Solar type III radio bursts are an important diagnostic tool in the understanding of solar accelerated electron beams. They are a signature of propagating beams of nonthermal electrons in the solar atmosphere and the solar system. Consequently, they provide information on electron acceleration and transport, and the conditions of the background ambient plasma they travel through. We review the observational properties of type III bursts with an emphasis on recent results and how each property can help identify attributes of electron beams and the ambient background plasma. We also review some of the theoretical aspects of type III radio bursts and cover a number of numerical efforts that simulate electron beam transport through the solar corona and the heliosphere.

Context. Quasi-periodic pulsations (QPP) of the electromagnetic radiation emitted in solar and stellar flares are often detected in microwave, white light, X-ray, and gamma-ray bands. Mechanisms for QPP are intensively debated in the literature. Previous studies revealed that QPP may manifest non-linear, non-stationary and, perhaps, multi-modal processes operating in flares. Aims. We study QPP of the microwave emission generated in an X3.2-class solar flare on 14 May, 2013, observed with the Nobeyama Radioheliograph (NoRH), aiming to reveal signatures of the non-linear, non-stationary, and multi-modal processes in the signal. Methods. The NoRH correlation signal obtained at the 17 GHz intensity has a clear QPP pattern. The signal was analysed with the Hilbert-Huang transform (HHT) that allows one to determine its instant amplitude and frequency, and their time variation. Results. It was established that the QPP consists of at least three well-defined intrinsic modes, with the mean periods of 15, 45, and 100 s. All the modes have quasi-harmonic behaviour with different modulation patterns. The 100 s intrinsic mode is a decaying oscillation, with the decay time of 250 s. The 15 s intrinsic mode shows a similar behaviour, with the decay time of 90 s. The 45 s mode has a wave-train behaviour. Conclusions. Dynamical properties of detected intrinsic modes indicate that the 100 s and 15 s modes are likely to be associated with fundamental kink and sausage modes of the flaring loop, respectively. The 100 s oscillation could also be caused by the fundamental longitudinal mode, while this interpretation requires the plasma temperature of about 30 million K and hence is not likely. The 45 s mode could be the second standing harmonics of the kink mode.

Context. High-energy electrons accelerated during solar flares are abundant in the solar corona and in interplanetary space. Commonly, the number and energy of non-thermal electrons at the Sun is estimated through hard X-ray (HXR) spectral observations (e.g. RHESSI) and a single-particle collisional approximation. Aims. We aim to investigate the role of the spectrally evolving Langmuir turbulence on the population of energetic electrons in the solar corona. Methods. We numerically simulated 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 the Langmuir wave spectrum towards smaller wavenumbers, caused by 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 because of acceleration of non-thermal electrons through 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.

Test particle codes indicate that electron dynamics due to interactions with low amplitude incoherent whistler mode‐waves can be adequately described by quasi‐linear theory. However there is significant evidence indicating that higher amplitude waves cause electron dynamics not adequately described using quasi‐linear theory. Using the method that was introduced in Allanson et al. (2019, https://doi.org/10.1029/2019JA027088), we track the dynamical response of electrons due to interactions with incoherent whistler‐mode waves, across all energy and pitch angle space. We conduct five experiments each with different values of the electromagnetic wave amplitude. We find that the electron dynamics agree well with the quasi‐linear theory diffusion coefficients for low amplitude incoherent waves with (Bw,rms/B0)2≈3.7·10−10, over a time scale T of the order of 1,000 gyroperiods. However, the resonant interactions with higher amplitude waves cause significant nondiffusive dynamics as well as diffusive dynamics. When electron dynamics are extracted and analyzed over time scales shorter than T, we are able to isolate both the diffusive and nondiffusive (advective) dynamics. Interestingly, when considered over these appropriately shorter time scales (of the order of hundreds or tens of gyroperiods), the diffusive component of the dynamics agrees well with the predictions of quasi‐linear theory, even for wave amplitudes up to (Bw,rms/B0)2≈5.8·10−6. Quasi‐linear theory is based on fundamentally diffusive dynamics, but the evidence presented herein also indicates the existence of a distinct advective component. Therefore, the proper description of electron dynamics in response to wave‐particle interactions with higher amplitude whistler‐mode waves may require Fokker‐Planck equations that incorporate diffusive and advective terms.

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 non-linear processes of wave-wave interaction. We develop a self-consistent model to calculate radio emission from a non-thermal electron population over a 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. By comparing these large-scale simulations with the observations, we can identify the processes governing the major type III solar radio burst characteristics.