Timo Laitinen | University of Central Lancashire (original) (raw)

Papers by Timo Laitinen

Particle acceleration by coronal shock waves is studied. Efficient acceleration requires particle... more Particle acceleration by coronal shock waves is studied. Efficient acceleration requires particles to interact with the shock many times before substantial energy gains can be expected. In diffusive shock acceleration models, particles scatter off low-frequency plasma waves or turbulence around the shock, which results in particle trajectories crossing the shock front many times. We study an alternative to the standard diffusive shock acceleration model: an oblique coronal shock wave propagating toward the solar surface on open field lines without upstream turbulence but with a large magnetic mirror ratio between the footpoint and the shock location. Such shocks can be either freely propagating or driven shock waves, and they would be related to the initial phases of particle events, when the erupting plasma has scales of the order of a solar radius. Our simulations reveal that the modeled shocks are able to efficiently accelerate ions up to energies from a few to a few tens of MeVs per nucleon, depending on the parameters of the shock wave and of the underlying magnetic field. These energies can be further increased by allowing particle scattering off upstream turbulence.

Astron Astrophys, 2003

Alfvén wave transport in the solar wind, including non-linear spectral energy transfer, is studie... more Alfvén wave transport in the solar wind, including non-linear spectral energy transfer, is studied. We present numerical solutions of wave transport using a diffusive flux function previously introduced for spectral energy transfer, and compare it with the analytical solution obtained for a convective flux function. The two models of cascading produce very similar behavior of a power spectrum initially of 1/f-form at the solar surface, provided that the cascading constants are tuned to produce the same spectral flux in the inertial range. We present an analytical expression for the power spectrum of the diffusively-cascading Alfvén waves in the solar wind derived from a solution of the wave transport equation and show that it compares well with the exact solutions. Our expression enables (semi) analytical evaluation of the cyclotron heating rate, the wave pressure gradient, and the energetic-particle mean free path related to the Alfvén waves in the corona and solar wind.

The Astrophysical Journal, Jul 5, 2013

Drifts are known to play a role in galactic cosmic ray transport within the heliosphere and are a... more Drifts are known to play a role in galactic cosmic ray transport within the heliosphere and are a standard component of cosmic ray propagation models. However, the current paradigm of Solar Energetic Particle (SEP) propagation holds the effects of drifts to be negligible, and they are not accounted for in most current SEP modelling efforts. We present full-orbit test particle simulations of SEP propagation in a Parker spiral interplanetary magnetic field which demonstrate that high energy particle drifts cause significant asymmetric propagation perpendicular to the interplanetary magnetic field. Thus in many cases the assumption of field aligned propagation of SEPs may not be valid. We show that SEP drifts have dependencies on energy, heliographic latitude, and charge to mass ratio, that are capable of transporting energetic particles perpendicular to the field over significant distances within interplanetary space, e.g. protons of initial energy 100 MeV propagate distances across the field on the order of 1 AU, over timescales typical of a gradual SEP event. Our results demonstrate the need for current models of SEP events to include the effects of particle drift. We show that the drift is considerably stronger for heavy ion SEPs due to their larger mass to charge ratio. This paradigm shift has important consequences for the modelling of SEP events and is crucial to the understanding and interpretation of in-situ observations.

Astronomische Nachrichten Supplement, Jul 1, 2003

The Astrophysical Journal

We investigate the deceleration of Solar Energetic Particles (SEPs) during their propagation from... more 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.

Wave damping and cascading processes have been found to be important for the heating and accelera... more Wave damping and cascading processes have been found to be important for the heating and acceleration of the solar wind. However, it remains a difficult task to extract details of these processes from observations of the thermal plasma only. The wave power required for efficient heating and acceleration of the solar wind also affects the acceleration and transport of solar energetic particles. Thus, their observation could provide valuable clues for the actual evolution of the wave power close to the coronal base and, in turn, give constraints for solar wind modeling. Pursuing this idea, we have developed a steady‐state two‐fluid model for the wave heating and acceleration of the solar wind. The dissipation frequency determining the heating is obtained from a cyclotron damping rate that depends on the plasma beta and, thus, differs from the usual assumption, a fixed fraction of the ion cyclotron frequency. We present first results obtained with the two‐fluid code and, in particular,...

We have developed a steady-state two-fluid description of the radial solar wind expan- sion close... more We have developed a steady-state two-fluid description of the radial solar wind expan- sion close to the coronal base. The model is formulated self-consistently with respect to the radial evolution of turbulence by supplementing the moment equations of the plasma with an equation describing the evolution of the (cyclotron) wave power due to damping and cascading processes as originally suggested by Tu et al. (1984). The resulting acceleration and heating rates of the thermal plasma are determined by as- suming a dissipation frequency that, in difference to earlier models, exhibits a thermal dependence on the plasma. We will present first results and compare them with wind profiles obtained previously by other authors. We will then discuss the implications of the improved formulation of the dissipation frequency and of the wave cascading.

The research of turbulence has benefited from recent MHD simulation studies. These simulations ar... more The research of turbulence has benefited from recent MHD simulation studies. These simulations are typically limited to small spatial domains by computational requirements, and are not easily applicable to all fields of research, such as studies on solar wind heating and energetic particle transport. A different approach, employing spectral transfer of turbulence energy by diffusive or convective cascading, is often used to describe the evolution of the turbulence in large-scale systems. The descriptions of the turbulence, used in this approach, however, are often not fully consistent, and typically contain some ad-hoc form for the cascade strength, which is related to the power in inward and outward propagating waves. We study the evolution of turbulence by employing a two-equation model for diffusive cascading. For the source of inward waves, we formulate a simple approximation for the reflection of the waves from large-scale gradients. The implications of the resulting turbulence...

Some recent modeling efforts to understand the transport and acceleration of solar energetic part... more Some recent modeling efforts to understand the transport and acceleration of solar energetic particles (SEPs) in corona and interplanetary medium are reviewed. We will present results from analytical calculations and from particle simulations employing the Monte Carlo method. Our modeling efforts concentrate on ions. Specifically, we have considered (i) velocity dispersion analysis of particles observed during the initial rise of an SEP event as obtained from particle transport simulations; (ii) particle acceleration in coronal shock waves during the initial phases of an SEP event; and (iii) the role of the generation of turbulence by the accelerated particles themselves. Ion acceleration by coronal shocks is shown to be consistent with the typical observational results on SEP event onsets. This holds true for both small gradual SEP events, which can be treated under the test-particle approximation, and for the largest SEP events, in which the accelerated particles significantly enh...

The onset of a Solar Energetic Particle (SEP) event has been traditionally determined by using th... more The onset of a Solar Energetic Particle (SEP) event has been traditionally determined by using the velocity dispersion analysis (VDA). In this method the injection of the first particles at the Sun is determined by fitting the solar injection time and the particles' path length to match the observed event onset at 1 AU for several SEP energy channels. Recently, this approach has been questioned by simulation studies, which take into account the effect of the interplanetary scattering on the arrival time of the first particles to 1 AU. Particularly when the pre-event particle background is strong, significant errors for the onset can be expected, up to tens of minutes for protons of energies 1-100 MeV. In this work, we continue to study the effect of the pre-event background to the SEP event onset at 1 AU, and its consequences to the determination of the SEP event evolution at the Sun. We study the use of the steepness of the event onset, as observed at 1 AU, as a parameter for t...

The capability to predict the parameters of an SEP event such as its onset, peak flux, and durati... more 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 operational modelling system simulating the propagation of Solar Energetic Particles (SEPs) from locations near the Sun to any given location in the heliosphere. 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 are obtained within a forecasting context are described. The first results from the modelling system are presented. These results demonstrate that corotation and drift of SEP streams play an essential role in shaping SEP flux profiles.

AIP Conference Proceedings, 2010

ABSTRACT The onset of a Solar Energetic Particle (SEP) event has been traditionally determined by... more ABSTRACT The onset of a Solar Energetic Particle (SEP) event has been traditionally determined by using the velocity dispersion analysis (VDA), where the event onset at the Sun is determined by fitting the solar onset time and the particles' path length to match the observed event onset at 1 AU for several SEP energy channels. This approach has been studied by using energetic particle simulations, in order to understand the effect of the interplanetary scattering on the arrival time of the first particles to 1 AU. In these studies, the SEP event onset at 1 AU has been defined as the time when the intensities reach certain percentage of the maximum of the event. This is often not feasible for practical work, as a real event may be complex in its structure, and the pre-event background may mask the SEP onset to differing degrees in different energies. In order to estimate the usability of the VDA method, we study the simulated SEP onset on a pre-existing particle background by varying the pre-event background level, the difference of the pre-event background and the simulated event maximum spectral indices, the interplanetary mean free path and the injection profile. As in the previous studies, we find that large path length variation can be explained as an artifact resulting from the use of the VDA method. More importantly, the error in the obtained solar onset time depends strongly on the properties of the pre-event background.

Space Weather: the Space Radiation Environment, 2012

ABSTRACT The results of full-orbit test-particle simulations of SEPs propagating through an IMF w... more ABSTRACT The results of full-orbit test-particle simulations of SEPs propagating through an IMF which exhibits large-scale fluctuations are presented. A variety of propagation conditions are simulated - scatter-free, and scattering with mean free path, λ, of 0.3 and 2.0 AU - and the cross-field transport of SEPs is investigated. When calculating cross-field displacements the Parker spiral geometry is accounted for and the role of magnetic field expansion is taken into account. It is found that transport across the magnetic field is enhanced in the λ =0.3 AU and λ =2 AU cases, compared to the scatter-free case, with the λ =2 AU case in particular containing outlying particles that had strayed a large distance across the IMF. Outliers are catergorized by means of Chauvenet's criterion and it is found that typically between 1 and 2% of the population falls within this category. The ratio of latitudinal to longitudinal diffusion coefficient perpendicular to the magnetic field is typically 0.2, suggesting that transport in latitude is less efficient.

The Astrophysical Journal, 2013

Drifts are known to play a role in galactic cosmic ray transport within the heliosphere and are a... more Drifts are known to play a role in galactic cosmic ray transport within the heliosphere and are a standard component of cosmic ray propagation models. However, the current paradigm of Solar Energetic Particle (SEP) propagation holds the effects of drifts to be negligible, and they are not accounted for in most current SEP modelling efforts. We present full-orbit test particle simulations of SEP propagation in a Parker spiral interplanetary magnetic field which demonstrate that high energy particle drifts cause significant asymmetric propagation perpendicular to the interplanetary magnetic field. Thus in many cases the assumption of field aligned propagation of SEPs may not be valid. We show that SEP drifts have dependencies on energy, heliographic latitude, and charge to mass ratio, that are capable of transporting energetic particles perpendicular to the field over significant distances within interplanetary space, e.g. protons of initial energy 100 MeV propagate distances across the field on the order of 1 AU, over timescales typical of a gradual SEP event. Our results demonstrate the need for current models of SEP events to include the effects of particle drift. We show that the drift is considerably stronger for heavy ion SEPs due to their larger mass to charge ratio. This paradigm shift has important consequences for the modelling of SEP events and is crucial to the understanding and interpretation of in-situ observations.

The Astrophysical Journal, 2012

In the full-orbit particle simulations of energetic particle transport in plasmas, the plasma tur... more In the full-orbit particle simulations of energetic particle transport in plasmas, the plasma turbulence is typically described as a homogeneous superposition of linear Fourier modes. The turbulence evolution is, however, typically a nonlinear process, and, particularly in the heliospheric context, the solar wind plasma is inhomogeneous due to the transient structures, as observed by remote and insitu measurements. In this work, we study the effects of the inhomogeneities on energetic particle transport by using spatially distributed, superposed turbulence envelopes. We find that the cross-field transport is significantly reduced, when compared to the results obtained with homogeneous turbulence. The reduction can reach an order of magnitude when the enveloping breaks the wave phase coherence along the mean magnetic field direction.

The Astrophysical Journal, 2012

The trajectories of Solar Energetic Particles (SEPs) in an Interplanetary Magnetic Field (IMF) ex... more The trajectories of Solar Energetic Particles (SEPs) in an Interplanetary Magnetic Field (IMF) exhibiting large-scale fluctuations due to footpoint motions originating in the photosphere, are simulated using a full-orbit test-particle code. The cross-field transport experienced by the particles in three propagation conditions (scatter-free, with scattering mean free path λ=0.3 AU and λ=2 AU) is characterized in the Parker spiral geometry. The role of expansion of the magnetic field with radial distance from the Sun is taken into consideration in the calculation of particle displacements and diffusion coefficients from the output of the simulations. It is found that transport across the magnetic field is enhanced in the λ=0.3 AU and λ=2 AU cases, compared to the scatter-free case. Values of the ratios of perpendicular to parallel diffusion coefficients vary between 0.01 and 0.08. The ratio of latitudinal to longitudinal diffusion coefficient perpendicular to the magnetic field is typically 0.2, suggesting that transport in latitude may be less efficient.

The Astrophysical Journal, 2013

Observations and modelling suggest that the fluctuations in magnetised plasmas exhibit scaledepen... more Observations and modelling suggest that the fluctuations in magnetised plasmas exhibit scaledependent anisotropy, with more energy in the fluctuations perpendicular to the mean magnetic field than in the parallel fluctuations and the anisotropy increasing at smaller scales. The scale-dependence of the anisotropy has not been studied in full-orbit simulations of particle transport in turbulent plasmas so far. In this paper, we construct a model of critically balanced turbulence, as suggested by , and calculate energetic particle spatial diffusion coefficients using fullorbit simulations. The model uses an enveloped turbulence approach, where each 2-dimensional wave mode with wavenumber k ⊥ is packed into envelopes of length L following the critical balance condition, L ∝ k −2/3 ⊥ , with the wave mode parameters changing between envelopes. Using full-orbit particle simulations, we find that both the parallel and perpendicular diffusion coefficients increase by a factor 2, compared to previous models with scale-independent anisotropy.

Particle acceleration by coronal shock waves is studied. Efficient acceleration requires particle... more Particle acceleration by coronal shock waves is studied. Efficient acceleration requires particles to interact with the shock many times before substantial energy gains can be expected. In diffusive shock acceleration models, particles scatter off low-frequency plasma waves or turbulence around the shock, which results in particle trajectories crossing the shock front many times. We study an alternative to the standard diffusive shock acceleration model: an oblique coronal shock wave propagating toward the solar surface on open field lines without upstream turbulence but with a large magnetic mirror ratio between the footpoint and the shock location. Such shocks can be either freely propagating or driven shock waves, and they would be related to the initial phases of particle events, when the erupting plasma has scales of the order of a solar radius. Our simulations reveal that the modeled shocks are able to efficiently accelerate ions up to energies from a few to a few tens of MeVs...

The Astrophysical Journal, 2013

Solar energetic particles (SEPs) have been observed to easily spread across heliographic longitud... more Solar energetic particles (SEPs) have been observed to easily spread across heliographic longitudes, and the mechanisms responsible for this behaviour remain unclear. We use full-orbit simulations of a 10 MeV proton beam in a turbulent magnetic field to study to what extent the spread across the mean field can be described as diffusion early in a particle event. We compare the full-orbit code results to solutions of a Fokker-Planck equation including spatial and pitch angle diffusion, and of one including also propagation of the particles along random-walking magnetic field lines. We find that propagation of the particles along meandering field lines is the key process determining their cross-field spread at 1 AU at the beginning of the simulated event. The mean square displacement of the particles an hour after injection is an order of magnitude larger than that given by the diffusion model, indicating that models employing spatial cross-field diffusion cannot be used to describe early evolution of an SEP event. On the other hand, the diffusion of the particles from their initial field lines is negligible during the first 5 hours, which is consistent with the observations of SEP intensity dropouts. We conclude that modelling SEP events must take into account the particle propagation along meandering field lines for the first 20 hours of the event.

Particle acceleration by coronal shock waves is studied. Efficient acceleration requires particle... more Particle acceleration by coronal shock waves is studied. Efficient acceleration requires particles to interact with the shock many times before substantial energy gains can be expected. In diffusive shock acceleration models, particles scatter off low-frequency plasma waves or turbulence around the shock, which results in particle trajectories crossing the shock front many times. We study an alternative to the standard diffusive shock acceleration model: an oblique coronal shock wave propagating toward the solar surface on open field lines without upstream turbulence but with a large magnetic mirror ratio between the footpoint and the shock location. Such shocks can be either freely propagating or driven shock waves, and they would be related to the initial phases of particle events, when the erupting plasma has scales of the order of a solar radius. Our simulations reveal that the modeled shocks are able to efficiently accelerate ions up to energies from a few to a few tens of MeVs per nucleon, depending on the parameters of the shock wave and of the underlying magnetic field. These energies can be further increased by allowing particle scattering off upstream turbulence.

Astron Astrophys, 2003

Alfvén wave transport in the solar wind, including non-linear spectral energy transfer, is studie... more Alfvén wave transport in the solar wind, including non-linear spectral energy transfer, is studied. We present numerical solutions of wave transport using a diffusive flux function previously introduced for spectral energy transfer, and compare it with the analytical solution obtained for a convective flux function. The two models of cascading produce very similar behavior of a power spectrum initially of 1/f-form at the solar surface, provided that the cascading constants are tuned to produce the same spectral flux in the inertial range. We present an analytical expression for the power spectrum of the diffusively-cascading Alfvén waves in the solar wind derived from a solution of the wave transport equation and show that it compares well with the exact solutions. Our expression enables (semi) analytical evaluation of the cyclotron heating rate, the wave pressure gradient, and the energetic-particle mean free path related to the Alfvén waves in the corona and solar wind.

The Astrophysical Journal, Jul 5, 2013

Drifts are known to play a role in galactic cosmic ray transport within the heliosphere and are a... more Drifts are known to play a role in galactic cosmic ray transport within the heliosphere and are a standard component of cosmic ray propagation models. However, the current paradigm of Solar Energetic Particle (SEP) propagation holds the effects of drifts to be negligible, and they are not accounted for in most current SEP modelling efforts. We present full-orbit test particle simulations of SEP propagation in a Parker spiral interplanetary magnetic field which demonstrate that high energy particle drifts cause significant asymmetric propagation perpendicular to the interplanetary magnetic field. Thus in many cases the assumption of field aligned propagation of SEPs may not be valid. We show that SEP drifts have dependencies on energy, heliographic latitude, and charge to mass ratio, that are capable of transporting energetic particles perpendicular to the field over significant distances within interplanetary space, e.g. protons of initial energy 100 MeV propagate distances across the field on the order of 1 AU, over timescales typical of a gradual SEP event. Our results demonstrate the need for current models of SEP events to include the effects of particle drift. We show that the drift is considerably stronger for heavy ion SEPs due to their larger mass to charge ratio. This paradigm shift has important consequences for the modelling of SEP events and is crucial to the understanding and interpretation of in-situ observations.

Astronomische Nachrichten Supplement, Jul 1, 2003

The Astrophysical Journal

We investigate the deceleration of Solar Energetic Particles (SEPs) during their propagation from... more 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.

Wave damping and cascading processes have been found to be important for the heating and accelera... more Wave damping and cascading processes have been found to be important for the heating and acceleration of the solar wind. However, it remains a difficult task to extract details of these processes from observations of the thermal plasma only. The wave power required for efficient heating and acceleration of the solar wind also affects the acceleration and transport of solar energetic particles. Thus, their observation could provide valuable clues for the actual evolution of the wave power close to the coronal base and, in turn, give constraints for solar wind modeling. Pursuing this idea, we have developed a steady‐state two‐fluid model for the wave heating and acceleration of the solar wind. The dissipation frequency determining the heating is obtained from a cyclotron damping rate that depends on the plasma beta and, thus, differs from the usual assumption, a fixed fraction of the ion cyclotron frequency. We present first results obtained with the two‐fluid code and, in particular,...

We have developed a steady-state two-fluid description of the radial solar wind expan- sion close... more We have developed a steady-state two-fluid description of the radial solar wind expan- sion close to the coronal base. The model is formulated self-consistently with respect to the radial evolution of turbulence by supplementing the moment equations of the plasma with an equation describing the evolution of the (cyclotron) wave power due to damping and cascading processes as originally suggested by Tu et al. (1984). The resulting acceleration and heating rates of the thermal plasma are determined by as- suming a dissipation frequency that, in difference to earlier models, exhibits a thermal dependence on the plasma. We will present first results and compare them with wind profiles obtained previously by other authors. We will then discuss the implications of the improved formulation of the dissipation frequency and of the wave cascading.

The research of turbulence has benefited from recent MHD simulation studies. These simulations ar... more The research of turbulence has benefited from recent MHD simulation studies. These simulations are typically limited to small spatial domains by computational requirements, and are not easily applicable to all fields of research, such as studies on solar wind heating and energetic particle transport. A different approach, employing spectral transfer of turbulence energy by diffusive or convective cascading, is often used to describe the evolution of the turbulence in large-scale systems. The descriptions of the turbulence, used in this approach, however, are often not fully consistent, and typically contain some ad-hoc form for the cascade strength, which is related to the power in inward and outward propagating waves. We study the evolution of turbulence by employing a two-equation model for diffusive cascading. For the source of inward waves, we formulate a simple approximation for the reflection of the waves from large-scale gradients. The implications of the resulting turbulence...

Some recent modeling efforts to understand the transport and acceleration of solar energetic part... more Some recent modeling efforts to understand the transport and acceleration of solar energetic particles (SEPs) in corona and interplanetary medium are reviewed. We will present results from analytical calculations and from particle simulations employing the Monte Carlo method. Our modeling efforts concentrate on ions. Specifically, we have considered (i) velocity dispersion analysis of particles observed during the initial rise of an SEP event as obtained from particle transport simulations; (ii) particle acceleration in coronal shock waves during the initial phases of an SEP event; and (iii) the role of the generation of turbulence by the accelerated particles themselves. Ion acceleration by coronal shocks is shown to be consistent with the typical observational results on SEP event onsets. This holds true for both small gradual SEP events, which can be treated under the test-particle approximation, and for the largest SEP events, in which the accelerated particles significantly enh...

The onset of a Solar Energetic Particle (SEP) event has been traditionally determined by using th... more The onset of a Solar Energetic Particle (SEP) event has been traditionally determined by using the velocity dispersion analysis (VDA). In this method the injection of the first particles at the Sun is determined by fitting the solar injection time and the particles' path length to match the observed event onset at 1 AU for several SEP energy channels. Recently, this approach has been questioned by simulation studies, which take into account the effect of the interplanetary scattering on the arrival time of the first particles to 1 AU. Particularly when the pre-event particle background is strong, significant errors for the onset can be expected, up to tens of minutes for protons of energies 1-100 MeV. In this work, we continue to study the effect of the pre-event background to the SEP event onset at 1 AU, and its consequences to the determination of the SEP event evolution at the Sun. We study the use of the steepness of the event onset, as observed at 1 AU, as a parameter for t...

The capability to predict the parameters of an SEP event such as its onset, peak flux, and durati... more 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 operational modelling system simulating the propagation of Solar Energetic Particles (SEPs) from locations near the Sun to any given location in the heliosphere. 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 are obtained within a forecasting context are described. The first results from the modelling system are presented. These results demonstrate that corotation and drift of SEP streams play an essential role in shaping SEP flux profiles.

AIP Conference Proceedings, 2010

ABSTRACT The onset of a Solar Energetic Particle (SEP) event has been traditionally determined by... more ABSTRACT The onset of a Solar Energetic Particle (SEP) event has been traditionally determined by using the velocity dispersion analysis (VDA), where the event onset at the Sun is determined by fitting the solar onset time and the particles' path length to match the observed event onset at 1 AU for several SEP energy channels. This approach has been studied by using energetic particle simulations, in order to understand the effect of the interplanetary scattering on the arrival time of the first particles to 1 AU. In these studies, the SEP event onset at 1 AU has been defined as the time when the intensities reach certain percentage of the maximum of the event. This is often not feasible for practical work, as a real event may be complex in its structure, and the pre-event background may mask the SEP onset to differing degrees in different energies. In order to estimate the usability of the VDA method, we study the simulated SEP onset on a pre-existing particle background by varying the pre-event background level, the difference of the pre-event background and the simulated event maximum spectral indices, the interplanetary mean free path and the injection profile. As in the previous studies, we find that large path length variation can be explained as an artifact resulting from the use of the VDA method. More importantly, the error in the obtained solar onset time depends strongly on the properties of the pre-event background.

Space Weather: the Space Radiation Environment, 2012

ABSTRACT The results of full-orbit test-particle simulations of SEPs propagating through an IMF w... more ABSTRACT The results of full-orbit test-particle simulations of SEPs propagating through an IMF which exhibits large-scale fluctuations are presented. A variety of propagation conditions are simulated - scatter-free, and scattering with mean free path, λ, of 0.3 and 2.0 AU - and the cross-field transport of SEPs is investigated. When calculating cross-field displacements the Parker spiral geometry is accounted for and the role of magnetic field expansion is taken into account. It is found that transport across the magnetic field is enhanced in the λ =0.3 AU and λ =2 AU cases, compared to the scatter-free case, with the λ =2 AU case in particular containing outlying particles that had strayed a large distance across the IMF. Outliers are catergorized by means of Chauvenet's criterion and it is found that typically between 1 and 2% of the population falls within this category. The ratio of latitudinal to longitudinal diffusion coefficient perpendicular to the magnetic field is typically 0.2, suggesting that transport in latitude is less efficient.

The Astrophysical Journal, 2013

Drifts are known to play a role in galactic cosmic ray transport within the heliosphere and are a... more Drifts are known to play a role in galactic cosmic ray transport within the heliosphere and are a standard component of cosmic ray propagation models. However, the current paradigm of Solar Energetic Particle (SEP) propagation holds the effects of drifts to be negligible, and they are not accounted for in most current SEP modelling efforts. We present full-orbit test particle simulations of SEP propagation in a Parker spiral interplanetary magnetic field which demonstrate that high energy particle drifts cause significant asymmetric propagation perpendicular to the interplanetary magnetic field. Thus in many cases the assumption of field aligned propagation of SEPs may not be valid. We show that SEP drifts have dependencies on energy, heliographic latitude, and charge to mass ratio, that are capable of transporting energetic particles perpendicular to the field over significant distances within interplanetary space, e.g. protons of initial energy 100 MeV propagate distances across the field on the order of 1 AU, over timescales typical of a gradual SEP event. Our results demonstrate the need for current models of SEP events to include the effects of particle drift. We show that the drift is considerably stronger for heavy ion SEPs due to their larger mass to charge ratio. This paradigm shift has important consequences for the modelling of SEP events and is crucial to the understanding and interpretation of in-situ observations.

The Astrophysical Journal, 2012

In the full-orbit particle simulations of energetic particle transport in plasmas, the plasma tur... more In the full-orbit particle simulations of energetic particle transport in plasmas, the plasma turbulence is typically described as a homogeneous superposition of linear Fourier modes. The turbulence evolution is, however, typically a nonlinear process, and, particularly in the heliospheric context, the solar wind plasma is inhomogeneous due to the transient structures, as observed by remote and insitu measurements. In this work, we study the effects of the inhomogeneities on energetic particle transport by using spatially distributed, superposed turbulence envelopes. We find that the cross-field transport is significantly reduced, when compared to the results obtained with homogeneous turbulence. The reduction can reach an order of magnitude when the enveloping breaks the wave phase coherence along the mean magnetic field direction.

The Astrophysical Journal, 2012

The trajectories of Solar Energetic Particles (SEPs) in an Interplanetary Magnetic Field (IMF) ex... more The trajectories of Solar Energetic Particles (SEPs) in an Interplanetary Magnetic Field (IMF) exhibiting large-scale fluctuations due to footpoint motions originating in the photosphere, are simulated using a full-orbit test-particle code. The cross-field transport experienced by the particles in three propagation conditions (scatter-free, with scattering mean free path λ=0.3 AU and λ=2 AU) is characterized in the Parker spiral geometry. The role of expansion of the magnetic field with radial distance from the Sun is taken into consideration in the calculation of particle displacements and diffusion coefficients from the output of the simulations. It is found that transport across the magnetic field is enhanced in the λ=0.3 AU and λ=2 AU cases, compared to the scatter-free case. Values of the ratios of perpendicular to parallel diffusion coefficients vary between 0.01 and 0.08. The ratio of latitudinal to longitudinal diffusion coefficient perpendicular to the magnetic field is typically 0.2, suggesting that transport in latitude may be less efficient.

The Astrophysical Journal, 2013

Observations and modelling suggest that the fluctuations in magnetised plasmas exhibit scaledepen... more Observations and modelling suggest that the fluctuations in magnetised plasmas exhibit scaledependent anisotropy, with more energy in the fluctuations perpendicular to the mean magnetic field than in the parallel fluctuations and the anisotropy increasing at smaller scales. The scale-dependence of the anisotropy has not been studied in full-orbit simulations of particle transport in turbulent plasmas so far. In this paper, we construct a model of critically balanced turbulence, as suggested by , and calculate energetic particle spatial diffusion coefficients using fullorbit simulations. The model uses an enveloped turbulence approach, where each 2-dimensional wave mode with wavenumber k ⊥ is packed into envelopes of length L following the critical balance condition, L ∝ k −2/3 ⊥ , with the wave mode parameters changing between envelopes. Using full-orbit particle simulations, we find that both the parallel and perpendicular diffusion coefficients increase by a factor 2, compared to previous models with scale-independent anisotropy.

Particle acceleration by coronal shock waves is studied. Efficient acceleration requires particle... more Particle acceleration by coronal shock waves is studied. Efficient acceleration requires particles to interact with the shock many times before substantial energy gains can be expected. In diffusive shock acceleration models, particles scatter off low-frequency plasma waves or turbulence around the shock, which results in particle trajectories crossing the shock front many times. We study an alternative to the standard diffusive shock acceleration model: an oblique coronal shock wave propagating toward the solar surface on open field lines without upstream turbulence but with a large magnetic mirror ratio between the footpoint and the shock location. Such shocks can be either freely propagating or driven shock waves, and they would be related to the initial phases of particle events, when the erupting plasma has scales of the order of a solar radius. Our simulations reveal that the modeled shocks are able to efficiently accelerate ions up to energies from a few to a few tens of MeVs...

The Astrophysical Journal, 2013

Solar energetic particles (SEPs) have been observed to easily spread across heliographic longitud... more Solar energetic particles (SEPs) have been observed to easily spread across heliographic longitudes, and the mechanisms responsible for this behaviour remain unclear. We use full-orbit simulations of a 10 MeV proton beam in a turbulent magnetic field to study to what extent the spread across the mean field can be described as diffusion early in a particle event. We compare the full-orbit code results to solutions of a Fokker-Planck equation including spatial and pitch angle diffusion, and of one including also propagation of the particles along random-walking magnetic field lines. We find that propagation of the particles along meandering field lines is the key process determining their cross-field spread at 1 AU at the beginning of the simulated event. The mean square displacement of the particles an hour after injection is an order of magnitude larger than that given by the diffusion model, indicating that models employing spatial cross-field diffusion cannot be used to describe early evolution of an SEP event. On the other hand, the diffusion of the particles from their initial field lines is negligible during the first 5 hours, which is consistent with the observations of SEP intensity dropouts. We conclude that modelling SEP events must take into account the particle propagation along meandering field lines for the first 20 hours of the event.