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 prop- agate 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 environ- ment 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 so- lar energetic particle event origins, particle transport modelling must include non-diffusive particle propagation along meandering field lines. Key words: Sun: particle emission – diffusion – magnetic fields – turbulenc

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◦ , while current diffusion theory can only explain extents of 11◦ 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 fieldline 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

Drift induced perpendicular transport of solar energetic particles

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 modeling efforts. We present full-orbit test particle simulations of SEP propagation in a Parker spiral interplanetary magnetic field (IMF), which demonstrate that high-energy particle drifts cause significant asymmetric propagation perpendicular to the IMF. 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 modeling of SEP events and is crucial to the understanding and interpretation of in situ observations. © 2013. The American Astronomical Society. All rights reserved.

ENERGETIC PARTICLE DIFFUSION IN CRITICALLY BALANCED TURBULENCE

Observations and modeling suggest that the fluctuations in magnetized plasmas exhibit scale-dependent 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 Goldreich & Sridhar, and calculate energetic particle spatial diffusion coefficients using full-orbit simulations. The model uses an enveloped turbulence approach, where each two-dimensional wave mode with wavenumber k ⊥ is packed into envelopes of length L following the critical balance condition, Lk –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 of two, compared to previous models with scale-independent anisotropy

Comparison of embedded and added motor imagery training in patients after stroke: Study protocol of a randomised controlled pilot trial using a mixed methods approach

Copyright @ 2009 Schuster et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background: Two different approaches have been adopted when applying motor imagery (MI) to stroke patients. MI can be conducted either added to conventional physiotherapy or integrated within therapy sessions. The proposed study aims to compare the efficacy of embedded MI to an added MI intervention. Evidence from pilot studies reported in the literature suggests that both approaches can improve performance of a complex motor skill involving whole body movements, however, it remains to be demonstrated, which is the more effective one.Methods/Design: A single blinded, randomised controlled trial (RCT) with a pre-post intervention design will be carried out. The study design includes two experimental groups and a control group (CG). Both experimental groups (EG1, EG2) will receive physical practice of a clinical relevant motor task ('Going down, laying on the floor, and getting up again') over a two week intervention period: EG1 with embedded MI training, EG2 with MI training added after physiotherapy. The CG will receive standard physiotherapy intervention and an additional control intervention not related to MI.The primary study outcome is the time difference to perform the task from pre to post-intervention. Secondary outcomes include level of help needed, stages of motor task completion, degree of motor impairment, balance ability, fear of falling measure, motivation score, and motor imagery ability score. Four data collection points are proposed: twice during baseline phase, once following the intervention period, and once after a two week follow up. A nested qualitative part should add an important insight into patients' experience and attitudes towards MI. Semi-structured interviews of six to ten patients, who participate in the RCT, will be conducted to investigate patients' previous experience with MI and their expectations towards the MI intervention in the study. Patients will be interviewed prior and after the intervention period.Discussion: Results will determine whether embedded MI is superior to added MI. Findings of the semi-structured interviews will help to integrate patient's expectations of MI interventions in the design of research studies to improve practical applicability using MI as an adjunct therapy technique

The large longitudinal spread of solar energetic particles during the January 17, 2010 solar event

We investigate multi-spacecraft observations of the January 17, 2010 solar energetic particle event. Energetic electrons and protons have been observed over a remarkable large longitudinal range at the two STEREO spacecraft and SOHO suggesting a longitudinal spread of nearly 360 degrees at 1AU. The flaring active region, which was on the backside of the Sun as seen from Earth, was separated by more than 100 degrees in longitude from the magnetic footpoints of each of the three spacecraft. The event is characterized by strongly delayed energetic particle onsets with respect to the flare and only small or no anisotropies in the intensity measurements at all three locations. The presence of a coronal shock is evidenced by the observation of a type II radio burst from the Earth and STEREO B. In order to describe the observations in terms of particle transport in the interplanetary medium, including perpendicular diffusion, a 1D model describing the propagation along a magnetic field line (model 1) (Dr\"oge, 2003) and the 3D propagation model (model 2) by (Dr\"oge et al., 2010) including perpendicular diffusion in the interplanetary medium have been applied, respectively. While both models are capable of reproducing the observations, model 1 requires injection functions at the Sun of several hours. Model 2, which includes lateral transport in the solar wind, reveals high values for the ratio of perpendicular to parallel diffusion. Because we do not find evidence for unusual long injection functions at the Sun we favor a scenario with strong perpendicular transport in the interplanetary medium as explanation for the observations.Comment: The final publication is available at http://www.springerlink.co

A detailed survey of the parallel mean free path of solar energetic particle protons and electrons

In this work, more than a dozen solar energetic particle (SEP) events are identified where the source region is magnetically well-connected to at least one spacecraft at 1~au. The observed intensity-time profiles, for all available proton and electron energy channels, are compared to results computed using a numerical 1D SEP transport model in order to derive the parallel mean free paths (pMFPs) as a function of energy (or rigidity) at 1~au. These inversion results are then compared to theoretical estimates of the pMFP, using observed turbulence quantities with observationally-motivated variations as input. For protons, a very good comparison between inversion and theoretical results is obtained. It is shown that the observed inter-event variations in the inversion pMFP values can be explained by natural variations in the background turbulence values. For electrons, there is relatively good agreement with pMFPs derived assuming the damping model of dynamical turbulence, although the theoretical values are extremely sensitive to the details of the turbulence dissipation range which themselves display a high level of variation.Comment: Accepted to Ap

Temporal evolution of solar energetic particle spectra

During solar flares and coronal mass ejections, solar energetic par- ticles (SEPs) may be released into the interplanetary medium and near-Earth locations. The energy spectra of SEP events at 1 AU are typically averaged over the entire event or studied in a few snapshots. In this paper we analyze the time evolution of the energy spectra of four large selected SEP events using a large number of snapshots. We use a multi-spacecraft and multi-instrument approach for the observations, obtained over a wide SEP energy range. We find large differences in the spectra at the beginning of the events as measured by different instruments. We show that over time, a wave-like structure is observed traveling through the spectra from the highest energies to the lowest energies, creating an “arch” shape which then straightens into a power law later in the event, after times of the order of 10 hours. We discuss the processes that determine SEP intensities and their role in shaping the spectral time evolution

Tracking a beam of electrons from the low solar corona into interplanetary space with the Low Frequency Array, Parker Solar Probe and 1 au spacecraft

Type III radio bursts are the result of plasma emission from mildly relativistic electron beams propagating from the low solar corona into the heliosphere where they can eventually be detected in situ if they align with the location of a heliospheric spacecraft. Here we observe a type III radio burst from 0.1-16 MHz using the Parker Solar Probe (PSP) FIELDS Radio Frequency Spectrometer (RFS), and from 10-80 MHz using the Low Frequency Array (LOFAR). This event was not associated with any detectable flare activity but was part of an ongoing noise storm that occurred during PSP encounter 2. A deprojection of the LOFAR radio sources into 3D space shows that the type III radio burst sources were located on open magnetic field from 1.6-3 $R_\odot$ and originated from a specific active region near the East limb. Combining PSP/RFS observations with WIND/WAVES and Solar Terrestrial Relations Observatory (STEREO)/WAVES, we reconstruct the type III radio source trajectory in the heliosphere interior to PSP's position, assuming ecliptic confinement. An energetic electron enhancement is subsequently detected in situ at the STEREO-A spacecraft at compatible times although the onset and duration suggests the individual burst contributes a subset of the enhancement. This work shows relatively small-scale flux emergence in the corona can cause the injection of electron beams from the low corona into the heliosphere, without needing a strong solar flare. The complementary nature of combined ground and space-based radio observations, especially in the era of PSP, is also clearly highlighted by this study.Comment: 17 pages, 10 figures, Submitted to ApJ, April 15 202

Observations of a Solar Energetic Particle Event From Inside and Outside the Coma of Comet 67P

Publisher Copyright: ©2022. The Authors.We analyze observations of a solar energetic particle (SEP) event at Rosetta's target comet 67P/Churyumov-Gerasimenko during 6–10 March 2015. The comet was 2.15 AU from the Sun, with the Rosetta spacecraft approximately 70 km from the nucleus placing it deep inside the comet's coma and allowing us to study its response. The Eastern flank of an interplanetary coronal mass ejection (ICME) also encountered Rosetta on 6 and 7 March. Rosetta Plasma Consortium data indicate increases in ionization rates, and cometary water group pickup ions exceeding 1 keV. Increased charge exchange reactions between solar wind ions and cometary neutrals also indicate increased upstream neutral populations consistent with enhanced SEP induced surface activity. In addition, the most intense parts of the event coincide with observations interpreted as an infant cometary bow shock, indicating that the SEPs may have enhanced the formation and/or intensified the observations. These solar transient events may also have pushed the cometopause closer to the nucleus. We track and discuss characteristics of the SEP event using remote observations by SOHO, WIND, and GOES at the Sun, in situ measurements at Solar Terrestrial Relations Observatory Ahead, Mars and Rosetta, and ENLIL modeling. Based on its relatively prolonged duration, gradual and anisotropic nature, and broad angular spread in the heliosphere, we determine the main particle acceleration source to be a distant ICME which emerged from the Sun on 6 March 2015 and was detected locally in the Martian ionosphere but was never encountered by 67P directly. The ICME's shock produced SEPs for several days which traveled to the in situ observation sites via magnetic field line connections.Peer reviewe