David Pace

Thesis - Chapter 1: Introduction

Sun, 08 Mar 2009 20:27:10 +0000

Introduction

1.1 Motivation

Anomalous transport is an area of great interest within the plasma physics research community. The field of magnetically confined thermonuclear fusion may benefit significantly from an improved understanding of this topic. It has already been shown that turbulent fluctuations increase the transport of mass and energy [Horton, 1999] in magnetically confined laboratory plasmas. Improved confinement can expedite the development of fusion reactors as controllable energy sources.

Space plasma research also encounters anomalous transport [Committee on Solar and Space Physics, 2004] across naturally occurring boundaries in temperature, density, and magnetic field. The modeling of space weather can be beneficially impacted by improvements in plasma transport understanding.

Figure 1.1: Coronal loops on the Sun as imaged by the Transition Region and Coronal Explorer (TRACE) satellite. Filamentary structures form along the magnetic field lines emanating from the Sun. Image taken from Stanford-Lockheed Institute for Space Research. [Full Size]

Filamentary pressure structures, meaning structures that are aligned along magnetic field lines with narrow radial extent compared to their length, are prevalent in both space and fusion plasmas. Figure 1.1 is a satellite photograph of the solar corona in which bright filaments are seen flowing along looping magnetic field lines. Energy transport along these filaments, and even through the solar wind en route to interaction with the Earth's magnetic field, are ongoing areas of research. An example of filamentary structures from a fusion device is seen in Fig. 1.2, a photograph from the MAST fusion device. This image shows bright filaments in the outer edges of the device. They are the manifestation of edge-localized modes (ELMs) that transport hot plasma from the center of the device out to the walls. Controlling ELMs to minimize their transport or to avoid them altogether is presently a major effort within the fusion community [Evans et al., 2008].

Figure 1.2: Photograph of filamentary structures in the MAST fusion device. Edge-localized modes appear as bright filaments as they conduct large amounts of energy and particles out of the confinement region. Image taken from UKAEA. [Full Size]

Many features of filamentary structures remain unknown, including their capacity for transport, mechanisms leading to their generation, and which plasma waves they may produce. A difficulty in studying these issues within the space and fusion examples above is that the resulting systems are actually a mixture of many individual filaments. Interactions between the filaments and the existence of background instabilities complicate the interpretation of observations. This thesis utilizes an experiment in which a single filamentary structure is generated in the background of a quiescent plasma. The resulting system may be imagined as the isolation of one of the many structures seen in the previous two images. The fluctuation spectra and associated transport generated by this single filament proves rich with dynamic behavior. Studies related to plasma turbulence, spontaneously generated temperature waves, and non-linear interactions of drift-Alfvén waves are all performed within this configuration.

The experimental configuration used in this project was originally motivated by the desire to present experimental evidence for classical heat transport in magnetized plasmas. A summary of that successful effort is available as a Ph.D. thesis [Burke, 1999]. The theory of heat transport due to Coulomb collisions [Landshoff, 1949; Spitzer and Härm, 1953a; Rosenbluth and Kaufman, 1958; Braginskii, 1965] was developed nearly 50 years before it was quantitatively validated in a laboratory plasma [Burke et al., 1998; 2000b] using this configuration. The experiment consists of a narrow cylindrical region of warm plasma (Te ≈ 5 eV) embedded in a cold background plasma. The heated filament of plasma is manipulated to control the temperature gradient, thus driving classically described heat transport. Classical transport is always initially observed in this experiment, but if the heating is applied over a longer time interval or above a certain temperature threshold, the system transitions to a regime of enhanced, or anomalous, transport greater than that predicted by classical theory. Turbulent fluctuations are observed in this regime, and while some of their features have been investigated [Burke et al., 2000a], a mature understanding requires more detailed experimentation.

A summary of the transition from classical to anomalous transport in this experiment is provided by Fig. 1.3, a spectrogram of Isat power spectra (color contour) with the fluctuating component of a single Isat trace (I~sat, solid white) overplotted. The heated filament is generated at time t = 0 ms and maintained until t = 12 ms. Prior to t = 6 ms there is one well defined mode between 25 and 45 kHz. This is a drift-Alfvén eigenmode that has been detailed extensively both theoretically [Peñano et al., 2000] and experimentally [Burke et al., 2000a]. The presence of this coherent mode does not alter the transport levels, i.e., the observed transport remains classical during the presence of the drift-Alfvén wave. After t = 6 ms, a transition from coherent spectra to broadband spectra occurs. The transition is delineated by the disappearance of the coherent drift-Alfvén line into a broad region of power spread across many frequencies. Transport levels are enhanced, or anomalous, during times after this transition. All of this behavior occurs within a range corresponding to low frequency turbulence. The low frequency range is an area of active research within plasma physics, as discussed in the following section.

Figure 1.3: Time evolution of the power spectrum (color contour) with an overplot of the fluctuating component of an Isat signal (solid white) from the same spatial position. Coherent fluctuations of the drift-Alfvén eigenmode are visible for t ≤ 5.5 ms. After 5.5 ms there is a sharp transition to broadband spectra that correlates with the appearance of large relative amplitude pulses in the Isat signal. [Full Size]

1.2 Low Frequency Turbulence

Identification of the processes underlying low frequency turbulence in magnetized plasmas is an ongoing challenge within plasma physics [Krommes, 2002]. By “low frequency” it is meant that the frequency of the fluctuating quantity, ω, is less than the ion cyclotron frequency, Ωi. This topic is relevant to the magnetically confined fusion research community because turbulent fluctuations can enhance the transport of mass and energy [Horton, 1999], thereby degrading tokamak performance. The topic is also of interest in space plasma efforts [Committee on Solar and Space Physics, 2004] in which enhanced transport across naturally occurring boundaries in temperature, density, and magnetic field can result in major effects observable by space and ground-based instruments.

A significant effort has been devoted to the identification of universal behaviors in the spectra of turbulent fluctuations. A rich literature exists for both laboratory [Chen, 1965, Kamataki et al., 2007, Labit et al., 2007, Škoric and Rajkovic, 2008, Budaev et al., 2008, Pedrosa et al., 1999, Stroth et al., 2004, Carreras et al., 1999, Zweben et al., 2007] and space [Tchen, 1973, Kuo and Chou, 2001, Milano et al., 2004, Zimbardo, 2006, Bale et al., 2005] plasmas. The cited references are merely a representative sample of the available literature. Kolmogorov's early contribution [Kolmogorov, 1941] has had a major influence in these activities [Frisch, 1995]. In particular, that pioneering work makes a general prediction of algebraic spectral dependencies that has resulted in most modern spectral results being presented in a log-log format. Piecewise fits are then applied in order to extract power-law values for comparison to the Kolmogorov prediction. A large dynamic range is compressed by the log-log display, however, and important features related to the turbulence may be obscured. An exponential frequency spectrum is one such important feature, and its presence and underlying mechanism are described in this thesis.

1.3 Summary of Thesis Results

In the following an abbreviated description is presented regarding the major results obtained in this thesis. These are:

Confirmation of previous results due to filamentary geometry.
Observation of a spontaneous thermal wave in the absence of an externally driven source.
Observation of exponential power spectra associated with anomalous transport that are generated by Lorentzian pulses in measured time series data.

1.3.1 Confirmation of Physics Results Due to Plasma Geometry

The previously cited work of Burke, et al. was performed in the LAPD device prior to 2000. The present studies are performed in the machine that replaced the original LAPD, which has been named the LAPD-U, signifying it as an “upgrade” over the original. With similar plasma production sources and plasma properties, the major difference between these two machines is their length along the applied background magnetic field. The LAPD featured a plasma of less than 9.4 m in length. The LAPD-U plasma length is approximately 15 m. Throughout this thesis the LAPD-U designation will be used to emphasize the completely different linear device used for this work compared to the foundational efforts conducted on the LAPD.

Precisely because the LAPD-U is a different machine, all of the results in this thesis confirm that fundamental plasma physics is responsible for the observed phenomena, rather than the geometry of a particular device. The LAPD-U provides boundary conditions that were not present in the previous device, yet the coherent modes observed are the same, along with the important features of transport that have been re-observed.

1.3.2 Thermal Wave

The existence of low frequency, coherent, fluctuations is documented in the earlier work within this experimental environment [Burke et al., 2000a]. Observations show this is a coherent mode that, while seemingly unrelated to the generation of low frequency turbulence, is capable of strongly modulating the drift-Alfvén modes that are excited by the filament. These fluctuations are identified here as representing a spontaneously excited thermal wave. A thermal wave is the diffusive propagation of a temperature oscillation driven by a similarly oscillating source. Although thermal waves in plasmas have been studied [Gentle, 1988, Jacchia et al., 1991], and even manipulated to deduce subtle issues of anomalous transport in tokamaks [Mantica et al., 2006, Casati et al., 2007], controlled experiments in basic plasma devices are made difficult by the geometry of a magnetized plasma. The complexity arises due to the large difference in the thermal conductivities along and across the magnetic field, κ|| >> κ⊥, requiring plasmas with significant length along the magnetic field direction.

The discrepancy in thermal conductivities results in an extended structure that acts as the cavity for a thermal wave resonator [Shen and Mandelis, 1995]. The results presented here represent thermal wave oscillations that appear without the setting of a driver. Other experimental work involving this phenomenon, including those referenced, drive the wave with a controllable heat source. The drive source is as yet unidentified here, though it is demonstrated that the electron beam heating is not the direct cause, i.e., there are no coherent low frequency oscillations in the beam source. A possible candidate for the drive source is the heat-flux instability that is found in the solar wind [Forslund, 1970] and in laser-plasma interactions [Tikhonchuk et al., 1995]. This work has been summarized in Pace et al., [2008b].

1.3.3 Exponential Spectra

Figure 1.4: Semi-log plot of an Isatpower spectrum. Coherent modes, due to the presence of drift-Alfvén waves, can be seen in the range 20 ≤ f ≤ 120 kHz and coexist with the exponential in the range 20 ≤ f ≤ 200 kHz. [Full Size]

Figure 1.4 provides an example of an exponential power spectrum from the experiment. In a semi-log display, an exponential dependence appears as a straight line. This behavior is used to calculate the scaling frequency (decay constant) of the spectra for comparison with the time width of the Lorentzian pulses. The coherent peaks in Fig. 1.4 (located at approximately f = 30, 60, 90, and 120 kHz) coexist with the exponential behavior that extends from 20 ≤ f ≤ 200 kHz.

Exponential spectra from a variety of experiments are found throughout the published literature. This is made possible by the semi-log display some researchers have chosen to use for the results. Figure 1a of Xia and Shats [2003] exhibits exponential behavior over four orders of magnitude from floating potential measurements. This experiment was performed in a helical device that reported proof of an inverse cascade. Figure 1 of Fiksel et al [1995] features an exponential dependence in an experiment observing magnetic fluctuation-induced heat transport. Figure 6b in Kauschke et al. [1990] shows an exponential spectrum with embedded coherent modes for a nonlinear dynamics experiment in a low pressure arc discharge plasma. Figure 7 of Maggs and Morales [2003] presents an exponential spectrum from magnetic fluctuations at the free edge of the LAPD-U. The exponential spectra in these examples are readily identified because of the semi-log plot display. The appearance of such spectra in a wide variety of experiments suggests that it may also be present in other results where it is simply compressed by a log-log display.

The power spectra, P, of measured fluctuations display an exponential dependence in frequency, P(f) ∝ exp(-2f / fs), where fs is a scaling frequency. This exponential feature is only observed after the temperature filament transitions into the enhanced, or anomalous, transport regime. Concomitant with the exponential spectrum is the observation of pulses or spikes in the time series data. These pulses, which can be either upward or downward going in amplitude depending on the measurement location, are Lorentzian in temporal shape. A Lorentzian pulse has an exponential power spectrum, leading to the conclusion that the appearance of these pulses causes the exponential spectrum. A brief summary of this work may be found in Pace et al. [2008a].

1.4 Thesis Outline

This thesis is composed of five chapters. Chapter 2 presents the laboratory device in which this study is performed, along with a review of the various diagnostics employed to measure plasma properties. Chapter 3 details the results surrounding the identification of a spontaneously generated thermal wave in the filament. This is the culmination of an effort to identify coherent oscillations featuring a lower frequency than the other previously known modes of the system. The thermal wave is likely to be supported in many filamentary plasma systems including the solar corona. Modification of the temperature profile by the thermal wave leads to large amplitude pulses in time series signals. These pulses are discussed in Chapter 4, which also presents evidence for a universal characteristic of power spectra in turbulent plasmas. Such spectra exhibit exponential dependencies in frequency and are found to result from the Lorentzian shape of the measured pulses. Similar spectra, and in many cases similar pulses, are observed in the existing plasma literature and in ongoing research at linear machines and tokamaks. A density gradient experiment performed in the same device as this thesis work also exhibits these pulses and exponential spectra. Chapter 5 compares the density gradient experiment to the temperature filament experiment as part of the argument for the universal nature of the exponential spectra and Lorentzian pulses. Conclusions and a unifying summary of these topics are presented in Chapter 7. Finally, the appendices present results on plasma flows in relation to the primary topics, techniques of wavelet analysis that have been applied in power spectra calculations, and a summary of techniques employed to detect the Lorentzian pulses that generate exponential power spectra.

Review: Exponential Frequency Spectrum and Lorentzian Pulses in Magnetized Plasmas

Thu, 08 Jan 2009 19:04:36 +0000

Sections

Details and Download

Previous Work

Modeling Lorentzian Pulses

What is the Relevance?

Discuss this Item

This is a review of a paper recently published by my group. Here, the paper is paraphrased to reach a wider audience. The plasma physics community can read the original publication, so my goal is to provide an example of current plasma physics research to the general public. The following review should be at a high school level and I appreciate any comments you may have regarding how to clarify it further. If you are interested in physics research, then I hope this helps to feed your curiosity.

Details and Download

This is a review of the paper titled, “Exponential Frequency Spectrum and Lorentzian Pulses in Magnetized Plasmas”. The published version of the paper can be downloaded from the following links.

Basic Information:

Citation: D. C. Pace, M. Shi, J. E. Maggs, G. J. Morales, and T. A. Carter, “Exponential Frequency Spectrum and Lorentzian Pulses in Magnetized Plasmas,” Phys. Plasmas 15, 122304 (2008)
Download: From DavidPace.com (free, no registration required)
Statements Required by the Publisher: Copyright (2008) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
The following article appeared in Phys. Plasmas 15, 122304 (2008) and may be found at http://link.aip.org/link/?PHP/15/122304.

Previous Work

Figure 14a from the paper, example of a pulse in the time series data.

An introduction to this work is provided on this page and the downloadable publication provided there. That first paper will hereafter be referred to as the PRL. The paper reviewed here (the POP) is longer and contains new material concerning the modeling of exponential power spectra as generated by the presence of Lorentzian shaped pulses in the time series data.

The basic idea behind all of this work is that we observe pulses, or spikes, in the plasma. These pulses are not always present, but whenever they are, the power spectrum of the data features an exponential dependence in frequency. The figure to the right provides an example of a pulse that was measured in one of the experiments. There are some background fluctuations, but the labeled pulse is clearly a unique feature of this signal. This is figure 14a from the paper.

Figure 6 from the paper, example of an exponential spectrum (such a spectrum appears as a straight line when plotted semi-log as in this figure).

In the next figure (figure 6 in the paper) an example of an exponential power spectrum is shown. The amplitude of the power spectrum decays exponentially with respect to the frequency. When such a spectrum is plotted in a semi-log format (logarithmic y-axis and linear x-axis), the exponential behavior appears as a straight region. In this particular example there are peaks in the spectrum that correspond to coherent waves. The exponential part of the spectrum is identified through the linear fit (a fit to the logarithmic format of the result) shown as the dashed red line.

The first paper (PDF) focused on demonstrating the connection between the pulses and the exponential spectra. The paper discussed in this review provides additional evidence for this connection by way of new modeling work. Some natural questions arise from the statements made thus far and are addresses by the more recent paper, including:

Can other pulse shapes generate exponential spectra (how do you know these pulses are Lorentzian)?
Is it possible to observe an exponential spectra with just about any combination of pulse-like features?
The data appear to show some non-symmetric pulses, can these be accounted for in the resulting spectra?

Modeling Lorentzian Pulses

The three questions above can all be addressed through analytic models of the pulses and spectra. Beginning with the question of whether non-Lorentzian shapes can generate exponential, the answer is yes. The argument in favor of the observed pulses being Lorentzian is that other pulse shapes, while potentially generating exponential spectra, do not produce the agreement between the pulse width and the exponential decay constant. As the PRL showed, there is a relationship between the temporal width of a Lorentzian pulse and the exponential decay constant of the power spectrum it produces. Presently, only the Lorentzian shape satisfies this relationship.

Figure 16 from the paper, showing the different spectral shapes resulting from different pulses.

The figure to the right is figure 16 from the POP. It plots the power spectra resulting from three different pulse shapes: Lorentzian, Gaussian, and hyperbolic-secant squared. While not shown in the paper, these three shapes are all very similar near their peaks. The differences between them are realized in the wings, away from their centers. Looking at the raw data from the experiments it would be reasonable to attempt to fit the pulses to any of these shapes. To compare their resulting power spectra, we analytically calculated the spectrum resulting from each pulse after giving them all the same temporal width. The figure shows that the Gaussian spectrum is not exponential across any frequency range. The hyperbolic-secant squared spectrum is exponential at the higher end of the frequency range, but not at the lower frequencies. The Lorentzian spectrum is exponential across all frequencies.

This initially seems to indicate that the hyperbolic-secant squared is a viable candidate for the pulse shape. It turns out that this is not the case, however, because the relationship between the pulse time-width and the exponential decay of the spectrum is not consistent. The spectra plotted in the figure all come from pulses with the same temporal width. The exponential parts of the Lorentzian and hyperbolic-secant squared spectra exhibit different slopes (the exponential part of the hyperbolic-secant squared spectrum is plotted as the dashed black line). This means that the spectrum produced by the hyperbolic-secant squared pulse would not allow for the calculation and prediction of the pulse width. In the experiments, however, we have shown that calculating the exponential behavior of the spectra allows for the determination of the widths of the pulses that generated it. Therefore, while this is not an exhaustive study of every single mathematical pulse shape in existence, it does show that there are no obvious examples of pulses other than Lorentzians that generate the same agreement between pulse and spectral characteristics.

Figure 17 from the paper, showing the different spectral shapes resulting from pulse sets with different distributions of time widths.

The next question addressed by the POP is whether exponential spectra are generated from any collection of pulse-like features. A model of Lorentzian pulses is constructed to test the sensitivity of the exponential spectral behavior with respect to the temporal widths of the pulses. In the figure to the left, two power spectra are plotted from different model sets. The Broad spectrum (dotted red line) is produced from a set of Lorentzian pulses in which the temporal widths vary between 2 and 10 microseconds. The Narrow spectrum (solid black line) is the result from a set of Lorentzian pulses in which the temporal widths vary only between 2.5 and 4.5 microseconds. For the same total number of pulses in each set, the Narrow set features a much more consistent range of pulses (i.e., the pulses are much more similar to each other within this set).

The figure shows that the power spectrum from the Narrow set exhibits exponential behavior over a greater frequency range than that of the Broad set. The Broad set loses its exponential behavior at lower frequencies. The relevance to the experiments is that since we measure exponential spectra over wide frequency ranges (see figure 6 as shown above), that implies the pulses in the experiment feature a narrow distribution of temporal widths. A consequence of this result is that if the pulses feature such consistent widths, then there is likely a generation mechanism that can explain the production of the pulses themselves. There are measurements of hundreds of pulses for a given experimental setup, and thousands of pulses overall, so the observation that exponential spectra are only observed when these pulses are reproducible and consistent in width is a powerful conclusion. In fact, it appears as though a completely random collection of pulses does not spontaneously result in an exponential power spectrum. The pulses need to feature the same shape and similar time widths.

Figure 14b from the paper, example of a Lorentzian fit to the pulse from figure 14a.

The final question covered in the POP concerns the observation of non-symmetric pulses. We claim that Lorentzian pulses generate the exponential power spectra, yet there are clearly examples of pulses that are not perfect Lorentzian shapes. One such example is shown in figure 14b from the paper, which is reproduced to the right. The measured pulse (solid red) is analytically fit to a Lorentzian shape (dashed black). It is clear that the fit is not perfect because the measured pulse is asymmetric. The leading edge (left side) of the measured pulse is steeper than a Lorentzian. While the trailing edge (right side) of the measured pulse is a very good fit, this still leads to the question of whether asymmetric, or skewed, Lorentzian pulse shapes can generate an exponential spectrum.

Figure 18a from the paper, fitting a skewed Lorentzian pulse to a measured pulse.

To model the behavior of non-symmetric Lorentzian pulses we modified the standard pulse shape with a multiplicative term shown as equation 9 in the paper. The result of this modification is that the pulse features a steepened edge. The figure to the left takes one of these modified Lorentzian fits as applied to a pulse from one of the experiments. Notice that even though this measured pulse is negative polarity (compared to the positive polarity of the pulse at the beginning of this review), the leading edge is once again steeper than the trailing edge. The measured pulse (solid black) is fit exceptionally well by the skewed Lorentzian (dashed red). Furthermore, figure 18b of the paper plots the resulting power spectra from models of either a pure or a skewed Lorentzian and shows that the resulting exponential shape is not changed by the skewing. The conclusion is that non-symmetric pulses in the measured data do not prevent the exponential spectrum from being observed.

What is the Relevance?

In a physics paper the relevance of the work is established in the beginning. In a review like this, however, it works better to explain the physics first and then put the results into context. This work experimentally observes pulse structures of a particular shape that only arise when the system has transitioned to a turbulent state (that is all shown in the PRL). The structures exhibit consistent time widths, implying that the generation mechanism is constant during their production. Turbulence is generally associated with the loss of coherent waves and the production of a broad spectrum of fluctuations. Here, however, it is shown that a very narrow-band behavior (the narrow distribution of pulse widths) is required to observe the broadband feature (the wide ranging exponential frequency behavior). This is a unique result that may be the beginning of new developments in plasma turbulence and transport. The bigger picture still needs to be determined. For example, what causes the pulses? If they are produced by a non-linear interaction of electromagnetic plasma waves, then it is likely that this same behavior occurs in other plasmas, both in space and in the laboratory. As such, we suggest that the pulses and exponential power spectra are a universal feature of plasma turbulence. If a Lorentzian shape is the result, then perhaps we can now work backwards to describe plasma turbulence with a set of solvable equations. What differential equations feature Lorentzian pulses as their solution? Perhaps these same equations can describe plasma transport in a new way. Plasma transport is important for understanding phenomena such as the solar wind and aurora in addition to the present challenge of developing nuclear fusion as an energy source.

Defense Date Set

Thu, 06 Nov 2008 19:29:00 +0000

The end of my time in graduate school at UCLA is fast approaching. On December 10, 2008 I will present a defense of my thesis to my committee. The Physics Department holds closed defenses, meaning that only the committee is allowed in the room. Some departments have open defenses in which guests and other interested people are allowed to observe (I have even heard of some departments requiring two defenses in which the first is closed and tough while the second one is open and friendly). It is a mad dash to the finish because I have to provide the committee with copies of the thesis right after the APS conference. Once it is finished, I will post a PDF of it on this website and also provide an HTML version to replace this.

A Sign that it is Time to Graduate

I recently received an accidental hint that it is time for me to finish school. A few weeks ago my department email mysteriously stopped working. Outages happen infrequently, so I let it go for a day and a half to see whether it would itself out. If the system goes down on a Sunday there is no point filing a help ticket with the department's IT group because odds are that they will see it when the come in to work on Monday. In this case, however, the problem never resolved itself and I submitted a help request. Help arrived immediately.

The department's email system automatically assigns accounts a six year lifetime. My six years passed and the system simply turned off my account! The IT group logged in to their system, probably checked a box labeled “Activate”, and I was back online. Everyone in the lab had a good time joshing me about running out my email lifetime. My account returned to full functionality, allowing me to receive the following image from another graduate student.

Now it's time to get back to work.

My Thesis Project

Mon, 20 Mar 2006 08:18:57 +0000

I completed my Ph.D. thesis in December 2008 (the conferral date is 2009). Copies of it are available in both PDF and HTML format. The PDF is the source for the printed copies that were turned in to the UCLA Library as part of the requirements for completion. The web version omits the front matter but does present every chapter and the full appendices. A link to the downloadable PDF is provided below, along with the Table of Contents for the web version.

General Information

Title: Spontaneous Thermal Waves and Exponential Spectra Associated with a Filamentary Pressure Structure in a Magnetized Plasma
Department: Physics and Astronomy
Institution: University of California, Los Angeles
Download: PDF (5.5 MB, 162 pages)

This is a work in progress. I will upload sections as I finish converting them to HTML. The PDF download is the complete version, however, so the web version will not provide anything new.

Abstract

1 Introduction

Abstract

An experimental study of plasma turbulence and transport is performed in the fundamental geometry of a narrow pressure filament in a magnetized plasma. An electron beam is used to heat a cold background plasma in a linear device, the Large Plasma Device (LAPD-U) [W. Gekelman et al. Rev. Sci. Instrum. 62, 2875 (1991)] operated by the Basic Plasma Science Facility at the University of California, Los Angeles. This results in the generation of a filamentary structure (~ 1000 cm in length and 1 cm in diameter) exhibiting a controllable radial temperature gradient embedded in a large plasma. The filament serves as a resonance cavity for a thermal (diffusive) wave manifested by large amplitude, coherent oscillations in electron temperature. Properties of this wave are used to determine the electron collision time of the plasma and suggest that a diagnostic method for studying plasma transport can be designed in a similar manner. For short times and low heating powers the filament conducts away thermal energy through particle collisions, consistent with classical theory. Experiments performed with longer heating times or greater injected power feature a transition from the classical transport regime to a regime of enhanced transport levels. During the anomalous transport regime, fluctuations exhibit an exponential power spectrum for frequencies below the ion cyclotron frequency. The exponential feature has been traced to the presence of solitary pulses having a Lorentzian temporal signature. These pulses arise from nonlinear interactions of drift-Alfvén waves driven by the pressure gradients. The temporal width of the pulses is measured to be a fraction of a period of the drift-Alfvén waves. A second experiment involves a macroscopic (3.5 cm gradient length) limiter-edge geometry in which a density gradient is established by inserting a metallic plate at the edge of the nominal plasma column of the LAPD-U. In both experiments the width of the pulses is narrowly distributed, resulting in exponential spectra with a single characteristic time scale. The temperature filament experiment permits a detailed study of the transition from coherent to turbulent behavior and the concomitant change from classical to anomalous transport. In the limiter experiment the turbulence sampled is always fully developed. The similarity of the pulse shapes and fluctuation spectra in the two experiments strongly suggests a universal feature of pressure-gradient driven turbulence in magnetized plasmas that results in non-diffusive cross-field transport. This may explain previous observations in helical confinement devices, research tokamaks and arc-plasmas.