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Modelling the transport of cosmic rays (CRs) in the heliosphere represents a global challenge in the field of heliophysics, in that such a study, if it were to be performed from first principles, requires the careful modelling of both large scale heliospheric plasma quantities (such as the global structure of the heliosphere, or the heliospheric magnetic field) and small scale plasma quantities (such as various turbulence-related quantities). Here, recent advances in our understanding of the transport of galactic cosmic rays are reviewed, with an emphasis on new developments pertaining to their transport coefficients, with a special emphasis on novel theoretical and numerical simulation results, as well as the CR transport studies that employ them. Furthermore, brief reviews are given of recent progress in CR focused transport modelling, as well as the modelling of non-diffusive CR transport.

Solar polar fields are essential for the solar cycle and the heliospheric magnetic field. Cycle 25 is now entering its declining phase, the critical period during which most of the cycle’s polar fields are established. Therefore, reliable polar-field prediction is now especially important. Polar-field evolution is governed by the poleward transport of already-emerged active-region (AR) flux over a timescale of a few years. Thus, surface flux-transport models can reliably provide 1 yr predictions without requiring information about future AR emergence. Our prediction method is validated using simulations of the surface magnetic field from 2020 to 2025 and hindcasts of the 2023–2024 polar fields, employing a newly constrained profile of the meridional flow. Using the most recent Helioseismic and Magnetic Imager synoptic magnetogram as the initial condition, we predict the polar-field evolution from 2025 October to 2026 October. The southern polar field is predicted to strengthen gradually, while the northern field is expected to decline sharply until 2026 March due to some ARs with abnormal polarity. By that time, the northern polar field becomes exceptionally weak, and the southern field remains relatively weak, raising concerns about the polar-field strength at the cycle 25/26 minimum and the amplitude of cycle 26.

The interplanetary magnetic field (IMF) measured near Earth can be up to 2 times greater than that derived from models using remote solar observations. We investigate this discrepancy by modeling the IMF using a potential field source surface (PFSS) model using synoptic maps of the photospheric magnetic field from 2010 May to 2024 April. Five types of radial field synoptic maps are used in this work: the Br synoptic maps from vector magnetic field data, the Mr synoptic maps from the line-of-sight field data, the rescaled Mr synoptic maps rescaled from the Mr maps by a center-to-limb distance dependent rescaling factor of Br/Mr, and composite and rescaled composite synoptic maps comprised of a combination of strong-field pixels from the Br maps and the rest from either the original Mr or rescaled Mr maps. The modeled IMFs from all five types of synoptic maps agree with each other well in the solar maximum phase, when they are about 2 times smaller than in situ measurements. The IMF calculated from the Br and both composite and rescaled composite synoptic maps match well with in situ observations during solar minimum from 2017 to 2022. The IMF values modeled from both the Mr and rescaled Mr synoptic maps are still significantly smaller in this time interval. This suggests that (1) the Br maps represent the radial field better than the Mr; and (2) the PFSS model is appropriate to model the heliospheric magnetic field in solar minimum, but has limitations when used near solar maximum.

Galactic cosmic rays suffer from solar modulation when they propagate through the heliosphere. The transfer of the local interstellar spectrum (LIS) to the top-of-atmosphere spectra is influenced by solar wind convection, and diffusion on the heliospheric magnetic field (HMF), among other factors. In this work, we derive the LIS of proton (p) and helium (He) covering energies from a few MeV/n to TeV/n, using a nonparameterization method. The study utilizes monthly AMS-02 data on proton and helium fluxes and their ratio to examine the evolution of solar modulation from 2011 May to 2017 May. To improve the fitting, the force-field approximation is modified by assigning different solar modulation potentials for high (ϕ h ) and low (ϕ l ) energy ranges. A sigmoid function is employed to describe the transition between these energy ranges. The analysis reveals that the break in proton and helium fluxes occurs at the same rigidity value, with a mean of approximately 6 GV and this break is more pronounced during the HMF reversal period. The ϕ l is close to the result of Advanced Composition Explorer while the ϕ h is close to the result of neutron monitor data. Furthermore, the long-term behavior of the proton-to-helium ratio ratio is found to naturally arise from the model when considering different Z/A values and the LISs for proton and helium.

We analyze the normal (N) component of the heliospheric magnetic field observed by the Interplanetary Monitoring Platform and the Advanced Composition Explorer spacecraft for the period 1973–2020. Parameters characterizing the frequency spectrum are calculated with a novel technique, which is based on calculating variances at incremental lags to yield the integral of a turbulence spectrum. We compare this technique with the standard second-order structure function to show their similarity in the inertial range, and use the latter to calculate correlation functions. We find that the yearly average for magnetic field magnitude and the variance attained their lowest values since spacecraft observations began for the period that includes the 2020 solar minimum, 4.2 nT and 3.3 nT2, respectively. The ratio of the magnitude of fluctuations of the N component to the field magnitude shows little variation, with an average value of 0.43 ± 0.04. The average value of the spectral index of the energy range for the whole data set is −1.0 ± 0.1, and shows some solar-cycle dependence. The average value for the inertial range is an almost constant −1.69 ± 0.04. While the break between the energy and the inertial range is difficult to determine accurately to search for a solar-cycle dependence, an indirect indication of such a dependence follows when the ratio of spectral levels in the energy and in the inertial range is calculated. The e-folding correlation length has an average value of 1.1 ± 0.3 Mkm, with a clear solar-cycle dependence.

We test the use of the Mg ii resonant lines for measurement of the magnetic field at the top of the chromosphere of polar coronal holes (CHs). The Hanle effect in the core of Mg II k enables access to a regime of field strengths where the Zeeman effect has little diagnostic value (especially at the solar poles, where most of the field is transverse to the line of sight). Synthetic Stokes spectra computed from a radiation magnetohydrodynamic simulation of a CH emulating a high viewing angle are inverted with the HanleRT Tenerife Inversion Code, which accounts for the physical processes that lead to scattering-induced polarization and its modification due to the magnetic field and other symmetry-breaking mechanisms. We find that, while degeneracies in the atmospheric model lead to poor inferences of the thermodynamical properties, the magnetic inferences are highly consistent with the model values. The mean magnetic field strength in the simulation cube is typically retrieved with a relative error of δB ∼ 20% and an absolute error of ΔB ∼ 2 G at the top of the chromosphere. This opens up an avenue for promising chromospheric constraints for magnetic extrapolation models that ingest photospheric magnetograms, whose biases and uncertainties are troublesome to the reconstruction of the heliospheric magnetic field.

Solar wind backmapping is a critical technique for analyzing the origin of the solar wind and space weather events by correlating in situ measurements with solar remote-sensing observations. This technique typically traces magnetic field lines using a heliospheric magnetic field (HMF) model coupled with a coronal magnetic field (CMF). However, the impact of different HMF and CMF configurations on backmapping uncertainty—particularly regarding high-latitude solar wind—remains inadequately quantified. This study comprehensively evaluates solar wind backmapping by combining two HMF models (Parker spiral, Fisk-type) with three CMF models (potential field source surface (PFSS), potential field current sheet (PFCS), current sheet source surface (CSSS)). Our analysis primarily uses in situ measurements from Ulysses and remote-sensing data from STEREO-A. Key findings are that: (1) While both Fisk and Parker HMF models show comparable consistency with measured magnetic field strength and polarity, they produce certain longitudinal displacements in their backmapped footpoints on the source surface (2.5R⊙); (2) For CMF models (PFSS, PFCS, CSSS), predicted photospheric footpoints exhibit minor variations for high-/midlatitude solar wind but some divergences for ecliptic/low-latitude wind; (3) All three CMF models link high-/midlatitude wind to active regions or coronal holes, yet associate a fraction of ecliptic/low-latitude wind with quiet-Sun regions; (4) Ecliptic/low-latitude sources show significantly stronger dependence on the PFSS source surface height compared to high-latitude wind. These results demonstrate that simpler models (PFSS + Parker) appear reasonably adequate for polar coronal hole wind studies, while low-latitude/ecliptic solar wind exhibits the heightened sensitivity to model choices.

Galactic cosmic rays (GCRs), consisting predominantly of fully stripped nuclei, are significantly modulated by solar activity and represent a major radiation hazard for long-duration human space exploration. This study presents a comprehensive GCR modulation model based on a modified force-field approach, extending previous work by Z. Shen et al. to heavier nuclei. The local interstellar spectra (LIS) for elements from hydrogen to nickel are derived by fitting observations from Voyager, Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics, Alpha Magnetic Spectrometer-02, Advanced Composition Explorer Cosmic Ray Isotope Spectrometer, HEAO3-C2, and others. The solar modulation potential ϕ(E) is described by a double power-law function with an exponential tail. Due to differences in LIS spectral shapes and mass-to-charge ratio-dependent modulation effects, protons and helium have distinct ϕ values, while heavier nuclei share the same ϕ as helium. The time-dependent parameters within the ϕ expression are determined by fitting selected GCR measurements and subsequently reconstructed using sunspot number, heliospheric current sheet tilt angle, and heliospheric magnetic field polarity, enabling the development of a predictive GCR model. The results successfully reproduce the 11 and 22 yr GCR cycles, with good agreement with observations since Solar Cycle 19 across different particle species and energies. Additionally, this study investigates long-term solar modulation over millennial timescales utilizing cosmogenic 14C isotope records and assesses radiation dose rates relevant for deep space missions, showing good agreement with Cosmic Ray Telescope for the Effects of Radiation/D1D2 measurements. This work thus provides a new framework for predicting GCR fluxes and associated radiation exposure in deep space.

Magnetohydrodynamic (MHD) simulations are a useful tool for understanding the propagation of coronal mass ejections (CMEs) in the inner heliosphere and their interaction with the background solar wind. This understanding is important for improving our ability to predict CME properties at Earth. A common approach in models of the inner heliosphere starting from ≈0.1 astronomical unit (au) is to inject CMEs with analytically prescribed magnetic structures—such as magnetic spheromaks—by superimposing the CME’s magnetic field onto the heliospheric magnetic field. However, the superposition method leads to the heliospheric magnetic field penetrating the CME, immediately distorting the CME’s magnetic structure during the injection. In this work, we introduce a new, more physically accurate displacement method for the CME injection into the inner heliosphere by dynamically bending the heliospheric magnetic field around the incoming CME. Using the GAMERA-Helio MHD model of the inner heliosphere (0.1–1 au) and a Gibson–Low model of a CME with an internal magnetic field, we demonstrate that the displacement method preserves the CME’s internal structure, unlike superposition. Moreover, the displacement method produces a current distribution around the CME that is consistent with results from previous coronal MHD simulations with a self-consistent description of CME initiation and evolution. The displacement approach represents a step forward in modeling magnetized CMEs in the inner heliosphere to study their evolution and impacts at Earth.

Galactic cosmic rays (GCRs), the highly energetic particles that may raise critical health issues for astronauts in space, are modulated by solar activity, with their intensity lagging behind the variation in sunspot number (SSN) by about one year. Previously, this lag has been attributed to the combined effect of outward convecting solar wind and inward propagating GCRs. However, the lag’s amplitude and its solar-cycle dependence are still not fully understood. By investigating the solar surface magnetic field, we find that the source of heliospheric magnetic field—the open magnetic flux on the Sun—already lags behind SSN before it convects into the heliosphere along with the solar wind. The delay during odd cycles is longer than that during sequential even cycles. Thus, we propose that the GCR lag is primarily due to the very late opening of the solar magnetic field with respect to SSN, though solar wind convection and particle transport in the heliosphere also matter. We further investigate the origin of the open flux from different latitudes of the Sun and find that the total open flux is significantly contributed by that from low latitudes, where coronal mass ejections frequently occur and also show an odd–even cyclic pattern. Our findings challenge existing theories, and may serve as the physical basis of long-term forecasts of radiation dose estimates for manned deep-space exploration missions.