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Page 14 2 Scientific Progress and the Development of Predictive Capability Early experimental efforts to harness fusion energy quickly came up against the complex, nonlinear nature of plasmas. More often than not, these experiments ended with the plasma splattering against the walls of the containment vessel rather than being confined inside the magnetic bottle. Scientific advances were needed to produce a high-temperature plasma at 100 million degrees. Tools had to be developed to describe plasma equilibrium (the balance between plasma pressure and the forces of the confining magnetic fields) and plasma stability. Even after significant advances had been made on these topics, other fundamental questions remained—how large-scale instabilities cause the plasma to break up whereas small-scale instabilities cause energy leakage across the magnetic field; how an essentially collisionless plasma can be heated hot enough for fusion reactions to occur; and how phenomena at both large and small scales can be remotely measured with enough accuracy to test the understanding of plasma behavior. A measure of the maturity of this knowledge base—and, also, of the quality of the science—is the ability to predict the performance of experiments from a fundamental understanding of the characteristic dynamics of plasmas in the laboratory and in nature. Such predictive capability goes beyond simple performance metrics such as the energy containment time, temperature, or the plasma pressure, which, although important, do not necessarily reflect the degree to which the fusion program has broadly impacted plasma science and related fields. Predictive capability also permits the confident design of future large experiments, perhaps even the optimum magnetic container (see Chapter 3 for a more complete description of the various magnetic configurations being explored within the program). The following sections discuss progress in the understanding of plasma science and the predictive capability that follows from this understanding. The material is presented in three categories: equilibrium, stability, and transport. It must be emphasized that while the overview of science issues that follows attempts to assess some of the important accomplishments of the program as well as the challenges it faces, all areas are not given equal treatment. It is simply not possible to cover all of the scientific topics of the program in depth. In the interest of addressing at least some topics with enough
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Page 15 detail to convey a sense of the science being done, the impact of program decisions on the science, and the scientific culture of the program, a few representative areas have been selected. One complication in assessing the specific contributions of the U.S. Fusion Energy Sciences program to the overall fusion effort is the need to separate and compare the U.S. effort and the broader international effort. From the very beginning of the program, in the 1950s, there has been a close collaboration internationally on all aspects of magnetic confinement fusion (collaboration on inertial fusion was constrained by security issues). Large U.S. facilities have had international collaborators and vice versa. These close interactions often make it difficult to clearly separate U.S. contributions from international contributions. The science in this chapter generally refers to activities in which the United States has, at the least, played a very significant role. Where foreign programs clearly played the dominant role, this is noted. Many of the important experimental and theoretical tools developed during the four-decade history of the program are now converging to produce a qualitative change in the program's approach to scientific discovery. Theoretical models are now sufficiently mature to describe much of the complex nonlinear dynamics of plasmas. Quantitative comparison with experimental observations is beginning to facilitate a first-principles understanding and interpretation of the behavior of plasmas. One consequence of the emerging scientific understanding of these systems is the development of techniques for manipulating turbulence and therefore controlling the energy-containment properties of the magnetic bottles. The suppression of small-scale turbulence and transport in a 100-million-degree medium is an accomplishment that is by any scientific standard a significant achievement and a sign of the high level of the science generally carried out under this program. SUMMARY Significant advances have been made in each of the traditional foci of plasma physics research: equilibrium, stability, heating, and transport. Over the past decade, a high level of predictive capability has been developed in several key areas. The program is moving into a new era in which the tight integration of theoretical predictions and experimental observations is enabling the control of plasma dynamics, including the suppression of turbulence and transport. Equilibrium and Heating The theoretical and computational tools needed for studying plasma equilibria in complex magnetic containers are now well developed and extensively used in the design of new experiments and in the analysis of existing experiments. A number of techniques, including high-power ion beams and driven waves at frequencies from kilohertz to multigigahertz, generally referred to as radio-frequency waves, have been developed to heat plasmas and also to generate and sustain plasma currents. The basic propagation and absorption physics for beams and waves are well understood. These techniques are being used to control pressure, current, and flow profiles and thus to optimize plasma performance in present-day large experiments, but techniques applicable to future high-pressure plasmas require further development. Diagnostics for remotely measuring important equilibrium-related quantities such as plasma density, electron and ion temperatures, and magnetic field are now available in major plasma experiments. Tools to measure electric fields and associated equilibrium flows, which are increasingly recognized as having an important influence on stability and transport, are less well developed. For future novel plasma configurations, these measurement techniques will have to be extended or new approaches invented.
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Page 16 Stability Pressure and current in magnetically confined plasma are limited by large-scale, ideal (zero resistivity) magnetohydrodynamic (MHD) instabilities. Standard tools for calculating these stability limits in complex magnetic geometries are widely available, and their predictions have been benchmarked with observations, aided by mature diagnostics. Dissipative instabilities (nonzero resistivity), such as magnetic reconnection, are not as well understood because their growth rates are low. Consequently, fluid drifts and flows can strongly modify the conditions under which these instabilities begin to grow. Once reconnection sets in, however, the dynamics is better understood, and the critical role of dispersive waves acting at small scale-lengths has been identified; similar physical processes control magnetic reconnection in magnetospheric and astro-physical plasmas. Pressure-driven reconnection, which can limit the pressure in magnetic containers below the ideal limit, is inherently nonlinear and therefore challenging to model. Single-mode evolution is largely understood, but the dynamics of multiple modes, their interactions, and the related transport are not. The existence of a density limit for plasma stability is a robust feature of magnetically confined plasmas and is well described by a simple scaling law (for tokamaks). While the final termination of discharges that exceed the density limit is described by a mechanism involving edge cooling, the apparent increase in transport at the limit is not well understood, and a predictive theory has remained elusive. The destabilization of plasma waves by energetic alpha particles and the resulting transport of these particles and their energy are central issues for energy-producing plasmas. Experiments have verified theoretical models for stability and for the single-wave nonlinear behavior. Learning about the interaction of energetic particles with a broad spectrum of waves and the self-consistent interplay among plasma equilibrium, stability, and transport in the presence of strong local self-heating requires access to a fully ignited plasma experiment. Transport It has been well documented that plasma transport is mainly caused by an anomalous process in which the free energy from gradients in the density and temperature profiles drives instabilities. These instabilities lead to vortices, which in turn cause the ions and electrons to wander across the confining magnetic field and eventually escape from the container. Anomalous transport of the same sort has also been invoked in other plasma systems, ranging from Earth's magnetopause to astrophysical accretion disks. Historically, the rate of transport and its dependence on plasma parameters were described by empirical scaling laws derived from experimental data. While the empirical laws were useful for comparing the performance of different machines and for benchmarking the testing of ideas for improving confinement, they provided little insight into physical processes. Moreover, the scaling laws had to be continually modified as plasmas progressively entered new operating regimes. This eroded confidence in the strictly empirical approach to describing transport. In place of scaling laws, a first-principles physics approach is now being developed that treats the detailed dynamics of the microscopic turbulence that drives transport. The enormous range of space- and timescales and the complexity of the magnetic geometry make the numerical simulation of turbulent transport a true “grand challenge.” Recent key discoveries in plasma transport research include the recognition that zonal flow plays a crucial role in determining nonlinear saturation and in identifying avalanches and associated fast radial propagation of disturbances. An important advance occurred when transport barriers (local regions of strongly suppressed transport) were observed to spontaneously form at the edge of a tokamak plasma.
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Page 17 Following a long and sustained effort to understand this phenomenon, a major breakthough occurred recently when these barriers were generated in the core of a confined plasma. The formation of these barriers marked a paradigm shift in the program, since their existence was a sign that turbulence—and hence transport—in high-temperature plasmas could be controlled. There is now substantial evidence that these barriers are generic, occurring in a variety of confinement devices. While experimental data support the idea that transport barriers arise because self-generated plasma flow suppresses the local turbulence, the actual dynamics of and threshold for barrier formation remain poorly understood. A complete understanding will require simulating barrier formation in the presence of self-consistently evolving turbulence. Direct measurement of fluctuations is required to understand turbulence-driven transport. Experimental techniques have been developed for remotely measuring fluctuations in the temperature and density at the length of the ion gyroradius (radius of gyration around the magnetic field) or larger. However, fluctuations at the much smaller electron-scale lengths have not yet been measured. Also, the measurement of fluctuations in the electric potential and the magnetic field is difficult. Although many instabilities can be present in modern plasma experiments, one particular instability—driven by the ion temperature gradient—has been identified as the dominant mechanism for ion thermal transport in the core of tokamak plasmas. The nonlinear behavior of this instability requires further investigation. In addition, agreement between key predictions of the models for this instability and experimental observations remains weak. The understanding of electron thermal and particle transport as well as the impact of magnetic perturbations, which are known to be important in high-pressure plasmas, also remains poor. Fluid models have advanced our understanding of transport at the cool edge of confined plasmas. The dominant instabilities here are distinct from those in the core region. More focused experiments dedicated to comparing theory and simulation models with experimental results are needed to gain confidence in the models and to pin down the threshold for the formation of the edge transport barrier. EQUILIBRIUM AND HEATING: DESIGNING, CONTROLLING, AND DIAGNOSING A CONFINED PLASMA Plasmas at the extremely high temperatures and densities at which fusion occurs need to be contained in magnetic bottles that can insulate the plasma from its cold surrounding wall material. These containers must be “strong” enough to hold in the pressure of the hot plasma gas, and their magnetic field lines must have “good” topology so that hot plasma particles—especially electrons—cannot wander along the lines and escape. Typically, the field lines of good containers form closed surfaces as they wind through space, the result being that particles moving along the field lines cannot easily leave the system. Generally, the most desirable containment configurations have large values of the parameter β, which is the ratio of the pressure of the plasma to the “pressure” (actually the energy density) of the confining magnetic field. For any given configuration, there is an upper limit on β for which an equilibrium, or balance of pressures, can exist. Above this limiting β, the plasma blows apart and strikes the walls of the confinement vessel, quenching the discharge. Hence the creation of equilibrium is the necessary first step to achieving high-temperature plasma containment. A number of techniques, including high-power ion beams and driven waves at frequencies from kilohertz to multigigahertz, generally referred to as radio-frequency waves, have been developed to heat plasmas and also to generate and sustain plasma currents. The basic propagation and absorption physics for beams and waves are well understood. These techniques are being used in present-day large
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Page 18 experiments for the control of pressure, current, and flow profiles in order to optimize plasma performance, but techniques applicable to future high-pressure plasmas require further development. The theoretical and computational tools for studying equilibria in complex magnetic bottles are now well developed and extensively used. Similarly, highly developed techniques for measuring important equilibrium quantifies such as the plasma density and temperature and the magnetic field are now standard on plasma experiments. Diagnostic tools to measure electric fields and associated equilibrium plasma flows are, however, less well developed. Tools for Calculating Equilibria The theoretical and computational tools for calculating the magnetohydrodynamic equilibria of plasmas confined in complex magnetic bottles are quite mature. The various equilibrium codes give reproducible and verifiable results for the same configuration. These codes are routinely used for the design of new experiments, analysis of data from present experiments, determination of equilibria for stability analysis, and even analysis for real-time feedback control of complex plasma shapes. Their robustness and high level of development reflect the relative simplicity of the underlying physics, which involves only Maxwell equations and the force balance for a conducting fluid in a magnetic field. In particular, two-dimensional equilibrium codes—for configurations with an axis of symmetry— are highly developed, extensively benchmarked against experiments (especially for tokamaks, less well so for other symmetric configurations), and widely used. Some extensions are still being pursued: for example, allowing for the presence of currents outside the last closed magnetic flux surface (called the separatrix). Three-dimensional equilibrium modeling codes are required for confinement configurations that are not axisymmetric. The outstanding example is the stellarator configuration, which has coils wound into a helical torus (see Figure 2.1). The stellarator does not have simple toroidal symmetry, although it may have helical symmetry or some useful form of quasi-symmetry. The state of the art in these codes continues to evolve, but they still provide a reasonably mature set of tools for plasma modeling and analysis. A challenge for the three-dimensional equilibrium codes is to be able to represent multiply connected regions, such as stochastic field regions (where magnetic field lines fill the volume without forming flux surfaces) or magnetic islands. Whether equilibria really exist when there are no flux surfaces is a question peculiar to the three-dimensional configurations. As long as this issue can be avoided, the equilibrium codes and vacuum magnetic field solvers provide the basic tools for design of complex three-dimensional stellarator configurations. A modest amount of experimental benchmarking has been pursued for the stellarator equilibria, and more is anticipated in the near future. To date, equilibrium code results and two-dimensional maps of the magnetic flux surfaces and their spatial shifts are in good agreement. Much of this work has been carried out in Germany as part of the Wendelstein stellarator experiments. Not much information has yet been obtained at high β, where the pressure-driven currents are so large that the measured fields are no longer close to the vacuum fields produced by external coils. Operation at higher values of β is expected in the next generation of these experiments. The predictive capability of equilibrium codes is contingent on the input of reliable profiles of the plasma pressure and current. The current profile can usually be satisfactorily obtained from classical calculations for current diffusion. Obtaining the pressure profile, on the other hand, requires a reliable understanding of plasma transport, which has not yet been achieved. Heuristic transport models are available, and these have often been adequate for predicting the equilibria to be realized in experiments. The equilibrium codes are also used in hindsight to interpret experimental data. In this case, the current
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Page 19 ~ enlarge ~ FIGURE 2.1 Pressure surface of a three-dimensional stellarator equilibrium illustrates the complex equilibria that can be studied and manipulated to maximize confinement and other properties. Courtesy of M. Zarnstorff, Princeton Plasma Physics Laboratory (PPPL). and plasma profiles can even be extracted from measurements and applied to generate self-consistent equilibria. These solutions are then routinely utilized to analyze stability and, recently, to control the plasma with real-time feedback. Tools for Measuring Equilibrium Pressure and Magnetic and Electric Fields Measurements of the internal pressure and the magnetic and electric fields in high-temperature confined plasmas are critical to understanding the equilibrium and stability properties of these plasmas. Probes are useless for measuring these important quantities since they vaporize if inserted into the interior of plasmas whose electron temperature is 10 to 30 keV. Thus, the challenge has been to invent remote measurement techniques. Very early in the fusion program, Thomson scattering techniques were developed to measure the electron temperature and density profiles. Later, when time-dependent measurements were required to understand macroscopic instability and magnetohydrodynamics (MHD), electron cyclotron emission techniques were developed to obtain accurate electron temperature measurements with high time resolution. Ion temperature measurements are more difficult and less widely available. In well-diagnosed experimental facilities, these data are provided from measurements of charge exchange between hightemperature ions and cold neutral particles.
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Page 20 Extensive progress has been made over the past decade in developing ways to measure the structure of the magnetic and electric fields inside magnetically confined toroidal plasmas. Most of this work was done for the tokamak configuration but is now being extended to other plasma configurations. The magnetic field at the edge of a plasma can readily be measured with simple external magnetic probes and loops. In the case of relatively cold or short-lived plasmas, the internal magnetic field has been measured with magnetic pickup loops inserted into the plasma. In general, however, remote measurements are required. An example of successful diagnostic development is the Motional Stark effect, a remote method that can measure the internal structure of the equilibrium magnetic field, at least in plasma configurations where the magnetic field is strong. This method measures the polarization of light emitted from high-energy neutral hydrogen atoms injected into the hot plasma core region. The light is polarized as a result of the Stark splitting of the energy levels, caused by the induced electric field that the atom experiences in its Lorentz-transformed rest frame. Care must be taken to account for contributions from the intrinsic electric field in the plasma, which can often be comparable to the induced field. Such measurements typically provide spatial resolutions of a few centimeters and a time resolution of 5 to 10 ms. The tilt angles of magnetic field lines are measured to an accuracy of 0.1 deg. This accuracy is sufficient for evaluating the global stability of plasmas but not their local stability. The measurements are sufficient to confirm the existence of the theoretically predicted “bootstrap” current, which is a self-generated current present in weakly collisional plasmas. These self-generated currents aid the steady-state operation of a number of confinement approaches. With high-temperature plasma experiments now being pursued in configurations that have weak magnetic fields and small, rapidly evolving plasmas, there is an increasing need for new or improved techniques to determine the internal magnetic field structure. In addition to the Motional Stark effect, techniques that use microwave polarimetry, emission from the ablation clouds of injected pellets, Zeeman splitting of energetic lithium neutrals, flux surface imaging, and Stark line broadening have either already been employed in special situations or are under active development. These and other concepts will have to be further developed in order to measure the magnetic field in modern high-pressure plasma experiments. New techniques are also needed to measure the profile of the current density in the cold edge region since the stability of the edge, which depends sensitively on this profile, is crucial for understanding energy containment. Over the past several years there has been an accumulation of evidence that plasma flows, driven by electric fields that point perpendicular to the magnetic flux surfaces, can have a strong influence on plasma stability with respect to both large-scale and small-scale disturbances. These electric fields can be directly measured by a beam of heavy ions injected into the magnetized plasma. However, because it is expensive, this technique has not been deployed in large plasma experiments, where the required energy of the ions would be very high. Two alternative methods for electric field measurements in large, hot plasmas have been developed. The first measures the plasma fluid velocity and then indirectly deduces the local electric field in the radial direction from force balance. The second method uses a variation of the Motional Stark effect to simultaneously solve for the pitch angle of the local magnetic field and the local electric field strength, from which the local electric field structure can be determined with reasonable accuracy. However, the extension of the latter method to plasma configurations with weak magnetic fields is problematic and is a topic of ongoing diagnostic development. Tools for Controlling Plasma Properties The eventual success of any magnetic fusion approach will depend on controlling several tightly coupled processes: transport, turbulence, macroscopic stability, alpha-particle dynamics, and plasma-wall
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Page 21 interactions. Their control, in turn, requires that one be able to control several plasma parameters: density, temperature, and the profiles for pressure, current (or magnetic geometry), flow, electric field, and so forth. Consequently, the development of techniques for plasma heating and control has always been a topic of considerable interest, including issues in plasma production, heating, current drive, flow drive, plasma stabilization, and the basic plasma physics needed for these applications. The most fully developed techniques for heating and control use either high-power neutral atomic beams or radio-frequency waves (see Figure 2.2), which are injected into the plasma. The basic physics of bulk heating and current drive has been established for the most common applications of both approaches, but techniques for detailed control of pressure and current profiles and applications to plasmas with high dielectric constants are still in development. In neutral beam heating and current drive, energetic neutrals injected across the magnetic field deposit energy and directed momentum in the confined plasma. The generation, propagation, and deposition of ~ enlarge ~ FIGURE 2.2 A gyrotron from the DIII-D tokamak experiment at General Atomics (GA) in San Diego. A gyrotron is a source of high-frequency radio waves for heating electrons. Courtesy of General Atomics.
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Page 22 the beam energy in the plasma are determined mainly by atomic processes and hence are well understood and predictable. Detailed measurements of the resultant ion distributions and beam deposition profiles have confirmed the models used to describe beam heating, while neutral beam current drive techniques have been reasonably confirmed with current profile measurements and detailed Monte Carlo deposition calculations. Nevertheless, the limitations of neutral beam injection for application to the large, high-temperature plasmas expected in fusion reactors have spurred work on alternative techniques for heating and control. The interaction of radio-frequency waves with magnetized plasmas promises a wide range of plasma and fusion applications and yields a wealth of challenging scientific issues. The main issues in these applications are launching the waves, propagation into the plasma in a complex magnetic geometry, absorption of the energy (and possibly the momentum) by the plasma, and generation of the nonlinear effects that perturb the plasma and alter the wave properties. The propagation of radio-frequency waves in magnetized plasmas is arguably one of the most quantitative and best-understood branches of plasma science. However, collisionless interactions with particles, relevant to wave heating in high-temperature plasmas, were not understood in the original studies of electromagnetic wave propagation in the 1930s and 1940s. Modern wave studies for fusion applications, begun in the 1950s and 1960s, were plagued by disappointing results owing to the poor confinement of energetic particles. Around the same time, theorists developed an understanding of wave-particle interactions (collisionless damping) and other kinetic effects. This was followed by a wealth of basic experimental work that catalogued a multitude of longitudinal plasma waves in warm, magnetized, and nearly collisionless plasmas and validated the nonlinear theory of plasma-wave interactions. As a new generation of large plasma devices with improved confinement was deployed in the 1970s and 1980s, tests of wave-plasma interactions were carried out at the megawatt power level, confirming the predictions of ion and electron bulk heating. Over the past decade, moreover, the use of radio-frequency waves to drive plasma currents at the mega-ampere level has been demonstrated at efficiencies consistent with theoretical predictions. The applications of radio-frequency waves extend beyond bulk heating and current drive to precise and localized plasma control. For such applications to be successful, an integrated understanding must be acquired of the various aspects of wave launching, propagation, and absorption and response of the plasma distribution function to the wave. A variety of tools have been constructed for this task, especially for application to tokamak-like plasmas, but new models will be needed as new confinement schemes and plasma conditions are considered. For example, spherical torus plasmas with very high pressures have wave propagation and absorption characteristics that are quite different from those in conventional tokamak plasmas. Launching the correct spectrum of waves into the desired plasma mode of oscillation is the first challenge. Low-frequency waves, typically associated with ion modes, require complex three-dimensional launching antennae, which are modeled numerically. The numerical models typically include some three-dimensional aspects, but a one-dimensional plasma, linear plasma response, and rectilinear antenna geometry are usually assumed. When the antenna shape does not closely match the plasma shape, the models become less accurate and less useful. An additional difficulty arises from the interaction of the antenna with the edge plasma. Nevertheless, good agreement with experimental results has been obtained for cases where the model approximations are valid. Wave-guide arrays for launching higher frequency waves, associated with electron modes, are much less sensitive to proximity to the plasma edge. Wave propagation is modeled in one of two ways, depending on the frequency range of interest. For high-frequency, short-wavelength modes, the well-established model of geometrical optics is usually
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Page 23 valid. At low frequencies, the wavelength is typically of the same order of magnitude as the plasma size, so the full wave equation must be solved directly. Computationally tractable two- and three-dimensional models can be formulated by means of various simplifying assumptions (such as a small gyroradius and restricting the particle cyclotron frequency to low harmonics). Such modeling yields useful and accurate predictive capability within the limits of the assumptions. However, applications to low-field devices, large reactor-scale devices, and high-pressure plasmas will require a significant increase in numerical resolution and a scale-up in computer power. In many cases, the injected radio-frequency power does not cause the velocity distribution functions to be significantly distorted away from the Maxwellian form. Rather, it essentially provides macroscopic sources of heat, current, and/or plasma flows. Given the radio-frequency fields from the propagation models, well-developed theories can be used to calculate the local deposition of power and current. More work is needed, however, to describe plasma flows driven by radio-frequency fields. At very high powers, the distribution often deviates significantly from Maxwellian, and direct solution of the velocity-space diffusion equation is necessary to produce the resultant particle distribution functions and to calculate the associated heating and current drive. Finite difference and Monte Carlo techniques are reasonably well established for these purposes. All of the above theories or models are computationally feasible only with idealizations and approximations, and determining or demonstrating the range of validity for a particular model is quite a challenge. To date, the most well-developed radio-frequency wave models have not been integrated into the transport and stability codes used to interpret experimental data. Tighter connection to experiments is needed. STABILITY: PREDICTING OPERATIONAL BEHAVIOR Fusion experiments in the early days were plagued by gross instabilities that caused catastrophic loss of plasma containment. These observations stimulated research on large-scale unstable motions. Energy principles—based initially on the MHD model of plasma as a fluid and later on kinetic models—were developed that provided a theoretical framework for understanding the plasma's stability. Subsequent experiments were then able to avoid gross instability. These energy principles are now widely used in the fusion program and also in the fields of space physics and astrophysics. Indeed, the assessment of linear stability, using computer codes that evaluate the ideal (with “ideal” indicating the limit of zero resistivity or dissipation in which the plasma and magnetic field move together, a significant constraint that maximizes the stability of the configuration) MHD energy principles in multidimensional geometry, has become a routine component of all plasma fusion experiments during both design and operation. Modern high-temperature experiments, however, have operational limits that arise not only from ideal MHD stability but also from nonideal (nonzero resistivity) stability and from excessive radiated power (density limit). The limits associated with ideal MHD stability are typically well understood, whereas those linked to nonideal effects are still being explored. The operational limit at high density has been well characterized empirically, but a basic understanding of it remains elusive. Also critical to predicting plasma operation, especially in configurations that could support high plasma pressure, is the ongoing effort to develop reliable codes for solving the nonlinear equations, fluid or kinetic, that describe the dynamics when linear stability boundaries are violated. In some cases, a linear instability will saturate benignly, causing only modest plasma transport that restabilizes the plasma, but in other cases, global confinement is lost. There are also purely nonlinear instabilities, which self-amplify only after the amplitude of motion exceeds a finite level and therefore cannot be analyzed with linear stability theory.
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Page 24 Ideal Stability of Confined Plasmas Strong coupling between experiment, theory, and computation has, in general, led to a solid basic physics understanding and predictive capability for ideal MHD stability limits in toroidal magnetic confinement experiments. This symbiosis has resulted in innovative ideas for configurations—a notable example being the spherical torus (a doughnut-shaped axisymmetric configuration in which the major and minor radii are comparable)—that have very high pressures as measured by the plasma β. High values of β would allow fusion reactors to be compact and efficiently use the externally applied magnetic field to contain the high-temperature plasma. The U.S. fusion program strongly supported the development of codes to evaluate local and global plasma stability from the ideal MHD energy principle. Parallel efforts were supported by the Europeans. Global stability involves unstable disturbances with large scale-lengths; these disturbances are sensitive to the profiles for the current and pressure and hence must be calculated in the full geometry of the confinement configuration. The calculation of the shape of the disturbance and how fast it grows can be reduced to a two-dimensional analysis if the configuration is toroidally symmetric. Existing codes are able to handle either “fixed” (i.e., conducting metal walls) or “free” (i.e., vacuum) boundary conditions at the edge of the plasma. The global stability codes become limited in resolution, however, when the scale-length of the perturbation becomes smaller than about 20 percent of the characteristic plasma size—in technical terms, when the toroidal mode number exceeds approximately 5. For analyzing these small-scale motions, local stability methods are faster and less computationally demanding. The best known is the so-called ballooning representation, which exploits the near-invariance resulting from the short scale-length across the magnetic field and reduces stability to a one-dimensional calculation, readily soluble even in complex magnetic configurations. The ballooning representation was developed simultaneously by scientists in the United States and the United Kingdom. Global stability calculations based on the ideal MHD model have been quite successful in predicting the operational limits for a variety of confinement devices. For example, excessive current in a plasma can cause a kinking motion that terminates the discharge. These current limits, which were early on predicted theoretically and observed experimentally, can be avoided fairly easily by operating below the limit (in a tokamak) or by imposing a conducting shell (in a spheromak or a reversed-field pinch). Another example is the scaling for the β limit from pressure-driven instabilities, initially identified from ideal MHD calculations by European scientists in the early 1980s and soon thereafter shown experimentally in all major tokamak facilities to be consistent with the maximum achievable β value. For example, see Figure 2.3 . Present ideal stability predictions of the limits for individual tokamak discharges are accurate to better than 10 percent. These types of calculation have become essential for identifying promising innovative confinement schemes, not only in tokamaks but also in stellarators and spherical tori. Examples of discoveries that are strongly impacting the design of current experiments are “second stability” (a parameter regime in which stability—surprisingly—improves with increased plasma pressure), strong tailoring of the plasma shape, and the structure of the current profile. Key to the successful application of ideal MHD equilibrium and stability models to experiments have been marked improvements in diagnostic and computational capabilities. Improved diagnostic measurements, especially for the tokamak, have enabled accurate reconstruction of the equilibrium current, pressure, and density profiles, which are necessary to accurately assess MHD stability. The stability of the reconstructed equilibria is now analyzed routinely and rapidly. The structure of the instabilities themselves can now be reliably obtained from measurements of the temperature, density, and magnetic fields; the disturbance in the plasma resulting from the instability typically sweeps past the
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Page 34 first discovered in the ASDEX tokamak experiment in Germany, with increased energy input (by ohmic heating, neutral-beam heating, or radio-frequency wave heating) the plasma discharge spontaneously enters a new regime in which the pressure profile becomes very steep near the edge, raising the stored energy over the entire central plasma and approximately doubling the energy confinement. Nearly a decade passed before the essential ingredients of the H-mode transition were understood—namely, that plasma rotation, locally generated at the edge, shears apart the vortices driving transport, allowing the pressure gradient to steepen, which facilitates a further increase in the plasma rotation. Nevertheless, once the results were confirmed by other experiments, there was immediate recognition of the far-reaching conclusion that anomalous transport is not intrinsic to a magnetically confined plasma but can be manipulated if the appropriate control knobs are identified. The discovery of the H-mode further eroded confidence in the scaling law approach, since no scaling law could predict bifurcation, in which the plasma confinement makes a transition from one regime to another. Other discoveries with significant implications for confinement were also made: injecting pellets or altering the twist of the central magnetic field (magnetic field shear) can induce a transport barrier in the core of the plasma; supplying auxiliary power on top of the ohmic heating degrades confinement (this unfavorable scaling of confinement with energy input is referred to as L-mode scaling); injecting trace amounts of heavy ions can boost confinement; the shape of the plasma cross section can affect confinement; and toroidal rotation induced by the injection of high-energy neutral beam ions can tear apart turbulence, as in the H-mode transition. The scaling law approach was improved somewhat by using normalized (or dimensionless) local plasma parameters as the variables against which the plasma confinement is compared. Nevertheless, scaling laws for describing energy containment carried more and more qualifiers, requiring that only discharges with, say, matching shapes or density profiles could be compared. The growing complexity of anomalous transport from the experimental perspective, coupled with the opportunities provided by an array of control techniques, undermined the scaling law approach to confinement predictability. At the same time, the ability of scientists to measure, understand, and model plasma turbulence was evolving rapidly, providing hope that a truly physics-based approach to understanding anomalous transport could be successfully pursued. Development of Tools for Calculating Stability and Simulating Nonlinear Microturbulence In the early years of fusion science research, theories for anomalous transport used simple mixing length estimates based on linear instability properties. These estimates assume that during a few growth times, the turbulence increases to a level sufficient to mix or relax the gradients (of, for example, density or temperature) that drive the turbulence. This approach was generally inadequate to describe the observations or provide useful predictions—estimates of the linear growth rates of instabilities were often inaccurate and the postulated fluctuation levels did not reflect the nonlinear processes that are important in high-temperature plasma systems. A variety of theoretical tools therefore needed to be developed to have a useful description of small-scale turbulence in high-temperature plasmas—tools to understand the linear stability of fluctuations and also to understand the nonlinear behavior. The unstable fluctuations of interest are those excited by the gradients of density, temperature, and velocity flow and also by the presence of multiple ion species, as often is the case in current experiments and will be in future experiments. Analyzing linear stability, especially in a complex magnetic geometry, is nontrivial. The ballooning mode formulation, which exploits the local invariance properties of plasmas with respect to translations across the magnetic flux surfaces, allows a two-dimensional linear stability problem to be reduced to a one-dimensional system. The resulting equations can be solved even in a
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Page 35 kinetic representation. Codes based on the ballooning mode formulation, which have been benchmarked to ensure reliability, are now widely available. They are flexible so that stability can be explored not only for model plasma equilibria but also for the equilibria obtained from actual experiments. Stability results can therefore be used either to gain a fundamental theoretical understanding of a problem of interest or to analyze the stability of particular regions of the experimental profiles to help interpret the observations. Describing the nonlinear, three-dimensional turbulent state is even more challenging. Nonlinear simulations are required, the computational algorithms for which are still under development. A wide range of instabilities can exist in a magnetically confined plasma, and their interaction is usually complicated and not well understood. A particular challenge has been the treatment of the relatively fast motion of electrons parallel to the magnetic field in conjunction with the much more slowly moving ions and the relatively slow evolution of the turbulent spectra. Thus, taking into account the perturbations of the magnetic field, which depend sensitively on parallel electron currents, is computationally prohibitive in the high-temperature core of a plasma. At the cold plasma edge, codes based on less demanding fluid-type models can be used. The description of the hot, collisionless plasma core region has therefore been largely limited to electrostatic turbulence, in which magnetic field perturbations are neglected. A few exceptions to these generalizations are discussed below. Two key advances were important for developing the capability to simulate turbulence in magnetically confined plasmas. The first was the formulation of a reduced set of equations for which the motion of plasma particles as they gyrate around a magnetic field line, which is very rapid compared to all frequencies characterizing turbulence associated with pressure-gradient-driven instabilities, is averaged away. These so-called gyrokinetic equations can be solved without the time step constraints (and the computer memory storage requirements) imposed by the fast gyromotion. A further reduction led to a set of “gyrofluid” equations, which, although fluid in nature (that is, they are based on velocity moments that integrate out the wave-particle resonance information), still capture some of the collisionless dissipation contained in the full kinetic equations. The advantage of the gyrofluid equations is that they can be solved much more quickly than the gyrokinetic equations. Recently, however, the utility of these gyrofluid equations has been called into question because they do not adequately treat the damping of plasma rotation. Nevertheless, these equations did play an instrumental role in developing the first credible models of the turbulence driven by the ion temperature gradient instability in tokamak plasmas. The second key advance in the ability to simulate fine-scale turbulence was the development of “flux tube” codes in the early 1990s. These codes took advantage of the same near-invariance properties as in the ballooning mode representation in order to be able to describe accurately both large scale-lengths (1 m) along the magnetic field and short scale-lengths (0.001 m) across it. For the first time, turbulence in three-dimensional systems could be simulated with normalized parameters (for example, the ratio of the ion gyroradius to the plasma size) that correspond to realistic experimental values. These flux tube codes led to the first simulation-based predictions of the transport of ion energy in the core region of magnetically confined plasmas. While electrostatic turbulence has been the focus of study in the high-temperature interior of a plasma, magnetic field perturbations have been explored in two contexts: at the plasma edge and in very-short-scale turbulence driven by the electron temperature gradient. At the low-temperature plasma edge, since collisions are important, three-dimensional models of turbulence based on the collisional fluid equations were derived. These models have also been used to study the pedestal in the temperature profile at the plasma edge, which occurs during the transition to H-mode behavior. Because they are simpler than kinetic models, these edge-turbulence models can describe magnetic perturbations, as well as include both ion and electron temperature gradient drives for instability and correctly treat the neoclassical
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Page 36 damping of flows, which is important for studying how stabilizing flows are generated during the H-mode transition. In a sense, therefore, these edge-turbulence models are the most complete of all plasma turbulence models. Magnetic field perturbations and the required dynamics of the very-high-speed electrons parallel to the magnetic field have also been included in studies of short-wavelength turbulence driven by the electron temperature gradient in the hot plasma core. Since the characteristic scale-length of this turbulence ranges between the electron gyroradius and the electron electromagnetic skin depth and is therefore very small compared to the ion gyroradius, static behavior for the ions is a valid approximation. With ion-scale turbulence neglected, it becomes computationally feasible to explore the turbulence spectrum and the associated plasma transport. Development of Tools for Remote Measurement of Fluctuations and Transient Phenomena On the experimental front, the evolving understanding of plasma confinement has been paced by the development of sophisticated diagnostics that can remotely measure hot plasma properties. For instance, the understanding of the dominant form of transport, that of ions, as well as the ability to suppress that transport, became possible only after new techniques were invented (mainly in the 1980s) to measure in detail the ion temperature, plasma flow velocity, and plasma current profile. Similarly, to fully understand microturbulence and its relation to the anomalous transport of heat and particles requires remote measurements of local fluctuations in density, temperature, magnetic field, and electrostatic potential. Impressive strides have been made, but further development of diagnostic tools is needed to allow detailed comparisons with turbulence theory. Early diagnostics of plasma turbulence used electromagnetic wave scattering to measure density fluctuation amplitudes over a wide range of wavelengths. Though limited in spatial resolution, these measurements did show that the power increased with the fluctuation wavelength. There was, as a result, a concentrated effort to develop new techniques to measure fluctuation spectra in the region of long wavelengths (i.e., larger than the ion gyroradius). Techniques based on the reflection of microwaves at critical density layers and on the collisionally induced fluorescence of injected neutral atomic beams now provide detailed measurements of density turbulence in high-temperature plasmas. The amplitudes of turbulent fluctuations can be measured to within 0.1 percent (relative to the equilibrium density value), and their temporal and spatial correlations are available for wave numbers from 0.1 to 10 cm−1. Temperature and also electric and magnetic field fluctuations are less well diagnosed than density turbulence. Under some circumstances, local fluctuations in both the ion and electron temperatures have been measured, allowing theoretical predictions to be tested. Even more difficult are measurements of the fluctuating electrostatic potential and magnetic field; these have been done only in particular experimental devices. Electrostatic potential fluctuations have been measured in small tokamaks and stellarators by means of the heavy-ion beam probe. Magnetic fluctuations have been measured in the reversed-field pinch device, where they are especially large (~1 percent of the equilibrium magnetic field). Though incomplete, these new measurement techniques have already provided a wealth of information about plasma microturbulence. The peak in the wave number spectrum for density turbulence was identified and the measured spectra were fairly well reproduced from gyrokinetic calculations. A specialized diagnostic was able to demonstrate that ion thermal fluctuations have larger amplitudes than ion density fluctuations, confirming a crucial theoretical prediction related to the ion-temperature-gradient instability. Turbulence correlation lengths and times estimated from simple random-walk transport models with step size given by the turbulent eddy dimension and time by the eddy correlation time can account for the observed cross-field transport. These findings have led to the conclusion that ion transport
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Page 37 loss is probably caused by drift wave turbulence from ion-temperature-gradient instabilities. Electron turbulence is not as well diagnosed; only recently has this transport channel received new attention. Detailed comparisons with theory will require further advances in experimental technique: for example, in nonlinear spectral analysis (to measure growth rates); two-dimensional visualization of turbulent density fluctuations; high-resolution measurements of intermittency; and very high spatially and temporally resolved studies of transport barriers and how they suppress turbulence. Key ingredients for the formation of transport barriers are self-generated plasma flows and fluctuations in the electrostatic potential, whose exploration will require new methods to measure flow velocity fluctuations. In order to visualize turbulence, probe arrays are being developed for cold plasmas and the edge of hot plasmas, while several techniques—neutral beam fluorescence imaging, multidimensional microwave reflectometry, and phase contrast imaging—show promise for the high-temperature interior region. Nonlinear spectral analysis may soon be able to measure the transfer of energy among fluctuating modes, which will make it easier to confront theory with experimental results. Transport Barriers and Confinement Control The discovery of the H-mode transition—and the associated sudden improvement in global plasma confinement—marked a paradigm shift in the fusion science program. It was proof that anomalous transport is not intrinsic to a magnetic confinement configuration but can actually be reduced. First discovered on the ASDEX tokamak in Germany, the H-mode was soon thereafter observed experimentally in the United States and around the world. More daunting was the task of identifying the cause of the H-mode transition, in which transport at the plasma edge bifurcates, leading to the creation of a narrow layer (“transport barrier”) within which the density and temperature profiles are very steep. New diagnostics, which were needed to measure the fine structure of the barrier and the local gradient-driven turbulence, revealed that the fluctuations driving transport drop precipitously at the location of the barrier. This observation led to sheared plasma rotation being identified as the mechanism for suppressing turbulence. Strong support for this conclusion was provided by experimental measurements indicating that these flows develop immediately before the barrier forms. Finally, the bifurcation nature of the H-mode transition is explained by a feedback loop in which suppression of turbulence leads to local steepening of the pressure profile and enhancement of the sheared rotation. A complete three-dimensional computer simulation of the bifurcation (based on a fluid model), including the turbulence and self-generated flows, further confirmed this picture, as illustrated in Figure 2.5 . Another paradigm shift occurred with the discovery that a transport barrier can also be formed in the hot plasma core. Worldwide, experimentalists found that by manipulating the twist of the magnetic field and injecting frozen hydrogen pellets they could form “internal transport barriers” and suppress turbulence. Conversely, in experiments where the plasma rotation was created by injected neutral beams, a reduction of sheared rotation (by adjustments to the beams) caused the internal barriers to disappear. The result from experiments on the DIII-D tokamak—that anomalous ion transport was completely suppressed over the entire cross section of the plasma—cemented the current view that turbulence and transport can in fact be controlled. The theoretical picture of transport barriers now needs to be tested in sufficient detail to achieve predictive capability. Additional challenges are to extend ion transport suppression to the electron loss channel and to ensure that the resulting pressure profiles are MHD-stable and sustainable in steady state (i.e., not transient). Transport barriers are not unique to the tokamak configuration but appear to be a generic phenomenon in nearly all magnetic confinement systems. The stellarator configuration, in which external helical coils
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Page 38 ~ enlarge ~ FIGURE 2.5 Simulation of ion energy transport in a tokamak plasma. Surfaces show the vortices that develop both with and without large-scale poloidal rotation, which acts to break up the flow patterns, reducing transport in magnetic confinement systems. Courtesy of W.M. Tang (PPPL). A similar image first appeared in Science, 1998, vol. 281, pp. 1835-1837. (rather than internal plasma currents, as in a tokamak) are responsible for creating the equilibrium magnetic field, is currently a major focus of the European and Japanese fusion programs owing to its intrinsically good stability and steady-state nature. In both European and Japanese stellarator experiments, the H-mode transition has been observed. An important component of the reversed-field pinch experimental program is the manipulation of transport by driving currents to maintain the configuration in its minimum energy state. Improvements in confinement by a factor of 6 were documented. There is also evidence that a transport barrier induced by sheared flow can form at the edge of a reversed-field pinch plasma.
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Page 39 Although the basic idea that sheared rotation can induce transport barriers and reduce turbulence is now well established, this understanding has not yet been translated into full predictive capability for the formation of these barriers or for their properties. Balancing the calculated linear growth rate of relevant instabilities with the estimated damping rate induced by the measured sheared rotation has had some success in predicting when internal barriers form. However, in notable cases, this procedure fails. Direct numerical simulations of the internal transport barriers with the turbulence evolving in time have yet to be completed. Such simulations are necessary to understand the full dynamics of barrier formation. They may also shed light on how barriers affect electron transport—experimentally, electron energy confinement sometimes improves when a barrier forms, but sometimes it does not. Simulations of edge barrier formation during the H-mode transition have been completed, and they give onset criteria that show some correspondence with the observations. Still, the sensitivity of the H-mode transition to factors such as the direction of the toroidal magnetic field has not been convincingly explained, which calls into question the current understanding of barrier onset. Evaluation of the Present Understanding of Turbulent Transport The understanding of turbulent transport has evolved rapidly over the past decade, driven by the development of computational techniques for directly simulating turbulence and the increasing precision by which turbulence and transport in experiments can be accurately measured and manipulated. The greatest progress has been made in the understanding of ion thermal transport in the plasma core and transport in the colder edge plasma of tokamaks. Core particle transport and electron energy transport remain poorly understood. Although confinement in tokamaks has received the most attention, the tools developed to study this problem are general to any toroidal magnetic confinement system. With the growth of interest in nontokamak approaches, it is expected that transport in these other configurations will be explored more thoroughly in the near future. Already, for example, efforts have been made to address the confinement issue in the reversed field pinch. A number of important, fundamental discoveries have been made in the effort to understand plasma turbulence and transport. These discoveries include the identification of the short-wavelength instabilities driven by ion temperature gradients as the most probable mechanism for anomalous ion transport; the self-generation of zonal flows as the primary mechanism for saturating the linear growth of instabilities driven by magnetic field line curvature; the creation of avalanches, associated with fast radial propagation of heat pulses and cold pulses; the role of velocity shear fields in stabilizing local turbulence; and the self-generation of transport barriers, which locally suppress turbulence and transport. It is important to call attention to these discoveries because they could have broad importance beyond the fusion science program. At the same time it is important to note that some of these concepts have roots in other areas of physics and are not wholly the invention of the plasma community. There is now substantial, but not overwhelming, evidence that turbulence driven by the ion temperature gradient is the dominant mechanism for ion thermal transport in the core of tokamak plasmas. It has long been recognized that, above a certain threshold, the ion temperature gradient could drive turbulence of relatively long wavelength (10 ion gyroradii) and that such large-scale turbulence would drive substantial transport. The observed sensitivity of transport to the density profile in the Alcator C and TFTR experiments was qualitatively consistent with a model of transport based on this instability. Measured wave number spectra are consistent with simulations of this instability, although much more detailed comparisons of theory with experimental results should be completed. An anomalous transport rate predicted from three-dimensional turbulence simulations gave a global energy confinement time that agreed well with experimental data. This comparison provided the first evidence that direct numerical
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Page 40 simulations could compete with empirical models in reproducing the confinement trends in present experiments. Finally, the ion-temperature-gradient instability has the property that it produces stiff profiles—that is, because the transport rapidly becomes very large when the temperature gradient exceeds a threshold, typically the gradient remains near the threshold. The stiffness of the ion temperature profiles has been confirmed in experiments that demonstrated a direct correlation between the central and edge ion temperatures. In spite of the substantial effort to test and document the ion-temperature-gradient picture of core confinement, the weight of confirming experimental evidence remains surprisingly and unacceptably thin by normal scientific standards. The verification of a transport theory on the basis of its steady-state predictions is too far removed from the basic physics to be of great value. An ongoing effort to compare the predictions of theory with an oscillating energy source in the DIII-D tokamak experiment is a positive development, but it is still somewhat indirect. Much more direct comparison between predicted turbulence properties and detailed measurements is needed to confirm the theoretical picture being developed. To date, measurements have concentrated on first-order spectral properties of the local turbulence, such as fluctuation amplitudes, correlation lengths and times, and corresponding wave number spectra, usually in one spatial dimension. Consistent data sets and relevant parametric scans of even these first-order quantities are very rare. For example, turbulence properties as a function of the critical ion-temperature-gradient scale-length are not available from any experiment. There is a need for expansion of diagnostics to measure higher order spectral properties that can provide direct quantitative tests of local growth rates and stabilizing shear flow rates and direct measurements of energy flow between fluctuating modes to evaluate nonlinear energy transfer between stable and unstable modes. In addition, multifield (e.g., density and electrostatic potential, or temperature) turbulence measurements are required to directly measure transport. An ongoing question is how the very large volume of data now available from the simulation community in the form of movies and other diagnostics can be compared with measurements from real experiments. Visualization is a powerful tool for comparing theory and data, at least qualitatively. Data from simulations very clearly reveal the development of extended radial fingers associated with the curvature-driven instability. Self-generated plasma flows (i.e., zonal flows) break up the radial streams. Suppression of these zonal flows in numerical simulations causes the transport to rise by an order of magnitude; accordingly, the importance of zonal flows in controlling the fluctuation levels is widely accepted. Experimental efforts in visualization can help confirm or challenge theoretical predictions. Initial results from visualization experiments are just now becoming available on a limited scale. In pursuit of these goals, there needs to be renewed commitment to the development of appropriate experimental tools and to dedicated experimental run time. On the theoretical side, the key ingredients that control the saturation of the ion-temperature-gradient instability and its wave spectrum are not fully understood. There are no theoretical predictions of the shape of the wave spectrum as the instability exceeds the threshold. At the threshold the spectrum is peaked near the ion gyroradius scale, and above the threshold the spectrum shifts toward long wavelengths—but how this shift evolves has not been quantified. Does a cascade process drive it, or is the long-wavelength turbulence locally driven? Does the measurement of the fast propagation of hot and cold pulses imply that studies of local transport are invalid? Is transport dominated by avalanches? These basic questions remain to be answered. Sharp scientific questions about the nature of the turbulence must be formulated and their answers pursued. An emphasis on simply producing a transport rate is superficial and is inhibiting the attack on these central issues and reducing the scientific impact on other fields. The impressive powerful computation tools that have been developed in the fusion science
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Page 41 program to model turbulence should be fully used to address more of the fundamental processes that control plasma turbulence. Addressing such issues is necessary to achieve predictive capability. Evidence is accumulating that the energy loss through electron scale-length modes is substantial and cannot be neglected in comparison with that through the ion channel, especially since control techniques for the ion channel have been developed. In some cases, the electron energy transport exceeds that through the ion channel. For example, an analysis of core transport barriers reveals that even when the ion energy transport is suppressed, the electron energy transport is not and may remain large. Surprisingly, electron thermal transport in the core of the TFTR tokamak remained large even though the electron temperature gradient was essentially zero and the density gradient was nonzero, a configuration that is apparently stable to all linear modes. Can a nonlinear instability sustain turbulence in the core of tokamak plasmas? This is a challenging but important research topic. As discussed earlier, the inclusion of electromagnetic perturbations and the evaluation of electron thermal and particle transport are difficult because the full parallel dynamics of electrons must be included. The time step limitations associated with the high electron thermal velocity, combined with the generally slow time evolution of wave spectra, conspire to make such calculations prohibitive in global simulation models. A flux tube simulation code based on a gyrokinetic electromagnetic model has recently been developed. Electron scale instabilities driven by the electron temperature gradient produce surprisingly high transport rates—the zonal flow dynamics, so important for ion-temperature-gradient turbulence, is absent and allows the fluctuations to grow to very large amplitude. Simulations that span the electron and ion scales but that do not address the global transport issues are now becoming feasible. Such models will, for the first time, facilitate the exploration of cross coupling between electron- and ion-scale turbulence in the plasma core. Turbulence simulations of the colder plasma edge have been proceeding in parallel with simulations of the core. The increased collisionality associated with lower edge temperatures justifies a model based on the collisional two-fluid equations. Several codes have been under development for nearly a decade and now include a broad spectrum of physical effects: equations for the electron and ion temperatures, the density, and the electromagnetic fields, including the magnetic perturbations and associated transport. A number of linear instabilities are described by these equations for the plasma edge, including ideal and dissipative ballooning modes and the ion-temperature-gradient modes that dominate the core. The ballooning modes are localized in the region of “bad” magnetic field line curvature. At the edge, the short scale-lengths of the ambient temperature and density profiles conspire to force the ion-temperature-gradient modes to very short wavelengths, and the resulting transport is typically smaller than from dissipative ballooning modes and drift waves. A surprise from the study of edge turbulence was the emergence of a nonlinear drift-wave instability, which dominates linear instabilities over a range of parameters at the plasma edge. For initial perturbations of very small amplitude, the turbulence simply decays away; however, above a critical amplitude the turbulence is self-sustaining. The parameters for which dissipative ballooning modes dominate drift waves and vice versa have been delineated. A second surprise was the strong impact of magnetic perturbations on edge turbulence. At high density, the magnetic perturbations dramatically increase transport, and there is some indirect evidence that this strong transport enhancement may be linked to the density limit that was discussed earlier. At low density and high temperature, the magnetic perturbations have the opposite effect. They weaken the turbulence to the extent that transport barriers spontaneously form above a threshold in β. A complete turbulence-based simulation of the transition to the H-mode has been completed. There is good correlation between the theoretical predictions of the onset of the H-mode and observations in a number of tokamak experiments. Nevertheless, as in the case of core turbulence, a solid scientific case has not yet been made that the existing theories are a valid description of edge turbulence.
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Page 42 There has also recently been a substantial effort to experimentally understand and control transport in the reversed-field pinch configuration. It has been demonstrated that in the core of a reversed-field pinch, the magnetic fluctuations associated with MHD dynamo action are the primary driver of transport, and that in the edge, shorter-wavelength “electrostatic” fluctuations are the primary driver of transport. There has as yet been no substantial effort to model thermal and particle transport in these systems. FINDINGS AND RECOMMENDATIONS Findings 1. The quality of the science that has been deployed in pursuit of a practical fusion power source (the fusion energy goal) is easily on a par with that displayed in other leading areas of contemporary basic and applied physical science. Learning to produce, confine, heat, and manipulate high-temperature plasma in the fusion regime is one of the most scientifically challenging endeavors in the history of mankind. The challenge is a consequence of the strong nonlinearities intrinsic to the plasma medium and the difficulty of diagnosing a medium whose temperatures greatly exceed those at the surface of the Sun—physical probes inside the plasma cannot survive the intense thermal energy fluxes. The complexity of the plasma medium is reflected in the scientific richness of the field. The fusion program has been the fundamental driver for the development of the field of plasma science, including energy principles for exploring plasma stability, wave dynamics, resonant wave-particle interactions, chaos, magnetic reconnection, plasma turbulence, and transport. The techniques it uses have broadly spun off to allied areas of science (see Chapter 4). While the significant scientific achievements of the fusion program are many, particularly impressive has been the development of techniques for suppressing and manipulating the small-scale turbulence that governs the leakage of stored energy from the magnetic container. Remotely controlling turbulence in a 300-million-degree medium is a premier scientific achievement by any measure and reflects the generally high quality of the science being carried out within the program. 2. The study of high-temperature plasma has historically had a strong empirical emphasis. With the development of new theoretical, computational, and experimental capabilities, a fundamental transition away from the empirically dominated approach is now taking place. Scientific computation, allied with theoretical insight, is becoming an integral and necessary component in the formulation and interpretation of experimental results. The process of confronting computational and theoretical results with experiment is creating new opportunities for achieving fundamental insight into the dynamics of plasma from the macroscale to the microscale. 3. Scientific discovery has played and continues to play a critical role in shaping the direction of research and facilitating the significant enhancements in the energy containment properties of magnetic bottles that have been achieved over the history of the fusion program. Notable examples include the following: The concept of “second stability,” in which higher-pressure plasma actually becomes more stable than low-pressure plasma. This, for example, led to the development of the spherical torus confinement configuration, which now holds the record for the highest value of β (the ratio of plasma to magnetic pressure), which is a measure of the efficiency with which the externally applied magnetic field contains the high-temperature plasma.
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Page 43 The idea that high-pressure plasma in a torus can drive its own current. Such current, known as bootstrap current, is critical to the development of steady-state (as opposed to pulsed) confinement in tokamaks and other configurations. The formation of transport barriers (which enhance containment) first in the edge of tokamaks (H-mode) and later in the plasma core and in other devices. This discovery produced a paradigm shift: The widespread belief that energy leakage from magnetic bottles was intrinsic crumbled as increasingly sophisticated techniques for controlling small-scale turbulence were developed. 4. Since the redirection of the fusion program in 1996 toward establishing the scientific knowledge base for fusion, there has been more emphasis on understanding the plasma dynamics underlying the operation of the various confinement configurations. However, performance goals rather than scientific overarching goals continue to be the primary driver for the allocation of resources in the program. (See Chapter 3 for further discussion.) This emphasis is reflected, for example, in the categorization of experiments as concept exploration, proof of principle, and performance extension. All of these categories pertain strictly to the reactor potential of an experiment rather than its scientific merit—there is no parallel measure of scientific worth. The result is that experiments designed to explore an important scientific topic, even though it may be critical to the program, are at a competitive disadvantage, so that some scientific topics remain inadequately explored. Given the historical impact of scientific discovery on the program, the absence of a science-based strategic planning process is inhibiting progress. Recent efforts to rectify this deficiency are to be applauded. One example is the experimental program for DIII-D, which awards device time to thrust areas that are, for the most part, performance oriented. A parallel set of scientific topics now introduces scientific goals that cut across the various performance thrusts, raising the priority of specific scientific topics in the program. The committee is encouraged by the use of parallel scientific goals and the inclusion of outside scientists, although for the most part, time is still allocated based on performance thrusts. 5. The U.S. program traditionally played a central role as a source of innovation and discovery for the international fusion energy effort. The program has been distinguished by its goal of understanding at a fundamental level the physical processes governing observed plasma behavior. This feature, a strength of the program, was formalized in the 1996 restructuring, which placed a new emphasis on establishing the knowledge base for fusion energy. The quantitative detail in which experiments are designed and executed in the United States has become a benchmark for the rest of the world. The forte of the U.S. program is the confrontation of theoretical results with experimental data, along with the development of advanced computational physics codes for the quantitative exploration of novel physical concepts. Recommendations Increasing our scientific understanding of fusion-relevant plasmas should become a central goal of the U.S. fusion energy program on a par with the goal of developing fusion energy technology, and decision-making should reflect these dual and related goals. Since the redirection of the fusion program in 1996, a greater emphasis has been placed on understanding the basic plasma dynamics underlying the operation of the various confinement configurations. The new emphasis on exploring scientific issues has been effectively implemented at the level of individual experiments. However, at the programmatic level, performance goals rather than overarching
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Page 44 scientific goals continue to act as the primary driver for the allocation of resources. (See Chapter 3 for further discussion.) This emphasis is reflected, for example, in the categorization of experiments as concept exploration, proof of principle, and performance extension, which appear to measure the reactor potential of an experiment rather than its scientific merit—there is no parallel measure of scientific worth. Given the significant historical impact of scientific discovery on the program, the absence of a science-based strategic planning process is inhibiting progress. The program direction should be determined by a focused set of scientific goals. DOE, in full consultation with the scientific community, needs to define this limited set of important scientific goals for fusion energy science. The goals should be realistic and specific so that a concrete strategy can be formulated to attack an issue and the theoretical/experimental/diagnostic tools can be marshaled. It is expected that many of the goals will transcend specific devices and therefore will serve to strengthen the linkages between different elements of the program. The committee understands that such a scientific planning process is under discussion but declines to make a judgement about the new process since it has not yet been implemented. The achievement of scientific goals should serve as a metric for defining success within the program and should replace the previous emphasis on performance as the primary measure of progress. Improvements in scientific understanding and progress towards fusion energy are coupled, and both should serve as measures of program success and be given equal weight. The program planning and budgetary justification carried out by DOE must be organized around answering key scientific questions as well as around progress toward the eventual energy goal. This applies to the confinement configuration program, as well as to programs of a more general nature (see Chapter 3). Public and congressional advocacy should emphasize progress in science as well as progress toward a practical fusion power source. Success in increasing the extent to which theory, computation, and experiment can be compared and used to validate scientific ideas will require a concerted effort. The key elements of theoretical models must be confronted with experimental observations at a level that uncovers the essential dynamics. Essential to this effort are the following: An expanded effort to identify and implement the diagnostic tools required to compare experiments with theoretical models and The allocation of sufficient time on existing experiments to address key scientific issues or the construction of dedicated experiments to explore a specific scientific issue.
Representative terms from entire chapter: