Periodic Reporting for period 1 - TerraVirtualE (Planetary space simulations based on the particle description for electrons and ions.)
Période du rapport: 2023-09-01 au 2025-05-31
The question of how solar storms affect Earth holds both fundamental scientific importance and considerable societal relevance, particularly with regard to protecting infrastructure from the most intense solar events. Current models typically employ a fluid representation of electrons, primarily due to algorithmic and computational limitations. The main objective of the TerraVirtualE project is to develop a model of Earth’s near-space environment based on a particle-based description of both ions and electrons.
TerraVirtualE aims to utilise a Particle-in-Cell (PIC) model, in which ions and electrons are treated explicitly as particles. This approach will enable a detailed investigation of the role of electrons in the transfer of energy and matter from the solar wind to Earth’s near-space environment.
This endeavour is made possible by the Energy-Conserving Semi-Implicit Method (ECsim) algorithm, developed by the Principal Investigator, Professor Giovanni Lapenta. ECsim conserves the total energy of particles and electromagnetic fields in PIC simulations—a crucial element for analysing energy flow from the solar wind. In addition, the algorithm’s energy conservation properties significantly improve numerical stability, greatly enhancing ECsim’s capacity to simulate large-scale systems, such as planetary atmospheres.
Building on this foundation, we will demonstrate that a comprehensive particle-based representation of planetary space, incorporating both electrons and ions, is viable using the ECsim algorithm (Objective 1). To enhance the physical realism of solar wind dynamics within the heliosphere, these PIC simulations will be coupled with the heliospheric model in EUHFORIA (Objective 2). Furthermore, we will show that machine learning algorithms can be used to cluster in situ observations of the solar wind and analyse the outputs of PIC simulations (Objective 4).
TerraVirtualE aims to utilise a Particle-in-Cell (PIC) model, in which ions and electrons are treated explicitly as particles. This approach will enable a detailed investigation of the role of electrons in the transfer of energy and matter from the solar wind to Earth’s near-space environment.
This endeavour is made possible by the Energy-Conserving Semi-Implicit Method (ECsim) algorithm, developed by the Principal Investigator, Professor Giovanni Lapenta. ECsim conserves the total energy of particles and electromagnetic fields in PIC simulations—a crucial element for analysing energy flow from the solar wind. In addition, the algorithm’s energy conservation properties significantly improve numerical stability, greatly enhancing ECsim’s capacity to simulate large-scale systems, such as planetary atmospheres.
Building on this foundation, we will demonstrate that a comprehensive particle-based representation of planetary space, incorporating both electrons and ions, is viable using the ECsim algorithm (Objective 1). To enhance the physical realism of solar wind dynamics within the heliosphere, these PIC simulations will be coupled with the heliospheric model in EUHFORIA (Objective 2). Furthermore, we will show that machine learning algorithms can be used to cluster in situ observations of the solar wind and analyse the outputs of PIC simulations (Objective 4).
Objective 1
Electrons play a crucial role in magnetic reconnection — a process in which magnetic energy is transformed into kinetic energy and heat. Particle-in-Cell (PIC) simulations of magnetic reconnection in Earth’s magnetotail were conducted to investigate the resulting plasma turbulence. The newly developed ECsim algorithm was applied to model the behaviour of charged particles (electrons and ions) in Earth’s magnetotail.
The contribution of magnetic reconnection to the acceleration of charged particles was also examined. PIC simulations of magnetic reconnection in Earth’s magnetotail were performed, and the resulting energy distributions of electrons and protons were compared with those derived from observational data from the Magnetospheric Multiscale (MMS) mission (Figure 1). The influence of various simulation parameters — including the ion-to-electron mass ratio, simulation domain dimensions, and initial plasma temperature anisotropy — was thoroughly analysed.
Objective 2
Planetary-scale PIC simulations and the newly developed ECsim algorithm were applied to model Earth's magnetosphere with unprecedented accuracy. For the first time, successful coupling was achieved between the heliospheric model within EUHFORIA and PIC simulations of Earth's magnetosphere. This advancement is expected to significantly enhance the physical realism of solar wind dynamics within the heliosphere.
EUHFORIA integrates a coronal model with a heliospheric model and is employed to simulate the propagation of coronal mass ejections (CMEs) and the solar wind through interplanetary space, as well as their impact on Earth. Within EUHFORIA, a novel CME model was developed, introducing a data-driven approach in which the magnetic field distribution of the CME is computed using a Physics-Informed Neural Network (PINN).
Furthermore, EUHFORIA’s traditional semi-empirical WSA (Wang–Sheeley–Arge) coronal model was replaced by the physics-based COCONUT (COolfluid COroNal UnsTructured) model. This new implementation enables time-dependent coupling between the solar corona and the heliosphere, allowing for continuous simulation of CMEs propagating from the Sun to Earth. The results of this work were published in Linan et al. (2025).
Objective 4
Self-Organising Maps — an unsupervised machine learning technique — were used to cluster in situ observations of the solar wind. These Self-Organising Maps were used to differentiate between fast and slow solar wind streams and to identify Coronal Mass Ejections (CMEs) and Stream Interaction Regions (SIRs).
Plasma behaviour may be characterised using fluid models, which treat plasma as a continuous medium governed by fluid equations. However, solving these equations requires the representation of unknown higher-order terms using known lower-order quantities — a formulation known as the plasma closure relationship. Sparse Identification of Nonlinear Dynamics (SINDy) was employed to derive this relationship from PIC simulation data.
Electrons play a crucial role in magnetic reconnection — a process in which magnetic energy is transformed into kinetic energy and heat. Particle-in-Cell (PIC) simulations of magnetic reconnection in Earth’s magnetotail were conducted to investigate the resulting plasma turbulence. The newly developed ECsim algorithm was applied to model the behaviour of charged particles (electrons and ions) in Earth’s magnetotail.
The contribution of magnetic reconnection to the acceleration of charged particles was also examined. PIC simulations of magnetic reconnection in Earth’s magnetotail were performed, and the resulting energy distributions of electrons and protons were compared with those derived from observational data from the Magnetospheric Multiscale (MMS) mission (Figure 1). The influence of various simulation parameters — including the ion-to-electron mass ratio, simulation domain dimensions, and initial plasma temperature anisotropy — was thoroughly analysed.
Objective 2
Planetary-scale PIC simulations and the newly developed ECsim algorithm were applied to model Earth's magnetosphere with unprecedented accuracy. For the first time, successful coupling was achieved between the heliospheric model within EUHFORIA and PIC simulations of Earth's magnetosphere. This advancement is expected to significantly enhance the physical realism of solar wind dynamics within the heliosphere.
EUHFORIA integrates a coronal model with a heliospheric model and is employed to simulate the propagation of coronal mass ejections (CMEs) and the solar wind through interplanetary space, as well as their impact on Earth. Within EUHFORIA, a novel CME model was developed, introducing a data-driven approach in which the magnetic field distribution of the CME is computed using a Physics-Informed Neural Network (PINN).
Furthermore, EUHFORIA’s traditional semi-empirical WSA (Wang–Sheeley–Arge) coronal model was replaced by the physics-based COCONUT (COolfluid COroNal UnsTructured) model. This new implementation enables time-dependent coupling between the solar corona and the heliosphere, allowing for continuous simulation of CMEs propagating from the Sun to Earth. The results of this work were published in Linan et al. (2025).
Objective 4
Self-Organising Maps — an unsupervised machine learning technique — were used to cluster in situ observations of the solar wind. These Self-Organising Maps were used to differentiate between fast and slow solar wind streams and to identify Coronal Mass Ejections (CMEs) and Stream Interaction Regions (SIRs).
Plasma behaviour may be characterised using fluid models, which treat plasma as a continuous medium governed by fluid equations. However, solving these equations requires the representation of unknown higher-order terms using known lower-order quantities — a formulation known as the plasma closure relationship. Sparse Identification of Nonlinear Dynamics (SINDy) was employed to derive this relationship from PIC simulation data.
The successful coupling between the heliospheric model within EUHFORIA and the Particle-in-Cell (PIC) simulation of Earth's magnetosphere will significantly enhance the physical realism of solar wind dynamics within the heliosphere.
EUHFORIA’s traditional semi-empirical Wang–Sheeley–Arge (WSA) coronal model has been replaced by the physics-based COCONUT model. This novel implementation enables time-dependent coupling between the solar corona and the heliosphere, facilitating the continuous simulation of coronal mass ejections (CMEs) as they propagate from the Sun to Earth. Both advancement are crucial for improving predictions of the impact of space weather events on satellites, communication systems, and power grids.
EUHFORIA’s traditional semi-empirical Wang–Sheeley–Arge (WSA) coronal model has been replaced by the physics-based COCONUT model. This novel implementation enables time-dependent coupling between the solar corona and the heliosphere, facilitating the continuous simulation of coronal mass ejections (CMEs) as they propagate from the Sun to Earth. Both advancement are crucial for improving predictions of the impact of space weather events on satellites, communication systems, and power grids.