Thesis – Chapter 7: Conclusions

Thesis – Table of Contents


Studies of filamentary pressure structures are an ongoing work within the LAPD-U laboratory. The work of Burke, et al. [1998, 2000a, b] (and [Burke, 1999]) established the ability of this experimental geometry to observe classical transport in magnetically confined plasmas. An increase in transport and the loss of classical confinement for larger pressure gradients and/or longer heating periods naturally provided an opportunity to study turbulence. A reproducible characteristic of power spectra from measurements made during the anomalous transport phase of the experiment led to the identification of Lorentzian pulses in time series data. Large amplitude examples of these pulses emphasized the role of low frequency oscillations and led to the identification of a spontaneous thermal wave.

Spontaneous Thermal Waves

The temperature filament acts as a resonance cavity for spontaneous thermal waves [Pace, et al., 2008b]. Thermal waves result from the diffusive propagation of thermal energy across boundaries that separate regions of largely differing thermal conductivity. In the filament, this wave manifests itself as coherent fluctuations in electron temperature near the filament center. A drive source has not been identified, though it is clear that the input heating does not oscillate in such a manner as to be solely responsible.

The wave number vectors of thermal waves depend on the thermal conductivity of the medium. Wavelength measurements, in the form of phase velocity or amplitude decay measurements, allow for calculation of these plasma parameters. From Eq. 3.5 it is seen that the electron collision frequency can also be calculated based on knowledge of the thermal wave’s properties. Given that the measurement of temperature fluctuations due to the presence of a thermal wave can be considerably simpler than measurement or modeling of fundamental plasma parameters, it is natural to suggest that a purposely driven thermal wave may be useful as a diagnostic instrument. Such a wave can be driven by external heating (e.g., electron cyclotron resonance heating) or with an electron beam setup similar to the one used here.

Exponential Power Spectra Related to Lorentzian Pulses

The power spectra calculated from time series measurements of plasma properties are found to exhibit an exponential dependence in frequency that is the result of Lorentzian shaped pulses in the raw signals [Pace et al., 2008a]. The exponential constant of the spectral shape is found to agree with the time width of the generating pulses, thereby providing support for the relation between the pulses and spectra. In the temperature filament experiment it is observed that the pulses appear only after the system transitions from classical transport into a turbulent regime of enhanced transport. Observations of exponential power spectra from many different plasma experiments suggest that Lorentzian pulses are a universal feature of plasma turbulence driven by cross-field pressure gradients. Comparison with a density gradient experiment of different scale length shows similar observations and demonstrates that this phenomenon is a general consequence of systems featuring pressure gradients.

Coherent drift-Alfvén eigenmodes present in the temperature filament suggest a generation mechanism for the Lorentzian pulses. The pulses appear to result from convective bursts of a nonlinear interaction between two drift-Alfvén modes of different m-number. Work on this topic is detailed in Shi [2008].

Future Work

Just as this thesis extends the earlier work performed by Burke [1999], it is possible that future thesis projects remain to be completed within this versatile experimental geometry.

Thermal Waves

The initial study of the thermal wave presented here should be expanded. Diagnostic difficulties prevented the complete elucidation of the wave’s properties by limiting measurements of the wave vectors. In order to minimize perturbations, an imaging diagnostic should be considered. There is a considerable amount of visible light emanating from the temperature filament and it may be possible to detect oscillations caused by the thermal wave. It is unclear how this may be implemented in a manner that provides axial resolution.

During this study of the thermal wave, multiple attempts were made to forcibly drive the wave by modulating the input beam heating. These attempts were unsuccessful due to the difficulty in modulating the beam current during the afterglow phase. This difficulty might be overcome by building an anode onto the existing beam structure. The LAPD-U anode is 16 m away from the crystal, creating a weak electrical connection even in the presence of the plasma. Finer control of beam emission will likely be achieved by bringing the anode closer to the crystal. Since the LAPD-U anode cannot be adjusted to this end, a change to the beam structure is warranted. Controlled experiments of driven thermal waves will be useful for further developing the diagnostic capabilities of this wave.

Exponential Spectra

While there is a wide range of theoretical work to be performed with regard to the exponential spectra, there is still a contribution to be made by experiments. The next phase of experimental research will likely focus on spatial measurements of the Lorentzian pulses. Some measurements indicate that these pulses are azimuthally localized, but the lack of a radial or azimuthal array of probes makes it difficult to reach any certain conclusions in this regard. The spatial behavior of the pulses is vital in order to understand their generation. This will also help in determining the similarities and differences between the time series pulses from other types of plasmas. Filamentary structures in fusion devices are generally known to be coherent structures that propagate radially outward. The pulses in the temperature filament experiment do not appear to feature similar behavior and it will be instructive to determine this with certainty.

Filamentary Structures

Nonlinear interactions between drift-Alfvén waves might be studied by the inclusion of a second filament. Experimentally, this is accomplished by adding a second electron beam to the existing setup. The two beams, with an adjustable radial separation, each generate a filamentary structure that supports coherent drift-Alfvén eigenmodes. Adjustments to the amount of overlap of these modes should allow for control over the types and amplitudes of their interactions. The resulting system may begin to accurately model that of the limiter-edge experiment discussed in Ch. 5. The pressure gradient of that experiment creates a full range of drift-Alfvén modes simultaneously. Plasma edges in other devices may have the same quality. As the single temperature filament aids in describing the behavior of these waves and plasma transport in general, so too might the double-filament experiment begin to reproduce the behavior of plasmas in which turbulence is always fully developed.

The temperature filament experiment provides a basic plasma environment that can simulate the situation encountered in other devices. The physics uncovered in this geometry is applicable to space and laboratory plasmas. Many research topics remain to be explored within this experimental setup and a wealth of “future work” will certainly add to the field of plasma physics.

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