arXiv subjects

T. Laitinen

Publications and source records attributed to T. Laitinen.

At least 19 recordsLinked to original sources

arXiv2026

Velocity dispersion of Solar Energetic Particles in turbulent heliosphere

Solar Energetic Particles (SEPs) are a signature of solar eruptions, and to link them to acceleration mechanisms many studies investigate their injection time at the Sun, $t_{sun}$. We assess velocity dispersion analysis (VDA), an often-used method to derive $t_{sun}$. We use full-orbit simulations of 1--100 MeV SEP protons in a novel model of the interplanetary magnetic turbulence superposed on a Parker Spiral magnetic field. The turbulence is described analytically as dominant transverse fluctuations that are 2D with respect to the mean field, supplemented with a minor contribution of asymptotically slab turbulence modes. We determine simulated SEP intensities for three turbulence strengths and use VDA to obtain $t_{sun}$ and the apparent path length $s$ of the SEPs, employing an SEP onset threshold to mimic a realistic energetic proton background before the SEP event. We find that turbulence strongly affects $t_{sun}$ and $s$. For weak and moderate turbulence, VDA estimates of $t_{sun}$ are 2-16 minutes after the actual solar injection time, and the path lengths are 0.2-0.3 au longer than the Parker spiral. For strong turbulence, the path lengths are $>5$ au, considerably longer than those typically obtained from SEP observations. We also investigate the effect of energy-dependence of the pre-event proton background, and find that different background spectra result in 5-20-minute difference in VDA injection times, depending on the heliolongitude. We conclude that in many cases VDA-derived injection times include a significant contribution from turbulence and/or the pre-event background and are not an accurate estimate of the acceleration time.

astro-ph.SR↗

arXiv2024

Interplay of large-scale drift and turbulence in the heliospheric propagation of solar energetic particles

The gradient and curvature of the Parker spiral interplanetary magnetic field give rise to curvature and gradient guiding centre drifts on cosmic rays. The plasma turbulence present in the interplanetary space is thought to suppress the drifts, however the extent to which they are reduced is not clear. We investigate the reduction of the drifts using a new analytic model of heliospheric turbulence where the dominant 2D component has both the wave vector and the magnetic field vector normal to the Parker spiral, thus fulfilling the main criterion of 2D turbulence. We use full-orbit test particle simulations of energetic protons in the modelled interplanetary turbulence, and analyse the mean drift velocity of the particles in heliolatitude. We release energetic proton populations of 10, 100 and 1000~MeV close to Sun and introduce a new method to assess their drift. We compare the drift in the turbulent heliosphere to drift in a configuration without turbulence, and to theoretical estimates of drift reduction. We find that drifts are reduced by a factor 0.2-0.9 of that expected for the heliospheric configuration without turbulence. This corresponds to a much less efficient suppression than what is predicted by theoretical estimates, particularly at low proton energies. We conclude that guiding centre drifts are a significant factor for the evolution of cosmic ray intensities in the heliosphere including the propagation of solar energetic particles in the inner heliosphere.

astro-ph.SR↗

arXiv2024

Detection asymmetry in solar energetic particle events

Context. Solar energetic particles (SEPs) are detected in interplanetary space in association with solar flares and coronal mass ejections (CMEs). The magnetic connection between the observing spacecraft and the solar active region (AR) source of the event is a key parameter in determining whether SEPs are observed and the particle event's properties. Aims. We investigate whether an east-west asymmetry in the detection of SEP events is present in observations and discuss its possible link to corotation of magnetic flux tubes with the Sun. Methods. We used a published dataset of 239 CMEs recorded between 2006 and 2017 and having source regions both on the Sun's front and far sides as seen from Earth. We produced distributions of occurrence of in-situ SEP intensity enhancements associated with the CME events, versus \Delta\phi, the longitudinal separation between source active region and spacecraft magnetic footpoint based on the nominal Parker spiral. We focused on protons of energy >10 MeV measured by STEREO A, STEREO B and GOES at 1 au. We also considered occurrences of 71-112 keV electron events detected by MESSENGER between 0.31 and 0.47 au. Results. We find an east-west asymmetry with respect to the best magnetic connection (\Delta\phi=0) in the detection of >10 MeV proton events and of 71-112 keV electron events. For protons, observers for which the source AR is on the east side of the spacecraft footpoint and not well connected (-180<\Delta\phi<-40) are 93% more likely to detect an SEP event compared to observers with +40<\Delta\phi<+180. The asymmetry may be a signature of corotation of magnetic flux tubes with the Sun, since for events with \Delta\phi<0 corotation sweeps particle-filled flux tubes towards the observing spacecraft, while for \Delta\phi>0 it takes them away from it. Alternatively it may be related to asymmetric acceleration or propagation effects.

astro-ph.SR↗

arXiv2024

Multi-spacecraft observations of the decay phase of solar energetic particle events

Context: Parameters of solar energetic particle (SEP) event profiles such as the onset time and peak time have been researched extensively to obtain information on acceleration and transport of SEPs. Corotation of particle-filled magnetic flux tubes with the Sun is generally thought to play a minor role in determining intensity profiles. However recent simulations have suggested that corotation has an effect on SEP decay phases, depending on the location of the observer with respect to the active region (AR) associated with the event. Aims: We aim to determine whether signatures of corotation are present in observations of decay phases of SEP events and study how the parameters of the decay phase depend on the properties of the flares and coronal mass ejections (CMEs) associated with the events. Methods: We analyse multi-spacecraft observations of SEP intensity profiles from 11 events between 2020 and 2022, using data from SOLO, PSP, STEREO-A, and SOHO. We determine the decay time constant, \tau in 3 energy channels; electrons ~ 1 MeV, protons ~ 25 MeV, and protons ~ 60 MeV. We study the dependence of \tau on the longitudinal separation, \Delta \phi, between source active region (AR) and the spacecraft magnetic footpoint on the Sun. Results: Within individual events there is a tendency for the decay time constant to decrease with increasing $\Delta \phi$, in agreement with test particle simulations. The intensity of the associated flare and speed of the associated CMEs have a strong effect on the measured $\tau$ values and are likely the cause of the observed large inter-event variability. Conclusions: We conclude that corotation has a significant effect on the decay phase of a solar energetic particle event and should be included in future simulations and interpretations of these events.

astro-ph.SR↗

arXiv2024

Solar energetic particles injected inside and outside a magnetic cloud: The widespread solar energetic particle event on 2022 January 20

Context. On 2022 January 20, the Energetic Particle Detector (EPD) on board Solar Orbiter measured a solar energetic particle (SEP) event showing unusual first arriving particles from the anti-Sun direction. Near-Earth spacecraft separated 17{\deg} in longitude to the west from Solar Orbiter measured classic antisunward-directed fluxes. STEREO-A and MAVEN, separated 18{\deg} to the east and 143{\deg} to the west from Solar Orbiter respectively, also observed the event, suggesting that particles spread over at least 160{\deg} in the heliosphere. Results. Solar Orbiter was embedded in a MC erupting on 16 January from the same active region as that related to the SEP event on 20 January. The SEP event is related to a M5.5 flare and a fast CME-driven shock of 1433 km/s, which injected particles within and outside the MC. Taken together, the hard SEP spectra, the presence of a Type II radio burst, and the co-temporal Type III radio burst being observed from 80 MHz that appears to emanate from the Type II burst, suggest that the shock is likely the main accelerator of the particles. Conclusions. Our detailed analysis of the SEP event strongly suggests that the energetic particles are mainly accelerated by a CME-driven shock and are injected into and outside of a previous MC present in the heliosphere at the time of the particle onset. The sunward-propagating SEPs measured by Solar Orbiter are produced by the injection of particles along the longer (western) leg of the MC still connected to the Sun at the time of the release of the particles. The determined electron propagation path length inside the MC is around 30% longer than the estimated length of the loop leg of the MC itself (based on the graduated cylindrical shell model), which is consistent with the low number of field line rotations.

astro-ph.SR↗

arXiv2023

Solar Energetic Particle event onsets at different heliolongitudes: The effect of turbulence in Parker Spiral Geometry

Solar energetic particles (SEPs), accelerated during solar eruptions, are observed to rapidly reach a wide heliolongitudinal range in the interplanetary space. To access these locations, the SEPs must have either been accelerated at a wide particle source, or propagated across the mean Parker spiral magnetic field. We study the propagation of SEPs in a new model of heliospheric turbulence which takes the spiral geometry of the average magnetic field into account, to evaluate how this improved description affects the SEP path lengths and the overall evolution of SEP intensities at 1~au. We use full-orbit test particle simulations of 100-MeV protons in a turbulence model dominated by modes that are transverse and 2D with respect to the Parker spiral. We find that the SEPs spread along the meandering field lines to arrive at a 60$^\circ$ heliolongitudinal range at 1~au within an hour of their injection at the Sun, consistent with the extent of the meandering field lines. The SEP onset times are asymmetric with respect to the location connected to the source along the Parker spiral, with westward locations seeing earlier arrival and higher peak intensity. The inferred path length of the first-arriving SEPs is 1.5-1.7~au, 30-50\% longer than the Parker spiral, and 20\% longer than the length of the meandering field lines. Subsequently, the SEP distribution broadens, consistent with diffusive spreading of SEPs across the field lines. Our results indicate that SEPs can propagate rapidly across the mean Parker Spiral field to arrive at wide range of longitudes, even without a wide particle source. The modelled SEP onset times, the peak intensity and subsequent heliolongitudinal evolution replicate several observed SEP event features. Further studies are be required to investigate the relative importance of interplanetary transport and source size in different turbulence environments.

astro-ph.SR↗

arXiv2022

An analytical model of turbulence in Parker spiral geometry and associated magnetic field line lengths

Understanding the magnetic connections from the Sun to interplanetary space is crucial for linking in situ particle observations with the solar source regions of the particles. A simple connection along the large-scale Parker spiral magnetic field is made complex by the turbulent random-walk of field lines. In this paper, we present the first analytical model of heliospheric magnetic fields where the dominant 2D component of the turbulence is transverse to the Parker spiral. The 2D wave field is supplemented with a minor wave field component that has asymptotically slab geometry at small and large heliocentric distances. We show that turbulence spreads field lines from a small source region at the Sun to a 60$^\circ$ heliolongitudinal and -latitudinal range at 1~au, with standard deviation of the angular spread of the field lines $14^\circ$. Small source regions map to an intermittent range of longitudes and latitudes at 1~au, consistent with dropouts in solar energetic particle intensities. The lengths of the field lines are significantly extended from the nominal Parker spiral length of 1.17~au up to 1.6~au, with field lines from sources at and behind the west limb considerably longer than those closer to the solar disk centre. We discuss the implications of our findings on understanding charged particle propagation, and the importance of understanding the turbulence properties close to the Sun.

astro-ph.SR↗

arXiv2020

3D propagation of relativistic solar protons through interplanetary space

Context. Solar Energetic Particles (SEPs) with energy in the GeV range can propagate to Earth from their acceleration region near the Sun and produce Ground Level Enhancements (GLEs). The traditional approach to interpreting and modelling GLE observations assumes particle propagation only parallel to the magnetic field lines of interplanetary space, i.e. it is spatially 1D. Recent measurements by PAMELA have characterised SEP properties at 1 AU for the ~100 MeV-1 GeV range at high spectral resolution. Aims. We model the transport of GLE-energy solar protons through the Interplanetary Magnetic Field (IMF) using a 3D approach, to assess the effect of the Heliospheric Current Sheet (HCS) and drifts associated to the gradient and curvature of the Parker spiral. The latter are influenced by the IMF polarity. We derive 1 AU observables and compare the simulation results with data from PAMELA. Methods. We use a 3D test particle model including a HCS. Monoenergetic populations are studied first to obtain a qualitative picture of propagation patterns and numbers of crossings of the 1 AU sphere. Simulations for power law injection are used to derive intensity profiles and fluence spectra at 1 AU. A simulation for a specific event, GLE 71, is used to compare with PAMELA data. Results. Spatial patterns of 1 AU crossings and the average number of crossings are strongly influenced by 3D effects, with significant differences between periods of A+ and A- polarities. The decay time constant of 1 AU intensity profiles varies depending on the polarity and position of the observer, and it is not a simple function of the mean free path as in 1D models. Energy dependent leakage from the injection flux tube is particularly important for GLE energy particles, in many cases resulting in a roll-over in the fluence spectrum.

astro-ph.SR↗

arXiv2019

From Sun to interplanetary space: What is the pathlength of Solar Energetic Particles?

Solar energetic particles (SEPs), accelerated during solar eruptions, propagate in turbulent solar wind before being observed with in situ instruments. In order to interpret their origin through comparison with remote-sensing observations of the solar eruption, we thus must deconvolve the transport effects due to the turbulent magnetic fields from the SEP observations. Recent research suggests that the SEP propagation is guided by the turbulent meandering of the magnetic fieldlines across the mean magnetic field. However, the lengthening of the distance the SEPs travel, due to the fieldline meandering, has so far not been included in SEP event analysis. This omission can cause significant errors in estimation of the release times of SEPs at the Sun. We investigate the distance travelled by the SEPs by considering them to propagate along fieldlines that meander around closed magnetic islands that are inherent in turbulent plasma. We introduce a fieldline randow walk model which takes into account the physical scales associated to the magnetic islands. Our method remedies the problem of the diffusion equation resulting in unrealistically short pathlengths, and the fractal dependence of the pathlength of random walk on the length of the random-walk step. We find that the pathlength from the Sun to 1 au can be below the nominal Parker spiral length for SEP events taking place at solar longitudes 45E to 60W, whereas the western and behind-the-limb particles can experience pathlengths longer than 2 au due to fieldline meandering.

astro-ph.SR↗

arXiv2018

Forecasting Solar Energetic Particle Fluence with Multi-Spacecraft Observations

Forecasting Solar Energetic Particle (SEP) fluence, as integrated over an SEP event, is an important element when estimating the effect of solar eruptions on humans and technology in space. Current real-time estimates are based on SEP measurements at a single location in space. However, the interplanetary magnetic field corotates with the Sun approximately 13$^\circ$ each day with respect to Earth, thus in 4 days a near-Earth spacecraft will have changed their connection about 60$^\circ$ from the original SEP source. We estimate the effect of the corotation on particle fluence using a simple particle transport model, and show that ignoring corotation can cause up to an order of magnitude error in fluence estimations, depending on the interplanetary particle transport conditions. We compare the model predictions with STEREO observations of SEP events.

physics.space-ph↗

arXiv2018

The effect of turbulence strength on meandering field lines and Solar Energetic Particle event extents

Insights into the processes of Solar Energetic Particle (SEP) propagation are essential for understanding how solar eruptions affect the radiation environment of near-Earth space. SEP propagation is influenced by turbulent magnetic fields in the solar wind, resulting in stochastic transport of SEPs to Earth. Multi-spacecraft observations suggest that the cross-field propagation shapes the SEP fluxes at Earth strongly. However, modelling SEP cross-field transport as spatial diffusion has been shown to be insufficient without use of unrealistically large cross-field diffusion coefficients. Recent work has shown that the early-time propagation of energetic particles across the mean field direction in turbulent fields is not diffusive, as the particles propagating along meandering field lines. This early-time transport mode results in fast access of the particles across the mean field direction, in agreement with the SEP observations. In this work, we demonstrate the significance of turbulence strength on evolution of the SEP radiation environment near Earth. We calculate the transport parameters with a turbulence transport model, parametrised by the SEP parallel scattering mean free path at 1~AU, $λ_{\parallel}^{*}$, and show that the parallel and cross-field transport are connected, with conditions resulting in slow parallel transport corresponding to wider events. We find a scaling $σ_{ϕ,\, \mathrm{max}}\propto (1/λ_{\parallel}^{*})^{1/4}$ for the Gaussian fitting of the longitudinal distribution of maximum intensities. The longitudes with highest intensities are shifted towards the west for strong scattering conditions. Our results emphasise the importance of understanding both the SEP transport and the interplanetary turbulence conditions for modelling and predicting the SEP radiation environment at Earth.

astro-ph.SR↗

arXiv2017

Early propagation of energetic particles across the mean field in turbulent plasmas

Propagation of energetic particles across the mean field direction in turbulent magnetic fields is often described as spatial diffusion. Recently, it has been suggested that initially the particles propagate systematically along meandering field lines, and only later reach the time-asymptotic diffusive cross-field propagation. In this paper, we analyse cross-field propagation of 1--100 MeV protons in composite 2D-slab turbulence superposed on a constant background magnetic field, using full-orbit particle simulations, to study the non-diffusive phase of particle propagation with a wide range of turbulence parameters. We show that the early-time non-diffusive propagation of the particles is consistent with particle propagation along turbulently meandering field lines. This results in a wide cross-field extent of the particles already at the initial arrival of particles to a given distance along the mean field direction, unlike when using spatial diffusion particle transport models. The cross-field extent of the particle distribution remains constant for up to tens of hours in turbulence environment consistent with the inner heliosphere during solar energetic particle events. Subsequently, the particles escape from their initial meandering field lines, and the particle propagation across the mean field reaches time-asymptotic diffusion. Our analysis shows that in order to understand solar energetic particle event origins, particle transport modelling must include non-diffusive particle propagation along meandering field lines.

physics.space-ph↗

arXiv2017

Experimental overview on Future Solar and Heliospheric research

Solar and heliospheric cosmic rays provide a unique perspective in cosmic ray research: we can observe not only the particles, but also the properties of the plasmas in which the they are accelerated and propagate, using in situ and high-resolution remote sensing instruments. The heliospheric cosmic ray observations typically require space missions, which face stern competition against planetary and astrophysics missions, and it can take up to decades from the initial concept proposal until the actual observing of the cosmic rays can commence. Therefore it is important to have continuity in the cosmic ray mission timeline. In this overview, we review the current status and the future outlook in the experimental solar and heliospheric research. We find that the current status of the available cosmic ray observations is good, but that many of the spacecraft are near the end of their feasible mission life. We describe the three missions currently being prepared for launch, and discuss the future outlook of the solar and heliospheric cosmic ray missions.

physics.space-ph↗

arXiv2016

Energetic particle transport across the mean magnetic field: before diffusion

Current particle transport models describe the propagation of charged particles across the mean field direction in turbulent plasmas as diffusion. However, recent studies suggest that at short time-scales, such as soon after solar energetic particle (SEP) injection, particles remain on turbulently meandering field lines, which results in non-diffusive initial propagation across the mean magnetic field. In this work, we use a new technique to investigate how the particles are displaced from their original field lines, and quantify the parameters of the transition from field-aligned particle propagation along meandering field lines to particle diffusion across the mean magnetic field. We show that the initial decoupling of the particles from the field lines is slow, and particles remain within a Larmor radius from their initial meandering field lines for tens to hundreds of Larmor periods, for 0.1-10 MeV protons in turbulence conditions typical of the solar wind at 1~AU. Subsequently, particles decouple from their initial field lines and after hundreds to thousands of Larmor periods reach time-asymptotic diffusive behaviour consistent with particle diffusion across the mean field caused by the meandering of the field lines. We show that the typical duration of the pre-diffusive phase, hours to tens of hours for 10 MeV protons in 1~AU solar wind turbulence conditions, is significant for SEP propagation to 1~AU and must be taken into account when modelling SEP propagation in the interplanetary space.

astro-ph.SR↗

arXiv2016

Time dependence of Fe/O ratio within a 3D Solar Energetic Particle propagation model including drift

Context. The intensity profiles of iron and oxygen in Solar Energetic Particle (SEP) events often display differences that result in a decreasing Fe/O ratio over time. The physical mechanisms behind this behaviour are not fully understood, but these observational signatures provide important tests of physical modelling efforts. Aims. In this paper we study the propagation of iron and oxygen SEP ions using a 3D model of propagation which includes the effect of guiding centre drift in a Parker spiral magnetic field. We derive time intensity profiles for a variety of observer locations and study the temporal evolution of the Fe/O ratio. Methods. We use a 3D full orbit test particle model which includes scattering. The configuration of the interplanetary magnetic field is a unipolar Parker spiral. Particles are released instantaneously from a compact region at 2 solar radii and allowed to propagate in 3D. Results. Both Fe and O experience significant transport across the magnetic field due to gradient and curvature drifts. We find that Fe ions drift more than O ions due to their larger mass-to-charge ratio, so that an observer that is not magnetically well connected to the source region will observe Fe arriving before O, for particles within the same range in energy per nucleon. As a result, for the majority of observer locations, the Fe/O ratio displays a decrease in time. Conclusions. We conclude that propagation effects associated with drifts produce a decay over time of the Fe/O ratio, qualitatively reproducing that observed in SEP event profiles.

astro-ph.SR↗

arXiv2016

Solar energetic particle access to distant longitudes through turbulent field-line meandering

Context. Current solar energetic particle (SEP) propagation models describe the effects of interplanetary plasma turbulence on SEPs as diffusion, using a Fokker-Planck (FP) equation. However, FP models cannot explain the observed fast access of SEPs across the average magnetic field to regions that are widely separated in longitude within the heliosphere without using unrealistically strong cross-field diffusion. Aims. We study whether the recently suggested early non-diffusive phase of SEP propagation can explain the wide SEP events with realistic particle transport parameters. Methods. We used a novel model that accounts for the SEP propagation along field lines that meander as a result of plasma turbulence. Such a non-diffusive propagation mode has been shown to dominate the SEP cross-field propagation early in the SEP event history. We compare the new model to the traditional approach, and to SEP observations. Results. Using the new model, we reproduce the observed longitudinal extent of SEP peak fluxes that are characterised by a Gaussian profile with $σ=30-50^\circ$, while current diffusion theory can only explain extents of 11$^\circ$ with realistic diffusion coefficients. Our model also reproduces the timing of SEP arrival at distant longitudes, which cannot be explained using the diffusion model. Conclusions. The early onset of SEPs over a wide range of longitudes can be understood as a result of the effects of magnetic field-line random walk in the interplanetary medium and requires an SEP transport model that properly describes the non-diffusive early phase of SEP cross-field propagation.

astro-ph.SR↗

arXiv2015

Drift-induced deceleration of Solar Energetic Particles

We investigate the deceleration of Solar Energetic Particles (SEPs) during their propagation from the Sun through interplanetary space, in the presence of weak to strong scattering in a Parker spiral configuration, using relativistic full orbit test particle simulations. The calculations retain all three spatial variables describing particles' trajectories, allowing to model any transport across the magnetic field. Large energy change is shown to occur for protons, due to the combined effect of standard adiabatic deceleration and a significant contribution from particle drift in the direction opposite to that of the solar wind electric field. The latter drift-induced deceleration is found to have a stronger effect for SEP energies than for galactic cosmic rays. The kinetic energy of protons injected at 1 MeV is found to be reduced by between 35 and 90% after four days, and for protons injected at 100 MeV by between 20 and 55%. The overall degree of deceleration is a weak function of the scattering mean free path, showing that, although adiabatic deceleration plays a role, a large contribution is due to particle drift. Current SEP transport models are found to account for drift-induced deceleration in an approximate way and their accuracy will need to be assessed in future work.

astro-ph.SR↗

arXiv2015

SPARX: a modelling system for Solar Energetic Particle Radiation Space Weather forecasting

The capability to predict the parameters of an SEP event such as its onset, peak flux, and duration is critical to assessing any potential space weather impact. We present a new flexible modelling system simulating the propagation of Solar Energetic Particles (SEPs) from locations near the Sun to any given location in the heliosphere to forecast the SEP flux profiles. SPARX uses an innovative methodology, that allows implementation within an operational framework, to overcome the time constraints of test particle modelling of SEP profiles, allowing the production of near real time SEP nowcasts and forecasts, when paired with appropriate near real time triggers. SPARX has the capability to produce SEP forecasts within minutes of being triggered by observations of a solar eruptive event. The model is based on the test particle approach and is spatially 3D, thus allowing for the possibility of transport in the direction perpendicular to the magnetic field. The model naturally includes the effects of perpendicular propagation due to drifts and drift-induced deceleration. The modelling framework and the way in which parameters of relevance for Space Weather forecasting are obtained are described. The first results from the modelling system are presented. These results demonstrate that corotation and drift of SEP streams play an important role in shaping SEP flux profiles.

astro-ph.SR↗