McClements, Kenneth George
(1987)
*The Generation of Langmuir Waves by Thick Target Electron Beams in Solar Flares.*
PhD thesis, University of Glasgow.

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## Abstract

Hard X-rays, observed during the impulsive phase of solar flares, are commonly believed to be produced by the bremsstrahlung of collimated beams of electrons, which lose their energy collisionally in the dense chromosphere. This thesis is concerned with the generation of Langmuir waves by such beams. In Chapter 1 we review observations of solar flares across the electromagnetic spectrum. Particular emphasis is given to the impulsive phase, and to those observations which provide strong evidence for the existence of electron beams. Solar flare theory, insofar as it is pertinent to the original work of this thesis, is reviewed in Chapter 2. After briefly discussing models of primary energy release and particle acceleration, we consider in detail the theoretical interpretation of hard X-ray and microwave observations. Emissions at these wavelengths are believed to contain the most direct information on the electron distribution function in the flaring region. In Chapter 3 we use the quasi-linear theory to determine the conditions required for the stability of a steady state electron beam propagating in the solar corona. The growth rate for electron plasma waves in a magnetized plasma is evaluated, with the electron distribution being given by an analytic solution of the linearized Fokker-Planck equation. A stability boundary in parameter space is determined, indicating that electron beams must be highly collimated at injection to be Langmuir unstable at any point in space. The implications of this result for alternative models of hard X-ray emission are discussed and it is argued that Langmuir instability will not occur in either the trap model or the dissipative thermal model. Such models would therefore be refuted by the detection of a large flux of plasma microwave emission associated with hard X-ray emission. In Chapters 4 and 5 we investigate the quasi-linear dynamics of thick target electron beams, using a combination of analytical and numerical techniques. In Chapter 4, one dimensional quasi-linear equations are derived from the general three dimensional equations for an axisymmetric beam in a magnetized collisional plasma. Asymptotic analytical solutions are discussed, and it is shown that the energy density of Langmuir waves excited by a steady state thick target beam is negligible compared with the beam energy density, although the waves heat the plasma at a rate which is comparable to that of the fast electrons. We also describe an approximate method of incorporating quasi-linear interactions into the collisional treatment of thick target beam evolution, based on the assumption that the asymptotic state is a plateau distribution. Numerical computations of the thick target electron distribution and the associated Langmuir wavelevel are presented in Chapter 5. It is shown that the energy deposition rate and bremsstrahlung X-ray signature of a thick target beam are essentially unaffected by the presence of Langmuir turbulence. We also show that reverse current energy losses can reduce the wavelevel by as much as a factor of 2, depending on the beam and plasma parameters. Finally, we consider the possible plasma radiation signature of a relaxed beam, and show that an observable flux of 2nd harmonic radiation will be produced if the Langmuir waves are close to being isotropic. In Chapter 6 we consider Langmuir wave generation by a time dependent beam. It is shown that the steady state model remains valid if the electrons are injected on a timescale greater than about Is. If the injection timescale is as short as 100ms, however, the energy density of Langmuir waves produced by a given instantaneous flux of electrons may be amplified by as much as an order of magnitude. We argue that the wavelevel is nevertheless unlikely to exceed the threshold for strong turbulence (i.e. the modulational instability), and that the propagation of thick target beams can therefore be adequately described using the quasi-linear theory. In Chapter 7 we briefly discuss two possible ways of extending the work described in previous chapters. Specifically, we consider thick target beam relaxation in an inhomogeneous plasma, and the induced scattering of Langmuir waves on thermal ions.

Item Type: | Thesis (PhD) |
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Qualification Level: | Doctoral |

Keywords: | Astronomy |

Date of Award: | 1987 |

Depositing User: | Enlighten Team |

Unique ID: | glathesis:1987-77559 |

Copyright: | Copyright of this thesis is held by the author. |

Date Deposited: | 14 Jan 2020 09:05 |

Last Modified: | 14 Jan 2020 09:05 |

URI: | https://theses.gla.ac.uk/id/eprint/77559 |

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