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Register a new userTurbulent pitch-angle scattering and diffusive transport of hard-X-ray producing electrons in flaring coronal loops
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Recent observations from {em RHESSI} have revealed that the number of non-thermal electrons in the coronal part of a flaring loop can exceed the number of electrons required to explain the hard X-ray-emitting footpoints of the same flaring loop. Such sources cannot, therefore, be interpreted on the basis of the standard collisional transport model, in which electrons stream along the loop while losing their energy through collisions with the ambient plasma; additional physical processes, to either trap or scatter the energetic electrons, are required. Motivated by this and other observations that suggest that high energy electrons are confined to the coronal region of the source, we consider turbulent pitch angle scattering of fast electrons off low frequency magnetic fluctuations as a confinement mechanism, modeled as a spatial diffusion parallel to the mean magnetic field. In general, turbulent scattering leads to a reduction of the collisional stopping distance of non-thermal electrons along the loop and hence to an enhancement of the coronal HXR source relative to the footpoints. The variation of source size $L$ with electron energy $E$ becomes weaker than the quadratic behavior pertinent to collisional transport, with the slope of $L(E)$ depending directly on the mean free path $lambda$ again pitch angle scattering. Comparing the predictions of the model with observations, we find that $lambda sim$$(10^8-10^9)$ cm for $sim30$ keV, less than the length of a typical flaring loop and smaller than, or comparable to, the size of the electron acceleration region.
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Energetic electrons with power-law spectrum are most commonly observed in astrophysics. This paper investigates electron cyclotron maser emission (ECME) from the power-law electrons, in which strong pitch-angle anisotropy is emphasized. The electron distribution function proposed in this paper can describe various types of pitch-angle anisotropy. Results show that the emission properties of ECME, including radiation growth, propagation, and frequency properties, depend considerably on the types of electron pitch-angle anisotropy, and different wave modes show different dependences on the pitch angle of electrons. In particular, the maximum growth rate of X2 mode rapidly decreases with respect to the electron pitch-angle cosine $mu_0$ at which the electron distribution peaks, while the growth rates for other modes (X1, O1, O2) initially increase before decreasing as $mu_0$ increases. Moreover, the O mode as well as the X mode can be the fastest growth mode, in terms of not only the plasma parameter but also the type of electron pitch-angle distribution. This result presents a significant extension of the recent researches on ECME driven by the lower-energy cutoff of power-law electrons, in which the X mode is generally the fastest growth mode.
A fundamental problem in astrophysics is the interaction between magnetic turbulence and charged particles. It is now possible to use emph{Ramaty High Energy Solar Spectroscopic Imager (RHESSI)} observations of hard X-rays (HXR) emitted by electrons to identify the presence of turbulence and to estimate the magnitude of the magnetic field line diffusion coefficient at least in dense coronal flaring loops.} {We discuss the various possible regimes of cross-field transport of non-thermal electrons resulting from broadband magnetic turbulence in coronal loops. The importance of the Kubo number $K$ as a governing parameter is emphasized and results applicable in both the large and small Kubo number limits are collected.} {Generic models, based on concepts and insights developed in the statistical theory of transport, are applied to the coronal loops and to the interpretation of hard X-ray imaging data in solar flares. The role of trapping effects, which become important in the non-linear regime of transport, is taken into account in the interpretation of the data.} For this flaring solar loop, we constrain the ranges of parallel and perpendicular correlation lengths of turbulent magnetic fields and possible Kubo numbers. We show that a substantial amount of magnetic fluctuations with energy $sim 1%$ (or more) of the background field can be inferred from the measurements of the magnetic diffusion coefficient inside thick-target coronal loops.
X-radiation from energetic electrons is the prime diagnostic of flare-accelerated electrons. The observed X-ray flux (and polarization state) is fundamentally a convolution of the cross-section for the hard X-ray emission process(es) in question with the electron distribution function, which is in turn a function of energy, direction, spatial location and time. To address the problems of particle propagation and acceleration one needs to infer as much information as possible on this electron distribution function, through a deconvolution of this fundamental relationship. This review presents recent progress toward this goal using spectroscopic, imaging and polarization measurements, primarily from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Previous conclusions regarding the energy, angular (pitch angle) and spatial distributions of energetic electrons in solar flares are critically reviewed. We discuss the role and the observational evidence of several radiation processes: free-free electron-ion, free-free electron-electron, free-bound electron-ion bremsstrahlung, photoelectric absorption and Compton back-scatter (albedo), using both spectroscopic and imaging techniques. This unprecedented quality of data allows for the first time inference of the angular distributions of the X-ray-emitting electrons using albedo, improved model-independent inference of electron energy spectra and emission measures of thermal plasma. Moreover, imaging spectroscopy has revealed hitherto unknown details of solar flare morphology and detailed spectroscopy of coronal, footpoint and extended sources in flaring regions. Additional attempts to measure hard X-ray polarization were not sufficient to put constraints on the degree of anisotropy of electrons, but point to the importance of obtaining good quality polarization data.
Pitch-angle scattering rates for cosmic-ray particles in magnetohydrodynamic (MHD) simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence with propagating Alfven waves, but an effect of the spatial structure of electric fields in cross-helical MHD turbulence.
We present the first results of a search for transient hard X-ray (HXR) emission in the quiet solar corona with the textit{Nuclear Spectroscopic Telescope Array} (textit{NuSTAR}) satellite. While textit{NuSTAR} was designed as an astrophysics mission, it can observe the Sun above 2~keV with unprecedented sensitivity due to its pioneering use of focusing optics. textit{NuSTAR} first observed quiet Sun regions on 2014 November 1, although out-of-view active regions contributed a notable amount of background in the form of single-bounce (unfocused) X-rays. We conducted a search for quiet Sun transient brightenings on time scales of 100 s and set upper limits on emission in two energy bands. We set 2.5--4~keV limits on brightenings with time scales of 100 s, expressed as the temperature T and emission measure EM of a thermal plasma. We also set 10--20~keV limits on brightenings with time scales of 30, 60, and 100 s, expressed as model-independent photon fluxes. The limits in both bands are well below previous HXR microflare detections, though not low enough to detect events of equivalent T and EM as quiet Sun brightenings seen in soft X-ray observations. We expect future observations during solar minimum to increase the textit{NuSTAR} sensitivity by over two orders of magnitude due to higher instrument livetime and reduced solar background.
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