arXiv subjects

J. P. van den Berg

Publications and source records attributed to J. P. van den Berg.

8 recordsLinked to original sources

arXiv2026

Are the Parker and Focused Transport Equations Equivalent for Galactic Cosmic Ray Modulation?

The Parker transport equation (TPE) has been the equation of choice for the past 60 years in studies of galactic cosmic ray (GCR) modulation. Conversely, the focused TPE describes the same processes on a more fundamental level than the Parker TPE by modelling an anisotropic distribution rather than an isotropic one. It is usually assumed that the Parker TPE is valid for modelling GCRs, but the two TPEs have not been tested against each other in this context. We conduct a first-of-its-kind comparison of these TPEs without particle drifts to test whether they produce the same results under identical diffusion conditions. A new model for protons during solar minimum conditions is developed to numerically solve the TPEs using stochastic differential equations. The TPEs are designed to be as consistent as possible for diffusion by normalising the pitch-angle-dependent diffusion coefficients (DCs) used in the focused TPE to the isotropic DCs used in the Parker TPE. The Parker TPE overestimates the GCR intensity at Earth's orbit for low energies by ~30%, and by ~40% over the poles. This stems from a small first-order anisotropy caused by particle fluxes over the poles. Particles gain easier access to the inner heliosphere by streaming in over the poles, where pitch-angle scattering is generally weaker, and the magnetic field is typically less wound. The focused TPE also yields nearly identical results for different pitch-angle dependencies of the DCs. The description of particle streaming and weak pitch-angle scattering as effective parallel diffusion in the Parker TPE makes it overly diffusive. This suggests that DCs derived from fitting the Parker TPE to observations are likely underestimated. Furthermore, GCR spectral and anisotropy data alone cannot distinguish between scattering theories with similar mean free paths but different pitch-angle dependencies.

physics.space-ph↗

arXiv2024

An Evaluation of Different Numerical Methods to Calculate the Pitch-angle Diffusion Coefficient from Full-orbit Simulations: disentangling a rope of sand

The pitch-angle diffusion coefficient quantifies the effect of pitch-angle scattering on charged particles propagating through turbulent magnetic fields and is a key ingredient in understanding the diffusion of these particles along the background magnetic field. Despite its significance, only a limited number of studies have calculated the pitch-angle diffusion coefficient from test particle simulations in synthetic magnetic turbulence, employing various, often quite different, techniques for this purpose. In this study, we undertake a comparative analysis of nine different methods for calculating the pitch-angle diffusion coefficient from full-orbit simulations. Our objective is to find the strengths and limitations of each method and to determine the most reliable approach. Although all nine methods should theoretically yield comparable results, certain methods may be ill-suited for numerical investigations, while others may not be applicable under conditions of strong turbulence. Through this investigation, we aim to provide recommendations for best practices when employing these methods in future numerical studies of pitch-angle scattering.

physics.space-ph↗

arXiv2024

A detailed survey of the parallel mean free path of solar energetic particle protons and electrons

In this work, more than a dozen solar energetic particle (SEP) events are identified where the source region is magnetically well-connected to at least one spacecraft at 1~au. The observed intensity-time profiles, for all available proton and electron energy channels, are compared to results computed using a numerical 1D SEP transport model in order to derive the parallel mean free paths (pMFPs) as a function of energy (or rigidity) at 1~au. These inversion results are then compared to theoretical estimates of the pMFP, using observed turbulence quantities with observationally-motivated variations as input. For protons, a very good comparison between inversion and theoretical results is obtained. It is shown that the observed inter-event variations in the inversion pMFP values can be explained by natural variations in the background turbulence values. For electrons, there is relatively good agreement with pMFPs derived assuming the damping model of dynamical turbulence, although the theoretical values are extremely sensitive to the details of the turbulence dissipation range which themselves display a high level of variation.

astro-ph.SR↗

arXiv2023

Jovian electrons in the inner heliosphere: Opportunities for Multi-spacecraft Observations and Modeling

In this paper we explore the idea of using multi-spacecraft observations of Jovian electrons to measure the 3D distribution of these particles in the inner heliosphere. We present simulations of Jovian electron intensities along selected spacecraft trajectories for 2021 and compare these, admittedly qualitatively, to these measurements. Using the data-model comparison we emphasize how such a study can be used to constrain the transport parameters in the inner heliosphere, and how this can lead to additional insight into energetic particle transport. Model results are also shown along the expected trajectories of selected spacecraft, including the off-ecliptic phase of the Solar Orbiter mission from 2025 onward. Lastly, we revisit the use of historical data and discuss upcoming missions that may contribute to Jovian electron measurements.

physics.space-ph↗

arXiv2023

On the onset delays of solar energetic electrons and protons: Evidence for a common accelerator

The processes responsible for the acceleration of solar energetic particles (SEPs) are still not well understood, including whether SEP electrons and protons are accelerated by common or separate processes. Using a numerical particle transport model that includes both pitch-angle and perpendicular spatial diffusion, we simulate, amongst other quantities, the onset delay for MeV electrons and protons and compare the results to observations of SEPs from widely-separated spacecraft. Such observations have previously been interpreted, in a simple scenario assuming no perpendicular diffusion, as evidence for different electron and proton sources. We show that, by assuming a common particle source together with perpendicular diffusion, we are able to simultaneously reproduce the onset delays for both electrons and protons. We argue that this points towards a common accelerator for these particles. Moreover, a relatively broad particle source is required in the model to correctly describe the observations. This is suggestive of diffusive shock acceleration occurring at large shock structures playing a significant role in the acceleration of these SEPs.

astro-ph.SR↗

arXiv2022

Cosmic ray transport near the Sun

The strongly diverging magnetic field lines in the very inner heliosphere, through the associated magnetic focusing/mirroring forces, can, potentially, lead to highly anisotropic galactic cosmic ray distributions close to the Sun. Using a simplified analytical approach, validated by numerical simulations, we study the behaviour of the galactic cosmic ray distribution in this newly explored region of the heliosphere and find that significant anisotropies can be expected inside 0.2 au.

physics.space-ph↗

arXiv2021

On the Turbulent Reduction of Drifts for Solar Energetic Particles

Particle drifts perpendicular to the background magnetic field have been proposed by some authors as an explanation for the very efficient perpendicular transport of solar energetic particles (SEPs). This process, however, competes with perpendicular diffusion caused by magnetic turbulence, which can also disrupt the drift patterns and reduce the efficiency of drift effects. The latter phenomenon is well known in cosmic ray studies, but not yet considered in SEP models. Additionally, SEP models which do not include drifts, especially for electrons, use turbulent drift reduction as a justification of this omission, without critically evaluating or testing this assumption. This article presents the first theoretical step for a theory of drift suppression in SEP transport. This is done by deriving the turbulence-dependent drift reduction function with a pitch-angle dependence, as applicable for anisotropic particle distributions, and by investigating to what extent drifts will be reduced in the inner heliosphere for realistic turbulence conditions and different pitch-angle dependencies of the perpendicular diffusion coefficient. The influence of the derived turbulent drift reduction factors on the transport of SEPs are tested, using a state-of-the-art SEP transport code, for several expressions of theoretically-derived perpendicular diffusion coefficients. It is found, for realistic turbulence conditions in the inner heliosphere, that cross-field diffusion will have the largest influence on the perpendicular transport of SEPs, as opposed to particle drifts.

physics.space-ph↗

arXiv2020

A Primer on Focused Solar Energetic Particle Transport: Basic physics and recent modelling results

The basics of focused transport as applied to solar energetic particles are reviewed, paying special attention to areas of common misconception. The micro-physics of charged particles interacting with slab turbulence are investigated to illustrate the concept of pitch-angle scattering, where after the distribution function and focused transport equation are introduced as theoretical tools to describe the transport processes and it is discussed how observable quantities can be calculated from the distribution function. In particular, two approximations, the diffusion-advection and the telegraph equation, are compared in simplified situations to the full solution of the focused transport equation describing particle motion along a magnetic field line. It is shown that these approximations are insufficient to capture the complexity of the physical processes involved. To overcome such limitations, a finite-difference model, which is open for use by the public, is introduced to solve the focused transport equation. The use of the model is briefly discussed and it is shown how the model can be applied to reproduce an observed solar energetic electron event, providing insights into the acceleration and transport processes involved. Past work and literature on the application of these concepts are also reviewed, starting with the most basic models and building up to more complex models.

physics.space-ph↗