We investigate the combined effects of solar energetic particle propagation, parallel and perpendicular to the large-scale magnetic field in the solar wind. Numerical methods employing stochastic differential equations are used incorporating pitch-angle diffusion, focusing, and pitch-angle-dependent diffusion perpendicular to the magnetic field. We compute spatial distributions of ~100?keV electrons and 4?MeV protons in the inner heliosphere, assuming impulsive injection near the Sun over a limited range of solar longitude and latitude. In addition, spatial distributions and intensity-time profiles for various combinations of the parallel and perpendicular mean free path, with different assumptions for the dependence of ?? on the radial distance and pitch angle, are investigated. We find that realistic results can be obtained when we assume that the perpendicular mean free path scales in the inner heliosphere with the gyroradius of the particles. Step-like decreases of particle intensities as frequently observed in impulsive events at 1?AU can be reproduced for a ratio of ??/?? a few times 10?5.

http://iopscience.iop.org/article/10.1088/0004-637X/709/2/912/pdf

Anisotropic three-dimensional focused transport of solar energetic particles in the inner heliosphere

Relativistic charged particles (CRs for cosmic rays) produced by supernova explosion of the first generation of massive stars that are responsible for the reionization of the universe escape into the intergalactic medium, carrying an electric current. Charge imbalance and induction give rise to a return current, , carried by the cold thermal plasma which tends to cancel the CR current. The electric field, , required to draw the collisional return current opposes the outflow of low-energy CRs and ohmically heats the cold plasma. Owing to inhomogeneities in the resistivity, ?(T), caused by a structure in the temperature, T, of the intergalactic plasma, the electric field possesses a rotational component which sustains Faraday's induction. It is found that a magnetic field is robustly generated throughout intergalactic space at a rate of 10?17 to 10?16?G?Gyr?1, until the temperature of the intergalactic medium is raised by cosmic reionization. The magnetic field may seed the subsequent growth of magnetic fields in the intergalactic environment. The role of CR-driven instabilities is discussed, and nonlinear effects are briefly considered.

https://iopscience.iop.org/article/10.1088/0004-637X/729/1/73/pdf

Resistive Magnetic Field Generation at Cosmic Dawn

We analyze 65–105 keV electrons in the 7 February 2010 solar electron event observed simultaneously by STEREO-A, STEREO-B, and ACE. A method to reconstruct the full-electron pitch angle distributions from the four Solar Electron and Proton Telescope sensors on STEREO-A/B and the Solar Electron and Proton Telescope instrument on ACE in the energy range of approximately 60–300 keV for periods of incomplete angular coverage is presented. A transport modeling based on numerical solutions of a three-dimensional particle propagation model which includes pitch angle scattering and focused transport is applied to the intensity and anisotropy profiles measured on all three spacecraft. Based on an analysis of intensity gradients observed between the three spacecraft, we find that the lateral transport of the electrons occurs partially close to the Sun, due to effects of nonradial divergence of magnetic field lines or particle diffusion, and partially in the interplanetary medium. For the mean free paths characterizing the electron diffusion parallel and perpendicular to the interplanetary magnetic field, we derive values of λ∥∼ 0.1 AU and λ⟂∼ 0.01 AU. In comparison with results from other particle events which we had previously analyzed in a similar manner we discuss whether the diffusion mean free paths parallel and perpendicular to the average magnetic field might be related with each other, and whether the particle transport perpendicular to the average magnetic field is more likely due to particles following meandering magnetic field lines, or due to particles being scattered off individual field lines.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2014JA019933

Wide longitudinal distribution of interplanetary electrons following the 7 February 2010 solar event: Observations and transport modeling

Aims. We investigate pitch-angle scattering, which is a fundamental process in the physics of cosmic rays. Methods. By employing the second-order quasilinear theory, the pitch-angle Fokker-Planck coefficient is calculated analytically for the first time. Results. We demonstrate that for sufficiently strong turbulence the pitch-angle Fokker-Planck coefficient is isotropic. The derived results can be used to compute the parallel mean free path for all forms of the turbulence spectrum. We also consider applications, namely the transport of solar energetic particles and the propagation of cosmic rays in the Galaxy. Conclusions. The previously used assumption of isotropic pitch-angle diffusion is indeed correct for sufficiently strong turbulence. An analytical description of nonlinear particle scattering is possible.

/pdf/analytical-description-of-nonlinear-cosmic-ray-scattering-1uks0ws542.pdf

Analytical description of nonlinear cosmic ray scattering: isotropic and quasilinear regimes of pitch-angle diffusion

Perpendicular diffusion coefficients and mean free paths of cosmic particles are computed for an anisotropic Alfvenic turbulence spectrum corresponding to the Goldreich-Sridhar model by employing an enhanced nonlinear guiding center theory. The calculations are important for understanding cosmic ray propagation in the Galaxy and in the solar system. In addition, the knowledge of diffusion coefficients is also useful for modeling charged particles which experience diffusive shock acceleration in supernova remnants and at interplanetary shock waves. To replace the parallel diffusion coefficient in our equation for the perpendicular diffusion coefficient, we employ different models such as quasilinear results and phenomenological models. The results are compared with those derived earlier. We demonstrate that the choice of the turbulence model as well as the choice of the model for the parallel diffusion coefficient has a strong influence on the perpendicular diffusion coefficient.

https://iopscience.iop.org/article/10.1088/0004-637X/725/2/2117/pdf

Perpendicular diffusion of cosmic rays for a goldreich-sridhar spectrum

The detailed modeling of solar particle events offers the possibility of deriving coefficients describing the propagation of energetic particles in the inner heliosphere such as scattering mean free paths and thus to test the validity of different theories for the interaction of the particles with magnetic field fluctuations. In addition, information about the three-dimensional structure and the dynamical properties of the fluctuations can be obtained and compared with results from direct magnetic field observations. We apply different methods to numerically solve the focused transport equation for pitch angle diffusion coefficients calculated from standard and dynamical quasi-linear theory, and investigate the resulting pitch angle distributions for 100 keV electrons and for MeV protons. We find that pitch angle distributions predicted for electrons from a model comprising dynamical quasi-linear theory and the assumption that the fluctuations are composed of a 20% slab and an 80% two-dimensional component differ significantly from those predicted for protons. A comparison with particle observations from the solar event of 2000 February 18 reveals that these predictions are also in strong disagreement with the observed electron pitch angle distributions. Our findings indicate that the above model, inspite of its recent success in making quantitatively correct predictions for the particle's scattering mean free path parallel to the average magnetic field from observations of solar wind turbulence, is still not complete.

Testing transport theories with solar energetic particles

The detailed modeling of solar particle events offers the possibility of deriving coefficients describing the propagation of energetic particles in the inner heliosphere such as scattering mean free paths and thus to test the validity of different theories for the interaction of the particles with magnetic field fluctuations. In addition, information about the three-dimensional structure and the dynamical properties of the fluctuations can be obtained and compared with results from direct magnetic field observations. We apply different methods to numerically solve the focused transport equation for pitch angle diffusion coefficients calculated from standard and dynamical quasi-linear theory, and investigate the resulting pitch angle distributions for 100 keV electrons and for MeV protons. We find that pitch angle distributions predicted for electrons from a model comprising dynamical quasi-linear theory and the assumption that the fluctuations are composed of a 20% slab and an 80% two-dimensional component differ significantly from those predicted for protons. A comparison with particle observations from the solar event of 2000 February 18 reveals that these predictions are also in strong disagreement with the observed electron pitch angle distributions. Our findings indicate that the above model, inspite of its recent success in making quantitatively correct predictions for the particle’s scattering mean free path parallel to the average magnetic field from observations of solar wind turbulence, is still not complete.

Y. Y. Kartavykh

Papers

Testing transport theories with solar energetic particles

Testing transport theories with solar energetic particles