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Abstract We present the HelioCubed, a high-order magnetohydrodynamic (MHD) code designed for modeling the inner heliosphere. The code is designed to achieve 4th order accuracy both in space and in time. In addition, HelioCubed can perform simulations on mapped grids, such as those based on cubed spheres, which makes it possible to overcome stability limitations caused by the geometrical singularity at the polar axis of a spherical grid, thus enabling substantially larger time steps. HelioCubed has been developed using the high-level Proto library, ensures performance portability across CPU and GPU architectures, and supports back-end implementations, e.g., CUDA, HIP, OpenMP, and MPI. The code is compatible with the HDF5 library, which facilitates seamless data handling for simulations and boundary conditions derived from semi-empirical and MHD models of the solar corona. While presenting the results of preliminary simulations, we demonstrate that our simulations are indeed performed with 4th order of accuracy. Our approach ensures that HelioCubed solves the MHD equations preserving the radial flow to machine round-off error even on cubed-sphere grids. Solar wind simulations are performed using the boundary conditions provided by the Wang–Sheeley–Arge coronal model of the ambient solar wind. It also allows us to to simulate coronal mass ejections using observation-driven flux rope models. These capabilities make HelioCubed a versatile and powerful tool to advance heliophysics research and space weather forecasting. 

Abstract Interplanetary coronal mass ejections (ICMEs) are the primary sources of geomagnetic storms at Earth. The negative out-of-ecliptic component (B_z) of magnetic field in the ICME or its associated sheath region is necessary for it to be geoeffective. For this reason, magnetohydrodynamic simulations of CMEs containing data-constrained flux ropes are more suitable for forecasting their geoeffectiveness as compared to hydrodynamic models of the CME. ICMEs observed in situ by radially aligned spacecraft can provide an important setup to validate the physics-based heliospheric modeling of CMEs. In this work, we use the constant-turn flux rope (CTFR) model to study an ICME that was observed in situ by Solar Orbiter (SolO) and at Earth, when they were in a near-radial alignment. This was a stealth CME that erupted on 2020 April 14 and reached Earth on 2020 April 20 with a weak shock and a smoothly rotating magnetic field signature. We found that the CTFR model was able to reproduce the rotating magnetic field signature at both SolO and Earth with very good accuracy. The simulated ICME arrived 5 hr late at SolO and 5 hr ahead at Earth, when compared to the observed ICME. We compare the propagation of the CME front through the inner heliosphere using synthetic J-maps and those observed in the heliospheric imager data and discuss the role of incorrect ambient solar wind background on kinematics of the simulated CME. This study supports the choice of the CTFR model for reproducing the magnetic field of ICMEs. 

Abstract We introduce the first solar-cycle simulations from our 3D, global MHD-plasma/kinetic-neutrals model, where both hydrogen and helium atoms are treated kinetically, while electrons and helium ions are described as individual fluids. Using Voyager/PWS observations of electron density up to 160 au from the Sun for validation of several different global models, we conclude that the current estimates for the proton density in the local interstellar medium (LISM) need a revision. Our findings indicate that the commonly accepted value of 0.054 cm⁻³may need to be increased to values exceeding 0.07 cm⁻³. We also show how different assumptions regarding the proton velocity distribution function in the outer heliosheath may affect the global solution. A new feature revealed by our simulations is that the helium ion flow may be significantly compressed and heated in the heliotail at heliocentric distances exceeding ∼400 au. Additionally, we identify a Kelvin–Helmholtz instability at the boundary of the slow and fast solar wind in the inner heliosheath, which acts as a driver of turbulence in the heliotail. These results are crucial for inferring the properties of the LISM and of the global heliosphere structure. 

Abstract We present recent advancements in our 3D modeling of the interaction between the solar wind and the local interstellar medium (LISM). The latest model results (Fraternale et al., ApJ, 2023) have raised a question about the electron density of the LISM near the heliopause. We have shown that the presence of helium ions leads to a significant underestimation of this parameter compared to the past simulations and Voyager 1 PWS observations. The latter observations, with over 12 years’ worth of LISM data, offers a robust constraint on our models. Here we present additional simulations in support of the idea that the LISM proton density may need to be revised from approximately 0.054 cm^–3to values around 0.07 cm^–3or higher. Additionally, we have developed and successfully tested a new version of the kinetic code suitable for simulating time-dependent solutions. 

Diffusive shock acceleration requires the production of backstreaming superthermal ions (injection) as a first step. Such ions can be generated in the process of scattering of ions in the superthermal tail off the shock front. Knowledge of the scattering of high-energy ions is essential for matching conditions of upstream and downstream distributions at the shock transition. Here we analyze the generation of backstreaming ions as a function of their initial energy in a model stationary shock and in a similar rippled shock. Rippling substantially enhances ion reflection and the generation of backstreaming ions for slightly and moderately superthermal energies, and thus is capable of ensuring ion injection into a further diffusive shock acceleration process. For high-energy ions, there is almost no difference in the fraction of backstreaming ions produced and the ion distributions between the planar stationary shock and the rippled shock. 

Abstract In a collisionless shock the energy of the directed flow is converted to heating and acceleration of charged particles, and to magnetic compression. In low-Mach number shocks the downstream ion distribution is made of directly transmitted ions. In higher-Mach number shocks ion reflection is important. With the increase of the Mach number, rippling develops, which is expected to affect ion dynamics. Using ion tracing in a model shock front, downstream distributions of ions are analyzed and compared for a planar stationary shock with an overshoot and a similar shock with ripples propagating along the shock front. It is shown that rippling results in the distributions, which are substantially broader and more diffuse in the phase space. Gyrotropization is sped up. Rippling is able to generate backstreaming ions, which are absent in the planar stationary case. 

Abstract Using ion tracing in a model shock front we study heating of thermal (Maxwellian) and superthermal (Vasyliunas–Siscoe) populations of protons, singly charged helium, and alpha particles. It is found that heating of thermal and superthermal populations is different, mainly because of substantially higher ion reflection in the superthermal populations. Accordingly, the temperature increase of initially superthermal populations is substantially higher than that of the thermal ions. Heating per mass decreases with the increase of the mass-to-charge ratio because of the reduced effect of the cross-shock potential and, accordingly, weaker ion reflection. The findings are supported by two-dimensional hybrid simulations. 

A collisionless shock is a self-organized structure where fields and particle distributions are mutually adjusted to ensure a stable mass, momentum and energy transfer from the upstream to the downstream region. This adjustment may involve rippling, reformation or whatever else is needed to maintain the shock. The fields inside the shock front are produced due to the motion of charged particles, which is in turn governed by the fields. The overshoot arises due to the deceleration of the ion flow by the increasing magnetic field, so that the drop of the dynamic pressure should be compensated by the increase of the magnetic pressure. The role of the overshoot is to regulate ion reflection, thus properly adjusting the downstream ion temperature and kinetic pressure and also speeding up the collisionless relaxation and reducing the anisotropy of the eventually gyrotropized distributions. 

Abstract To address Objective II of the National Space Weather Strategy and Action Plan “Develop and Disseminate Accurate and Timely Space Weather Characterization and Forecasts” and US Congress PROSWIFT Act 116–181, our team is developing a new set of open-source software that would ensure substantial improvements of Space Weather (SWx) predictions. On the one hand, our focus is on the development of data-driven solar wind models. On the other hand, each individual component of our software is designed to have accuracy higher than any existing SWx prediction tools with a dramatically improved performance. This is done by the application of new computational technologies and enhanced data sources. The development of such software paves way for improved SWx predictions accompanied with an appropriate uncertainty quantification. This makes it possible to forecast hazardous SWx effects on the space-borne and ground-based technological systems, and on human health. Our models include (1) a new, open-source solar magnetic flux model (OFT), which evolves information to the back side of the Sun and its poles, and updates the model flux with new observations using data assimilation methods; (2) a new potential field solver (POT3D) associated with the Wang–Sheeley–Arge coronal model, and (3) a new adaptive, 4-th order of accuracy solver (HelioCubed) for the Reynolds-averaged MHD equations implemented on mapped multiblock grids (cubed spheres). We describe the software and results obtained with it, including the application of machine learning to modeling coronal mass ejections, which makes it possible to improve SWx predictions by decreasing the time-of-arrival mismatch. The tests show that our software is formally more accurate and performs much faster than its predecessors used for SWx predictions. 

Abstract Collisionless shocks channel the energy of the directed plasma flow into the heating of the plasma species and magnetic field enhancement. The kinetic processes at the shock transition cause the ion distributions just behind the shock to be nongyrotropic. Gyrotropization and subsequent isotropization occur at different spatial scales. Accordingly, for a given upstream plasma and magnetic field state, there would be different downstream states corresponding to the anisotropic and isotropic regions. Thus, at least two sets of Rankine–Hugoniot relations are needed, in general, to describe the connection of the downstream measurable parameters to the upstream ones. We establish the relation between the two sets.