This dissertation explores several aspects of a temperature filament in a magnetized plasma and the instabilities and turbulence related to it. This theoretical and numerical study is related to the temperature filament experiment performed in the Large Plasma Device (LAPD-U) operated by the Basic Plasma Science Facility (BaPSF) at UCLA.

The classical heat transport equations are solved using proper numerical schemes along with the parallel flow and density evolutions. Factors that affect the quantitative properties of the classical transport are examined. The results of the simulation are compared to the experimental observations in LAPD-U. The comparison yields a good agreement on the temporal evolution of the temperature and radial profiles before the system becomes turbulent in the experiment. The agreement on the parallel measurements is also achieved in the classical stage.

The magnetized ion-acoustic wave excited by heat-flux-induced current is formulated and applied to the temperature filament structure. Factors that affect the properties of the ion-acoustic wave are examined. A spatially growing wave with a frequency similar to the experimental low-frequency oscillation is produced.

The concept of a thermal wave is introduced. The classical transport code is adapted to examine the properties of the thermal wave in the temperature filament structure in a magnetized plasma. Factors that affect the properties of the thermal wave are examined using the adapted classical transport code. The simulation result is compared to the observed temperature oscillation in the LAPD-U experiment to verify that the observation is a thermal wave.

It is discovered that the power spectrum during the turbulent stage shows an exponential frequency dependence for both the temperature filament experiment and the limiter-edge experiment in LAPD-U. It is also discovered that the time traces in both experiments contain pulses that can be fit by Lorentzian functions. A model study is performed to establish the relationship between the pulse-width and the slope of the exponential power spectrum. It is proved that the exponential power spectrum is the result of a series of Lorentzian pulses with narrow width distribution.

A model study is performed of the effect of the convective flows generated by large-amplitude drift-waves on the pressure gradient structure. The drift-wave is modeled by a potential structure that contains two components with different azimuthal mode numbers and radial profiles oscillating at the same frequency. For both the temperature and density filament it is found, at the amplitude large enough for the drift speed to exceed phase speed, that the spatial profile develops fine spiral structures and the time traces contain pulses. The pulses from the temperature filament can be fit well by Lorentzian functions. It is also discovered that an extra azimuthal counter-flow can suppress the spiral structure and the pulses. It is verified that the generation of the spiral structure and the pulses requires the interaction of the two modes. Two differential equations with Lorentzian-type solutions are introduced in order to approximate the Lorentzian pulses locally.