Energetic particles are accelerated in rich profusion at sites throughout the heliosphere. They come from solar flares in the low corona, from shock waves driven outward by coronal mass ejections (CMEs), from planetary magnetospheres and bow shocks. They come from corotating interaction regions (CIRs) produced by high-speed streams in the solar wind, and from the heliospheric termination shock at the outer edge of the heliospheric cavity. We sample all these populations near Earth, but can distinguish them readily by their element and isotope abundances, ionization states, energy spectra, angular distributions and time behavior. Remote spacecraft have probed the spatial distributions of the particles and examined new sources in situ. Most acceleration sources can be "seen" only by direct observation of the particles; few photons are produced at these sites. Wave-particle interactions are an essential feature in acceleration sources and, for shock acceleration, new evidence of energetic-proton-generated waves has come from abundance variations and from local cross-field scattering. Element abundances often tell us the physics the source plasma itself, prior to acceleration. By comparing different populations, we learn more about the sources, and about the physics of acceleration and transport, than we can possibly learn from one source alone.

/pdf/particle-acceleration-at-the-sun-and-in-the-heliosphere-2yha5t1u73.pdf

Particle Acceleration at the Sun and in the Heliosphere

We present an idealized model simulating the coupled evolution of the distributions of multispecies shock-accelerated energetic ions and interplanetary Alfven waves in gradual solar energetic particle (SEP) events. Particle pitch-angle diffusion coefficients are expressed in terms of wave intensities, and wave growth rates in terms of momentum gradients of SEP distributions, by the same quasilinear theory augmented with resonance broadening. The model takes into consideration various physical processes: for SEPs, particle motion, magnetic focusing, scattering by Alfven waves, solar wind convection, and adiabatic deceleration; for the waves, WKB transport and amplification by streaming SEPs. Shock acceleration is heuristically represented by continuous injection of prescribed spectra of SEPs at a moving shock front. We show the model predictions for two contrasting sets of SEP source spectra, fast weakening and softening in one case and long lasting and hard in the other. The results presented include concurrent time histories of multispecies SEP intensities and elemental abundance ratios, as well as sequential snapshots of the following: SEP intensity energy spectra, Alfven wave spectra, particle mean free paths as functions of rigidity, and spatial profiles of SEP intensities and mean free paths. Wave growth plays a key role in both cases, although the magnitude of the wave growth differs greatly, and quite different SEP abundance variations are obtained. In these simulations, the maximum wave growth rate is large, but small relative to the wave frequency, and everywhere the total wave magnetic energy density remains small relative to that of the background magnetic field. The simulations show that, as the energetic protons stream outward, they rapidly amplify the ambient Alfven waves, by several orders of magnitude in the inner heliosphere. Energetic minor ions find themselves traveling through resonant Alfven waves previously amplified by higher velocity protons. The nonuniformly growing wave spectra alter the rigidity dependence of particle scattering, resulting in complex time variations of SEP abundances at large distances from the Sun. The greatly amplified waves travel outward in an expanding and weakening shell, creating an expanding and falling reservoir of SEPs with flat spatial intensity profiles behind, while in and beyond the shell the intensities drop steeply. The wave-particle resonance relation dynamically links the evolving characteristics of the SEP and Alfven wave distributions in this new mode of SEP transport. We conclude that wave amplification, the counterpart to the scattering of streaming particles required by energy conservation, plays an essential role in the transport of SEPs in gradual SEP events. The steep proton-amplified wave spectra just upstream of the shock suggest that they may also be important in determining the elemental abundances of shock-accelerated SEP sources.

http://iopscience.iop.org/article/10.1086/375293/pdf

Modeling Shock-accelerated Solar Energetic Particles Coupled to Interplanetary Alfvén Waves

The problem of particle transport perpendicular to a magnetic background field is well known in cosmic-ray astrophysics. Whereas it is widely accepted that quasi-linear theory (QLT) of particle transport does not provide the correct results for perpendicular diffusion, it was assumed for a long time that QLT is the correct theory for parallel diffusion. In the current paper we demonstrate that QLT is in general also incorrect for parallel particle transport if we consider composite turbulence geometry. Motivated through the recent success of the so-called nonlinear guiding center theory of perpendicular diffusion, we present a new theory for parallel and perpendicular diffusion of cosmic rays. This new theory is a nonlinear extension of QLT and provides us with a coupled system of nonlinear Fokker-Planck coefficients. By solving the resulting system of integral equations we obtain new results for the pitch-angle Fokker-Planck coefficient and the Fokker-Planck coefficient of perpendicular diffusion. By integrating over pitch angle we calculate the parallel and perpendicular mean free path. To our knowledge the new theory is the first that can deal with both parallel and perpendicular diffusion in agreement with simulations.

/pdf/nonlinear-parallel-and-perpendicular-diffusion-of-charged-fnn0m8g0s3.pdf

Nonlinear Parallel and Perpendicular Diffusion of Charged Cosmic Rays in Weak Turbulence

We have studied the injection rate of shock-accelerated protons in long-lasting particle events by tracing back the magnetohydrodynamic conditions at the shock under which protons are accelerated. This tracing back is carried out by -tting the observed Nux and anisotropy pro-les at di†erent energies, considering the magnetic connection between the shock and the observer, and modeling the propagation of the shock and of the particles along the interplanetary magnetic -eld. A focused-di†usion transport equation that includes the e†ects of adiabatic deceleration and solar wind convection has been used to model the evolution of the particle population. The mean free path and the injection rate have been derived by requiring consistency with the observed Nux and anisotropy pro-les for di†erent energies, in the upstream region of the events. We have extended the energy range of previous models down to 50 keV and up to D100 MeV. We have analyzed four proton events, representative of west, central merid- ian, and east scenarios. The spectra of the injection rate of shock-accelerated protons derived for these events show that for energies higher than 2 MeV the shock becomes a less efficient proton accelerator. We have related the derived injection rates to the evolution of the strength of the shock, particularly to the normalized downstream-upstream velocity ratio (VR), the magnetic -eld ratio, and the angle As h Bn . a result, we have derived an empirical relation of the injection rate with respect to the normalized veloc- ity ratio (log Q P VR), but we have not succeeded with the other two parameters. The Q(VR) relation allows us to determine the injection rate of shock-accelerated particles along the shock front and throughout its dynamical expansion, reproducing multispacecraft observations for one of the simulated events. This relation allows us to analyze the inNuence of the corotation e†ect on the modeled particle Nux and anisotropy pro-les. Subject headings: acceleration of particles E interplanetary medium E MHD E shock waves E Sun: particle emission

http://iopscience.iop.org/article/10.1086/306461/pdf

Energetic Particle Events: Efficiency of Interplanetary Shocks as 50 keV < E < 100 MeV Proton Accelerators

We present a model of the coupled evolution of energetic ions and Alfven waves, incorporating magnetic focusing, pitch-angle diffusion, wave amplification, and a traveling ion source. Ion transport through proton-amplified waves with non-Kolmogorov spectra produces the contrasting three-stage evolution of Fe/O and He/H ratios at several MeV/amu observed by Wind/EPACT in the 20 April 1998 gradual solar energetic particle event [Tylka et al., 1999].

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999GL900459

C. K. Ng

Papers

Pitch Angle Diffusion Coefficient in an Extended Quasi-linear Theory