Three-wave interactions of dispersive plasma waves propagating parallel to the magnetic field

Three-wave interactions of plasma waves propagating parallel to the mean magnetic field at frequencies below the electron cyclotron frequency are considered. We consider Alfv\'en--ion-cyclotron waves, fast-magnetosonic--whistler waves, and ion-sound waves. Especially the weakly turbulent low-beta plasmas like the solar corona are studied, using the cold-plasma dispersion relation for the transverse waves and the fluid-description of the warm plasma for the longitudinal waves. We analyse the resonance conditions for the wave frequencies $\omega$ and wavenumbers $k$, and the interaction rates of the waves for all possible combinations of the three wave modes, and list those reactions that are not forbidden.Comment: accepted for publication in Advanced Science Letter

Iron-rich solar particle events measured by SOHO/ERNE during two solar cycles

We study the differences in the heavy ion composition of solar energetic particle (SEP) events between solar cycles 23 and 24. We have surveyed the SOHO/ERNE heavy ion data from the beginning of solar cycle 23 until the end of June 2015, that is, well into the declining phase of cycle 24. We used this long observation period to study the properties of heavy ions (from C to Fe) and to compare the two solar cycles in this respect. We surveyed the data for SEP events with enhancements in the Fe/C and Fe/O intensity ratios in the energy range 5-15 MeV per nucleon, and associated the events with solar flare and coronal mass ejections (CME) when possible. We studied the properties of heavy ions in these events and compared the average relative abundances of heavy ions between the two solar cycles. We found that fewer days had C and O intensities higher than ~10$^{-3}$ cm$^{-2}$sr$^{-1}$s$^{-1}$(MeVn$^{-1}$)$^{-1}$ during solar cycle 24 than during cycle 23. For Fe this difference was clear even at lower intensities. We also found that fewer days had Fe/(C+O) > 0.183 during cycle 24. We identified 86 SEP events with at least one Fe-rich day, 65 of which occurred during cycle 23 and only 21 during cycle 24. We found that impulsive events have been almost completely absent during cycle 24. Mean abundances of heavy ions in the events were found to be significantly lower during cycle 24 than in cycle 23. Our results reflect the reduced solar activity in cycle 24 and indicate lower efficiency of particle acceleration processes for both gradual and impulsive SEP events in cycle 24.Comment: 14 pages, 9 figures and 3 tables. To be published in A&

Stochastic Acceleration in Relativistic Parallel Shocks

(abridged) We present results of test-particle simulations on both the first and the second order Fermi acceleration at relativistic parallel shock waves. We consider two scenarios for particle injection: (i) particles injected at the shock front, then accelerated at the shock by the first order mechanism and subsequently by the stochastic process in the downstream region; and (ii) particles injected uniformly throughout the downstream region to the stochastic process. We show that regardless of the injection scenario, depending on the magnetic field strength, plasma composition, and the employed turbulence model, the stochastic mechanism can have considerable effects on the particle spectrum on temporal and spatial scales too short to be resolved in extragalactic jets. Stochastic acceleration is shown to be able to produce spectra that are significantly flatter than the limiting case of particle energy spectral index -1 of the first order mechanism. Our study also reveals a possibility of re-acceleration of the stochastically accelerated spectrum at the shock, as particles at high energies become more and more mobile as their mean free path increases with energy. Our findings suggest that the role of the second order mechanism in the turbulent downstream of a relativistic shock with respect to the first order mechanism at the shock front has been underestimated in the past, and that the second order mechanism may have significant effects on the form of the particle spectra and its evolution.Comment: 14 pages, 11 figures (9 black/white and 2 color postscripts). To be published in the ApJ (accepted 6 Nov 2004

Particle scattering in turbulent plasmas with amplified wave modes

High-energy particles stream during coronal mass ejections or flares through the plasma of the solar wind. This causes instabilities, which lead to wave growth at specific resonant wave numbers, especially within shock regions. These amplified wave modes influence the turbulent scattering process significantly. In this paper, results of particle transport and scattering in turbulent plasmas with excited wave modes are presented. The method used is a hybrid simulation code, which treats the heliospheric turbulence by an incompressible magnetohydrodynamic approach separately from a kinetic particle description. Furthermore, a semi-analytical model using quasilinear theory (QLT) is compared to the numerical results. This paper aims at a more fundamental understanding and interpretation of the pitch-angle scattering coefficients. Our calculations show a good agreement of particle simulations and the QLT for broad-band turbulent spectra; for higher turbulence levels and particle beam driven plasmas, the QLT approximation gets worse. Especially the resonance gap at μ = 0 poses a well-known problem for QLT for steep turbulence spectra, whereas test-particle computations show no problems for the particles to scatter across this region. The reason is that the sharp resonant wave-particle interactions in QLT are an oversimplification of the broader resonances in test-particle calculations, which result from nonlinear effects not included in the QLT. We emphasise the importance of these results for both numerical simulations and analytical particle transport approaches, especially the validity of the QLT. Appendices A-D are available in electronic form at http://www.aanda.or

Conversion of relativistic pair energy into radiation in the jets of active galactic nuclei

It is generally accepted that relativistic jet outflows power the nonthermal emission from active galactic nuclei (AGN). The composition of these jets -- leptonic versus hadronic -- is still under debate. We investigate the microphysical details of the conversion process of the kinetic energy in collimated relativistic pair outflows into radiation through interactions with the ambient interstellar medium. Viewed from the coordinate system comoving with the pair outflow, the interstellar protons and electrons represent a proton-electron beam propagating with relativistic speed in the pair plasma. We demonstrate that the beam excites both electrostatic and low-frequency magnetohydrodynamic Alfven-type waves via a two-stream instability in the pair background plasma, and we calculate the time evolution of the distribution functions of the beam particles and the generated plasma wave turbulence power spectra. For standard AGN jet outflow and environment parameters we show that the initial beam distributions of interstellar protons and electrons quickly relax to plateau-distributions in parallel momentum, transferring thereby one-half of the initial energy density of the beam particles to electric field fluctuations of the generated electrostatic turbulence. On considerably longer time scales, the plateaued interstellar electrons and protons will isotropise by their self-generated transverse turbulence and thus be picked-up in the outflow pair plasma. These longer time scales are also characteristic for the development of transverse hydromagnetic turbulence from the plateaued electrons and protons. This hydromagnetic turbulence upstream and downstream is crucial for diffusive shock acceleration to operate at external or internal shocks associated with pair outflows.Comment: A&A in pres

First analysis of GLE 72 event on 10 September 2017: Spectral and anisotropy characteristics

Using neutron monitor and space-borne data we performed an analysis of the second ground level enhancement of solar cycle 24, namely the event of 10 September 2017 (GLE 72) and derive the spectral and angular characteristics of GLE particles. We employ new neutron monitor yield function and a recently proposed model based on optimization procedure. The method consists of simulation of particle propagation in a model magnetosphere in order to derive the cut-off rigidity and neutron monitor asymptotic directions. Subsequently the rigidity spectrum and anisotropy of GLE particles are obtained in their dynamical evolution during the event on the basis of inverse problem solution. The derived angular distribution and spectra are briefly discussed.Comment: 21 pages, 10 figures, 1 tabl

Injection of thermal and suprathermal seed particles into coronal shocks of varying obliquity

Context. Diffusive shock acceleration in the solar corona can accelerate solar energetic particles to very high energies. Acceleration efficiency is increased by entrapment through self-generated waves, which is highly dependent on the amount of accelerated particles. This, in turn, is determined by the efficiency of particle injection into the acceleration process. Aims. We present an analysis of the injection efficiency at coronal shocks of varying obliquity.We assessed injection through reflection and downstream scattering, including the effect of a cross-shock potential. Both quasi-thermal and suprathermal seed populations were analysed. We present results on the effect of cross-field diffusion downstream of the shock on the injection efficiency. Methods. Using analytical methods, we present applicable injection speed thresholds that were compared with both semi-analytical flux integration and Monte Carlo simulations, which do not resort to binary thresholds. Shock-normal angle θBn and shock-normal velocity Vs were varied to assess the injection efficiency with respect to these parameters. Results. We present evidence of a significant bias of thermal seed particle injection at small shock-normal angles. We show that downstream isotropisation methods affect the θBn-dependence of this result. We show a non-negligible effect caused by the crossshock potential, and that the effect of downstream cross-field diffusion is highly dependent on boundary definitions. Conclusions. Our results show that for Monte Carlo simulations of coronal shock acceleration a full distribution function assessment with downstream isotropisation through scatterings is necessary to realistically model particle injection. Based on our results, seed particle injection at quasi-parallel coronal shocks can result in significant acceleration efficiency, especially when combined with varying field-line geometry

Diffusion of energetic particles in turbulent MHD plasmas

In this paper we investigate the transport of energetic particles in turbulent plasmas. A numerical approach is used to simulate the effect of the background plasma on the motion of energetic protons. The background plasma is in a dynamically turbulent state found from numerical MHD simulations, where we use parameters typical for the heliosphere. The implications for the transport parameters (i.e. pitch-angle diffusion coefficients and mean free path) are calculated and deviations from the quasi-linear theory are discussed.Comment: Accepted for publication in Ap

Solar interacting protons versus interplanetary protons in the core plus halo model of diffusive shock acceleration and stochastic re-acceleration

With the first observations of solar γ-rays from the decay of pions, the relationship of protons producing ground level enhancements (GLEs) on the Earth to those of similar energies producing the γ-rays on the Sun has been debated. These two populations may be either independent and simply coincident in large flares, or they may be, in fact, the same population stemming from a single accelerating agent and jointly distributed at the Sun and also in space. Assuming the latter, we model a scenario in which particles are accelerated near the Sun in a shock wave with a fraction transported back to the solar surface to radiate, while the remainder is detected at Earth in the form of a GLE. Interplanetary ions versus ions interacting at the Sun are studied for a spherical shock wave propagating in a radial magnetic field through a highly turbulent radial ray (the acceleration core) and surrounding weakly turbulent sector in which the accelerated particles can propagate toward or away from the Sun. The model presented here accounts for both the first-order Fermi acceleration at the shock front and the second-order, stochastic re-acceleration by the turbulence enhanced behind the shock. We find that the re-acceleration is important in generating the γ-radiation and we also find that up to 10% of the particle population can find its way to the Sun as compared to particles escaping to the interplanetary space

Growth dynamics of a Bose-Einstein condensate in a dimple trap without cooling

We study the formation of a Bose-Einstein condensate in a cigar-shaped three-dimensional harmonic trap, induced by the controlled addition of an attractive "dimple" potential along the weak axis. In this manner we are able to induce condensation without cooling due to a localized increase in the phase space density. We perform a quantitative analysis of the thermodynamic transformation in both the sudden and adiabatic regimes for a range of dimple widths and depths. We find good agreement with equilibrium calculations based on self-consistent semiclassical Hartree-Fock theory describing the condensate and thermal cloud. We observe there is an optimal dimple depth that results in a maximum in the condensate fraction. We also study the non-equilibrium dynamics of condensate formation in the sudden turn-on regime, finding good agreement for the observed time dependence of the condensate fraction with calculations based on quantum kinetic theory.Comment: v1: 9 pages, 7 figures, submitted to Phys. Rev. A; v2: 10 pages, 8 figures, fixed typos, added references, additional details on experimental procedure, values of phase-space density, new figure and discussion on effects of three-body loss in Appendix B (replaced with published version