Boris Vilhelm Gudiksen

• Cherry, George; Gudiksen, Boris Vilhelm; Finley, Adam J. & Noraz, Quentin (2026). Decomposing wave activity in the solar atmosphere: Shocks, jets, and swirls in the quiet Sun. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 705. doi: 10.1051/0004-6361/202557226. Fulltekst i vitenarkiv Vis sammendrag

  Context. There remains much mystery about how wave energy in the photosphere can be transferred sufficiently upward through the solar atmosphere to contribute to coronal heating. In light of a plethora of theoretical and idealised studies, we must complement our understanding with realistic and self-driven simulations in order to confidently quantify such contributions. Aims. In this study we aim to connect wave drivers in the photosphere with their impact on the low corona, transitions, and dissipation mechanisms. We analyse the effects of the presence of twisted magnetic features and vortical flows on the transport of such wave modes as the structures evolve. Methods. We adopted the most significant frequency (MSF) decomposition method to trace wave activity through a 3D realistic quiet Sun simulation. We focused on vertical and temporal evolution, identifying wave sources and shifts in the dominant modes. Results. We identify two frequencies, at 3.5 and 5 mHz, that connect oscillations in the upper convection zone to the dynamics in the solar atmosphere. We see distinct differences in the absence and presence of swirling structures on the upward propagation of these oscillations. Furthermore, we validate the use of the highest MSF bin as a proxy for the location of shocks in the chromosphere and use the results to understand the connection between shocks and the propagation of oscillations in the upper atmosphere. We discuss the relation of energy transfer via shocks, mode conversion, and jets. Finally, we find the contribution of 3.5 and 5 mHz signals to the overall wave power in the domain to be significant, up to 50%.

• Øyre, Eilif Sommer; Gudiksen, Boris Vilhelm & Fletcher, Lyndsay (2025). Test particle sampling and particle acceleration in a 2D coronal plasmoid-mediated reconnecting current sheet. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 703. doi: 10.1051/0004-6361/202555424. Fulltekst i vitenarkiv Vis sammendrag

  Context. Solar flares accelerate electrons, creating non-thermal energy distributions. However, the acceleration sites and dominant acceleration mechanisms remain largely unknown. Aims. We study the characteristics of electron acceleration and subsequent non-thermal energy distribution in a 2D coronal plasmoid-mediated reconnecting current sheet. Methods. We used test particles and the guiding centre approximation to transport electrons in a static coronal 2D fan-spine topology magnetohydrodynamic (MHD) snapshot. The snapshot was from a Bifrost simulation that featured plasmoid-mediated reconnection at a current sheet. To sample initial particle conditions that lead to non-thermal energies, we used importance sampling. In this way, the characteristics of the non-thermal electrons were statistically representative of the MHD plasma. Results. The energy distribution of the electrons forms a non-thermal power law that varies with our tolerance of the guiding centre approximation’s validity, from no obvious power law to a power law with an exponent of −4 (the power law also depends on the statistical weighing of the electrons). The non-thermal electrons gain energy through a gradual betatron acceleration close to magnetic null points associated with plasmoids. Conclusions. In this static, asymmetric, coronal, 2D fan-spine topology MHD configuration, non-thermal electron acceleration occurs only in the vicinity of null points associated with magnetic gradients and electric fields induced by plasmoid formation and ejection. However, the guiding centre approximation alone is not sufficient to properly estimate the shape of the non-thermal power law since, according to our results, electron acceleration is correlated with the adiabaticity of the particles’ motion. The results also show that the particle power law formation is biased by the test particle sampling procedure.

• Lamarre, Henri; Charbonneau, Paul; Noraz, Quentin; Strugarek, Antoine; Blaise, Alexis & Brun, Allan Sacha [Vis alle 8 forfattere av denne artikkelen] (2025). Avalanches in magnetohydrodynamical simulations. Physical Review E (PRE). ISSN 2470-0045. 112(6). doi: 10.1103/28ws-d57z. Fulltekst i vitenarkiv Vis sammendrag

  Scale invariance is a hallmark of many natural systems, including solar flares, where energy release spans a vast range of scales. Recent computational advances, at the level of both algorithmics and hardware, have enabled high-resolution magnetohydrodynamical (MHD) simulations to span multiple scales, offering new insights into magnetic energy dissipation processes. Here, we study the scale invariance of magnetic energy dissipation in two distinct MHD simulations. Current sheets are identified and analyzed over time. Results demonstrate that dissipative events exhibit scale invariance, with power-law distributions characterizing their energy dissipation and lifetimes. Remarkably, these distributions are consistent across the two simulations, despite differing numerical and physical setups, suggesting universality in the process of magnetic energy dissipation. Comparisons between the evolution of dissipation regions reveal distinct growth behaviors in high plasma-𝛽 regions (convective zone) and low plasma-𝛽 regions (atmosphere). The latter display spatiotemporal dynamics similar to those of avalanche models, suggesting self-organized criticality and a common universality class.

• Enerhaug, Elisabeth; Carlsson, M.; Szydlarski, Mikolaj; Gudiksen, Boris Vilhelm & Moortel, Ineke de (2025). Identifying magnetohydrodynamic wave modes in the solar atmosphere: Experiments in 2D. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 701. doi: 10.1051/0004-6361/202554210. Fulltekst i vitenarkiv Vis sammendrag

  Context. Magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. They are thought to play an important role in maintaining the temperature of the solar corona and are important components of coronal seismology. However, research into reliable wave mode identification schemes is still in its early stages. Such a scheme would be a valuable tool for understanding the role of waves in the coronal heating problem. A widely renowned 2003 study in 2D on magnetoacoustic gravity (MAG) waves crossing the β  = 1 layer in the atmosphere provided valuable insights into wave propagation, from the lower to the upper atmosphere. The in-depth analyses of wave propagation through the solar atmosphere offer a valuable reference, which can be used to test other wave mode identifier schemes that could subsequently be expanded to 3D. Aims. We aim to analyse a set of wave mode identification components designed to isolate properties of fast and slow MAG waves. Methods. We recreated the 2003 experiment using the numerical code Bifrost with simplified boundary conditions. We then compared the existing wave analysis to our own scheme. Results. We show that our wave mode identification scheme is equivalent to that of the scheme used in the 2003 study. We show how physical properties such as steepening, maximum, and minimum can be deduced from the scheme. As these wave mode identifiers can be expanded to 3D, the recreation of the piston experiment along with the careful analysis of the components opens the door for further studies into how MAG waves are transmitted across the β  = 1 layer.

• Haahr, Michael; Gudiksen, Boris Vilhelm & Nordlund, Åke (2025). Two-way coupled particle-in-cell and magnetohydrodynamic simulation of 2D fan-spine reconnection. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 701. doi: 10.1051/0004-6361/202555813. Fulltekst i vitenarkiv Vis sammendrag

  Context. Magnetic reconnection is a key mechanism for energy release in the solar atmosphere, but its kinetic-scale microphysics remains difficult to model in large-scale solar geometries. Aims. We investigate whether fully kinetic particle-in-cell (PIC) simulations can be stably and meaningfully embedded within global magnetohydrodynamic (MHD) models of the solar corona using a realistic fan-spine magnetic configuration. Methods. We employed a two-way coupled PIC-MHD scheme implemented in the DISPATCH code framework. The PIC solver is embedded within a reconnecting current sheet in a solar-like topology. A physical adjustment of constants is used to bridge kinetic and fluid scales while maintaining self-consistent plasma ordering. Results. The system evolves stably over more than 45 000 ion plasma periods, exhibiting clear kinetic signatures such as Hall-driven quadrupolar magnetic fields, a reconnection geometry reminiscent of the Petschek configuration, and supra-thermal particle populations. The reconnection rate in the PIC region remains steady and physically consistent, while coupling artefacts are effectively suppressed by fade-in/fade-out boundary weighting. Conclusions. Our results demonstrate that fully kinetic reconnection can be embedded in global solar MHD models with physical fidelity and computational efficiency. This hybrid approach offers a practical pathway to multi-scale kinetic modelling in realistic astrophysical environments.

• Haahr, Michael; Gudiksen, Boris Vilhelm & Nordlund, Åke (2025). Coupling particle-in-cell and magnetohydrodynamics methods for realistic solar flare models. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 696. doi: 10.1051/0004-6361/202452117. Fulltekst i vitenarkiv Vis sammendrag

  Context. Simulating solar flares requires capturing both large-scale magnetohydrodynamic (MHD) evolution and small-scale kinetic processes near reconnection sites. Bridging these scales has been a significant computational challenge. Aims. This study introduces a Particle-In-Cell (PIC) solver integrated within the DISPATCH framework, facilitating seamless embedding within MHD simulations. This development aims to enable self-consistent multi-scale solar flare simulations. Methods. Our PIC solver, inspired by the PhotonPlasma code, addresses the Vlasov-Maxwell equations in collisionless plasma. We validate its accuracy through fundamental plasma tests – including plasma oscillations, two-stream instability, and current sheet reconnection. To make kinetic simulations computationally feasible, we employ physical adjustment of constants (PAC), modifying the speed of light, elementary charge, and electron mass to shift plasma scales. Additionally, we implement and validate a coupling strategy that enables smooth transitions between kinetic and fluid regimes. Results. The PIC solver successfully recovers expected plasma dynamics and electromagnetic field behaviour. Our analysis highlights the effects of PAC on reconnection dynamics, underscoring the importance of transparent and well-documented scaling choices. Test cases involving propagating waves across PIC-MHD interfaces confirm the robustness of our coupling approach. Conclusions. The integration of the PIC solver into the DISPATCH framework makes it possible to run self-consistent, multiscale solar flare simulations. Our approach provides a computationally efficient foundation for investigating reconnection physics in large-scale astrophysical plasmas.

• Cherry, George; Gudiksen, Boris Vilhelm & Finley, Adam J. (2025). Detection of wave activity within a realistic 3D magnetohydrodynamic quiet Sun simulation. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 700. doi: 10.1051/0004-6361/202555110. Fulltekst i vitenarkiv Vis sammendrag

  Context. Tracing wave activity from the photosphere to the corona has important implications for coronal heating and prediction of the solar wind. Despite extensive theory and simulations, the detection of waves in realistic magnetohydrodynamic (MHD) simulations still presents a large challenge due to wave interaction, mode conversion, and damping mechanisms. Aims. We developed a method to address certain limitations of current wave decompositions. With this method, we aim to detect localised wave activity within a realistic MHD simulation of the solar atmosphere by the Bifrost code. Methods. We present a new method of detecting the most significant contributions of wave activity within localised areas of the domain, aided by discrete Fourier transforms and frequency filtering. We correlate oscillations in the vertical and horizontal magnetic field, velocities parallel and perpendicular to the magnetic field, and pressure to infer the nature of the dominant wave modes. Results. Our method captures the most powerful frequencies and wavenumbers, and provides a new diagnostic for damping processes. We infer the presence of magnetoacoustic waves in the boundaries of prominent chromospheric and coronal swirling features. We find these waves are likely damped by viscous heating in the swirl boundaries, contributing to heating in the upper atmosphere. Conclusions. Using the most significant frequency decomposition, we highlight that energy can be transported from the lower atmosphere to the upper atmosphere through waves and fluctuations along the swirl boundaries. Although further analysis is needed to confirm these findings, our new method provides a path forward to investigate wave activity in the solar atmosphere.

• Brchnelova, M.; Gudiksen, Boris Vilhelm; Carlsson, Mats; Lani, A. & Poedts, S. (2025). Constraining the inner boundaries of COCONUT through plasma β and Alfvén speed. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 693. doi: 10.1051/0004-6361/202451772. Fulltekst i vitenarkiv Vis sammendrag

  Context. Space weather modelling has been gaining importance due to our increasing dependency on technology sensitive to space weather effects, such as satellite services, air traffic and power grids. Improving the reliability, accuracy and numerical performance of space weather modelling tools, including global coronal models, is essential to develop timely and accurate forecasts and to help partly mitigate the space weather threat. Global corona models, however, require accurate boundary conditions, for the formulations of which we have very limited observational data. Unsuitable boundary condition prescriptions may lead to inconsistent features in the solution flow field and spoil the code’s accuracy and performance. Aims. In this paper, we develop an adjustment to the inner boundary condition of the COolfluid COrona uNstrUcTured (COCONUT) global corona model to better capture the dynamics over and around the regions of stronger magnetic fields by constraining the plasma β and the Alfvén speed. Methods. Using data from solar observations and solar atmospheric modelling codes such as Bifrost, we find that the baseline homogeneous boundary condition formulations for pressure and density do not capture the plasma conditions physically accurately. We develop a method to adjust these prescribed pressure and density values by placing constraints on the plasma β and the Alfvén speed that act as proxies. Results. We demonstrate that we can remove inexplicable fast streams from the solution by constraining the maximum Alfvén speed and the minimum plasma β on the boundary surface. We also show that the magnetic topology is not significantly affected by this treatment otherwise. Conclusions. The presented technique shows the potential to ease the modelling of solar maxima, especially removing inexplicable features while, at the same time, not significantly affecting the magnetic field topology around the affected regions.

• Cherry, George; Szydlarski, Mikolaj & Gudiksen, Boris Vilhelm (2024). Implementation of thermal conduction energy transfer models in the Bifrost solar atmosphere MHD code. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 692. doi: 10.1051/0004-6361/202452012. Fulltekst i vitenarkiv Vis sammendrag

  Context. Thermal conductivity provides important contributions to the energy evolution of the upper solar atmosphere, behaving as a non-linear concentration-dependent diffusion equation. Recently, different methods have been offered as best-fit solutions to these problems in specific situations, but their effectiveness and limitations are rarely discussed. Aims. We have rigorously tested the different implementations of solving the conductivity flux, in the massively parallel magnetohydrodynamics code, Bifrost, with the aim of specifying the best scenarios for the use of each method. Methods. We compared the differences and limitations of explicit versus implicit methods, and analyse the convergence of a hyperbolic approximation. Among the tests, we used a newly derived first-order self-similar approximation to compare the efficacy of each method analytically in a 1D pure-thermal test scenario. Results. We find that although the hyperbolic approximation proves the most accurate and the fastest to compute in long-running simulations, there is no optimal method to calculate the mid-term conductivity with both accuracy and efficiency. We also find that the solution of this approximation is sensitive to the initial conditions, and can lead to faster convergence if used correctly. Hyperdiffusivity is particularly useful in aiding the methods to perform optimally. Conclusions. We discuss recommendations for the use of each method within more complex simulations, whilst acknowledging the areas where there are opportunities for new methods to be developed.

• Frogner, Lars & Gudiksen, Boris Vilhelm (2024). Accelerated particle beams in a 3D simulation of the quiet Sun: Effects of advanced beam propagation modelling. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 683. doi: 10.1051/0004-6361/202348457. Fulltekst i vitenarkiv Vis sammendrag

  Context. Charged particles are constantly accelerated to non-thermal energies by the reconnecting magnetic field in the solar atmosphere. Our understanding of the interactions between the accelerated particles and their environment can benefit considerably from three-dimensional atmospheric simulations that account for non-thermal particle beam generation and propagation. In a previous publication, we presented the first results from such a simulation, which considers quiet Sun conditions. However, the original treatment of beam propagation ignores potentially important phenomena such as the magnetic gradient forces associated with a converging or diverging magnetic field. Aims. Here we present a more general beam propagation model incorporating magnetic gradient forces, the return current, acceleration by the ambient electric field, corrected collision rates due to the ambient temperature, and collisions with heavier elements than hydrogen and the free electrons they contribute. Neglecting collisional velocity randomisation makes the model sufficiently lightweight to simulate millions of beams. We investigate how each new physical effect in the model changes the non-thermal energy transport in a realistic three-dimensional atmosphere. Methods. We applied the method of characteristics to the steady-state continuity equation for electron flux to derive ordinary differential equations for the mean evolution of energy, pitch angle, and flux with distance. For each beam, we solved these numerically for a range of initial energies to obtain the evolving flux spectrum, from which we computed the energy deposited into the ambient plasma. Results. Magnetic gradient forces significantly influence the spatial distribution of deposited beam energy. The magnetic field converges strongly with depth in the corona above loop footpoints. This convergence leads to a small coronal peak in deposited energy followed by a heavy dip caused by the onset of magnetic mirroring. Magnetically reflected electrons carry away 5 to 10% of the injected beam energy on average. The remaining electrons are relatively energetic and produce a peak in deposited energy below the transition region a few hundred kilometres deeper than they would in a uniform magnetic field. A diverging magnetic field at the beginning of the trajectory, which is common in the simulation, enhances the subsequent impact of magnetic mirroring. The other new physical effects do not qualitatively alter the picture of non-thermal energy transport for the atmospheric conditions under consideration.

• Bakke, Helle; Frogner, Lars; Voort, Luc Rouppe van der; Gudiksen, Boris Vilhelm & Carlsson, Mats (2023). Accelerated particle beams in a 3D simulation of the quiet Sun: Lower atmospheric spectral diagnostics. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 675. doi: 10.1051/0004-6361/202346765. Fulltekst i vitenarkiv Vis sammendrag

  Context. Nanoflare heating through small-scale magnetic reconnection events is one of the prime candidates to explain heating of the solar corona. However, direct signatures of nanoflares are difficult to determine, and unambiguous observational evidence is still lacking. Numerical models that include accelerated electrons and can reproduce flaring conditions are essential in understanding how low-energetic events act as a heating mechanism of the corona, and how such events are able to produce signatures in the spectral lines that can be detected through observations. Aims. We investigate the effects of accelerated electrons in synthetic spectra from a 3D radiative magnetohydrodynamics simulation to better understand small-scale heating events and their impact on the solar atmosphere. Methods. We synthesised the chromospheric Ca  II and Mg  II lines and the transition region Si  IV resonance lines from a quiet Sun numerical simulation that includes accelerated electrons. We calculated the contribution function to the intensity to better understand how the lines are formed, and what factors are contributing to the detailed shape of the spectral profiles. Results. The synthetic spectra are highly affected by variations in temperature and vertical velocity. Beam heating exceeds conductive heating at the heights where the spectral lines form, indicating that the electrons should contribute to the heating of the lower atmosphere and hence affect the line profiles. However, we find that it is difficult to determine specific signatures from the non-thermal electrons due to the complexity of the atmospheric response to the heating in combination with the relatively low energy output (∼10 21 erg s −1 ). Even so, our results contribute to understanding small-scale heating events in the solar atmosphere, and give further guidance to future observations.

• Bakke, Helle; Carlsson, Mats; Voort, Luc Rouppe van der; Gudiksen, Boris Vilhelm; Polito, V. & Testa, Paola [Vis alle 7 forfattere av denne artikkelen] (2022). Chromospheric emission from nanoflare heating in RADYN simulations. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 659. doi: 10.1051/0004-6361/202142842. Fulltekst i vitenarkiv Vis sammendrag

  Context. Heating signatures from small-scale magnetic reconnection events in the solar atmosphere have proven to be difficult to detect through observations. Numerical models that reproduce flaring conditions are essential in understanding how nanoflares may act as a heating mechanism of the corona. Aims. We study the effects of non-thermal electrons in synthetic spectra from 1D hydrodynamic RADYN simulations of nanoflare heated loops to investigate the diagnostic potential of chromospheric emission from small-scale events. Methods. The Mg  II h and k, Ca  II H and K, Ca  II 854.2 nm, and H α and H β chromospheric lines were synthesised from various RADYN models of coronal loops subject to electron beams of nanoflare energies. The contribution function to the line intensity was computed to better understand how the atmospheric response to the non-thermal electrons affects the formation of spectral lines and the detailed shape of their spectral profiles. Results. The spectral line signatures arising from the electron beams highly depend on the density of the loop and the lower cutoff energy of the electrons. Low-energy (5 keV) electrons deposit their energy in the corona and transition region, producing strong plasma flows that cause both redshifts and blueshifts of the chromospheric spectra. Higher-energy (10 and 15 keV) electrons deposit their energy in the lower transition region and chromosphere, resulting in increased emission from local heating. Our results indicate that effects from small-scale events can be observed with ground-based telescopes, expanding the list of possible diagnostics for the presence and properties of nanoflares.

• Frogner, Lars; Gudiksen, Boris Vilhelm & Bakke, Helle (2020). Accelerated particle beams in a 3D simulation of the quiet Sun. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 643. doi: 10.1051/0004-6361/202038529. Fulltekst i vitenarkiv Vis sammendrag

  Context. Observational and theoretical evidence suggest that beams of accelerated particles are produced in flaring events of all sizes in the solar atmosphere, from X-class flares to nanoflares. Current models of these types of particles in flaring loops assume an isolated 1D atmosphere. Aims. A more realistic environment for modelling accelerated particles can be provided by 3D radiative magnetohydrodynamics codes. Here, we present a simple model for particle acceleration and propagation in the context of a 3D simulation of the quiet solar atmosphere, spanning from the convection zone to the corona. We then examine the additional transport of energy introduced by the particle beams. Methods. The locations of particle acceleration associated with magnetic reconnection were identified by detecting changes in magnetic topology. At each location, the parameters of the accelerated particle distribution were estimated from local conditions. The particle distributions were then propagated along the magnetic field, and the energy deposition due to Coulomb collisions with the ambient plasma was computed. Results. We find that particle beams originate in extended acceleration regions that are distributed across the corona. Upon reaching the transition region, they converge and produce strands of intense heating that penetrate the chromosphere. Within these strands, beam heating consistently dominates conductive heating below the bottom of the transition region. This indicates that particle beams qualitatively alter the energy transport even outside of active regions.

• Kanella, Charalambos & Gudiksen, Boris Vilhelm (2019). Emission of Joule heating events in simulations of the solar corona. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 621. doi: 10.1051/0004-6361/201833634. Fulltekst i vitenarkiv Vis sammendrag

  Context. Nanoscale events in cooperation with steady heating from a slow heating mechanism, such as slow-burning current-sheets, could be able to heat the corona; however, their observational traces are hard to detect via current instrumentation. After we locate heating events in magnetohydrodynamic (MHD) simulations and synthesise observational data, we extract observational signatures of small-scale events. Aims. Our mission is threefold. The first goal is to observe the manifestation of small-scale events via three observational tools: intensity maps of three extreme ultraviolet (EUV) filters in the Atmospheric Imaging Assembly (AIA) instrument with resolution better than that in AIA images, emission measure (EM) analysis, and time-lag maps. The second goal is to identify the reason why we cannot quantify the energy release from observed events. The third goal is to study the differences between the radiation from isolated heating events and that from the whole corona. Methods. We employed a three-dimensional magnetohydrodynamic (3D-MHD) simulation using the Bifrost code. We simulated the atmosphere of a network embedded in the quiet Sun (QS), and we identified 3D heating events in the corona in several time-steps. Then we synthesised the three observational tools for two cases. First, we considered information from the total column mass in the corona, and then we considered only regions that exhibit heating events. Results. We report on the differences between the two regions of investigation, which also consist of the evidence to justify why observers cannot identify small-scale heating events in observations. We found that the combination of multiple heating events at different cooling phases along the line of sight gives the impression of thin elongated threads of events. For this reason, the EM as a function of temperature has a multi-thermal distribution. Both the radiation and the emission measure of the isolated heating events have values at least ten times lower than the signal calculated from the total corona. We also found that heating events move together with diffuse emission from the slow heating mechanism, and for this reason we cannot differentiate between the two. In addition, we find that the frequency of heating events and their intensity affect the EM distribution as a function of temperature. We also find that the filter’s intensity, EM, and time-lag maps of heating events are different to those incorporating information from the total column mass of the corona. However, the two regions have, on average, comparable values, which are slightly smaller than the analytical cooling timescales calculated for an optically thin and radiation-dominated atmosphere.

• Cheung, M. C. M.; Rempel, M.; Chintzoglou, G.; Chen, F.; Testa, Paola & Martinez-Sykora, Juan [Vis alle 14 forfattere av denne artikkelen] (2019). A comprehensive three-dimensional radiative magnetohydrodynamic simulation of a solar flare. Nature Astronomy. 3, s. 160–166. doi: 10.1038/s41550-018-0629-3. Fulltekst i vitenarkiv
• Martinez-Sykora, Juan; Hansteen, Viggo; Gudiksen, Boris Vilhelm; Carlsson, Mats; Pontieu, Bart Walter De & Gošić, Milan (2019). On the Origin of the Magnetic Energy in the Quiet Solar Chromosphere. The Astrophysical Journal (ApJ). ISSN 0004-637X. 878(1). doi: 10.3847/1538-4357/ab1f0b. Fulltekst i vitenarkiv Vis sammendrag

  The presence of magnetic field is crucial in the transport of energy through the solar atmosphere. Recent ground-based and space-borne observations of the quiet Sun have revealed that magnetic field accumulates at photospheric heights, via a local dynamo or from small-scale flux emergence events. However, most of this small-scale magnetic field may not expand into the chromosphere due to the entropy drop with height at the photosphere. Here we present a study that uses a high-resolution 3D radiative MHD simulation of the solar atmosphere with non-gray and non-LTE radiative transfer and thermal conduction along the magnetic field to reveal that (1) the net magnetic flux from the simulated quiet photosphere is not sufficient to maintain a chromospheric magnetic field (on average), (2) processes in the lower chromosphere, in the region dominated by magnetoacoustic shocks, are able to convert kinetic energy into magnetic energy, (3) the magnetic energy in the chromosphere increases linearly in time until the rms of the magnetic field strength saturates at roughly 4–30 G (horizontal average) due to conversion from kinetic energy, (4) and that the magnetic features formed in the chromosphere are localized to this region.

• Kanella, Charalambos & Gudiksen, Boris Vilhelm (2018). Investigating 4D coronal heating events in magnetohydrodynamic simulations. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 617. doi: 10.1051/0004-6361/201732494. Fulltekst i vitenarkiv Vis sammendrag

  Context: One candidate model for heating the solar corona is magnetic reconnection that embodies Ohmic dissipation of current sheets. When numerous small-scale magnetic reconnection events occur, then it is possible to heat the corona; if ever observed, these events would have been the speculated nanoflares. Aims: Because of the limitations of current instrumentation, nanoflares cannot be resolved. But their importance is evaluated via statistics by finding the power-law index of energy distribution. This method is however biased for technical and physical reasons. We aim to overcome limitations imposed by observations and statistical analysis. This way, we identify, and study these small-scale impulsive events. Methods: We employed a three-dimensional magnetohydrodynamic (3D MHD) simulation using the Bifrost code. We also employed a new technique to identify the evolution of 3D joule heating events in the corona. Then, we derived parameters describing the heating events in these locations, studied their geometrical properties and where they occurred with respect to the magnetic field. Results: We report on the identification of heating events. We obtain the distribution of duration, released energy, and volume. We also find weak power-law correlation between these parameters. In addition, we extract information about geometrical parameters of 2D slices of 3D events, and about the evolution of resolved joule heating compared to the total joule heating and magnetic energy in the corona. Furthermore, we identify relations between the location of heating events and the magnetic field. Conclusions: Even though the energy power index is less than 2, when classifying the energy release into three categories with respect to the energy release (pico-, nano-, and micro-events), we find that nano-events release 82% of the resolved energy. This percentage corresponds to an energy flux larger than that needed to heat the corona. Although no direct conclusions can be drawn, it seems that the most popular population among small-scale events is the one that contains nano-scale energetic events that are short lived with small spatial extend. Generally, the locations and size of heating events are affected by the magnitude of the magnetic field. © 2018 ESO

• Zacharias, Pia; Hansteen, Viggo; Leenaarts, Jorrit; Carlsson, Mats & Gudiksen, Boris Vilhelm (2018). Disentangling flows in the solar transition region. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 614. doi: 10.1051/0004-6361/201732055. Fulltekst i vitenarkiv Vis sammendrag

  Context: The measured average velocities in solar and stellar spectral lines formed at transition region temperatures have been difficult to interpret. The dominant redshifts observed in the lower transition region naturally leads to the question of how the upper layers of the solar (and stellar) atmosphere can be maintained. Likewise, no ready explanation has been made for the average blueshifts often found in upper transition region lines. However, realistic three-dimensional radiation magnetohydrodynamics (3D rMHD) models of the solar atmosphere are able to reproduce the observed dominant line shifts and may thus hold the key to resolve these issues. Aims. These new 3D rMHD simulations aim to shed light on how mass flows between the chromosphere and corona and on how the coronal mass is maintained. These simulations give new insights into the coupling of various atmospheric layers and the origin of Doppler shifts in the solar transition region and corona. Methods: The passive tracer particles, so-called corks, allow the tracking of parcels of plasma over time and thus the study of changes in plasma temperature and velocity not only locally, but also in a co-moving frame. By following the trajectories of the corks, we can investigate mass and energy flows and understand the composition of the observed velocities. Results: Our findings show that most of the transition region mass is cooling. The preponderance of transition region redshifts in the model can be explained by the higher percentage of downflowing mass in the lower and middle transition region. The average upflows in the upper transition region can be explained by a combination of both stronger upflows than downflows and a higher percentage of upflowing mass. The most common combination at lower and middle transition region temperatures are corks that are cooling and traveling downward. For these corks, a strong correlation between the pressure gradient along the magnetic field line and the velocity along the magnetic field line has been observed, indicating a formation mechanism that is related to downward propagating pressure disturbances. Corks at upper transition region temperatures are subject to a rather slow and highly variable but continuous heating process. Conclusions: Corks are shown to be an essential tool in 3D rMHD models in order to study mass and energy flows. We have shown that most transition region plasma is cooling after having been heated slowly to upper transition region temperatures several minutes before. Downward propagating pressure disturbances are identified as one of the main mechanisms responsible for the observed redshifts at transition region temperatures. © 2018 ESO

• Bakke, Helle; Frogner, Lars & Gudiksen, Boris Vilhelm (2018). Non-thermal electrons from solar nanoflares In a 3D radiative MHD simulation. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 620. doi: 10.1051/0004-6361/201834129. Fulltekst i vitenarkiv Vis sammendrag

  Context: We introduce a model for including accelerated particles in pure magnetohydrodynamics (MHD) simulations of the solar atmosphere. Aims: We show that the method is viable and produces results that enhance the realism of MHD simulations of the solar atmosphere. Methods: The acceleration of high-energy electrons in solar flares is an accepted fact, but is not included in the most advanced 3D simulations of the solar atmosphere. The effect of the acceleration is not known, and here we introduce a simple method to account for the ability of the accelerated electrons to move energy from the reconnection sites and into the dense transition zone and chromosphere. Results: The method was only run for a short time and with low reconnection energies, but this showed that the reconnection process itself changes, and that there is a clear effect on the observables at the impact sites of the accelerated electrons. Further work will investigate the effect on the reconnection sites and the impact sites in detail.

• Kanella, Charalambos & Gudiksen, Boris Vilhelm (2017). Identification of coronal heating events in 3D simulations. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 603. doi: 10.1051/0004-6361/201730748. Fulltekst i vitenarkiv Vis sammendrag

  Context. The solar coronal heating problem has been an open question in the science community since 1939. One of the proposed models for the transport and release of mechanical energy generated in the sub-photospheric layers and photosphere is the magnetic reconnection model that incorporates Ohmic heating, which releases a part of the energy stored in the magnetic field. In this model many unresolved flaring events occur in the solar corona, releasing enough energy to heat the corona. Aims. The problem with the verification and quantification of this model is that we cannot resolve small scale events due to limitations of the current observational instrumentation. Flaring events have scaling behavior extending from large X-class flares down to the so far unobserved nanoflares. Histograms of observable characteristics of flares show powerlaw behavior for energy release rate, size, and total energy. Depending on the powerlaw index of the energy release, nanoflares might be an important candidate for coronal heating; we seek to find that index. Methods. In this paper we employ a numerical three-dimensional (3D)-magnetohydrodynamic (MHD) simulation produced by the numerical code Bifrost, which enables us to look into smaller structures, and a new technique to identify the 3D heating events at a specific instant. The quantity we explore is the Joule heating, a term calculated directly by the code, which is explicitly correlated with the magnetic reconnection because it depends on the curl of the magnetic field. Results. We are able to identify 4136 events in a volume 24 × 24 × 9.5 Mm3 (i.e., 768 × 786 × 331 grid cells) of a specific snapshot. We find a powerlaw slope of the released energy per second equal to αP = 1.5 ± 0.02, and two powerlaw slopes of the identified volume equal to αV = 1.53 ± 0.03 and αV = 2.53 ± 0.22. The identified energy events do not represent all the released energy, but of the identified events, the total energy of the largest events dominate the energy release. Most of the energy release happens in the lower corona, while heating drops with height. We find that with a specific identification method large events can be resolved into smaller ones, but at the expense of the total identified energy releases. The energy release that cannot be identified as an event favors a low energy release mechanism. Conclusions. This is the first step to quantitatively identify magnetic reconnection sites and measure the energy released by current sheet formation. © ESO, 2017

• Martinez-Sykora, Juan; Pontieu, Bart Walter De; Carlsson, Mats; Hansteen, Viggo; Nobrega-Siverio, Daniel & Gudiksen, Boris Vilhelm (2017). Two-dimensional Radiative Magnetohydrodynamic Simulations of Partial Ionization in the Chromosphere. II. Dynamics and Energetics of the Low Solar Atmosphere. The Astrophysical Journal (ApJ). ISSN 0004-637X. 847(1). doi: 10.3847/1538-4357/aa8866. Fulltekst i vitenarkiv Vis sammendrag

  We investigate the effects of interactions between ions and neutrals on the chromosphere and overlying corona using 2.5D radiative MHD simulations with the Bifrost code. We have extended the code capabilities implementing ion–neutral interaction effects using the generalized Ohm's law, i.e., we include the Hall term and the ambipolar diffusion (Pedersen dissipation) in the induction equation. Our models span from the upper convection zone to the corona, with the photosphere, chromosphere, and transition region partially ionized. Our simulations reveal that the interactions between ionized particles and neutral particles have important consequences for the magnetothermodynamics of these modeled layers: (1) ambipolar diffusion increases the temperature in the chromosphere; (2) sporadically the horizontal magnetic field in the photosphere is diffused into the chromosphere, due to the large ambipolar diffusion; (3) ambipolar diffusion concentrates electrical currents, leading to more violent jets and reconnection processes, resulting in (3a) the formation of longer and faster spicules, (3b) heating of plasma during the spicule evolution, and (3c) decoupling of the plasma and magnetic field in spicules. Our results indicate that ambipolar diffusion is a critical ingredient for understanding the magnetothermodynamic properties in the chromosphere and transition region. The numerical simulations have been made publicly available, similar to previous Bifrost simulations. This will allow the community to study realistic numerical simulations with a wider range of magnetic field configurations and physics modules than previously possible. © 2017. The American Astronomical Society. All rights reserved.

• Carlsson, Mats; Hansteen, Viggo; Gudiksen, Boris Vilhelm; Leenaarts, Jorrit & Pontieu, Bart Walter De (2016). A publicly available simulation of an enhanced network region of the Sun. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 585:A4. doi: 10.1051/0004-6361/201527226. Fulltekst i vitenarkiv Vis sammendrag

  Context. The solar chromosphere is the interface between the solar surface and the solar corona. Modelling of this region is difficult because it represents the transition from optically thick to thin radiation escape, from gas-pressure domination to magnetic-pressure domination, from a neutral to an ionised state, from MHD to plasma physics, and from near-equilibrium (LTE) to non-equilibrium conditions. Aims. Our aim is to provide the community with realistic simulations of the magnetic solar outer atmosphere. This will enable detailed comparison of existing and upcoming observations with synthetic observables from the simulations, thereby elucidating the complex interactions of magnetic fields and plasma that are crucial for our understanding of the dynamic outer atmosphere. Methods. We used the radiation magnetohydrodynamics code Bifrost to perform simulations of a computational volume with a magnetic field topology similar to an enhanced network area on the Sun. Results. The full simulation cubes are made available from the Hinode Science Data Centre Europe. The general properties of the simulation are discussed, and limitations are discussed. Reproduced with permission from Astronomy & Astrophysics, © ESO

• Kato, Yoshiaki; Steiner, Oskar; Hansteen, Viggo; Gudiksen, Boris Vilhelm; Wedemeyer, Sven & Carlsson, Mats (2016). Chromospheric and Coronal Wave Generation in a Magnetic Flux Sheath. The Astrophysical Journal (ApJ). ISSN 0004-637X. 827(1). doi: 10.3847/0004-637X/827/1/7. Fulltekst i vitenarkiv
• Martinez-Sykora, Juan; Pontieu, Bart Walter De; Hansteen, Viggo & Gudiksen, Boris Vilhelm (2016). TIME DEPENDENT NONEQUILIBRIUM IONIZATION of TRANSITION REGION LINES OBSERVED with IRIS. The Astrophysical Journal (ApJ). ISSN 0004-637X. 817(1). doi: 10.3847/0004-637X/817/1/46. Fulltekst i vitenarkiv Vis sammendrag

  The properties of nonstatistical equilibrium ionization of silicon and oxygen ions are analyzed in this work. We focus on five solar targets (quiet Sun; coronal hole; plage; quiescent active region, AR; and flaring AR) as observed with the Interface Region Imaging Spectrograph (IRIS). IRIS is best suited for this work owing to the high cadence (up to 0.5 s), high spatial resolution (up to 0farcs32), and high signal-to-noise ratios for O iv λ1401 and Si iv λ1402. We find that the observed intensity ratio between lines of three times ionized silicon and oxygen ions depends on their total intensity and that this correlation varies depending on the region observed (quiet Sun, coronal holes, plage, or active regions) and on the specific observational objects present (spicules, dynamic loops, jets, microflares, or umbra). In order to interpret the observations, we compare them with synthetic profiles taken from 2D self-consistent radiative MHD simulations of the solar atmosphere, where the statistical equilibrium or nonequilibrium treatment of silicon and oxygen is applied. These synthetic observations show vaguely similar correlations to those in the observations, i.e., between the intensity ratios and their intensities, but only in the nonequilibrium case do we find that (some of) the observations can be reproduced. We conclude that these lines are formed out of statistical equilibrium. We use our time-dependent nonequilibrium ionization simulations to describe the physical mechanisms behind these observed properties. Reproduced with permission from the Astrophysical Journal. © IOP Publishing

• Olluri, Kosovare; Gudiksen, Boris Vilhelm; Hansteen, Viggo & Pontieu, Bart Walter De (2015). Synthesized spectra of optically thin emission lines produced by the Bifrost stellar atmosphere code, including nonequilibrium ionization effects: A study of the intensity, nonthermal line widths, and Doppler shifts. The Astrophysical Journal (ApJ). ISSN 0004-637X. 802(1). doi: 10.1088/0004-637X/802/1/5. Fulltekst i vitenarkiv Vis sammendrag

  In recent years realistic 3D numerical models of the solar atmosphere have become available. The models attempt to recreate the solar atmosphere and mimic observations in the best way, in order to make it possible to couple complicated observations with physical properties such as the temperatures, densities, velocities, and magnetic fields. We here present a study of synthetic spectra created using the Bifrost code in order to assess how well they fit with previously taken solar data. A study of the synthetic intensity, nonthermal line widths, Doppler shifts, and correlations between any two of these three components of the spectra first assuming statistical equilibrium is made, followed by a report on some of the effects nonequilibrium ionization will have on the synthesized spectra. We find that the synthetic intensities compare well with the observations. The synthetic observations depend on the assumed resolution and point-spread function (PSF) of the instrument, and we find a large effect on the results, especially for intensity and nonthermal line width. The Doppler shifts produce the reported persistent redshifts for the transition region (TR) lines and blueshifts for the upper TR and corona lines. The nonthermal line widths reproduce the well-known turnoff point around (2–3) × 105 K, but with much lower values than those observed. The nonthermal line widths tend to increase with decreasing assumed instrumental resolution, also when nonequilibrium ionization is included. Correlations between the nonthermal line width of any two TR line studies as reported by Chae et al. are reproduced, while the correlations of intensity to line width are reproduced only after applying a PSF to the data. Doppler shift correlations reported by Doschek for the TR lines and correlations of Doppler shift to nonthermal line width of the Fe xii 19.5 line reported by Doschek et al. are reproduced. Reproduced with permission from the Astrophysical Journal. © IOP Publishing

• Fletcher, L.; Cargill, P. J.; Antiochos, S. K. & Gudiksen, Boris Vilhelm (2015). Structures in the Outer Solar Atmosphere. Space Science Reviews. ISSN 0038-6308. 188, s. 211–249. doi: 10.1007/s11214-014-0111-1. Fulltekst i vitenarkiv
• Hansteen, Viggo; Carlsson, Mats & Gudiksen, Boris Vilhelm (2015). IRIS observations and 3D `realistic' MHD models of the solar chromosphere. I Cenarro, A. J.; Figueras, F.; Hernández-Monteagudo, C.; Bueno, J. Trujillo & Valdivielso, L. (Red.), Highlights of Spanish Astrophysics VIII, Proceedings of the XI Scientific Meeting of the Spanish Astronomical Society (SEA) held in Teruel, September 8-12, 2014. Sociedad Española de Astronomía. ISSN 9788460687603. s. 19–28. Fulltekst i vitenarkiv
• Hansteen, Viggo; Carlsson, Mats & Gudiksen, Boris Vilhelm (2015). Numerical Modeling of the Solar Chromosphere and Corona: What Has Been Done? What Should Be Done? Astronomical Society of the Pacific Conference Series. ISSN 1050-3390. 498, s. 141–146. Fulltekst i vitenarkiv
• Olluri, Kosovare; Gudiksen, Boris Vilhelm & Hansteen, Viggo (2013). NON-EQUILIBRIUM IONIZATION EFFECTS ON THE DENSITY LINE RATIO DIAGNOSTICS OF O IV. The Astrophysical Journal (ApJ). ISSN 0004-637X. 767(1). doi: 10.1088/0004-637X/767/1/43. Fulltekst i vitenarkiv
• Olluri, Kosovare; Gudiksen, Boris Vilhelm & Hansteen, Viggo (2013). NON-EQUILIBRIUM IONIZATION IN THE BIFROST STELLAR ATMOSPHERE CODE. Astronomical Journal. ISSN 0004-6256. 145(3). doi: 10.1088/0004-6256/145/3/72. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm; Carlsson, Mats; Hayek, Wolfgang; Hansteen, Viggo; Leenaarts, Jorrit & Martinez-Sykora, Juan (2011). The stellar atmosphere simulation code Bifrost. Code description and validation. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 531. doi: 10.1051/0004-6361/201116520. Fulltekst i vitenarkiv
• Collet, R.; Hayek, Wolfgang; Asplund, Martin; Nordlund, Å.; Trampedach, R & Gudiksen, Boris Vilhelm (2011). Three-dimensional surface convection simulations of metal-poor stars. The effect of scattering on the photospheric temperature stratification. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 528. doi: 10.1051/0004-6361/201016151. Fulltekst i vitenarkiv
• Leenaarts, J.; Carlsson, Mats; Hansteen, Viggo & Gudiksen, Boris Vilhelm (2011). On the minimum temperature of the quiet solar chromosphere. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 530. doi: 10.1051/0004-6361/201016392. Fulltekst i vitenarkiv
• Hayek, Wolfgang Simon; Asplund, M; Carlsson, Mats; Trampedach, R; Collet, R. & Gudiksen, Boris Vilhelm [Vis alle 8 forfattere av denne artikkelen] (2010). Radiative transfer with scattering for domain-decomposed 3D MHD simulations of cool stellar atmospheres Numerical methods and application to the quiet, non-magnetic, surface of a solar-type star. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 517. doi: 10.1051/0004-6361/201014210. Fulltekst i vitenarkiv
• Bingert, Sven; Zacharias, P; Peter, Hardi & Gudiksen, Boris Vilhelm (2010). On the nature of coronal loops above the quiet sun network. Advances in Space Research. ISSN 0273-1177. 45(2), s. 310–313. doi: 10.1016/j.asr.2009.08.020. Fulltekst i vitenarkiv
• Carlsson, Mats; Hansteen, Viggo & Gudiksen, Boris Vilhelm (2010). Chromospheric heating and structure as determined from high resolution 3D simulations. MEMORIE DELLA SOCIETÀ ASTRONOMICA ITALIANA JOURNAL OF THE ITALIAN ASTRONOMICAL SOCIETY. ISSN 0037-8720. 81, s. 582–587. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2009). Coronal dynamics and heating theories. Advances in Space Research. ISSN 0273-1177. 43(1), s. 108–112. doi: 10.1016/j.asr.2008.05.012. Fulltekst i vitenarkiv
• Jesus, Leandro Filipe Gomes de & Gudiksen, Boris Vilhelm (2009). PHOTOSPHERIC MOTIONS AND THEIR EFFECTS ON THE CORONA: A NUMERICAL APPROACH. The Astrophysical Journal (ApJ). ISSN 0004-637X. 704(1), s. 705–714. doi: 10.1088/0004-637X/704/1/705. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2008). Coronal Dynamics and Heating Theories. Advances in Space Research. ISSN 0273-1177. 43(1), s. 108–112. doi: 10.1016/j.asr.2008.05.012. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2007). Topological Dissipation and the Solar Corona. I Shibata, K.; Nagata, S. & Sakurai, T. (Red.), New Solar Physics with Solar-B Mission. Astronomical Society of the Pacific. ISSN 9781583812372. s. 269–277. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2007). Heating the solar corona. MEMORIE DELLA SOCIETÀ ASTRONOMICA ITALIANA JOURNAL OF THE ITALIAN ASTRONOMICAL SOCIETY. ISSN 0037-8720. 78(2), s. 293–297. Fulltekst i vitenarkiv
• Hansteen, Viggo; Carlsson, Mats Per-Olof & Gudiksen, Boris Vilhelm (2007). 3D Numerical Models of the Chromosphere, Transition Region, and Corona. I Heinzel, Petr; Dorotovic, Ivan & Rutten, Robert (Red.), The Physics of Chromospheric Plasmas. Astronomical Society of the Pacific. ISSN 9781583812365. s. 107–114. Fulltekst i vitenarkiv
• Peter, H.; Gudiksen, Boris & Nordlund, Å. (2006). Forward modeling of the corona of the sun and solar-like stars: From a three-dimensional magnetohydrodynamic model to synthetic extreme-ultraviolet spectra. The Astrophysical Journal (ApJ). ISSN 0004-637X. 638, s. 1086–1100. Fulltekst i vitenarkiv
• Gudiksen, Boris & Nordlund, Å. (2005). An Ab Initio Approach to the Solar Coronal Heating Problem. The Astrophysical Journal (ApJ). ISSN 0004-637X. 618, s. 1020–1030. Fulltekst i vitenarkiv
• Gudiksen, Boris & Nordlund, Å. (2005). An Ab Initio Approach to Solar Coronal Loops. The Astrophysical Journal (ApJ). ISSN 0004-637X. 618, s. 1031–1038. doi: 10.1086/426064. Fulltekst i vitenarkiv
• Peter, Hardi; Gudiksen, Boris & Nordlund, Å. (2004). Coronal Heating through Braiding of Magnetic Field lines. The Astrophysical Journal (ApJ). ISSN 0004-637X. 617, s. L85–L88. Fulltekst i vitenarkiv

Se alle arbeider i NVA

• Gudiksen, Boris Vilhelm (2026). Large effect of small scales in the solar corona. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm; Haahr, Michael & Øyre, Eilif Sommer (2025). A multi-scale implementation. Fulltekst i vitenarkiv Vis sammendrag

  A description of the work on multi-physics modelling of the solar atmosphere happening at the Rosseland centre for Solar physics, University of Oslo

• Gudiksen, Boris Vilhelm (2025). Braiding in the solar atmosphere. Fulltekst i vitenarkiv Vis sammendrag

  Talk on the braiding of the magnetic field in the solar atmosphere. Details on how it is achieved, what consequences it has and what observable effects that will create. Special attention is given to what we don't know and how that affects our predictions.

• Cherry, George; Gudiksen, Boris Vilhelm & Finley, Adam J. (2024). Detecting waves in non-idealised quiet-sun simulations. Fulltekst i vitenarkiv
• Cherry, George; Gudiksen, Boris Vilhelm & Szydlarski, Mikolaj (2024). Implementation of thermal conduction energy transfer codes in the Bifrost Solar atmosphere MHD solver. Fulltekst i vitenarkiv Vis sammendrag

  Thermal conductivity provides important contributions to the energy evolution of the upper solar atmosphere, behaving as a non-linear concentration-dependent diffusion equation. Computational discretisation limits the operation of solving such terms due to numerical instabilities and other error build-up. Recently, different methods have been offered as best-fit solutions to these problems in specific situations, but their limitations and total range in other scenarios is rarely discussed. Therefore, we rigorously test the different implementations of solving the conductivity flux, in the massively parallel MHD solver code, Bifrost. We compare the differences and limitations of explicit vs. implicit methods, and analyse the convergence of a hyperbolic approximation. Among the tests, we use a newly derived 1st-order self-similar approximation to compare the efficacy of each method analytically in a 1D pure-thermal scenario. The results give guidelines for when to use each method, and the variables that might affect a certain method’s efficiency or accuracy. We discuss the optimisation of parameters in each method, and weaknesses that are not covered suitably by the current implementations.

• Gudiksen, Boris Vilhelm (2023). Supercomputing in solar physics The road to simulating the whole Sun. Fulltekst i vitenarkiv
• Frogner, Lars & Gudiksen, Boris Vilhelm (2023). Accelerated particles in the solar atmosphere. Fulltekst i vitenarkiv
• Frogner, Lars & Gudiksen, Boris Vilhelm (2023). Accelerated particles in the solar atmosphere. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2021). Hvorfor er koronaen så varm? Astronomi. ISSN 0802-7587. s. 21–23. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm; Frogner, Lars; Bakke, Helle & Clemmensen, Frederik (2020). Accelerated particles in the solar atmosphere. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2020). Our active Sun. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm; Frogner, Lars & Bakke, Helle (2020). Accelerated particles in the solar atmosphere. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2018). Nvidia Hackaton - The Bifrost Project. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2018). Solar Physics and HPC. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2017). News coverage of the naming of the Parker solar probe plus on Dansish national TV channel TV2. [TV]. Danish National TV. Fulltekst i vitenarkiv
• Kato, Yoshiaki; Steiner, Oskar; Hansteen, Viggo; Carlsson, Mats & Gudiksen, Boris Vilhelm (2014). Chromospheric and Corona Wave Generation in Flux Tubes. Fulltekst i vitenarkiv
• Carlsson, Mats; Hansteen, Viggo; Pereira, Tiago Mendes Domingos; Leenaarts, Jorrit; Gudiksen, Boris Vilhelm & Pontieu, Bart Walter De (2013). First Comparison between IRIS Data and Numerical Models. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2013). Advanced computer simulations helps understand the active solar atmosphere. META. ISSN 1890-1956. s. 18–21. Fulltekst i vitenarkiv
• Olluri, Kosovare; Gudiksen, Boris Vilhelm & Hansteen, Viggo (2012). non-equilibrium ionization in 3D numerical models. Fulltekst i vitenarkiv
• Olluri, Kosovare; Hansteen, Viggo & Gudiksen, Boris Vilhelm (2011). Non-equilibrium ionization in 3D numerical models. Fulltekst i vitenarkiv
• Olluri, Kosovare; Hansteen, Viggo & Gudiksen, Boris Vilhelm (2010). Non-equilibrium ionization of transition region elements in 3D numerical models. Fulltekst i vitenarkiv
• Carlsson, Mats; Hansteen, Viggo & Gudiksen, Boris Vilhelm (2010). 3D MHD modeling of the solar chromosphere. Fulltekst i vitenarkiv
• Carlsson, Mats; Hansteen, Viggo & Gudiksen, Boris Vilhelm (2009). Chromospheric heating and structure: 3D simulations. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2008). Solen. Fulltekst i vitenarkiv
• Carlsson, Mats; Hansteen, Viggo & Gudiksen, Boris Vilhelm (2008). Dynamic MHD models of the chromosphere and corona. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2008). Vapor. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2007). Coronal Loops. Fulltekst i vitenarkiv
• Hansteen, Viggo & Gudiksen, Boris (2005). 3d Numerical Models of Quiet Sun Coronal Heating. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2005). Connections: Photosphere - Chromosphere - Corona. Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2005). DC-Heating - Is it enough? Fulltekst i vitenarkiv
• Gudiksen, Boris Vilhelm (2005). Topological dissipation and the Solar Corona. Fulltekst i vitenarkiv
• Peter, Hardi; Gudiksen, Boris & Nordlund, Å. (2004). Analysis of Synthetic EUV Spectra from 3d Models of the Corona. Fulltekst i vitenarkiv
• Enerhaug, Elisabeth; Gudiksen, Boris Vilhelm; Carlsson, Mats; Moortel, Ineke de & Howson, Tom (2025). Identifying magnetohydrodynamic wave modes in the solar atmosphere. Universitetet i Oslo. Fulltekst i vitenarkiv
• Haahr, Michael; Gudiksen, Boris Vilhelm & Nordlund, Åke (2025). Multi-Scale Modelling of Magnetic Reconnection in the Solar Corona. A Two-Way Coupled PIC–MHD Model Bridging Microphysics and Global Dynamics in the Exascale Era. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  Solar flares are among the most energetic events in the solar system, powered by magnetic reconnection in the corona where stressed magnetic fields rapidly reorganise, releasing energy as heat, radiation, and accelerated particles. Understanding this multi-scale process is vital for advancing solar and space plasma physics, as well as for forecasting space weather that can disrupt satellites, communications, and power grids on Earth. A central challenge in modelling solar flares lies in the extreme disparity between global and kinetic scales. While magnetohydrodynamic (MHD) models efficiently describe large-scale coronal dynamics, they fail to resolve the microphysics of reconnection and particle acceleration. Fully kinetic methods, such as Particle-in-Cell (PIC) simulations, capture these effects but remain computationally unfeasible at global scales. This thesis presents the development and application of a two-way coupled PIC–MHD model within the DISPATCH framework, enabling localised kinetic resolution embedded within a global MHD domain. The PIC solver, developed and validated within DISPATCH, incorporates a flexible unit-agnostic formulation. To bridge fluid and kinetic scales, we employ the Physical Adjustment of Constants (PAC) method, rescaling key physical constants to enlarge kinetic scales without compromising dimensionless plasma parameters. A key result is the successful two-way coupling by averaging across patch interfaces, enabling stable and self-consistent hybrid simulations. The model is applied to a solar flare scenario involving a 2D fan–spine magnetic topology under solar-like plasma conditions. Simulations show that, even with PAC, the reconnection rate within the PIC region remains comparable to the MHD prediction and consistent with expectations for collisionless reconnection, albeit on the lower end of the range. PAC broadens the current sheet, stabilising it and suppressing secondary plasmoid formation in most cases. However, secondary plasmoids still emerge in the most realistic PAC setup, indicating a partial return of tearing activity. Crucially, the simulations demonstrate sustained acceleration of suprathermal particles, With non-thermal protons dominating the energy budget—an effect rarely explored in solar contexts. Kinetic signatures, notably quadrupolar Hall magnetic fields, extend beyond the PIC region and perturb the global magnetic field topology. These results demonstrate that hybrid PIC–MHD modelling with localised kinetic resolution and physics adjusted by PAC can capture the global dynamics and essential microphysics of solar flare reconnection. The framework developed here enables realistic, multiscale simulations that reveal how kinetic processes influence the release of magnetic energy in the solar corona.

• Cherry, George & Gudiksen, Boris Vilhelm (2025). Quantifying energy transfer in the solar atmosphere. A closer look at the displacement and deposition of energy from the photosphere to the corona through simulations. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  Simulations are a crucial part of solar research, supplementing solar observations and validating theoretical understanding. This dissertation takes a deep dive into the 3D rMHD solar atmosphere model, Bifrost, in a journey from cradle to grave – or more precisely, from the inner mechanisms and theory behind the model to how analysis of simulations can be used to improve real-world problems, such as space weather forecasting. The fundamental aim of this work has been to move us one step closer to understanding the energy transfer mechanisms that heat the corona and drive the solar wind. One of the main contributors to such heating is thought to be the deposition of wave-energy in the corona, although the original photospheric source of such waves is still contested. We aim to use a realistic simulation to study the path which such wave activity may take. Firstly, however, it is important understand the mechanisms at play in the code itself, in order to acknowledge and tackle the artificial limitations of our physical results. We start by refining and analysing the implementation of thermal conduction in Bifrost. Thermal conduction is an important additional term in the upper atmosphere, and as such is required as an additional energy term in the code under certain conditions. Of the three implementations of this term in the solver, we find that the optimal scheme is based on a balance of precision and computational expense. We discuss how the nature of these solutions affects the surrounding environment in the simulation domain, and is therefore an important numerical phenomenon to be aware of when calculating energy transport and deposition. With a clear understanding of the energetic mechanisms in the code, we then introduce a new decomposition method for detecting wave activity in the domain of a realistic simulation. We validate that our method detects the global oscillations of the solar atmosphere, as well as localised activity such as on the boundary of swirling vortices. Furthermore, we find that our method can detect areas of damping and dissipation, which is crucial for understanding the deposition of energy into the corona. With these characteristics in mind, we conclude that our method addresses several limitations in already established methods and offers a convincing alternative for wave decomposition. Finally, we apply our newly derived decomposition method in order to analyse the wave processes in a realistic quiet sun simulation from the photosphere to the low corona. We discuss the vertical propagation of global 3.5 and 5 mHz oscillations, and the energy transferred by these oscillations. We find interesting correlations between the locations of shocks and spicules to these global oscillations, and find also that swirling vortex structures can facilitate the propagation of these waves, if stable enough.

• Haahr, Michael; Gudiksen, Boris Vilhelm & Nordlund, Aake (2025). Multi-Scale Modelling of Magnetic Reconnection in the Solar Corona: A Two-Way Coupled PIC-MHD Model Bridging Microphysics and Global Dynamics in the Exascale Era. Universitetet i Oslo. Fulltekst i vitenarkiv
• Cherry, George & Gudiksen, Boris Vilhelm (2025). Quantifying energy transfer in the solar atmosphere. Universitetet i Oslo. Fulltekst i vitenarkiv
• Frogner, Lars; Gudiksen, Boris Vilhelm & Carlsson, Mats (2024). Modelling accelerated particles in the solar atmosphere. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  This thesis explores the Sun’s dynamic atmosphere, focusing on the role of accelerated particles. These particles are propelled to extremely high speeds during solar flares, which are bright, explosive events in the Sun’s atmosphere. Accelerated particle beams can contain much of the energy released during a flare. Traditionally, particle beams have been simulated individually in simplified, one-dimensional atmospheres. By including accelerated particles in an advanced three-dimensional simulation of the Sun’s atmosphere, we could simulate many particle beams in a more realistic setting. Our simulations demonstrate how the Sun’s intricate magnetic field influences how the beams emerge and evolve. These results show how important it is to consider the presence of many beams in a complex magnetic environment when trying to understand the role of accelerated particles. In addition to providing this new perspective on energy transport in the solar atmosphere, our research lays the groundwork for more accurate models in the future.

• Bakke, Helle; Voort, Luc Rouppe van der & Gudiksen, Boris Vilhelm (2023). Impact of nanoflare heating in the lower solar atmosphere. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  Understanding the mechanisms responsible for heating the solar atmosphere from a few thousand Kelvin in the photosphere to millions of degrees in the corona is a major challenge in solar physics. A number of potential heating mechanisms are continuously studied, and one of the leading candidates is called the nanoflare theory. Nanoflares are small-scale heating events associated with magnetic reconnection, and the heating mechanism is based on the theory that nanoflares occur frequently throughout the solar atmosphere and heat the corona consistently. However, proving this theory has been difficult because the energy released from nanoflares is below the detection threshold of current instrumentation and nanoflares have therefore not been observed yet. So how can we study a phenomenon that is not observable? In this work we utilize numerical simulations in order to investigate the presence and properties of nanoflares in the solar atmosphere. By analysing the atmospheric response to nanoflare heating, it is possible to probe potential heating signatures in simulations to get an idea of what to look for in observations. In our exploration of the nanoflare theory, we have investigated the diagnostic potential of nanoflares by analysing heating signatures in the lower atmosphere and compared our numerical results to an observation of a small-scale coronal heating event.

• Kanella, Charalambos & Gudiksen, Boris Vilhelm (2018). On the Identification of Small-Scaled Heating Events in MHD Simulations of the Solar Corona. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  The identification of small-scale 3-D heating events in numerical simulations brought us a step closer to solve one of the biggest mysteries in astrophysics. The identification of small scale 3-D heating events in the solar atmosphere is an extremely difficult task. Until we succeeded. This brought us a decisive step closer to solve a 70-year-old mystery in astrophysics: “Why the solar corona, the outer layer of the Sun’s atmosphere, is much hotter than the solar surface?” To succeed, we used a powerful code to simulate the solar atmosphere, and an innovative identification method used in medical imaging for multi-dimensional image analysis. We discovered that the largest population of heating events is energetically small events, with small-spatial extent that leave shortly. This finding is very important because it favored an old but famous theory: “Small scale events, but still unobserved due to the limitations of our telescopes, is the main heating mechanism of the solar corona.” Being able to identify 3D heating events allows us to study their geometrical characteristics in all spatial dimensions. For instance, we studied how rounded or how big they could be. This is important because in real observations we are doomed to capture 2-D images, and the process of combining 2-D images to create 3-D ones is always biased. Each event occupies a volume and has a duration. Knowing this information, we compared those parameters with the energy released from each event. This way, we found rough approximations between the parameters that could help observers deduce information by observing one parameter than another. Having identified heating events in numerical simulations allows to use parameters calculated in the simulation, such as temperature and electron density, and therefore synthesize images such those in real observations. But the most interesting aspect is the fact that we synthesized images of regions exhibiting only heating events. This way, we helped observers to understand the reasons they cannot identify small-scale events in real observations and show them how heating events would possibly look like. Even though the results are not conclusive, they point towards the correct direction: Further research and more brilliant ideas and methods are needed to solve the mystery.

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