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Astrophysical shocks, driven by explosive events such as supernovae, efficiently accelerate charged particles to relativistic energies. The majority of these shocks occur in collisionless plasmas where the energy transfer is dominated by particle-wave interactions.Strong nonrelativistic shocks found in supernova remnants are plausible sites of galactic cosmic ray production, and the observed emission indicates the presence of nonthermal electrons. To participate in the primary mechanism of energy gain - Diffusive Shock Acceleration - electrons must have a highly suprathermal energy, implying a need for very efficient pre-acceleration. This poorly understood aspect of the shock acceleration theory is known as the electron injection problem. Studying electron-scale phenomena requires the use of fully kinetic particle-in-cell (PIC) simulations, which describe collisionless plasma from first principles.
Most published studies consider a homogenous upstream medium, but turbulence is ubiquitous in astrophysical environments and is typically driven at magnetohydrodynamic scales, cascading down to kinetic scales. For the first time, I investigate how preexisting turbulence affects electron acceleration at nonrelativistic shocks using the fully kinetic approach. To accomplish this, I developed a novel simulation framework that allows the study of shocks propagating in turbulent media. It involves simulating slabs of turbulent plasma separately, which are further continuously inserted into a shock simulation. This demands matching of the plasma slabs at the interface. A new procedure of matching electromagnetic fields and currents prevents numerical transients, and the plasma evolves self-consistently. The versatility of this framework has the potential to render simulations more consistent with turbulent systems in various astrophysical environments.
In this Thesis, I present the results of 2D3V PIC simulations of high-Mach-number nonrelativistic shocks with preexisting compressive turbulence in an electron-ion plasma. The chosen amplitudes of the density fluctuations ($\lesssim15\%$) concord with \textit{in situ} measurements in the heliosphere and the local interstellar medium. I explored how these fluctuations impact the dynamics of upstream electrons, the driving of the plasma instabilities, electron heating and acceleration. My results indicate that while the presence of the turbulence enhances variations in the upstream magnetic field, their levels remain too low to influence the behavior of electrons at perpendicular shocks significantly. However, the situation is different at oblique shocks. The external magnetic field inclined at an angle between $50^\circ \lesssim \theta_\text{Bn} \lesssim 75^\circ$ relative to the shock normal allows the escape of fast electrons toward the upstream region. An extended electron foreshock region is formed, where these particles drive various instabilities. Results of an oblique shock with $\theta_\text{Bn}=60^\circ$ propagating in preexisting compressive turbulence show that the foreshock becomes significantly shorter, and the shock-reflected electrons have higher temperatures. Furthermore, the energy spectrum of downstream electrons shows a well-pronounced nonthermal tail that follows a power law with an index up to -2.3.
The methods and results presented in this Thesis could serve as a starting point for more realistic modeling of interactions between shocks and turbulence in plasmas from first principles.
The Sun is surrounded by a 10^6 K hot atmosphere, the corona. The corona and the solar wind are fully ionized, and therefore in the plasma state. Magnetic fields play an important role in a plasma, since they bind electrically charged particles to their field lines. EUV spectroscopes, like the SUMER instrument on-board the SOHO spacecraft, reveal a preferred heating of coronal ions and strong temperature anisotropies. Velocity distributions of electrons can be measured directly in the solar wind, e.g. with the 3DPlasma instrument on-board the WIND satellite. They show a thermal core, an anisotropic suprathermal halo, and an anti-solar, magnetic-field-aligned, beam or "strahl". For an understanding of the physical processes in the corona, an adequate description of the plasma is needed. Magnetohydrodynamics (MHD) treats the plasma simply as an electrically conductive fluid. Multi-fluid models consider e.g. protons and electrons as separate fluids. They enable a description of many macroscopic plasma processes. However, fluid models are based on the assumption of a plasma near thermodynamic equilibrium. But the solar corona is far away from this. Furthermore, fluid models cannot describe processes like the interaction with electromagnetic waves on a microscopic scale. Kinetic models, which are based on particle velocity distributions, do not show these limitations, and are therefore well-suited for an explanation of the observations listed above. For the simplest kinetic models, the mirror force in the interplanetary magnetic field focuses solar wind electrons into an extremely narrow beam, which is contradicted by observations. Therefore, a scattering mechanism must exist that counteracts the mirror force. In this thesis, a kinetic model for electrons in the solar corona and wind is presented that provides electron scattering by resonant interaction with whistler waves. The kinetic model reproduces the observed components of solar wind electron distributions, i.e. core, halo, and a "strahl" with finite width. But the model is not only applicable on the quiet Sun. The propagation of energetic electrons from a solar flare is studied, and it is found that scattering in the direction of propagation and energy diffusion influence the arrival times of flare electrons at Earth approximately to the same degree. In the corona, the interaction of electrons with whistler waves does not only lead to scattering, but also to the formation of a suprathermal halo, as it is observed in interplanetary space. This effect is studied both for the solar wind as well as the closed volume of a coronal magnetic loop. The result is of fundamental importance for solar-stellar relations. The quiet solar corona always produces suprathermal electrons. This process is closely related to coronal heating, and can therefore be expected in any hot stellar corona. In the second part of this thesis it is detailed how to calculate growth or damping rates of plasma waves from electron velocity distributions. The emission and propagation of electron cyclotron waves in the quiet solar corona, and that of whistler waves during solar flares, is studied. The latter can be observed as so-called fiber bursts in dynamic radio spectra, and the results are in good agreement with observed bursts.
This work reports about new high-resolution imaging and spectroscopic observations of solar type III radio bursts at low radio frequencies in the range from 30 to 80 MHz. Solar type III radio bursts are understood as result of the beam-plasma interaction of electron beams in the corona. The Sun provides a unique opportunity to study these plasma processes of an active star. Its activity appears in eruptive events like flares, coronal mass ejections and radio bursts which are all accompanied by enhanced radio emission. Therefore solar radio emission carries important information about plasma processes associated with the Sun’s activity. Moreover, the Sun’s atmosphere is a unique plasma laboratory with plasma processes under conditions not found in terrestrial laboratories. Because of the Sun’s proximity to Earth, it can be studied in greater detail than any other star but new knowledge about the Sun can be transfer to them. This “solar stellar connection” is important for the understanding of processes on other stars.
The novel radio interferometer LOFAR provides imaging and spectroscopic capabilities to study these processes at low frequencies. Here it was used for solar observations.
LOFAR, the characteristics of its solar data and the processing and analysis of the latter with the Solar Imaging Pipeline and Solar Data Center are described. The Solar Imaging Pipeline is the central software that allows using LOFAR for solar observations. So its development was necessary for the analysis of solar LOFAR data and realized here. Moreover a new density model with heat conduction and Alfvén waves was developed that provides the distance of radio bursts to the Sun from dynamic radio spectra.
Its application to the dynamic spectrum of a type III burst observed on March 16, 2016 by LOFAR shows a nonuniform radial propagation velocity of the radio emission. The analysis of an imaging observation of type III bursts on June 23, 2012 resolves a burst as bright, compact region localized in the corona propagating in radial direction along magnetic field lines with an average velocity of 0.23c. A nonuniform propagation velocity is revealed. A new beam model is presented that explains the nonuniform motion of the radio source as a propagation effect of an electron ensemble with a spread velocity distribution and rules out a monoenergetic electron distribution. The coronal electron number density is derived in the region from 1.5 to 2.5 R☉ and fitted with the newly developed density model. It determines the plasma density for the interplanetary space between Sun and Earth. The values correspond to a 1.25- and 5-fold Newkirk model for harmonic and fundamental emission, respectively. In comparison to data from other radio instruments the LOFAR data shows a high sensitivity and resolution in space, time and frequency.
The new results from LOFAR’s high resolution imaging spectroscopy are consistent with current theories of solar type III radio bursts and demonstrate its capability to track fast moving radio sources in the corona. LOFAR solar data is found to be a valuable source for solar radio physics and opens a new window for studying plasma processes associated with highly energetic electrons in the solar corona.