solar Energetic Particles in Coronal and Interplanetary Magnetic Fields

This paper describes a method of simulating solar energetic particle propagation through the magnetic fields of the solar corona and interplanetary medium. The simulation code is based on the focus transport equation of energetic particles in 3-d magnetic fields, which contains all the particle transport mechanisms, including streaming, convection, gradient/curvature drift, adiabatic focusing, pitch angle scattering by Alfvénic magnetic field fluctuations and perpendicular diffusion due to the random walk of field lines. In the simulation, particles are injected at their source in the corona, and their guiding center trajectories are calculated using stochastic differential equations. Because of the vastly different time scales of particle transport mechanisms included in the equation, we use the 4-th order Runge-Kutta method to integrate the particle streaming and adiabatic focusing terms, while the stochastic terms of pitch angle scattering and perpendicular diffusion are integrated with the Euler scheme. The model is applied to the 2017 September 10 solar energetic particle event. With perpendicular diffusion, we are able to explain SEP observations from Earth and STEREO-A. A pattern of SEP precipitation on the solar surface is also predicted.

Stellar Energetic Particles in the Magnetically Turbulent Habitable Zones of TRAPPIST-1-like Planetary Systems

Abstract Planets in close proximity to their parent star, such as those in the habitable zones around M dwarfs, could be subject to particularly high doses of particle radiation. We have carried out test-particle simulations of ∼GeV protons to investigate the propagation of energetic particles accelerated by flares or traveling shock waves within the stellar wind and magnetic field of a TRAPPIST-1-like system. Turbulence was simulated with small-scale magnetostatic perturbations with an isotropic power spectrum. We find that only a few percent of particles injected within half a stellar radius from the stellar surface escape, and that the escaping fraction increases strongly with increasing injection radius. Escaping particles are increasingly deflected and focused by the ambient spiraling magnetic field as the superimposed turbulence amplitude is increased. In our TRAPPIST-1-like simulations, regardless of the angular region of injection, particles are strongly focused onto two caps within the fast wind regions and centered on the equatorial planetary orbital plane. Based on a scaling relation between far-UV emission and energetic protons for solar flares applied to M dwarfs, the innermost putative habitable planet, TRAPPIST-1e, is bombarded by a proton flux up to 6 orders of magnitude larger than experienced by the present-day Earth. We note two mechanisms that could strongly limit EP fluxes from active stars: EPs from flares are contained by the stellar magnetic field; and potential CMEs that might generate EPs at larger distances also fail to escape.