Langmuir Wave Electric Fields Induced by Electron Beams in the Heliosphere

Solar electron beams responsible for type III radio emission generate Langmuir waves as they propagate out from the Sun. The Langmuir waves are observed via in-situ electric field measurements. These Langmuir waves are not smoothly distributed but occur in discrete clumps, commonly attributed to the turbulent nature of the solar wind electron density. Exactly how the density turbulence modulates the Langmuir wave electric fields is understood only qualitatively. Using weak turbulence simulations, we investigate how solar wind density turbulence changes the probability distribution functions, mean value and variance of the beam-driven electric field distributions. Simulations show rather complicated forms of the distribution that are dependent upon how the electric fields are sampled. Generally the higher magnitude of density fluctuations reduce the mean and increase the variance of the distribution in a consistent manor to the predictions from resonance broadening by density fluctuations. We also demonstrate how the properties of the electric field distribution should vary radially from the Sun to the Earth and provide a numerical prediction for the in-situ measurements of the upcoming Solar Orbiter and Solar Probe Plus spacecraft.Comment: 14 pages, 11 figures, published in Astronomy and Astrophysic

Spatial expansion and speeds of type III electron beam sources in the solar corona

A component of space weather, electron beams are routinely accelerated in the solar atmosphere and propagate through interplanetary space. Electron beams interact with Langmuir waves resulting in type III radio bursts. Electron beams expand along the trajectory, and using kinetic simulations, we explore the expansion as the electrons propagate away from the Sun. Specifically, we investigate the front, peak and back of the electron beam in space from derived radio brightness temperatures of fundamental type III emission. The front of the electron beams travelled at speeds from 0.2c--0.7c, significantly faster than the back of the beam that travelled between 0.12c--0.35c. The difference in speed between the front and the back elongates the electron beams in time. The rate of beam elongation has a 0.98 correlation coefficient with the peak velocity; in-line with predictions from type III observations. The inferred speeds of electron beams initially increase close to the acceleration region and then decrease through the solar corona. Larger starting densities and harder initial spectral indices result in longer and faster type III sources. Faster electron beams have higher beam energy densities, produce type IIIs with higher peak brightness temperatures and shorter FWHM durations. Higher background plasma temperatures also increase speeds, particularly at the back of the beam. We show how our predictions of electron beam evolution influences type III bandwidth and drift-rates. Our radial predictions of electron beam speed and expansion can be tested by the upcoming in situ electron beam measurements made by Solar Orbiter and Parker Solar Probe.Comment: 19 pages, 20 figures, submitted to Ap

LOFAR observations of fine spectral structure dynamics in type IIIb radio bursts

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

Stopping Frequency of Type III Solar Radio Bursts in Expanding Magnetic Flux Tubes

Understanding the properties of type III radio bursts in the solar corona and interplanetary space is one of the best ways to remotely deduce the characteristics of solar accelerated electron beams and the solar wind plasma. One feature of all type III bursts is the lowest frequency they reach (or stopping frequency). This feature reflects the distance from the Sun that an electron beam can drive the observable plasma emission mechanism. The stopping frequency has never been systematically studied before from a theoretical perspective. Using numerical kinetic simulations, we explore the different parameters that dictate how far an electron beam can travel before it stops inducing a significant level of Langmuir waves, responsible for plasma radio emission. We use the quasilinear approach to model self-consistently the resonant interaction between electrons and Langmuir waves in inhomogeneous plasma, and take into consideration the expansion of the guiding magnetic flux tube and the turbulent density of the interplanetary medium. We find that the rate of radial expansion has a significant effect on the distance an electron beam travels before enhanced leves of Langmuir waves, and hence radio waves, cease. Radial expansion of the guiding magnetic flux tube rarefies the electron stream to the extent that the density of non-thermal electrons is too low to drive Langmuir wave production. The initial conditions of the electron beam have a significant effect, where decreasing the beam density or increasing the spectral index of injected electrons would cause higher type III stopping frequencies. We also demonstrate how the intensity of large-scale density fluctuations increases the highest frequency that Langmuir waves can be driven by the beam and how the magnetic field geometry can be the cause of type III bursts only observed at high coronal frequencies.Comment: 11 pages, 8 figures, accepted in Astronomy and Astrophysic

Imaging Spectroscopy of Type U and J Solar Radio Bursts with LOFAR

Radio U-bursts and J-bursts are signatures of electron beams propagating along magnetic loops confined to the corona. The more commonly observed type III radio bursts are signatures of electron beams propagating along magnetic loops that extend into interplanetary space. Given the prevalence of solar magnetic flux to be closed in the corona, it is an outstanding question why type III bursts are more frequently observed than U-bursts or J-bursts. We use LOFAR imaging spectroscopy between 30-80 MHz of low-frequency U-bursts and J-bursts, for the first time, to understand why electron beams travelling along coronal loops produce radio emission less often. The different radio source positions were used to model the spatial structure of the guiding magnetic flux tube and then deduce the energy range of the exciting electron beams without the assumption of a standard density model. The radio sources infer a magnetic loop 1 solar radius in altitude, with the highest frequency sources starting around 0.6 solar radii. Electron velocities were found between 0.13 c and 0.24 c, with the front of the electron beam travelling faster than the back of the electron beam. The velocities correspond to energy ranges within the beam from 0.7-11 keV to 0.7-43 keV. The density along the loop is higher than typical coronal density models and the density gradient is smaller. We found that a more restrictive range of accelerated beam and background plasma parameters can result in U-bursts or J-bursts, causing type III bursts to be more frequently observed. The large instability distances required before Langmuir waves are produced by some electron beams, and the small magnitude of the background density gradients make closed loops less facilitating for radio emission than loops that extend into interplanetary space.Comment: 9 pages, 7 figure

Solar Physics with the Square Kilometre Array

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 Researc

Fast spectral fitting of hard X-ray bremsstrahlung from truncated power-law electron spectra

<p><b>Context:</b> Hard X-ray bremsstrahlung continuum spectra, such as from solar flares, are commonly described in terms of power-law fits, either to the photon spectra themselves or to the electron spectra responsible for them. In applications various approximate relations between electron and photon spectral indices are often used for energies both above and below electron low-energy cutoffs.</p> <p><b>Aims:</b> We examine the form of the exact relationships in various situations, and for various cross-sections, showing that empirical relations sometimes used can be highly misleading especially at energies below the low-energy cutoff, and consider how to improve fitting procedures.</p> <p><b>Methods:</b> We obtain expressions for photon spectra from single, double and truncated power-law electron spectra for a variety of cross-sections and for the thin and thick target models and simple analytic expressions for the non-relativistic Bethe-Heitler case.</p> <p><b>Results:</b> We show that below the low-energy cutoff Kramers and other constant spectral index forms commonly used are very poor approximations to accurate results, but that our analytical forms are a good match; and that above a low-energy cutoff, the Kramers and non-relativistic Bethe-Heitler results match reasonably well with results for up to energies around 100 keV.</p> <p><b>Conclusions:</b> Analytical forms of the non-relativistic Bethe-Heitler photon spectra from general power-law electron spectra are good match to exact results for both thin and thick targets and they enable much faster spectral fitting than evaluation of the full spectral integrations.</p&gt

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

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