Numerical and experimental investigations of instabilities in electron beams in plasmas

Student thesis: Doctoral Thesis

Abstract

Beam-plasma interactions can produce highly non-linear effects that can influence the dynamics of a system. Two-such systems have been investigated: Plasma moderated cyclotron instabilities relevant to the mechanisms of Auroral Kilometric Radiation (AKR) and the non-linear behaviour of the two-stream beam-plasma instability. In the first case numerical simulations were undertaken and compared to the measurements of a laboratory experiment conducted previously. Radio emissions from the Earth's polar regions, known as Auroral Kilometric Radiation (AKR) have been measured at a frequency of ~300kHz with an efficiency of ~1%.This emission is generated when particles are accelerated downwards along the Earth's increasing magnetic field. As they propagate they undergo magnetic compression and form a horseshoe distribution in velocity space. As these particles travel through an area of plasma depletion known as the auroral density cavity, it is believed that a form of cyclotron resonance m aser (CRM) instability causes them to emit the radio waves detected by a range of satellites. The University of Strathclyde has previously undertaken laboratory experiments to investigate this behaviour. This work numerically simulated the previous experimental setup with and without a background plasma. The simulated electron beam distribution was matched analytically to the measured beam in the previous laboratory experiment. This beam was then injected into a simulation of the laboratory geometry and predicted wave generation efficiency of ~1% which closely matched the previous measurements. The impact of adding a background plasma to the simulation was also investigated and successfully showed that the efficiency of the CRM instability falls off as the plasma frequency approaches a tenth of the cyclotron frequency (400MHz in these simulations). This again was in good agreement to the previous experimental measurements.Further work was undertaken to investigate the instabilities that form when a rectilinear electron beam is propagated through a plasma column. This is of potential relevance to fast-ignition inertial confinement fusion as in this form of fusion, a deuterium-tritium fuel pellet is compressed using uniform laser irradiation while a secondary laser pulse is then utilised to accelerate a highly relativistic electron beam into the core of the pellet to provide the heating necessary to initiate fusion. As the beam propagates it can potentially undergo the beam-plasma instability. This work presents a numerical study of the beam-plasma instability in a low-density environment using a 2.5D particle-in-cell code. This numerical model is then used to as a basis around which to construct a similar laboratory apparatus to ultimately benchmark the code. This will enhance confidence in the use of PiC codes in the simulation of these instabilities. The simulated beam-plasma instability correlated well to the predicted analytic growth rates in the linear regime. Typically after ~20-80ns of beam propagation, when the beam-plasma instability is saturated, periodic plasma cavities are formed. The spacing between these cavities increased linearly from ~2 to 6cm as the voltage of a 10A electron beam was increased from 10kV to 100kV, in a background hydrogen plasma of density 9x1016m-3. Ion density perturbations were found to propagate from these cavities in both the positive and negative axial directions, at speeds close to the local ion sound speed observed inside the cavity but faster than the mean ion sound speed (averaged across the plasma column).Spectra of the longitudinal electric field shows oscillations close to the electron plasma and ion acoustic frequencies close to these cavity structures suggesting that this behaviour relates to the modulational instability. An experimental apparatus was developed to reproduce major features of the numerica
Date of Award1 Apr 2013
LanguageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsEPSRC (Engineering and Physical Sciences Research Council)
SupervisorKevin Ronald (Supervisor) & Colin Whyte (Supervisor)

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