Mixing of shear Alfven wave packets

The propagation of shear Alfven wave packets in inhomogeneous magnetic fields, at the origin of their distortion, regardless of the occurrence of non-linear coupling, is considered. It is shown that the distortion mechanism can be regarded as mixing process and hence, standard "phase mixing" corresponds to the effect of an "Alfvenic" shear flow while enhanced dissipation at a magnetic X-point corresponds to mixing by an "Alfvenic" strain flow. The evolution of the global wave field is supposed to result from the dynamics of a superposition of wave packets and a kinetic equation for the wave energy is obtained following this eikonal (WKB) description. Since shear Alfven wave packets experience continuous shearing/straining while transported by an inhomogeneous Alfvenic flow $\mathbf{V}_{A}$, their mixing process, in physical space, is also a cascade of wave energy in k-space. The wave energy spectrum resulting from this linear mechanism of energy transfer is determined for the special case of waves propagating along chaotic magnetic field lines, the analog of a chaotic mixing process. The latter follows a $k^{-1}$ power-law, in the energy conserving range in $k$ space.Comment: revised, final version, Astron. Astrophys. in pres

A Classification Scheme For Turbulent Acceleration Processes In Solar Flares

We establish a classification scheme for stochastic acceleration models involving low-frequency plasma turbulence in a strongly magnetized plasma. This classification takes into account both the properties of the accelerating electromagnetic field, and the nature of the transport of charged particles in the acceleration region. We group the acceleration processes as either resonant, non-resonant or resonant-broadened, depending on whether the particle motion is free-streaming along the magnetic field, diffusive or a combination of the two. Stochastic acceleration by moving magnetic mirrors and adiabatic compressions are addressed as illustrative examples. We obtain expressions for the momentum-dependent diffusion coefficient $D(p)$, both for general forms of the accelerating force and for the situation when the electromagnetic force is wave-like, with a specified dispersion relation $\omega=\omega(k)$. Finally, for models considered, we calculate the energy-dependent acceleration time, a quantity that can be directly compared with observations of the time profile of the radiation field produced by the accelerated particles, such as during solar flares.Comment: 45 pages, submitted to Astrophysical Journa

The collisional relaxation of electrons in hot flaring plasma and inferring the properties of solar flare accelerated electrons from X-ray observations

X-ray observations are a direct diagnostic of fast electrons produced in solar flares, energized during the energy release process and directed towards the Sun. Since the properties of accelerated electrons can be substantially changed during their transport and interaction with the background plasma, a model must ultimately be applied to X-ray observations in order to understand the mechanism responsible for their acceleration. A cold thick target model is ubiquitously used for this task, since it provides a simple analytic relationship between the accelerated electron spectrum and the emitting electron spectrum in the X-ray source, with the latter quantity readily obtained from X-ray observations. However, such a model is inappropriate for the majority of solar flares in which the electrons propagate in a hot megaKelvin plasma, because it does not take into account the physics of thermalization of fast electrons. The use of a more realistic model, properly accounting for the properties of the background plasma, and the collisional diffusion and thermalization of electrons, can alleviate or even remove many of the traditional problems associated with the cold thick target model and the deduction of the accelerated electron spectrum from X-ray spectroscopy, such as the number problem and the need to impose an ad hoc low energy cut-off.Comment: 6 pages, 14th Annual International Astrophysics Conference Tampa proceeding

Particle acceleration and transport in reconnecting twisted loops in a stratified atmosphere

Twisted coronal loops should be ubiquitous in the solar corona. Twisted magnetic fields contain excess magnetic energy, which can be released during magnetic reconnection, causing solar flares. The aim of this work is to investigate magnetic reconnection, and particle acceleration and transport in kink-unstable twisted coronal loops, with a focus on the effects of resistivity, loop geometry and atmospheric stratification. Another aim is to perform forward-modelling of bremsstrahlung emission and determine the structure of hard X-ray sources. We use a combination of magnetohydrodynamic (MHD) and test-particle methods. First, the evolution of the kinking coronal loop is considered using resistive MHD model, incorporating atmospheric stratification and loop curvature. Then, the obtained electric and magnetic fields and density distributions are used to calculate electron and proton trajectories using a guiding-centre approximation, taking into account Coulomb collisions. It is shown that electric fields in twisted coronal loops can effectively accelerate protons and electrons to energies up to 10 MeV. High-energy particles have hard, nearly power-law energy spectra. The volume occupied by high-energy particles demonstrates radial expansion, which results in the expansion of the visible hard X-ray loop and a gradual increase in hard X-ray footpoint area. Synthesised hard X-ray emission reveals strong footpoint sources and the extended coronal source, whose intensity strongly depends on the coronal loop density

The role of diffusion in the transport of energetic electrons during solar flares

The transport of the energy contained in suprathermal electrons in solar flares plays a key role in our understanding of many aspects of flare physics, from the spatial distributions of hard X-ray emission and energy deposition in the ambient atmosphere to global energetics. Historically the transport of these particles has been largely treated through a deterministic approach, in which first-order secular energy loss to electrons in the ambient target is treated as the dominant effect, with second-order diffusive terms (in both energy and angle) being generally either treated as a small correction or even neglected. We here critically analyze this approach, and we show that spatial diffusion through pitch-angle scattering necessarily plays a very significant role in the transport of electrons. We further show that a satisfactory treatment of the diffusion process requires consideration of non-local effects, so that the electron flux depends not just on the local gradient of the electron distribution function but on the value of this gradient within an extended region encompassing a significant fraction of a mean free path. Our analysis applies generally to pitch-angle scattering by a variety of mechanisms, from Coulomb collisions to turbulent scattering. We further show that the spatial transport of electrons along the magnetic field of a flaring loop can be modeled rather effectively as a Continuous Time Random Walk with velocity-dependent probability distribution functions of jump sizes and occurrences, both of which can be expressed in terms of the scattering mean free path.Comment: 11 pages, to be published in Astrophysical Journa

Wigner function negativity and contextuality in quantum computation on rebits

We describe a universal scheme of quantum computation by state injection on rebits (states with real density matrices). For this scheme, we establish contextuality and Wigner function negativity as computational resources, extending results of [M. Howard et al., Nature 510, 351--355 (2014)] to two-level systems. For this purpose, we define a Wigner function suited to systems of $n$ rebits, and prove a corresponding discrete Hudson's theorem. We introduce contextuality witnesses for rebit states, and discuss the compatibility of our result with state-independent contextuality.Comment: 18 + 4 page

Suppression of parallel transport in turbulent magnetized plasmas and its impact on the non-thermal and thermal aspects of solar flares

The transport of the energy contained in electrons, both thermal and suprathermal, in solar flares plays a key role in our understanding of many aspects of the flare phenomenon, from the spatial distribution of hard X-ray emission to global energetics. Motivated by recent RHESSI observations that point to the existence of a mechanism that confines electrons to the coronal parts of flare loops more effectively than Coulomb collisions, we here consider the impact of pitch-angle scattering off turbulent magnetic fluctuations on the parallel transport of electrons in flaring coronal loops. It is shown that the presence of such a scattering mechanism in addition to Coulomb collisional scattering can significantly reduce the parallel thermal and electrical conductivities relative to their collisional values. We provide illustrative expressions for the resulting thermoelectric coefficients that relate the thermal flux and electrical current density to the temperature gradient and the applied electric field. We then evaluate the effect of these modified transport coefficients on the flare coronal temperature that can be attained, on the post-impulsive-phase cooling of heated coronal plasma, and on the importance of the beam-neutralizing return current on both ambient heating and the energy loss rate of accelerated electrons. We also discuss the possible ways in which anomalous transport processes have an impact on the required overall energy associated with accelerated electrons in solar flares

Solar plasma radio emission in the presence of imbalanced turbulence of kinetic-scale Alfv\'en waves

We study the influence of kinetic-scale Alfv\'enic turbulence on the generation of plasma radio emission in the solar coronal regions where the plasma/magnetic pressure ratio $\beta$ is smaller than the electron/ion mass ratio $m_{e}/m_{i}$. The present study is motivated by the phenomenon of solar type I radio storms associated with the strong magnetic field of active regions. The measured brightness temperature of the type I storms can be up to $10^{10}$ K for continuum emission, and can exceed $10^{11}$ K for type I bursts. At present, there is no generally accepted theory explaining such high brightness temperatures and some other properties of the type I storms. We propose the model with the imbalanced turbulence of kinetic-scale Alfv\'en waves producing an asymmetric quasilinear plateau on the upward half of the electron velocity distribution. The Landau damping of resonant Langmuir waves is suppressed and their amplitudes grow spontaneously above the thermal level. The estimated saturation level of Langmuir waves is high enough to generate observed type I radio emission at the fundamental plasma frequency. Harmonic emission does not appear in our model because the backward-propagating Langmuir waves undergo a strong Landau damping. Our model predicts $100\%$ polarization in the sense of the ordinary (o-) mode of type I emission.Comment: 27 pages, 8 figures, accepted for publication in Solar Physic

Heating and cooling of coronal loops with turbulent suppression of parallel heat conduction

Using the "enthalpy-based thermal evolution of loops" (EBTEL) model, we investigate the hydrodynamics of the plasma in a flaring coronal loop in which heat conduction is limited by turbulent scattering of the electrons that transport the thermal heat flux. The EBTEL equations are solved analytically in each of the two (conduction-dominated and radiation-dominated) cooling phases. Comparison of the results with typical observed cooling times in solar flares shows that the turbulent mean free-path $\lambda_T$ lies in a range corresponding to a regime in which classical (collision-dominated) conduction plays at most a limited role. We also consider the magnitude and duration of the heat input that is necessary to account for the enhanced values of temperature and density at the beginning of the cooling phase and for the observed cooling times. We find through numerical modeling that in order to produce a peak temperature $\simeq 1.5 \times 10^7$~K and a 200~s cooling time consistent with observations, the flare heating profile must extend over a significant period of time; in particular, its lingering role must be taken into consideration in any description of the cooling phase. Comparison with observationally-inferred values of post-flare loop temperatures, densities, and cooling times thus leads to useful constraints on both the magnitude and duration of the magnetic energy release in the loop, as well as on the value of the turbulent mean free-path $\lambda_T$.Comment: 16 pages, 4 figures, to be published in The Astrophysical Journa

On the variation of solar flare coronal x-ray source sizes with energy

Observations with {\em RHESSI} have enabled the detailed study of the structure of dense hard X-ray coronal sources in solar flares. The variation of source extent with electron energy has been discussed in the context of streaming of non-thermal particles in a one-dimensional cold-target model, and the results used to constrain both the physical extent of, and density within, the electron acceleration region. Here we extend this investigation to a more physically realistic model of electron transport that takes into account the finite temperature of the ambient plasma, the initial pitch-angle distribution of the accelerated electrons, and the effects of collisional pitch-angle scattering. The finite temperature results in the thermal diffusion of electrons, that leads to the observationally-inferred value of the acceleration region volume being an overestimate of its true value. The different directions of the electron trajectories, a consequence of both the non-zero injection pitch-angle and scattering within the target, cause the projected propagation distance parallel to the guiding magnetic field to be reduced, so that a one-dimensional interpretation can overestimate the actual density by a factor of up to $\sim 6$. The implications of these results for the determination of acceleration region properties (specific acceleration rate, filling factor, etc.) are discussed.Comment: 45 pages, 9 figures, accepted for publication in Ap