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In this Roadmap, we present a vision for the future of submillimetre and millimetre astronomy in the United Kingdom over the next decade and beyond. This Roadmap has been developed in response to the recommendation of the Astronomy Advisory Panel (AAP) of the STFC in the AAP Astronomy Roadmap 2022. In order to develop our stragetic priorities and recommendations, we surveyed the UK submillimetre and millimetre community to determine their key priorities for both the near-term and long-term future of the field. We further performed detailed reviews of UK leadership in submillimetre/millimetre science and instrumentation. Our key strategic priorities are as follows: 1. The UK must be a key partner in the forthcoming AtLAST telescope, for which it is essential that the UK remains a key partner in the JCMT in the intermediate term. 2. The UK must maintain, and if possible enhance, access to ALMA and aim to lead parts of instrument development for ALMA2040. Our strategic priorities complement one another: AtLAST (a 50m single-dish telescope) and an upgraded ALMA (a large configurable interferometric array) would be in synergy, not competition, with one another. Both have identified and are working towards the same overarching science goals, and both are required in order to fully address these goals., Comment: 91 pages plus cover, 38 figures. Submitted to the Science and Technology Facilities Council, August 2024. One figure corrected (v2); new appendix with STFC Q&A; corrected SMA access statement; updated references, acronyms & author list (v3)

In this study we examine the radial dependence of the inertial and dissipation range indices, as well as the spectral break separating the inertial and dissipation range in power density spectra of interplanetary magnetic field fluctuations using {\it Parker Solar Probe} data from the fifth solar encounter between $\sim$0.1 and $\sim$0.7 au. The derived break wavenumber compares reasonably well with previous estimates at larger radial distances and is consistent with gyro-resonant damping of Alfv\'enic fluctuations by thermal protons. We find that the inertial scale power law index varies between approximately -1.65 and -1.45. This is consistent with either the Kolmogorov (-5/3) or Iroshnikov-Kraichnan (-3/2) values, has a very weak radial dependence with a possible hint that the spectrum becomes steeper closer to the Sun. The dissipation range power law index, however, has a clear dependence on radial distance (and turbulence age), decreasing from -3 near 0.7 au (4 days) to -4 [$\pm$0.3] at 0.1 au (0.75 days) closer to the Sun., Comment: Accepted for publication in ApJ

Metric and decametric radio-emissions from the Sun are the only direct source of information about the dynamics of non-thermal electrons in the upper corona. In addition, the combination of spectral and imaging (sizes, shapes, and positions) observations of low-frequency radio sources can be used as a unique diagnostic tool to probe plasma turbulence in the solar corona and inner heliosphere. The geometry of the low-frequency sources and its variation with frequency are still not understood, primarily due to the relatively low spatial resolution available for solar observations. Here we report the first detailed multi-frequency analysis of the sizes of solar radio sources observed by the Low-Frequency Array (LOFAR). Furthermore, we investigate the source shapes by approximating the derived intensity distributions using 2D Gaussian profiles with elliptical half-maximum contours. These measurements have been made possible by a novel empirical method for evaluating the instrumental and ionospheric effects on radio maps based on known source observations. The obtained deconvolved sizes of the sources are found to be smaller than previous estimations, and often show higher ellipticity. The sizes and ellipticities of the sources inferred using 2D Gaussian approximation, and their variation with frequency are consistent with models of anisotropic radio-wave scattering in the solar corona., Comment: Accepted for publication in the Astrophysical Journal

We use multi-spacecraft observations of invididual type III radio bursts in order to calculate the directivity of the radio emission, to be compared to the results of ray-tracing simulations of the radio-wave propagation and probe the plasma properties of the inner heliosphere. Ray-tracing simulations of radio-wave propagation with anisotropic scattering on density inhomogeneities are used to study the directivity of radio emissions. Simultaneous observations of type III radio bursts by four widely-separated spacecraft are used to calculate the directivity and position of the radio sources. The shape of the directivity pattern deduced for individual events is compared to the directivity pattern resulting from the ray-tracing simulations. We show that simultaneous observations of type radio III bursts by 4 different probes provide the opportunity to estimate the radio source positions and the directivity of the radio emission. The shape of the directivity varies from one event to another, and is consistent with anisotropic scattering of the radio-waves.

Solar Orbiter is the first space mission observing the solar plasma both in situ and remotely, from a close distance, in and out of the ecliptic. The ultimate goal is to understand how the Sun produces and controls the heliosphere, filling the Solar System and driving the planetary environments. With six remote-sensing and four in-situ instrument suites, the coordination and planning of the operations are essential to address the following four top-level science questions: (1) What drives the solar wind and where does the coronal magnetic field originate? (2) How do solar transients drive heliospheric variability? (3) How do solar eruptions produce energetic particle radiation that fills the heliosphere? (4) How does the solar dynamo work and drive connections between the Sun and the heliosphere? Maximising the mission's science return requires considering the characteristics of each orbit, including the relative position of the spacecraft to Earth (affecting downlink rates), trajectory events (such as gravitational assist manoeuvres), and the phase of the solar activity cycle. Furthermore, since each orbit's science telemetry will be downloaded over the course of the following orbit, science operations must be planned at mission level, rather than at the level of individual orbits. It is important to explore the way in which those science questions are translated into an actual plan of observations that fits into the mission, thus ensuring that no opportunities are missed. First, the overarching goals are broken down into specific, answerable questions along with the required observations and the so-called Science Activity Plan (SAP) is developed to achieve this. The SAP groups objectives that require similar observations into Solar Orbiter Observing Plans (SOOPs), resulting in a strategic, top-level view of the optimal opportunities for science observations during the mission lifetime., Comment: 20 pages, 1 figure, accepted by Astronomy & Astrophysics

Incoherent radar scatter from the ionosphere will, for equilibrium conditions, show two symmetric ion-acoustic lines, one for each direction of wave propagation. Many observation, from the EISCAT Svalbard Radar (ESR) for instance, demonstrate that the symmetry of this ion line can be broken, accompanied by an enhanced, nonthermal, level of fluctuations, i.e., Naturally Enhanced Ion-Acoustic Lines (NEIALs). Several models have been proposed for explaining these naturally enhanced lines. Here, we consider one of these, suggesting that decay of electron beam excited Langmuir waves gives rise to enhanced asymmetric ion lines in the ionosphere. We use a weak-turbulence approximation, and identify crucial parameters for Langmuir decay processes to be effective in generating the observed signals., Comment: 4 figures

The self-consistent description of Langmuir wave and ion-sound wave turbulence in the presence of an electron beam is presented for inhomogeneous non-isothermal plasmas. Full numerical solutions of the complete set of kinetic equations for electrons, Langmuir waves, and ion-sound waves are obtained for a inhomogeneous unmagnetized plasma. The result show that the presence of inhomogeneity significantly changes the overall evolution of the system. The inhomogeneity is effective in shifting the wavenumbers of the Langmuir waves, and can thus switch between different process governing the weakly turbulent state. The results can be applied to a variety of plasma conditions, where we choose solar coronal parameters as an illustration, when performing the numerical analysis., Comment: 11 pages, 8 figures

Electromagnetic wave scattering off density inhomogeneities in the solar corona is an important process which determines both the apparent source size and the time profile of radio bursts observed at 1 AU. Here we model the scattering process using a Fokker-Planck equation and apply this formalism to several regimes of interest. In the first regime the density fluctuations are considered quasi-static and diffusion in wavevector space is dominated by angular diffusion on the surface of a constant energy sphere. In the small-angle ("pencil beam") approximation, this diffusion further occurs over a small solid angle in wavevector space. The second regime corresponds to a much later time, by which scattering has rendered the photon distribution near-isotropic resulting in a spatial diffusion of the radiation. The third regime involves time-dependent fluctuations and, therefore, Fermi acceleration of photons. Combined, these results provide a comprehensive theoretical framework within which to understand several important features of propagation of radio burst waves in the solar corona: emitted photons are accelerated in a relatively small inner region and then diffuse outwards to larger distances. En route, angular diffusion results both in source sizes which are substantially larger than the intrinsic source, and in observed intensity-versus-time profiles that are asymmetric, with a sharp rise and an exponential decay. Both of these features are consistent with observations of solar radio bursts., Comment: 28 pages , 1 figure, submitted to ApJ

The Square Kilometre Array (SKA) will be the largest radio telescope ever built, aiming to provide collecting area larger than 1 km$^2$. The SKA will have two independent instruments, SKA-LOW comprising of dipoles organized as aperture arrays in Australia and SKA-MID comprising of dishes in South Africa. Currently the phase-1 of SKA, referred to as SKA1, is in its late design stage and construction is expected to start in 2020. Both SKA1-LOW (frequency range of 50-350 MHz) and SKA1-MID Bands 1, 2, and 5 (frequency ranges of 350-1050, 950-1760, and 4600-15300 MHz, respectively) are important for solar observations. In this paper we present SKA's unique capabilities in terms of spatial, spectral, and temporal resolution, as well as sensitivity and show that they have the potential to provide major new insights in solar physics topics of capital importance including (i) the structure and evolution of the solar corona, (ii) coronal heating, (iii) solar flare dynamics including particle acceleration and transport, (iv) the dynamics and structure of coronal mass ejections, and (v) the solar aspects of space weather. Observations of the Sun jointly with the new generation of ground-based and space-borne instruments promise unprecedented discoveries., Comment: Accepted for publication in Advances in Space Research

Observations of solar flares at sub-THz frequencies (mm and sub-mm wavelengths) over the last two decades often show a spectral component rising with frequency. Unlike a typical gyrosynchrotron spectrum decreasing with frequency, or a weak thermal component from hot coronal plasma, the observations can demonstrate a high flux level (up to ~10^4 s.f.u. at 0.4 THz) and fast variability on sub-second time scales. Although, many models has been put forward to explain the puzzling observations, none of them have clear observational support. Here we propose a scenario to explain the intriguing sub-THz observations. We show that the model, based on free-free emission from the plasma of flare ribbons at temperatures 10^4-10^6 K, is consistent with all existing observations of frequency-rising sub-THz flare emission. The model provides a temperature diagnostic of the flaring chromosphere and suggests fast heating and cooling of the dense transition region plasma., Comment: 6 pages, 3 figures, 2 tables, A&A, accepted

A considerable fraction of the energy in a solar flare is released as suprathermal electrons; such electrons play a major role in energy deposition in the ambient atmosphere and hence the atmospheric response to flare heating. Historically the transport of these particles has been approximated 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 neglected. However, it has recently been pointed out that while neglect of diffusion in energy may indeed be negligible, diffusion in angle is of the same order as deterministic scattering and hence must be included. Here we therefore investigate the effect of angular scattering on the energy deposition profile in the flaring atmosphere. A relatively simple compact expression for the spatial distribution of energy deposition into the ambient plasma is presented and compared with the corresponding deterministic result. For unidirectional injection there is a significant shift in heating from the lower corona to the upper corona; this shift is much smaller for isotropic injection. We also compare the heating profiles due to return current Ohmic heating in the diffusional and deterministic models.

The phenomena observed at the Sun have a variety of unique radio signatures that can be used to diagnose the processes in the solar atmosphere. The insights provided by radio obervations are further enhanced when they are combined with observations from space-based telescopes. This special issue demonstrates the power of combination methodology at work and provides new results on i) type I solar radio bursts and thermal emission to study active regions; ii) type II and IV bursts to better understand the structure of coronal mass ejections; iii)~non-thermal gyro-synchrotron and/or type III bursts to improve characterization of particle acceleration in solar flares. The ongoing improvements in time, frequency, and spatial resolutions of ground-based telescopes reveal new levels of solar phenomena complexity and pose new questions.

Solar radio emission features a large number of fine structures demonstrating great variability in frequency and time. We present spatially resolved spectral radio observations of type IIIb bursts in the $30-80$ MHz range made by the Low Frequency Array (LOFAR). The bursts show well-defined fine frequency structuring called "stria" bursts. The spatial characteristics of the stria sources are determined by the propagation effects of radio waves; their movement and expansion speeds are in the range of 0.1-0.6c. Analysis of the dynamic spectra reveals that both the spectral bandwidth and the frequency drift rate of the striae increase with an increase of their central frequency; the striae bandwidths are in the range of ~20-100 kHz and the striae drift rates vary from zero to ~0.3 MHz s^-1. The observed spectral characteristics of the stria bursts are consistent with the model involving modulation of the type III burst emission mechanism by small-amplitude fluctuations of the plasma density along the electron beam path. We estimate that the relative amplitude of the density fluctuations is of dn/n~10^-3, their characteristic length scale is less than 1000 km, and the characteristic propagation speed is in the range of 400-800 km/s. These parameters indicate that the observed fine spectral structures could be produced by propagating magnetohydrodynamic waves.

Type II radio bursts are evidence of shocks in the solar atmosphere and inner heliosphere that emit radio waves ranging from sub-meter to kilometer lengths. These shocks may be associated with CMEs and reach speeds higher than the local magnetosonic speed. Radio imaging of decameter wavelengths (20-90 MHz) is now possible with LOFAR, opening a new radio window in which to study coronal shocks that leave the inner solar corona and enter the interplanetary medium and to understand their association with CMEs. To this end, we study a coronal shock associated with a CME and type II radio burst to determine the locations at which the radio emission is generated, and we investigate the origin of the band-splitting phenomenon., Comment: 7 Figures, 9 Pages

Imaging spectroscopy in X-rays with RHESSI provide the possibility to investigate the spatial evolution of the X-ray emitting electron distribution and therefore to study the transport effects on energetic electrons during solar flares. We study the energy dependence of the energetic electron scattering mean free path in the solar corona. We use the imaging spectroscopy technique with RHESSI to study the evolution of energetic electrons distribution in different part of the magnetic loop during the 2004 May 21 flare. These observations are compared with the radio observations of the gyrosynchrotron radiation of the same flare by Kuznetsov and Kontar (2015), and with the predictions of the diffusive transport model described by Kontar et al. (2014). The X-ray analysis shows a trapping of energetic electrons in the corona and a spectral hardening of the energetic electron distribution between the top of the loop and the footpoints. Coronal trapping of electrons is stronger for the radio-emitting electrons than for the X-ray-emitting electrons. These observations can be explained by the diffusive transport model derived by Kontar et al. (2014). We show that the combination of X-ray and radio diagnostics is a powerful tool to study electron transport in the solar corona in different energy domains. We show that the diffusive transport model can explain our observations; and in the range 25-500 keV, the electron scattering mean free path decreases with electron energy. We can estimate for the first time the scattering mean free path dependence on energy in the corona., Comment: 15 pages, accepted in A&A

Solar radio observations provide a unique diagnostic of the outer solar atmosphere. However, the inhomogeneous turbulent corona strongly affects the propagation of the emitted radio waves, so decoupling the intrinsic properties of the emitting source from the effects of radio-wave propagation has long been a major challenge in solar physics. Here we report quantitative spatial and frequency characterization of solar radio burst fine structures observed with the LOw Frequency Array (LOFAR), an instrument with high time resolution that also permits imaging at scales much shorter than those corresponding to radio-wave propagation in the corona. The observations demonstrate that radio-wave propagation effects, and not the properties of the intrinsic emission source, dominate the observed spatial characteristics of radio burst images. These results permit more accurate estimates of source brightness temperatures, and open opportunities for quantitative study of the mechanisms that create the turbulent coronal medium through which the emitted radiation propagates., Comment: 20 pages, 9 figures

The energy released in solar flares derives from a reconfiguration of magnetic fields to a lower energy state, and is manifested in several forms, including bulk kinetic energy of the coronal mass ejection, acceleration of electrons and ions, and enhanced thermal energy that is ultimately radiated away across the electromagnetic spectrum from optical to X-rays. Using an unprecedented set of coordinated observations, from a suite of instruments, we here report on a hitherto largely overlooked energy component -- the kinetic energy associated with small-scale turbulent mass motions. We show that the spatial location of, and timing of the peak in, turbulent kinetic energy together provide persuasive evidence that turbulent energy may play a key role in the transfer of energy in solar flares. Although the kinetic energy of turbulent motions accounts, at any given time, for only $\sim (0.5-1)$\% of the energy released, its relatively rapid ($\sim$$1-10$~s) energization and dissipation causes the associated throughput of energy (i.e., power) to rival that of major components of the released energy in solar flares, and thus presumably in other astrophysical acceleration sites., Comment: 5pages, 4 figures, to be published in Physical Review Letters

Flare-driven coronal rain can manifest from rapidly cooled plasma condensations near coronal loop-tops in thermally unstable post-flare arcades. We detect 5 phases that characterise the post-flare decay: heating, evaporation, conductive cooling dominance for ~120 s, radiative / enthalpy cooling dominance for ~4700 s and finally catastrophic cooling occurring within 35-124 s leading to rain strands with s periodicity of 55-70 s. We find an excellent agreement between the observations and model predictions of the dominant cooling timescales and the onset of catastrophic cooling. At the rain formation site we detect co-moving, multi-thermal rain clumps that undergo catastrophic cooling from ~1 MK to ~22000 K. During catastrophic cooling the plasma cools at a maximum rate of 22700 K s-1 in multiple loop-top sources. We calculated the density of the EUV plasma from the DEM of the multi-thermal source employing regularised inversion. Assuming a pressure balance, we estimate the density of the chromospheric component of rain to be 9.21x10^11 +-1.76x10^11 cm-3 which is comparable with quiescent coronal rain densities. With up to 8 parallel strands in the EUV loop cross section, we calculate the mass loss rate from the post-flare arcade to be as much as 1.98x10^12 +/-4.95x10^11 g s-1. Finally, we reveal a close proximity between the model predictions of 10^5.8 K and the observed properties between 10^5.9 K and 10^6.2 K, that defines the temperature onset of catastrophic cooling. The close correspondence between the observations and numerical models suggests that indeed acoustic waves (with a sound travel time of 68 s) could play an important role in redistributing energy and sustaining the enthalpy-based radiative cooling., Comment: 23 pages, 21 figures

To solve a number of problems in solar physics related to mechanisms of energy release in solar corona parameters of hot coronal plasma are required, such as energy distribution, emission measure, differential emission measure, and their evolution with time. Of special interest is the distribution of solar plasma by energies, which can evolve from a nearly Maxwellian distribution to a distribution with a more complex structure during a solar flare. The exact form of this distribution for low-energy particles, which receive the bulk of flare energy, is still poorly known; therefore, detailed investigations are required. We present a developed method of simultaneous fitting of data from two spacecrafts Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) and Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), using a differential emission measure and a thin target model for the August 14, 2010 flare event.

EUV (Extreme-Ultraviolet) waves are globally propagating disturbances that have been observed since the era of the SoHO/EIT instrument. Although the kinematics of the wave front and secondary wave components have been widely studied, there is not much known about the generation and plasma properties of the wave. In this paper we discuss the effect of an EUV wave on the local plasma as it passes through the corona. We studied the EUV wave, generated during the 2011 February 15 X-class flare/CME event, using Differential Emission Measure diagnostics. We analyzed regions on the path of the EUV wave and investigated the local density and temperature changes. From our study we have quantitatively confirmed previous results that during wave passage the plasma visible in the Atmospheric Imaging Assembly (AIA) 171A channel is getting heated to higher temperatures corresponding to AIA 193A and 211A channels. We have calculated an increase of 6 - 9% in density and 5 - 6% in temperature during the passage of the EUV wave. We have compared the variation in temperature with the adiabatic relationship and have quantitatively demonstrated the phenomenon of heating due to adiabatic compression at the wave front. However, the cooling phase does not follow adiabatic relaxation but shows slow decay indicating slow energy release being triggered by the wave passage. We have also identified that heating is taking place at the front of the wave pulse rather than at the rear. Our results provide support for the case that the event under study here is a compressive fast-mode wave or a shock., Comment: Accepted for publication in ApJ

Extending previous studies of nonthermal electron transport in solar flares which include the effects of collisional energy diffusion and thermalization of fast electrons, we present an analytic method to infer more accurate estimates of the accelerated electron spectrum in solar flares from observations of the hard X-ray spectrum. Unlike for the standard cold-target model, the spatial characteristics of the flaring region, especially the necessity to consider a finite volume of hot plasma in the source, need to be taken into account in order to correctly obtain the injected electron spectrum from the source-integrated electron flux spectrum (a quantity straightforwardly obtained from hard X-ray observations). We show that the effect of electron thermalization can be significant enough to nullify the need to introduce an {\it ad hoc} low-energy cutoff to the injected electron spectrum in order to keep the injected power in non-thermal electrons at a reasonable value. Rather the suppression of the inferred low-energy end of the injected spectrum compared to that deduced from a cold-target analysis allows the inference from hard X-ray observations of a more realistic energy in injected non-thermal electrons in solar flares., Comment: accepted for publication in ApJ

The Atacama Large Millimeter/submillimeter Array (ALMA) is a new powerful tool for observing the Sun at high spatial, temporal, and spectral resolution. These capabilities can address a broad range of fundamental scientific questions in solar physics. The radiation observed by ALMA originates mostly from the chromosphere - a complex and dynamic region between the photosphere and corona, which plays a crucial role in the transport of energy and matter and, ultimately, the heating of the outer layers of the solar atmosphere. Based on first solar test observations, strategies for regular solar campaigns are currently being developed. State-of-the-art numerical simulations of the solar atmosphere and modeling of instrumental effects can help constrain and optimize future observing modes for ALMA. Here we present a short technical description of ALMA and an overview of past efforts and future possibilities for solar observations at submillimeter and millimeter wavelengths. In addition, selected numerical simulations and observations at other wavelengths demonstrate ALMA's scientific potential for studying the Sun for a large range of science cases., Comment: 73 pages, 21 figures ; Space Science Reviews (accepted December 10th, 2015); accepted version

The Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) was initiated in 2014 in connection with two ALMA development studies. The Atacama Large Millimeter/submillimeter Array (ALMA) is a powerful new tool, which can also observe the Sun at high spatial, temporal, and spectral resolution. The international SSALMONetwork aims at coordinating the further development of solar observing modes for ALMA and at promoting scientific opportunities for solar physics with particular focus on numerical simulations, which can provide important constraints for the observing modes and can aid the interpretation of future observations. The radiation detected by ALMA originates mostly in the solar chromosphere - a complex and dynamic layer between the photosphere and corona, which plays an important role in the transport of energy and matter and the heating of the outer layers of the solar atmosphere. Potential targets include active regions, prominences, quiet Sun regions, flares. Here, we give a brief overview over the network and potential science cases for future solar observations with ALMA., Comment: 15 pages, 3 figures, to appear in Advances in Solar Physics (special issue of Advances in Space Research, AdSR), proceedings of the 14th European Solar Physics Meeting (ESPM-14, Dublin, Ireland, September 2014); (resubmitted version after minor revision)

We study a model of particle acceleration coupled with an MHD model of magnetic reconnection in unstable twisted coronal loops. The kink instability leads to the formation of helical currents with strong parallel electric fields resulting in electron acceleration. The motion of electrons in the electric and magnetic fields of the reconnecting loop is investigated using a test-particle approach taking into account collisional scattering. We discuss the effects of Coulomb collisions and magnetic convergence near loop footpoints on the spatial distribution and energy spectra of high-energy electron populations and possible implications on the hard X-ray emission in solar flares.

Non-thermal electrons accelerated in the solar corona can produce intense coherent radio emission, known as solar type III radio bursts. This intense radio emission is often observed from hundreds of MHz in the corona down to the tens of kHz range in interplanetary space. It involves a chain of physical processes from the generation of Langmuir waves to nonlinear processes of wave-wave interaction. We develop a self-consistent model to calculate radio emission from a non-thermal electron population over large frequency range, including the effects of electron transport, Langmuir wave-electron interaction, the evolution of Langmuir waves due to non-linear wave-wave interactions, Langmuir wave conversion into electromagnetic emission, and finally escape of the electromagnetic waves. For the first time we simulate escaping radio emission over a broad frequency range from 500~MHz down to a few MHz and infer key properties of the radio emission observed: the onset (starting) frequency, {identification as fundamental or harmonic emission}, peak flux density, instantaneous frequency bandwidth, and timescales for rise and decay. Comparing with the observations, these large scale simulations enable us to identify the processes governing the key type III solar radio burst characteristics.

We have performed a statistical study of $152$ Type III radio bursts observed by Solar TErrestrial RElations Observatory (STEREO)/Waves between May 2007 and February 2013. We have investigated the flux density between $125$kHz and $16$MHz. Both high- and low-frequency cutoffs have been observed in $60\,%$ of events suggesting an important role of propagation. As already reported by previous authors, we observed that the maximum flux density occurs at $1$MHz on both spacecraft. We have developed a simplified analytical model of the flux density as a function of radial distance and compared it to the STEREO/Waves data., Comment: published in Solar Physics

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., Comment: 25 pages, 5 figures, accepted for publication in Astrophysical Journal

The capability of maintaining two satellites in precise relative position, stable in a celestial coordinate system, would enable major advances in a number of scientific disciplines and with a variety of types of instrumentation. The common requirement is for formation flying of two spacecraft with the direction of their vector separation in inertial coordinates precisely controlled and accurately determined as a function of time. We consider here the scientific goals that could be achieved with such technology and review some of the proposals that have been made for specific missions. Types of instrumentation that will benefit from the development of this type of formation flying include 1) imaging systems, in which an optical element on one spacecraft forms a distant image recorded by a detector array on the other spacecraft, including telescopes capable of very high angular resolution; 2) systems in which the front spacecraft of a pair carries an occulting disk, allowing very high dynamic range observations of the solar corona and exoplanets; 3) interferometers, another class of instrument that aims at very high angular resolution and which, though usually requiring more than two spacecraft, demands very much the same developments., Comment: To be published in "Int. J. Space Science and Engineering". This is a revised and expanded version of a paper presented at the "5th International Conference on Spacecraft Formation Flying Missions and Technologies(SFFMT)", Munich, May 2013

Major solar eruptive events (SEEs), consisting of both a large flare and a near simultaneous large fast coronal mass ejection (CME), are the most powerful explosions and also the most powerful and energetic particle accelerators in the solar system, producing solar energetic particles (SEPs) up to tens of GeV for ions and hundreds of MeV for electrons. The intense fluxes of escaping SEPs are a major hazard for humans in space and for spacecraft. Furthermore, the solar plasma ejected at high speed in the fast CME completely restructures the interplanetary medium (IPM) - major SEEs therefore produce the most extreme space weather in geospace, the interplanetary medium, and at other planets. Thus, understanding the flare/CME energy release process(es) and the related particle acceleration processes are major goals in Heliophysics. To make the next major breakthroughs, we propose a new mission concept, SEE 2020, a single spacecraft with a complement of advanced new instruments that focus directly on the coronal energy release and particle acceleration sites, and provide the detailed diagnostics of the magnetic fields, plasmas, mass motions, and energetic particles required to understand the fundamental physical processes involved., Comment: White Paper submitted to the Heliophysics Decadal Survey. Available as LinRobertP-SH.pdf on p. 7 at http://www8.nationalacademies.org/SSBSurvey/publicviewHeliophysics.aspx

The aim of this work is to determine the multi-thermal characteristics and plasma energetics of an eruptive plasmoid and occulted flare observed by Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA). We study an event from 03-Nov-2010 (peaking at 12:20UT in GOES soft X-rays) of a coronal mass ejection and occulted flare which demonstrates the morphology of a classic erupting flux rope. The high spatial, and time resolution, and six coronal channels, of the SDO/AIA images allows the dynamics of the multi-thermal emission during the initial phases of eruption to be studied in detail. The Differential Emission Measure (DEM) is calculated, using an optimised version of a regularized inversion method (Hannah & Kontar 2012), for each pixel across the six channels at different times, resulting in emission measure maps and movies in a variety of temperature ranges. We find that the core of the erupting plasmoid is hot (8-11, 11-14MK) with a similarly hot filamentary "stem" structure connecting it to the lower atmosphere, which could be interpreted as the current sheet in the flux rope model, though is wider than these models suggest. The velocity of the leading edge of the eruption is 597-664 km s$^{-1}$ in the temperature range $\ge$3-4MK and between 1029-1246 km s$^{-1}$ for $\le$2-3MK. We estimate the density (in 11-14 MK) of the erupting core and stem during the impulsive phase to be about $3\times10^9$ cm$^{-3}$, $6\times10^9$ cm$^{-3}$, $9\times10^8$ cm$^{-3}$ in the plasmoid core, stem and surrounding envelope of material. This gives thermal energy estimates of $5\times10^{29}$ erg, $1\times10^{29}$ erg and $2\times10^{30}$ erg. The kinetic energy for the core and envelope is slightly smaller. The thermal energy of the core and current sheet grows during the eruption, suggesting continuous influx of energy presumably via reconnection., Comment: Submitted to A&A: in revision

The aim of this paper is to demonstrate the effect of turbulent background density fluctuations on flare-accelerated electron transport in the solar corona. Using the quasi-linear approximation, we numerically simulated the propagation of a beam of accelerated electrons from the solar corona to the chromosphere, including the self-consistent response of the inhomogeneous background plasma in the form of Langmuir waves. We calculated the X-ray spectrum from these simulations using the bremsstrahlung cross-section and fitted the footpoint spectrum using the collisional "thick-target" model, a standard approach adopted in observational studies. We find that the interaction of the Langmuir waves with the background electron density gradient shifts the waves to a higher phase velocity where they then resonate with higher velocity electrons. The consequence is that some of the electrons are shifted to higher energies, producing more high-energy X-rays than expected if the density inhomogeneity is not considered. We find that the level of energy gain is strongly dependent on the initial electron beam density at higher energy and the magnitude of the density gradient in the background plasma. The most significant gains are for steep (soft) spectra that initially had few electrons at higher energies. If the X-ray spectrum of the simulated footpoint emission are fitted with the standard "thick-target" model (as is routinely done with RHESSI observations) some simulation scenarios produce more than an order-of-magnitude overestimate of the number of electrons $>50$keV in the source coronal distribution., Comment: Accepted by A&A

We investigate the effects of acceleration during non-linear electron-beam relaxation in magnetized plasma in the case of electron transport in solar flares. The evolution of electron distribution functions is computed using a three-dimensional particle-in-cell electromagnetic code. Analytical estimations under simplified assumptions are made to provide comparisons. We show that, during the non-linear evolution of the beam-plasma system, the accelerated electron population appears. We found that, although the electron beam loses its energy efficiently to the thermal plasma, a noticeable part of the electron population is accelerated. For model cases with initially monoenergetic beams in uniform plasma, we found that the amount of energy in the accelerated electrons above the injected beam-electron energy varies depending the plasma conditions and could be around 10-30% of the initial beam energy. This type of acceleration could be important for the interpretation of non-thermal electron populations in solar flares. Its neglect could lead to the over-estimation of accelerated electron numbers. The results emphasize that collective plasma effects should not be treated simply as an additional energy-loss mechanism, when hard X-ray emission in solar flares is interpreted, notably in the case of RHESSI data., Comment: 9 pages, 8 figures, accepted to Astronomy and Astrophysics

We develop and apply an enhanced regularization algorithm, used in RHESSI X-ray spectral analysis, to constrain the ill-posed inverse problem that is determining the DEM from solar observations. We demonstrate this computationally fast technique applied to a range of DEM models simulating broadband imaging data from SDO/AIA and high resolution line spectra from Hinode/EIS, as well as actual active region observations with Hinode/EIS and XRT. As this regularization method naturally provides both vertical and horizontal (temperature resolution) error bars we are able to test the role of uncertainties in the data and response functions. The regularization method is able to successfully recover the DEM from simulated data of a variety of model DEMs (single Gaussian, multiple Gaussians and CHIANTI DEM models). It is able to do this, at best, to over four orders of magnitude in DEM space but typically over two orders of magnitude from peak emission. The combination of horizontal and vertical error bars and the regularized solution matrix allows us to easily determine the accuracy and robustness of the regularized DEM. We find that the typical range for the horizontal errors is $\Delta$log$T\approx 0.1 -0.5$ and this is dependent on the observed signal to noise, uncertainty in the response functions as well as the source model and temperature. With Hinode/EIS an uncertainty of 20% greatly broadens the regularized DEMs for both Gaussian and CHIANTI models although information about the underlying DEMs is still recoverable. When applied to real active region observations with Hinode/EIS and XRT the regularization method is able to recover a DEM similar to that found via a MCMC method but in considerably less computational time., Comment: 15 pages, 17 figures, accepted for publication in A&A

Context. High energy electrons accelerated during solar flare are abundant in the solar corona and in the interplanetary space. Commonly, the number and the energy of non-thermal electrons at the Sun is estimated using hard X-ray (HXR) spectral observations (e.g. RHESSI) and a single-particle collisional approximation. Aims. To investigate the role of the spectrally evolving Langmuir turbulence on the population of energetic electrons in the solar corona. Methods. We numerically simulate the relaxation of a power-law non-thermal electron population in a collisional inhomogeneous plasma including wave-particle, and wave-wave interactions. Results. The numerical simulations show that the long-time evolution of electron population above 20 keV deviates substantially from the collisional approximation when wave-particle interactions in non-uniform plasma are taken into account. The evolution of Langmuir wave spectrum towards smaller wavenumbers, due to large-scale density fluctuations and wave-wave interactions, leads to an effective acceleration of electrons. Furthermore, the time-integrated spectrum of non-thermal electrons, which is normally observed with HXR above 20 keV, is noticeably increased due to acceleration of non-thermal electrons by Langmuir waves. Conclusions. The results show that the observed HXR spectrum, when interpreted in terms of collisional relaxation, can lead to an overestimated number and energy of energetic electrons accelerated in the corona., Comment: 8 pages, 6 figures, submitted to Astronomy and Astrophysics Journal

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., Comment: This is an article for a monograph on the physics of solar flares, inspired by RHESSI observations. The individual articles are to appear in Space Science Reviews (2011); 10.1007/s11214-011-9804-x

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.

Investigate the spatial and spectral evolution of hard X-ray (HXR) emission from flare accelerated electron beams subject to collisional transport and wave-particle interactions in the solar atmosphere. We numerically follow the propagation of a power-law of accelerated electrons in 1D space and time with the response of the background plasma in the form of Langmuir waves using the quasilinear approximation.}{We find that the addition of wave-particle interactions to collisional transport for a transient initially injected electron beam flattens the spectrum of the footpoint source. The coronal source is unchanged and so the difference in the spectral indices between the coronal and footpoint sources is \Delta \gamma > 2, which is larger than expected from purely collisional transport. A steady-state beam shows little difference between the two cases, as has been previously found, as a transiently injected electron beam is required to produce significant wave growth, especially at higher velocities. With this transiently injected beam the wave-particle interactions dominate in the corona whereas the collisional losses dominate in the chromosphere. The shape of the spectrum is different with increasing electron beam density in the wave-particle interaction case whereas with purely collisional transport only the normalisation is changed. We also find that the starting height of the source electron beam above the photosphere affects the spectral index of the footpoint when Langmuir wave growth is included. This may account for the differing spectral indices found between double footpoints if asymmetrical injection has occurred in the flaring loop., Comment: 10 pages, 10 FIgures, accepted for publication in A&A

Aims: We seek to illustrate the analysis problems posed by RHESSI spacecraft motion by studying persistent instrumental oscillations found in the lightcurves measured by RHESSI's X-ray detectors in the 6-12 keV and 12-25 keV energy range during the decay phase of the flares of 2004 November 4 and 6. Methods: The various motions of the RHESSI spacecraft which may contribute to the manifestation of oscillations are studied. The response of each detector in turn is also investigated. Results: We find that on 2004 November 6 the observed oscillations correspond to the nutation period of the RHESSI instrument. These oscillations are also of greatest amplitude for detector 5, while in the lightcurves of many other detectors the oscillations are small or undetectable. We also find that the variation in detector pointing is much larger during this flare than the counterexample of 2004 November 4. Conclusions: Sufficiently large nutation motions of the RHESSI spacecraft lead to clearly observable oscillations in count rates, posing a significant hazard for data analysis. This issue is particularly problematic for detector 5 due to its design characteristics. Dynamic correction of the RHESSI counts, accounting for the livetime, data gaps, and the transmission of the bi-grid collimator of each detector, is required to overcome this issue. These corrections should be applied to all future oscillation studies., Comment: 8 pages, 10 figures

Plasma turbulence is thought to be associated with various physical processes involved in solar flares, including magnetic reconnection, particle acceleration and transport. Using Ramaty High Energy Solar Spectroscopic Imager ({\it RHESSI}) observations and the X-ray visibility analysis, we determine the spatial and spectral distributions of energetic electrons for a flare (GOES M3.7 class, April 14, 2002 23$:$55 UT), which was previously found to be consistent with a reconnection scenario. It is demonstrated that because of the high density plasma in the loop, electrons have to be continuously accelerated about the loop apex of length $\sim 2\times 10^9$cm and width $\sim 7\times 10^8$cm. Energy dependent transport of tens of keV electrons is observed to occur both along and across the guiding magnetic field of the loop. We show that the cross-field transport is consistent with the presence of magnetic turbulence in the loop, where electrons are accelerated, and estimate the magnitude of the field line diffusion coefficient for different phases of the flare. The energy density of magnetic fluctuations is calculated for given magnetic field correlation lengths and is larger than the energy density of the non-thermal electrons. The level of magnetic fluctuations peaks when the largest number of electrons is accelerated and is below detectability or absent at the decay phase. These hard X-ray observations provide the first observational evidence that magnetic turbulence governs the evolution of energetic electrons in a dense flaring loop and is suggestive of their turbulent acceleration., Comment: 6 pages, 4 figures, submitted to ApJL

We investigate the type III radio bursts and X-ray signatures of accelerated electrons in a well observed solar flare in order to find the spatial properties of the acceleration region. Combining simultaneous RHESSI hard X-ray flare data and radio data from Phoenix-2 and the Nan\c{c}ay radioheliograph, the outward transport of flare accelerated electrons is analyzed. The observations show that the starting frequencies of type III bursts are anti-correlated with the HXR spectral index of solar flare accelerated electrons. We demonstrate both analytically and numerically that the type III burst starting location is dependent upon the accelerated electron spectral index and the spatial acceleration region size, but weakly dependent on the density of energetic electrons for relatively intense electron beams. Using this relationship and the observed anti-correlation, we estimate the height and vertical extent of the acceleration region, giving values of around 50 Mm and 10 Mm respectively. The inferred acceleration height and size suggests that electrons are accelerated well above the soft X-ray loop-top, which could be consistent with the electron acceleration between 40 Mm and 60 Mm above the flaring loop., Comment: 9 pages, 7 figures, to be published in A+A

Solar flare accelerated electron beams propagating away from the Sun can interact with the turbulent interplanetary media, producing plasma waves and type III radio emission. These electron beams are detected near the Earth with a double power-law energy spectrum. We simulate electron beam propagation from the Sun to the Earth in the weak turbulent regime taking into account the self-consistent generation of plasma waves and subsequent wave interaction with density fluctuations from low frequency MHD turbulence. The rate at which plasma waves are induced by an unstable electron beam is reduced by background density fluctuations, most acutely when fluctuations have large amplitudes or small wavelengths. This suppression of plasma waves alters the wave distribution which changes the electron beam transport. Assuming a 5/3 Kolmogorov-type power density spectrum of fluctuations often observed near the Earth, we investigate the corresponding energy spectrum of the electron beam after it has propagated 1 AU. We find a direct correlation between the spectrum of the double power-law below the break energy and the turbulent intensity of the background plasma. For an initial spectral index of 3.5, we find a range of spectra below the break energy between 1.6-2.1, with higher levels of turbulence corresponding to higher spectral indices., Comment: 9 pages, 9 figures, to be published in ApJ

Previous numerical studies have identified "phase mixing" of low-frequency Alfven waves as a mean of parallel electric field amplification and acceleration of electrons in a collisionless plasma. Theoretical explanations are given of how this produces an amplification of the parallel electric field, and as a consequence, also leads to enhanced collisionless damping of the wave by energy transfer to the electrons. Our results are based on the properties of the Alfven waves in a warm plasma which are obtained from drift-kinetic theory, in particular, the rate of their electron Landau damping. Phase mixing in a collisionless low-$\beta$ plasma proceeds in a manner very similar to the visco-resistive case, except for the fact that electron Landau damping is the primary energy dissipation channel. The time and length scales involved are evaluated. We also focus on the evolution of the parallel electric field and calculate its maximum value in the course of its amplification.

Anisotropic Alfv\'{e}nic fluctuations with $k_{\parallel}/k_{\perp}\ll 1$ remain at frequencies much smaller than the ion cyclotron frequency in the presence of a strong background magnetic field. Based on the simplest truncation of the electromagnetic gyrofluid equations in a homogeneous plasma, a model for the energy cascade produced by Alfv\'{e}nic turbulence is constructed, which smoothly connect the large magnetohydrodynamics (MHD) scales and the small "kinetic" scales. Scaling relations are obtained for the electromagnetic fluctuations, as a function of $k_{\perp}$ and $k_{\parallel}$. Moreover, a particular attention is paid to the spectral structure of the parallel electric field which is produced by Alfv\'{e}nic turbulence. The reason is the potential implication of this parallel electric field in turbulent acceleration and transport of particles. For electromagnetic turbulence, this issue was raised some time ago in [A. Hasegawa, K. Mima, J. Geophys. Res. {\bf 83} 1117 (1978)].

{This work aims to investigate the spectral structure of the parallel electric field generated by strong anisotropic and balanced Alfvenic turbulence in relation with the problem of electron acceleration from the thermal population in solar flare plasma conditions.} {We consider anisotropic Alfvenic fluctuations in the presence of a strong background magnetic field. Exploiting this anisotropy, a set of reduced equations governing non-linear, two-fluid plasma dynamics is derived. The low-$\beta$ limit of this model is used to follow the turbulent cascade of the energy resulting from the non-linear interaction between kinetic Alfven waves, from the large magnetohydrodynamics (MHD) scales with $k_{\perp}\rho_{s}\ll 1$ down to the small "kinetic" scales with $k_{\perp}\rho_{s} \gg 1$, $\rho_{s}$ being the ion sound gyroradius.} {Scaling relations are obtained for the magnitude of the turbulent electromagnetic fluctuations, as a function of $k_{\perp}$ and $k_{\parallel}$, showing that the electric field develops a component parallel to the magnetic field at large MHD scales.} {The spectrum we derive for the parallel electric field fluctuations can be effectively used to model stochastic resonant acceleration and heating of electrons by Alfven waves in solar flare plasma conditions}

The newly developed X-ray visibility forward fitting technique is applied to Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) data of a limb flare to investigate the energy and height dependence on sizes, shapes, and position of hard X-ray chromospheric footpoint sources. This provides information about the electron transport and chromospheric density structure. The spatial distribution of two footpoint X-ray sources is analyzed using PIXON, Maximum Entropy Method, CLEAN and visibility forward fit algorithms at nonthermal energies from $\sim 20$ to $\sim 200$ keV. We report, for the first time, the vertical extents and widths of hard X-ray chromospheric sources measured as a function of energy for a limb event. Our observations suggest that both the vertical and horizontal sizes of footpoints are decreasing with energy. Higher energy emission originates progressively deeper in the chromosphere consistent with downward flare accelerated streaming electrons. The ellipticity of the footpoints grows with energy from $\sim 0.5$ at $ \sim 20$ keV to $\sim 0.9$ at $\sim 150$ keV. The positions of X-ray emission are in agreement with an exponential density profile of scale height $\sim 150$~km. The characteristic size of the hard X-ray footpoint source along the limb is decreasing with energy suggesting a converging magnetic field in the footpoint. The vertical sizes of X-ray sources are inconsistent with simple collisional transport in a single density scale height but can be explained using a multi-threaded density structure in the chromosphere., Comment: 7 pages, 7 figures, submitted to ApJ

We investigate the positions and source sizes of X-ray solar flare sources taking into account Compton backscattering (albedo). Using a Monte Carlo simulation of X-ray photon transport including photo-electric absorption and Compton scattering, we calculate the apparent source sizes and positions of X-ray sources at the solar disk for various source sizes, spectral indices and directivities of the primary source. We show that the albedo effect will alter the true source positions and substantially increase the measured source sizes. The source positions are shifted up to $\sim 0.5"$ radially towards the disk centre and 5 arcsecond source sizes can be two times larger even for an isotropic source (minimum albedo effect) at 1 Mm above the photosphere. X-ray sources therefore should have minimum observed sizes, thus FWHM source size (2.35 times second-moment) will be as large as $\sim 7"$ in the 20-50 keV range for a disk-centered point source at a height of 1 Mm ($\sim 1.4"$) above the photosphere. The source size and position change is the largest for flatter primary X-ray spectra, stronger downward anisotropy, for sources closer to the solar disk centre, and between the energies of 30 and 50 keV. Albedo should be taken into account when X-ray footpoint positions, footpoint motions or source sizes from e.g. RHESSI or Yohkoh data are interpreted, and suggest that footpoint sources should be larger in X-rays than in optical or EUV ranges., Comment: 4 pages, 2 figures, submitted to Astronomy and Astrophysics Letters

Using the potential of two unprecedented missions, STEREO and RHESSI, we study three well observed fast CMEs that occurred close to the limb together with their associated high energy flare emissions in terms of RHESSI HXR spectra and flux evolution. From STEREO/EUVI and STEREO/COR1 data the full CME kinematics of the impulsive acceleration phase up to 4 Rs is measured with a high time cadence of less equal 2.5 min. For deriving CME velocity and acceleration we apply and test a new algorithm based on regularization methods. The CME maximum acceleration is achieved at heights h < 0.4 Rs, the peak velocity at h < 2.1 Rs (in one case as small as 0.5 Rs). We find that the CME acceleration profile and the flare energy release as evidenced in the RHESSI hard X-ray flux evolve in a synchronized manner. These results support the standard flare/CME model which is characterized by a feed-back relationship between the large-scale CME acceleration process and the energy release in the associated flare., Comment: accepted for ApJ

Solar flare hard X-ray spectra from RHESSI are normally interpreted in terms of purely collisional electron beam propagation, ignoring spatial evolution and collective effects. In this paper we present self-consistent numerical simulations of the spatial and temporal evolution of an electron beam subject to collisional transport and beam-driven Langmuir wave turbulence. These wave-particle interactions represent the background plasma's response to the electron beam propagating from the corona to chromosphere and occur on a far faster timescale than coulomb collisions. From these simulations we derive the mean electron flux spectrum, comparable to such spectra recovered from high resolution hard X-rays observations of solar flares with RHESSI. We find that a negative spectral index (i.e. a spectrum that increases with energy), or local minima when including the expected thermal spectral component at low energies, occurs in the standard thick-target model, when coulomb collisions are only considered. The inclusion of wave-particle interactions does not produce a local minimum, maintaining a positive spectral index. These simulations are a step towards a more complete treatment of electron transport in solar flares and suggest that a flat spectrum (spectral index of 0 to 1) down to thermal energies maybe a better approximation instead of a sharp cut-off in the injected electron spectrum., Comment: 6 pages, 5 figures, accepted by ApJL

The collisional thick target model (CTTM) of solar hard X-ray (HXR) bursts has become an almost 'Standard Model' of flare impulsive phase energy transport and radiation. However, it faces various problems in the light of recent data, particularly the high electron beam density and anisotropy it involves.} {We consider how photon yield per electron can be increased, and hence fast electron beam intensity requirements reduced, by local re-acceleration of fast electrons throughout the HXR source itself, after injection.} {We show parametrically that, if net re-acceleration rates due to e.g. waves or local current sheet electric (${\cal E}$) fields are a significant fraction of collisional loss rates, electron lifetimes, and hence the net radiative HXR output per electron can be substantially increased over the CTTM values. In this local re-acceleration thick target model (LRTTM) fast electron number requirements and anisotropy are thus reduced. One specific possible scenario involving such re-acceleration is discussed, viz, a current sheet cascade (CSC) in a randomly stressed magnetic loop.} {Combined MHD and test particle simulations show that local ${\cal E}$ fields in CSCs can efficiently accelerate electrons in the corona and and re-accelerate them after injection into the chromosphere. In this HXR source scenario, rapid synchronisation and variability of impulsive footpoint emissions can still occur since primary electron acceleration is in the high Alfv\'{e}n speed corona with fast re-acceleration in chromospheric CSCs. It is also consistent with the energy-dependent time-of-flight delays in HXR features., Comment: 8 pages, 2 figures