scholarly journals Energetic Particle Superdiffusion in Solar System Plasmas: Which Fractional Transport Equation?

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2368
Author(s):  
Gaetano Zimbardo ◽  
Francesco Malara ◽  
Silvia Perri
Keyword(s):  
Solar System ◽  
Transport Equation ◽  
Pitch Angle ◽  
Energetic Particle ◽  
Time Derivative ◽  
Direction Parallel ◽  
Lévy Walks ◽  
Angle Scattering ◽  
Superdiffusive Transport ◽  
The Magnetic Field

Superdiffusive transport of energetic particles in the solar system and in other plasma environments is often inferred; while this can be described in terms of Lévy walks, a corresponding transport differential equation still calls for investigation. Here, we propose that superdiffusive transport can be described by means of a transport equation for pitch-angle scattering where the time derivative is fractional rather than integer. We show that this simply leads to superdiffusion in the direction parallel to the magnetic field, and we discuss some advantages with respect to approaches based on transport equations with symmetric spatial fractional derivates.

Determination of Solar Energetic Particle anisotropies based on four-sector measurements - Study based on STEREO/SEPT in preperation of SolO/EPT

2020 ◽  
Author(s):  
Maximilian Bruedern ◽  
Nina Dresing ◽  
Bernd Heber ◽  
Lars Berger ◽  
Alexander Kollhoff ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Pitch Angle ◽  
Radial Distance ◽  
Solar Energetic Particle ◽  
The Sun ◽  
Angle Scattering ◽  
Bootstrap Approach ◽  
The Magnetic Field ◽  
The Imf

<p>With the launch of Solar Orbiter (SolO) Solar Energetic Particles (SEPs) can be observed at a radial distance of 0.284 to 0.9 AU and an inclination out of the ecliptic up to 34 degree. The properties of SEP observations carry information about their source at the Sun as well as their transport through the interplanetary medium. Their energy is mostly determined close to the Sun. As SEPs propagate outward along the Interplanetary Magnetic Field (IMF) the pitch-angle with respect to the local field is systematically focused due to the radially decreasing IMF. However, stochastic changes are induced by scattering at fluctuations of the IMF. Often the first order anisotropy of SEPs is calculated to disentangle imprints of source and transport. Strong anisotropies indicate periods of weak pitch-angle scattering. Although many modeling and observational studies are based on the anisotropy, its uncertainty is often neglected which could result in inaccurate conclusions. Therefore, we propose a new method based on a bootstrap approach where we consider (1) directional instrument responses, (2) the variation of the magnetic field, and (3) the stochastic nature of detection. Here, we present our procedure and final results for different SEP events using measured data of the IMF and particle fluxes by the Solar Electron and Proton Telescope (SEPT) on board of each STEREO spacecraft. The SEPT provides four viewing directions with a view cone of 0.66 sr each on a three axis stabilized spacecraft. In contrast the Electron and Proton Telescope (EPT) on board SolO also consists of four viewing directions but each telescope has a much smaller view cone of 0.21 sr. Due to the very similar instrument setup we can apply our method both to the SEPT and EPT.</p>

scholarly journals The expected imprint of flux rope geometry on suprathermal electrons in magnetic clouds

2009 ◽  
Vol 27 (10) ◽  
pp. 4057-4067 ◽  
Author(s):  
M. J. Owens ◽  
N. U. Crooker ◽  
T. S. Horbury
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Pitch Angle ◽  
Flux Rope ◽  
Magnetic Clouds ◽  
Magnetic Field Direction ◽  
Magnetic Flux Rope ◽  
Suprathermal Electron ◽  
Angle Scattering ◽  
The Magnetic Field

Abstract. Magnetic clouds are a subset of interplanetary coronal mass ejections characterized by a smooth rotation in the magnetic field direction, which is interpreted as a signature of a magnetic flux rope. Suprathermal electron observations indicate that one or both ends of a magnetic cloud typically remain connected to the Sun as it moves out through the heliosphere. With distance from the axis of the flux rope, out toward its edge, the magnetic field winds more tightly about the axis and electrons must traverse longer magnetic field lines to reach the same heliocentric distance. This increased time of flight allows greater pitch-angle scattering to occur, meaning suprathermal electron pitch-angle distributions should be systematically broader at the edges of the flux rope than at the axis. We model this effect with an analytical magnetic flux rope model and a numerical scheme for suprathermal electron pitch-angle scattering and find that the signature of a magnetic flux rope should be observable with the typical pitch-angle resolution of suprathermal electron data provided ACE's SWEPAM instrument. Evidence of this signature in the observations, however, is weak, possibly because reconnection of magnetic fields within the flux rope acts to intermix flux tubes.

scholarly journals Energetic particles observed by ISEE-1 and ISEE-2 in a cusp diamagnetic cavity on 29 September 1978

2007 ◽  
Vol 25 (12) ◽  
pp. 2633-2640 ◽  
Author(s):  
B. M. Walsh ◽  
T. A. Fritz ◽  
N. M. Lender ◽  
J. Chen ◽  
K. E. Whitaker
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Pitch Angle ◽  
Energetic Particle ◽  
Electron Flux ◽  
Energetic Particles ◽  
Local Magnetic Field ◽  
Local Source ◽  
Magnetospheric Cusp ◽  
The Magnetic Field

Abstract. Observations by the ISEE-1 and ISEE-2 spacecraft on 29 September 1978 show large CEP (Cusp Energetic Particle) fluxes while passing through the dayside magnetospheric cusp in near coincident orbits. The event was observed around 11:00 MLT between roughly 12:30 and 13:00 UT by ISEE-1 and 12:00 and 13:00 UT by ISEE-2. During these periods, both electron and ion fluxes increased by more than two orders of magnitude, with the electron flux showing a strong peak at a pitch angle of 90°. The solar wind was ~710 km s−1 and the Dst was ~−200 nT, suggesting the occurrence of a strong geomagnetic storm. The ISEE-1 and ISEE-2 observations, however, show no time-energy dispersion of the CEPs, leading us to believe that these particles could not be the result of substorm processes in the magnetotail. The local magnetic field was depressed and extremely turbulent. Changes in the magnitude of the magnetic field anticorrelate closely to variations of the electron flux. The observations in electron flux peaking at 90° and the close anticorrelation between the local magnetic field strength and electron flux are unique and provide evidence of a potential local source for these energetic particles.

scholarly journals Parallel velocity mixing yielding enhanced electron heating during magnetic pumping

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
J. Egedal ◽  
J. Schroeder ◽  
E. Lichko
Keyword(s):  
Pitch Angle ◽  
Recent Theory ◽  
Heating Rates ◽  
Naturally Occurring ◽  
Parallel Diffusion ◽  
Angle Scattering ◽  
Magnetic Perturbations ◽  
Earth’S Bow Shock ◽  
Combined Mechanism ◽  
The Magnetic Field

Magnetic wave perturbations are observed in the solar wind and in the vicinity of Earth's bow shock. For such environments, recent work on magnetic pumping with electrons trapped in the magnetic perturbations has demonstrated the possibility of efficient energization of superthermal electrons. Here we also analyse the energization of such energetic electrons for which the transit time through the system is short compared with time scales associated with the magnetic field evolution. In particular, considering an idealized magnetic configuration we show how trapping/detrapping of energetic magnetized electrons can cause effective parallel velocity ( $v_{\parallel }$ -) diffusion. This parallel diffusion, combined with naturally occurring mechanisms known to cause pitch angle scattering, such as whistler waves, produces enhanced heating rates for magnetic pumping. We find that at low pitch angle scattering rates, the combined mechanism enhances the heating beyond the predictions of the recent theory for magnetic pumping with trapped electrons.

Nongyroresonant Pitch Angle Scattering

1999 ◽  
Vol 518 (2) ◽  
pp. 974-984 ◽  
Author(s):  
B. R. Ragot
Keyword(s):  
Pitch Angle ◽  
Angle Scattering

scholarly journals Calculation of Transient Magnetic Field and Induced Voltage in Photovoltaic Bracket System during a Lightning Stroke

2021 ◽  
Vol 11 (10) ◽  
pp. 4567
Author(s):  
Xiaoqing Zhang ◽  
Yaowu Wang
Keyword(s):  
Magnetic Field ◽  
Time Derivative ◽  
Equivalent Circuit Model ◽  
Magnetic Flux Density ◽  
Induced Voltage ◽  
Lightning Stroke ◽  
Transient Magnetic Field ◽  
Lightning Current ◽  
Time Space ◽  
The Magnetic Field

An effective method is proposed in this paper for calculating the transient magnetic field and induced voltage in the photovoltaic bracket system under lightning stroke. Considering the need for the lightning current responses on various branches of the photovoltaic bracket system, a brief outline is given to the equivalent circuit model of the photovoltaic bracket system. The analytic formulas of the transient magnetic field are derived from the vector potential for the tilted, vertical and horizontal branches in the photovoltaic bracket system. With a time–space discretization scheme put forward for theses formulas, the magnetic field distribution in an assigned spatial domain is determined on the basis of the lightning current responses. The magnetic linkage passing through a conductor loop is evaluated by the surface integral of the magnetic flux density and the induced voltage is obtained from the time derivative of the magnetic linkage. In order to check the validity of the proposed method, an experiment is made on a reduced-scale photovoltaic bracket system. Then, the proposed method is applied to an actual photovoltaic bracket system. The calculations are performed for the magnetic field distributions and induced voltages under positive and negative lightning strokes.

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