Self-generated Waves Research Articles

Review and outlook of solar energetic particle measurements on multispacecraft missions

The earliest evidence of spatial distributions of solar energetic particles (SEPs) compared events from many different source longitudes on the Sun, but the early Pioneers provided the first evidence of the large areas of equal SEP intensities across the magnetically confined “reservoirs” late in the events. More detailed measurements of the importance of self-generated waves and trapping structures around the shock waves that accelerate SEPs were obtained from the Helios mission plus IMP 8, especially during the year when the two Voyager spacecraft also happened by. The extent of the dozen widest SEP events in a solar cycle, which effectively wrap around the Sun, was revealed by the widely separated STEREO spacecraft with three-point intensities fit to Gaussians. Element abundances of the broadest SEP events favor average coronal element abundances with little evidence of heavy-element-enhanced “impulsive suprathermal” ions that often dominate the seed population of the shocks, even in extremely energetic local events. However, it is hard to define a distribution with two or three points. Advancing the physics of SEPs may require a return to the closer spacing of the Helios era with coverage mapped by a half-dozen spacecraft to help disentangle the distribution of the SEPs from the underlying structure of the magnetic field and the accelerating shock.

A nonlinear model of diffusive particle acceleration at a planar shock

We study the process of nonlinear shock acceleration based on a nonlinear diffusion–advection equation. The nonlinearity is introduced via a dependence of the spatial diffusion coefficient on the distribution function of accelerating particles. This dependence reflects the interaction of energetic particles with self-generated waves. After thoroughly testing the grid-based numerical setup with a well-known analytical solution for linear shock acceleration at a specific shock transition, we consider different nonlinear scenarios, assess the influence of various parameters, and discuss the differences of the solutions to those of the linear case. We focus on the following observable features of the acceleration process, for which we quantify the differences in the linear and nonlinear cases: (1) the shape of the momentum spectra of the accelerated particles, (2) the time evolution of the solutions, and (3) the spatial number density profiles.

Kinetic simulation of electron, proton and helium acceleration in a non-relativistic quasi-parallel shock

ABSTRACT In addition to accelerating electrons and protons, non-relativistic quasi-parallel shocks are expected to possess the ability to accelerate heavy ions. The shocks in supernova remnants are generally supposed to be accelerators of Galactic cosmic rays, which consist of many species of particles. We investigate the diffusive shock acceleration of electrons, protons and helium ions in a non-relativistic quasi-parallel shock through a 1D particle-in-cell simulation with a helium-to-proton number density ratio of 0.1, which is relevant for Galactic cosmic rays. The simulation indicates that waves can be excited by the flow of energetic protons and helium ions upstream of a non-relativistic quasi-parallel shock with a sonic Mach number of 14 and an Alfvén Mach number of 19.5 in the shock rest frame, and that the charged particles are scattered by the self-generated waves and accelerated gradually. Moreover, the spectra of the charged particles downstream of the shock are thermal with a non-thermal tail, and the acceleration is efficient, with about $7{{\ \rm per\ cent}}$ and $5.4{{\ \rm per\ cent}}$ of the bulk kinetic energy transferred into the non-thermal protons and helium ions, respectively, in the near downstream region by the end of the simulation.

The cosmic ray-driven streaming instability in astrophysical and space plasmas

Energetic non-thermal particles, or cosmic rays, are a major component of astrophysical plasmas next to magnetic fields, radiation, and thermal gas. Cosmic rays are usually sub-dominant in density but carry as much pressure as the thermal plasma background. In some cases, cosmic rays drift at faster speeds with respect to the normal modes' phase speeds of the background plasma. Because of this, cosmic rays are a strong source of free energy that causes new classes of kinetic or convective instabilities. Recent years have seen the development of intense analytical and numerical efforts to analyze the onset of an instability produced by the motion of these particles at fast bulk speeds: this is the streaming instability. The streaming instability has been applied to different space plasmas and astrophysical contexts like strong shocks, jets, or in interstellar and intergalactic medium studies. Streaming instabilities participate in the production of magnetic turbulence at scales corresponding to the gyroradius of the particles. By scattering off their self-generated waves, cosmic rays are coupled to the background thermal plasma. This mechanism is able to self-confine cosmic rays around sources and launch winds out of the disk of the galaxy, hence impacting galactic matter dynamics and ultimately the galactic star formation rate. We discuss a few science cases, which should be accessible in the near future for analytical calculations and numerical simulations.

Origin of the Cosmic Ray Galactic Halo Driven by Advected Turbulence and Self-Generated Waves.

The diffusive paradigm for the transport of Galactic cosmic rays is central to our understanding of the origin of these high energy particles. However, it is worth recalling that the normalization, energy dependence, and spatial extent of the diffusion coefficient in the interstellar medium are fitted to the data and typically are not derived from more basic principles. Here, we discuss a scenario in which the diffusion properties of cosmic rays are derived from a combination of wave self-generation and advection from the Galactic disc, where the sources of cosmic rays are assumed to be located. We show for the first time that a halo naturally arises from these phenomena, with a size of a few kiloparsecs, compatible with the value that typically best fits observations in simple parametric approaches to cosmic ray diffusion. We also show that transport in such a halo results in a hardening in the spectra of primary cosmic rays at ∼300 GV.

Nonlinear cosmic ray Galactic transport in the light of AMS-02 and Voyager data

Context: Features in the spectra of primary cosmic rays (CRs) provide invaluable information on the propagation of these particles in the Galaxy. In the rigidity region around a few hundred GV, such features have been measured in the proton and helium spectra by the PAMELA experiment and later confirmed with a higher significance by AMS-02. We investigate the implications of these datasets for the scenario in which CRs propagate under the action of self-generated waves. Aims: We show that the recent data on the spectrum of protons and helium nuclei as collected with AMS-02 and Voyager are in very good agreement with the predictions of a model in which the transport of Galactic CRs is regulated by self-generated waves. We also study the implications of the scenario for the boron-to-carbon ratio: although a good overall agreement is found, at high energy we find marginal support for a (quasi) energy independent contribution to the grammage, that we argue may come from the sources themselves Results: A break in the spectra of all nuclei is found at rigidity of a few hundred GV, as a result of a transition from self-generated waves to pre-existing waves with a Kolmogorov power spectrum. Neither the slope of the diffusion coefficient, nor its normalisation are free parameters. Moreover, at rigidities below a few GV, CRs are predicted to be advected with the self-generated waves at the local Alfv\'en speed. This effect, predicted in our previous work, provides an excellent fit to the Voyager data on the proton and helium spectra at low energies, providing additional support to the model.

NON-THERMAL ELECTRON ACCELERATION IN LOW MACH NUMBER COLLISIONLESS SHOCKS. I. PARTICLE ENERGY SPECTRA AND ACCELERATION MECHANISM

Electron acceleration to non-thermal energies in low Mach number (M<5) shocks is revealed by radio and X-ray observations of galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Diffusive shock acceleration, also known as first-order Fermi acceleration, cannot be directly invoked to explain the acceleration of electrons. Rather, an additional mechanism is required to pre-accelerate the electrons from thermal to supra-thermal energies, so they can then participate in the Fermi process. In this work, we use two- and three-dimensional particle-in-cell plasma simulations to study electron acceleration in low Mach number shocks. We focus on the particle energy spectra and the acceleration mechanism in a reference run with M=3 and a quasi-perpendicular pre-shock magnetic field. We find that about 15 percent of the electrons can be efficiently accelerated, forming a non-thermal power-law tail in the energy spectrum with a slope of p~2.4. Initially, thermal electrons are energized at the shock front via shock drift acceleration. The accelerated electrons are then reflected back upstream, where their interaction with the incoming flow generates magnetic waves. In turn, the waves scatter the electrons propagating upstream back toward the shock, for further energization via shock drift acceleration. In summary, the self-generated waves allow for repeated cycles of shock drift acceleration, similarly to a sustained Fermi-like process. This mechanism offers a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.

ON THE STABILITY OF PICK-UP ION RING DISTRIBUTIONS IN THE OUTER HELIOSHEATH

The energetic neutral atom (ENA) hypothesis for the ribbon feature observed by the Interstellar Boundary Explorer (IBEX) posits that the neutral component of the solar wind continues beyond the heliopause and charge exchanges with interstellar ions in the Outer Heliosheath (OHS). This creates pick-up ions that gyrate about the draped interstellar magnetic field (ISMF) lines at pitch angles near 90° on the locus where the ISMF lies tangential to the heliopause and perpendicular to the heliocentric radial direction. This location closely coincides with the location of the ribbon feature according to the prevailing inferences of the ISMF orientation and draping. The locally gyrating ions undergo additional charge exchange and escape as free-flying neutral atoms, many of which travel back toward the inner solar system and are imaged by IBEX as a ribbon tracing out the locus described above. For this mechanism to succeed, the pick-up ions must diffuse in pitch angle slowly enough to permit secondary charge exchange before their pitch angle distribution substantially broadens away from 90°. Previous work using linear Vlasov dispersion analysis of parallel propagating waves has suggested that the ring distribution in the OHS is highly unstable, which, if true, would make the secondary ENA hypothesis incapable of rendering the observed ribbon. In this paper, we extend this earlier work to more realistic ring distribution functions. We find that, at the low densities necessary to produce the observed IBEX ribbon via the secondary ENA hypothesis, growth rates are highly sensitive to the temperature of the beam and that even very modest temperatures of the ring beam corresponding to beam widths of <1° are sufficient to damp the self-generated waves associated with the ring beam. Thus, at least from the perspective of linear Vlasov dispersion analysis of parallel propagating waves, there is no reason to expect that the ring distributions necessary to produce the observed IBEX ENA flux via the secondary ENA hypothesis will be unstable to their own self-generated turbulence.

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 and shock-normal velocity 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 theta-dependence of this result. We show a non-negligible effect caused by the cross-shock 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.

MONTE CARLO SIMULATION MODEL OF ENERGETIC PROTON TRANSPORT THROUGH SELF-GENERATED ALFVÉN WAVES

A new Monte Carlo simulation model for the transport of energetic protons through self-generated Alfven waves is presented. The key point of the model is that, unlike the previous ones, it employs the full form (i.e., includes the dependence on the pitch-angle cosine) of the resonance condition governing the scattering of particles off Alfven waves—the process that approximates the wave-particle interactions in the framework of quasilinear theory. This allows us to model the wave-particle interactions in weak turbulence more adequately, in particular, to implement anisotropic particle scattering instead of isotropic scattering, which the previous Monte Carlo models were based on. The developed model is applied to study the transport of flare-accelerated protons in an open magnetic flux tube. Simulation results for the transport of monoenergetic protons through the spectrum of Alfven waves reveal that the anisotropic scattering leads to spatially more distributed wave growth than isotropic scattering. This result can have important implications for diffusive shock acceleration, e.g., affect the scattering mean free path of the accelerated particles in and the size of the foreshock region.

Heavy-ion acceleration and self-generated waves in coronal shocks

Context: Acceleration in coronal mass ejection driven shocks is currently considered the primary source of large solar energetic particle events. Aims: The solar wind, which feeds shock-accelerated particles, includes numerous ion populations, which offer much insight into acceleration processes. We present first simulations of shock-accelerated minor ions, in order to explore trapping dynamics and acceleration timescales in detail. Methods: We have simulated diffusive shock acceleration of minor ions (3He2+, 4He2+, 16O6+ and 56Fe14+) and protons using a Monte Carlo method, where self-generated Alfv\'enic turbulence allows for repeated shock crossings and acceleration to high energies. Results: We present the effect of minor ions on wave generation, especially at low wavenumbers, and show that it is significant. We find that maximum ion energy is determined by the competing effects of particle escape due to focusing in an expanding flux tube and trapping due to the amplified turbulence. We show the dependence of cut-off energy on the particle charge to mass ratio to be approximately (Q/A)^1.5. Conclusions: We suggest that understanding the acceleration of minor ions at coronal shocks requires simulations which allow us to explore trapping dynamics and acceleration timescales in detail, including evolution of the turbulent trapping boundary. We conclude that steady-state models do not adequately describe the acceleration of heavy ions in coronal shocks.

The transport of cosmic rays in self-excited magnetic turbulence

The process of diffusive shock acceleration relies on the efficacy with which hydromagnetic waves can scatter charged particles in the precursor of a shock. The growth of self-generated waves is driven by both resonant and non-resonant processes. We perform high-resolution magnetohydrodynamic simulations of the non-resonant cosmic ray driven instability, in which the unstable waves are excited beyond the linear regime. In a snapshot of the resultant field, particle transport simulations are carried out. The use of a static snapshot of the field is reasonable given that the Larmor period for particles is typically very short relative to the instability growth time. The diffusion rate is found to be close to, or below, the Bohm limit for a range of energies. This provides the first explicit demonstration that self-excited turbulence reduces the diffusion coefficient and has important implications for cosmic-ray transport and acceleration in supernova remnants.

Properties of dust and detection of Hα emission in LDN 1780

We present ISOPHOT observations between 60 and 200 μm and a near-infrared extinction map of the small intermediate-density cloud Lynds Dark Nebula (LDN) 1780 (Galactic coordinates l = 359° and b = 36°8). For an angular resolution of 4 arcmin, the visual extinction maximum is A V = 4.4 mag. We have used the ISOPHOT data together with the 25-, 60- and 100-μm IRIS maps to disentangle the warm and cold components of large dust grains that are observed in translucent clouds and dense clouds. The warm and cold components in LDN 1780 have different properties (temperature, emissivity) and spatial distributions, with the warm component surrounding the cold component. The warm component is mainly in the illuminated side of the cloud facing the Galactic plane and the Scorpius-Centaurus (Sco-Cen) OB association, as in the case of the H I excess emission. The cold component is associated with the 13 CO(J = 1-0) line integrated (W 13 ), which trace molecular gas at densities of ∼10 3 cm -3 . The warm component has a uniform colour temperature of 25 ± 1 K (assuming β = 2), and the colour temperature of the cold component slightly varies between 15.8 and 17.3 K (β = 2, AT = 0.5 K). The ratio between the emission at 200 μm of the cold component [I c v (200)] and A V is I c v (200)/A V = 12.1 ± 0.7 MJy sr -1 mag -1 and the average ratio τ 200 /A V = (2.0 ± 0.2) x 10 -4 mag -1 . The far-infrared emissivity of the warm component is significantly lower than that of the cold component. The Ha emission [I v (Hα)] and A V correlate very well; a ratio I v (Hα)/A V = 2.2 ± 0.1 Rayleigh mag -1 is observed. This correlation is observed for a relatively large range of column densities and indicates the presence of a source of ionization that can penetrate deep into the cloud (reaching zones with optical extinctions A v of 2 mag). Based on modelling predictions, we reject out a shock front as precursor of the observed Ha surface brightness although that process could be responsible of the formation of LDN 1780. Using the ratio I v (Hα)/A v , we have estimated an ionization rate for LDN 1780 that results to be ∼10 -16 γs -1 . We interpret this relatively high value as due to an enhanced cosmic ray radiation rate of ∼10 times the standard value. This is the first time such an enhancement is observed in a moderately dense molecular cloud. The enhancement in the ionization rate could be explained as the result of a confinement of low-energy (∼100 Mev) cosmic rays by self-generated magnetohydrodynamics waves in agreement with the recent modelling results of Padoan & Scalo. The origin of the cosmic rays could be from supernovae in the Sco-Cen OB association and/or the runaway ζ Ophiuchus. The observed low- 13 CO abundance and relatively high temperatures of the dust in LDN 1780 support the existence of a heating source that can come in through the denser regions of the cloud.

Large‐Scale Hybrid Simulations of Particle Acceleration at a Parallel Shock

Using one-dimensional hybrid simulations with very large spatial domains, we study the acceleration of protons by a parallel collisionless shock to energies higher than have been obtained previously with self-consistent plasma simulations of this type. Energy spectra and energetic particle fluxes are determined for four simulations with different-sized spatial domains. We find that the density of energetic particles upstream decays with distance from the shock and approaches a constant. The energetic particles also excite magnetic fluctuations. We find that the variance of these transverse fluctuations decreases with distance from the shock into the upstream region. This implies that the mean free path, λ, of the energetic particles increases with distance from the shock. Since our simulations are spatially limited, the downstream energy spectra are expected to deviate from a power law and become exponential at a characteristic energy Ec. However, we find that because λ increases with distance upstream, Ec is smaller than expected from a simple application of the diffusive theory (which assumes a constant mean free path and a free-escape boundary). Our results are qualitatively consistent with diffusive theories of the coupling of the particles and self-generated waves. However, in contrast to these theories, the hybrid-simulated energetic particle flux approaches a constant at some point far upstream, rather than vanishing, as assumed in the diffusion theory.

Conversion of bulk kinetic energy into radiation in AGNs and GRBs: Particle transport effects

We investigate the spatial structure of collisionless collision fronts in relativistic outflows interacting with ambient material. As a result of the interaction, ambient particles are picked up by the outflow and generate transverse plasma waves via streaming instabilities. Pick-up particle transport under the influence of self-generated turbulence inside such interaction regions is studied. We extend our previous momentum space modeling to include also a spatial dimension. We find that the following possibilities are consistent with quasi-linear equations of particle transport and wave generation: (i) if background waves have small intensities inside the outflow region, leading to inefficient scattering across the pitch-angle, θ , of $90^\circ$, particles are isotropized in the backward hemisphere (relative to the outflow velocity vector) and self-generated waves have a steep, ${\propto} k^{-3}$ wavenumber spectrum; (ii) if background waves have large intensities, enabling particles to cross $\theta=90^\circ$, particles can be fully isotropized. In case (i), however, the calculated self-generated wave amplitudes are close to the magnitude of the ordered field for reasonable choices of model parameters, giving the particles a chance to be scattered across the resonance gap by non-resonant processes. If the resonance gap is filled, a large fraction of the pick-up particles is expected to return to the upstream region, and an ultra-relativistic shock wave is predicted to form in front of the outflow, where the two relativistic particle populations (ambient and reflected) mix and form a relativistic plasma. Reflection of pick-up protons decreases the $\pi^0$-decay luminosity of relativistic outflows, leading to a need to update parameters of previous modeling. An example of outflow parameters reproducing typical TeV-blazar observations is presented.

Wave Damping by Magnetohydrodynamic Turbulence and Its Effect on Cosmic‐Ray Propagation in the Interstellar Medium

Cosmic rays scatter off magnetic irregularities (Alfven waves) with which they are resonant, that is, waves of wavelength comparable to their gyroradii. These waves may be generated either by the cosmic rays themselves, if they stream faster than the Alfven speed, or by sources of MHD turbulence. Waves excited by streaming cosmic rays are ideally shaped for scattering, whereas the scattering efficiency of MHD turbulence is severely diminished by its anisotropy. We show that MHD turbulence has an indirect effect on cosmic-ray propagation by acting as a damping mechanism for cosmic-ray-generated waves. The hot (coronal) phase of the interstellar medium is the best candidate location for cosmic-ray confinement by scattering from self-generated waves. We relate the streaming velocity of cosmic rays to the rate of turbulent dissipation in this medium for the case in which turbulent damping is the dominant damping mechanism. We conclude that cosmic rays with up to 10^2 GeV could not stream much faster than the Alfven speed but 10^6 GeV cosmic rays would stream unimpeded by self-generated waves, unless the coronal gas were remarkably turbulence-free.

Shock acceleration of energetic particles in wave heated corona

The solar wind wave heating models require substantial amount of wave power in order to efficiently heat and accelerate solar wind. The level of fluctuations is however limited by energetic particle observations. The simplest cyclotron sweep models result in convection-dominated transport, contradicting observations. However, models incorporating wave-wave -interactions, which cause wave energy to cascade in wavenumber, allow more reasonable energetic particle transport in the interplanetary space. The mean free path of the energetic particles remains still relatively short in the corona, providing favorable conditions for coronal mass ejection (CME) related shock acceleration. We study the consequences of this scenario on the energetic particle production related to CMEs. The role of self-generated waves is also discussed.

Shock acceleration of energetic particles in wave heated corona

The solar wind wave heating models require substantial amount of wave power in order to efficiently heat and accelerate solar wind. The level of fluctuations is however limited by energetic particle observations. The simplest cyclotron sweep models result in convection-dominated transport, contradicting observations. However, models incorporating wave-wave -interactions, which cause wave energy to cascade in wavenumber, allow more reasonable energetic particle transport in the interplanetary space. The mean free path of the energetic particles remains still relatively short in the corona, providing favorable conditions for coronal mass ejection (CME) related shock acceleration. We study the consequences of this scenario on the energetic particle production related to CMEs. The role of self-generated waves is also discussed.

On the Possible Reason for Nondetection of TeV Protons in Supernova Remnants

The theory of shock acceleration predicts the maximum particle energy to be limited only by the acceleration time and the size (geometry) of the shock. This led to optimistic estimates for the galactic cosmic-ray energy achievable in supernova remnant (SNR) shocks. The estimates imply that the accelerated particles, while making no strong impact on the shock structure (test-particle approach), are nevertheless scattered by the strong self-generated Alfven waves (turbulent boost) needed to accelerate them quickly. We demonstrate that these two assumptions are in conflict when applied to SNRs of the age required for cosmic-ray acceleration to the knee energy. We study the combined effect of acceleration nonlinearity (shock modification by accelerated particles) and wave generation on the acceleration process. We show that the refraction of self-generated waves resulting from the deceleration of the plasma flow by the pressure of energetic particles causes enhanced losses of these particles. This effect slows down the acceleration and changes the shape of the particle spectrum near the cutoff. The implications for observations of TeV emission from SNRs are also discussed.

Diffusive Shock Acceleration with Self-Consistent Injection

A numerical scheme that incorporates a self-consistent cosmic-ray (CR, hereafter) injection model into the combined gas dynamics and CR diffusion-convection code has been developed. The hydro/CR code can follow in a very cos-effective way the evolution of CR modified shocks by adopting subzone shock-tracking and multi-level Adaptive Mesh Refinement techniques. The injection model is based on interactions of the suprathermal particles with self-generated MHD waves in quasi-parallel shocks. The particle injection is followed numerically by filtering the diffusive flux of suprathermal particles across the shock to upstream region according to a velocity-dependent transparency function, which represents the fraction of leaking suprathermal particles. In the strong shock limit of Mach numbers 20, significant physical processes such as the injection and acceleration seem to become independent of M, while they are sensitively dependent on M for M