Nicholas Eugene Engelbrecht

The terrestrial production of cosmogenic radionuclides such as 10Be, 14C and 36Cl is triggered by spallation reactions of high-energy particles with atmospheric constituents such as oxygen, nitrogen and argon. After being produced and transported within the atmosphere, these radionuclides are deposited in natural archives, storing, for example, solar information over thousands of years. Therefore, records of 10Be, 14C and 36Cl can be used to reconstruct solar activity back in time. However, to understand the underlying physical processes that dominate production and interpret the observations, numerical modelling is crucial. Here, we shall discuss the dependencies of the numerically derived production rates on a variety of factors that include the effects of the choice of the local interstellar spectrum (LIS), the geomagnetic field and the production cross-sections available in the literature. We show that the investigated factors have modest to significant impacts on the modelled production rates of cosmogenic radionuclides and identify the discrepancies in the available cross-sections as the most crucial factor. This article is part of the Theo Murphy meeting issue ‘Radiocarbon and cosmic radiation events’.

Context. The Parker transport equation (TPE) has been the preferred equation for the past 60 years in studies of galactic cosmic ray (GCR) modulation. The focused TPE, however, describes the same processes on a more fundamental level than the Parker TPE by modelling an anisotropic rather than an isotropic distribution. 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. Aims. We conducted a first-of-its-kind comparison of these TPEs without particle drifts to test whether they produce the same results under identical diffusion conditions. Methods. We developed a new model to numerically solve the TPEs for protons under solar-minimum conditions, using stochastic differential equations. The model ensures that the TPEs are 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. Results. The Parker TPE overestimates the GCR intensity at Earth’s orbit by ∼30% at low energies 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. Conclusions. 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 fitting the Parker TPE to observations likely underestimates DCs. Furthermore, GCR spectral and anisotropy data alone cannot distinguish between scattering theories that have similar mean free paths but different pitch-angle dependencies.

Galactic cosmic-ray (GCR) modulation studies have suggested that the ratio between the parallel and perpendicular mean free paths (MFPs) of these particles is a key parameter governing the observed, steep increase in high-energy GCR intensities within the heliosheath. Here, GCR diffusion coefficients are computed for heliosheath turbulence through direct numerical test-particle simulations, using a grid-based Fourier-noise model for a turbulent magnetic field with an arbitrary fractional longitudinal (compressive) magnetic variance, which is introduced. In the case of purely compressive turbulence, the parallel MFP does not converge, suggesting free streaming along the background field. For levels of compressibility more in line with observations in the inner heliosheath, including significant isotropic as well as anisotropic transverse components, parallel diffusive behaviour is regained, with a strong dependence on compressibility. Perpendicular MFPs increase with energy, in line with theoretical expectations. Intriguingly, the computed ratios of parallel to perpendicular MFPs do not greatly differ from those expected in the inner heliosphere, but are sensitive to increases in compressibility. Finally, the addition of a compressive component to a turbulent field with a transverse variance, which is held constant, results in enhancements to both parallel and perpendicular transport, implying that compressive turbulence cannot be neglected when modelling particle transport coefficients in this region.

In addition to making near‐Earth observations, the THEMIS/ARTEMIS mission is uniquely positioned at lunar distance, in the deep magnetotail, reaching distances of 60 and further. This vantage point allows ARTEMIS to access the plasma sheet and measure entropy evolution across convective channels, plasma flow gradients, reconnection outflows, flow burst timing, and dipolarization fronts. In this study, we examine the thermodynamic behavior of the central plasma sheet (CPS) near‐Earth and at the distant magnetotail, across the northern and southern hemispheres, on the dusk and dawn sides, and also during geomagnetic quiet and active conditions. The specific entropy evolution and the mechanisms of the heating and cooling processes during mass and energy transport in the Earth's PS are also investigated. We use 10 years of THEMIS‐C/ARTEMIS‐P2 spacecraft data during CPS crossings and the polytropic index relation of Desta et al. (2024). Our results show that (a) the specific entropy and the polytropic index value vary radially in the CPS; (b) the thermodynamic process that takes place in the CPS at lunar distance is more likely a subadiabatic process; (c) near lunar distance, the northern and southern hemispheres, during quiet and active geomagnetic conditions, display nearly the same polytropic index. The results of this study can be used for modeling and simulation of magnetospheric substorms and also have implications relevant to the pressure catastrophe problem in substorm models.

In addition to making near-Earth observations, the THEMIS / ARTEMIS mission is uniquely positioned at lunar distance, in the deep magnetotail, reaching distances of 60 RE and fur- ther. This vantage point allows ARTEMIS to access the plasma sheet (PS) and measure entropy evolution across convective channels, plasma flow gradients, reconnection outflows, flow burst timing, and dipolarization fronts. In this study, we examine the thermodynamic behavior of the central plasma sheet (CPS) near-Earth and at the distant magnetotail, across the northern and southern hemispheres, on the dusk and dawn sides, and also during geomagnetic quiet and active conditions. The specific entropy evolution and the mechanisms of the heating and cooling processes during mass and energy transport in the Earth’s PS are also investigated. We use 10 years of THEMIS-C/ ARTEMIS-P2 spacecraft data during CPS crossings and the polytropic index relation of Desta et al. (2024). Our results show that (1) the specific entropy and the polytropic index value vary radially in the CPS; (2) the thermodynamic process that takes place in the CPS at lunar distance is more likely a subadiabatic process; (3) near lunar distance, the northern and southern hemispheres, during quiet and active geomagnetic conditions, display nearly the same polytropic index. The results of this study can be used for modeling and simulation of magnetospheric substorms and also have implications relevant to the pressure catastrophe problem in substorm models.

Due to solar wind turbulence, Parker spirals are stochastic. The dispersion of magnetic field lines is described by a convection–diffusion equation for the field line density distribution, which is a function of the two heliographic angles in addition to the radial distance. Taking into account the radial evolution of the turbulence, the three-dimensional convection–diffusion equation is transformed into a set of stochastic differential equations that is solved numerically using both a forward and a backward formulation. By tracing a large number of stochastic Parker spirals, the field line density distribution is constructed at any point in the heliosphere. It is shown that the angular part of the distribution function can be well-fitted by a two-dimensional Gaussian with standard deviation close to 25° at 1 au. The simulations also confirm that the magnetic field lines are underwound, on average, for strong enough turbulence intensity. Applying the backward approach, magnetic field lines are traced from an observer at 1 au back to the Sun, quantifying the probability of magnetic connection when interplanetary turbulence is accounted for. It is shown that the angular uncertainty of ∼25° is sharply reduced to ∼4° when the field lines are traced back to the solar wind source surface from 0.25 au.

In the heliosphere, solar cycle-related changes in galactic cosmic ray (GCR) intensities have long been known to arise as a direct consequence of solar cyclic changes in, for example, the heliospheric magnetic field and the solar tilt angle. In recent years, an increasing amount of observations of cyclic behaviour (especially in terms of stellar activity cycles like the solar cycle) in other stars has become available. The present study, for the first time, investigates the influence of a stellar activity cycle on the modulation of GCRs, taking as a case study the astrosphere of the exoplanet-hosting M-dwarf Proxima Centauri, using a 3D, physics-first GCR transport code. We demonstrate a modest stellar activity cycle-dependence of GCR proton and Helium intensities at Proxima Centauri b, which qualitatively resembles that seen at Earth. However, drift effect play a more significant role, even during periods of stellar maximum activity. For all levels of stellar activity, GCR intensities remain well above those observed at Earth. The influence of these variations on the atmospheric ionisation and radiation exposure of a presumably Earth-like Proxima Centauri b is also investigated. A moderate but non-negligible cyclic variation of up to 28% is found in the atmospheric ionisation profile at high altitudes. Since atmospheric ionisation and chemistry/climate changes are correlated, and with that might impact atmospheric transmission spectra, more precise information on the GCR-induced atmospheric background ionisation in exoplanetary atmospheres is crucial.

Although the drift effect is well known to play an important role in the transport process of energetic charged particles in the heliosphere, the widely adopted standard drift coefficient only reflects the uniformity of the large-scale magnetic field. The drift arising from the turbulent electromagnetic field was investigated by Stawicki with quasilinear theory. However, some higher-order terms in the Fokker–Planck coefficient were ignored in his model in order to simplify a laborious calculation. We revisit Stawicki’s model by incorporating higher-order terms and discuss extensively the properties of the general form of the drift coefficient. We propose a new parametric form of the suppression factor ( f _s ), defined as the ratio of the net and standard drift coefficients, which is very distinct from some previous models. According to the calculated f _s , we find that suppression occurs at a similar level during the solar minimum (2008/1–2010/12) and solar maximum (2013/1–2015/12).

Several studies of Galactic cosmic-ray (GCR) modulation within the astrospheres of stars deemed to be proxies for the young Sun have concluded that the intensities of these particles would, at early stages of the Sun’s evolution, be negligible at 1 au. These studies, however, do not take into account the varying interstellar conditions the young Sun would have encountered as it traversed its Galactic orbit, nor do they realistically model the transport of GCRs. The present study, for the first time, examines the influence of various interstellar parameters in the Galactic spiral arms on the astrosphere of κ ¹ Ceti, a young Sun proxy, through magnetohydrodynamic modelling. We demonstrate that these conditions lead to an astrosphere with considerably smaller dimensions than previous estimates. We also model the transport of turbulence parameters within said astrosphere for the first time, demonstrating that turbulence levels could be significantly higher than observed in the heliosphere. Finally, these insights are implemented in a 3D, ab initio GCR transport model to compute GCR intensities at 1 au, demonstrating the importance of drift effects in astrospheric modulation: full drift effects lead to GCR intensities comparable to modern observations, while turbulence-reduced drift coefficients lead to significantly smaller intensities.

The nature, and geometry, of the heliospheric magnetic field (HMF) plays a significant role in the transport of energetic charged particles, whether these be of solar or galactic origin. The present study investigates the winding angle of the HMF by analysing almost 60 years of spacecraft data, by employing methods based on the assumption of a Parker HMF from prior studies, as well as a 3D definition of the winding angle. The 2D results reveal an overwound (relative to the expected Parker field result) winding angle with a clear solar cycle dependence, in agreement with previous studies. The 3D results, however, indicate a consistently underwound field. It is further demonstrated that this winding can potentially be explained by the meandering of HMF lines due to the presence of turbulence. Furthermore, consequences of this phenomenon for energetic particle transport, particularly for magnetic focusing, are discussed.