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4 The Plasma Science of Magnetic Fusion Introduction A New Era in Magnetic Fusion Research The worldwide magnetic fusion research effort to develop a virtually unlimited, environment-friendly energy source is entering a new era. The first experiments to explore magnetically confined fusion burning plasmas will begin in the interna- tional fusion device ITER late in the next decade. This is of enormous scientific importance. Indeed, it will provide the first opportunity to study the rich and possibly unexpected physics of burning plasmas. Understanding and controlling burning plasmas is an essential step in developing fusion as a source of electricity. In addition to its scientific importance, ITER is expected to be the first magnetic fusion device to generate substantial levels (as much as 500 MW) of thermal fusion power for hundreds of secondsâa very significant step for future energy security. This chapter outlines the recent scientific progress that has brought magnetic fu- sion to this historic juncture. It also highlights the outstanding plasma science issues. These issues inform two key strategic questions facing the magnetic fusion community: âThe evolution of the worldwide fusion research program to the ITER project and key character- istics of the ITER device are summarized in Appendix B. 115
116 Plasma Science â¢ What plasma science must be developed to maximize the scientific output of ITER? â¢ What science and enabling technology must be developed to move beyond ITER to fusion-generated electricity? The nonplasma fusion sciences and enabling technologies needed to develop an electricity-producing fusion power system are beyond the scope of this report; they are discussed in the report of the Burning Plasma Assessment Committee. Magnetic Fusion: A Brief Description The design and proposed operation of ITER illustrates the key principles, phys- ical processes, and terminology involved in magnetic fusion. To introduce these basic ideas and give a context for recent developments, we will refer to the ITER design. The plasma is contained in a toroidal (doughnut-shaped) steel vacuum vessel of major radius 6.2 m and minor radius 2 m (Figure. 4.1). Wrapped around the vessel are superconducting coils that produce a toroidal magnetic field of 5.3 T (the coils are dark orange). The plasma (pink) consists of electrons, deuterium ions, and tritium ions. These charged particles carry an electrical current that creates part of the magnetic field. They travel along and spiral around the magnetic field linesâsee, for instance, Figure 4.2. The radii of the ion spirals, the ion Larmor radii, are typically a couple of millimeters (in ITER conditions)âa thousandth of the 2-m minor radius. The plasma is collisionless in the sense that a typical charged particle will circumnavigate the torus hundreds of times in a characteristic collision length. In the middle of the plasma the particles have temperatures of greater than 100 million degrees (10 kV) and densities of 1020 particles per cubic meter; these values decrease approaching the vacuum vessel wall. Deuterium and tritium ions fuse to form a helium nucleus (alpha particle) with 3.5 MV of energy and a neutron with 14.1 MV of energy. The fusion happens predominantly in the center of the plasma, where the ions have enough energy (over 10 kV) to overcome their mutual electrostatic repulsion. Most important to the burning plasma regime is the confinement of the energetic alpha particles, since collisional heating from the alphas is used to maintain the high plasma tem- perature. The neutron produced in the fusion reactions crosses the magnetic field and deposits four-fifths of the fusion energy in the external structure. In a future fusion reactor the neutrons will strike lithium nuclei in a blanket surrounding the plasma, splitting the lithium into helium nuclei and new tritium nuclei for fueling the plasma. Heat to power turbines and generate electricity will also be extracted âNRC, Burning Plasma: Bringing a Star to Earth, Washington, D.C.: The National Academies Press, 2004. Hereinafter referred to as Burning Plasma.
The Plasma Science of Magnetic Fusion 117 FIGURE 4.1â Cutaway drawing of the International Thermonuclear Experimental Reactor (ITER), to be built over the next decade in Cadarache, France. For the size scale, note the small blue standard person shown in the lower left portion of the figure. The hot plasma is enclosed in a magnetic doughnut, whose dominant magnetic field coils encircle the plasma. Detailed characteristics of the ITER device can be obtained from http://www.iter.org. Published with permission of ITER. from this blanket. Blanket prototypes will be tested to only a limited extent in ITER, and ITER will not produce electricity. The power balance of the plasma is the key issue for ITER. The plasma will be heated by up to 80 MW of fusion alpha particle heating, and up to about 100 MW of external heating can be added using injected neutral particle beams and externally excited plasma waves. To achieve the ITER design goal of Q â¥ 10, where Q is the ratio of total fusion power (500 MW at ITER) to external heating power, only 40-50 MW of external heating is expected to be needed. Heat is lost from the
118 Plasma Science (a) RFP (b) ST (c) AT (d) CS Magnetic field lines Self Organization External Organization Device Simplicity Intrinsic-Steady State Externally Driven Device Complexity FIGURE 4.2â The magnetic topology of the main U.S. magnetic fusion concept improvement experiments in decreasing order of plasma self-organization. (a) Reversed-field pinch (RFP), a high Î² (pressure) device where the fields are created mainly by plasma currentsfig rearranged by a self-organizing dynamo. (b) Spherical torus and 4-2 a,b,c (ST), also very high Î², which has seen rapid development in the last decade (see Figure 4.3). (c) Advanced to- kamak (AT), with research in the figure go having shown that with certain current5.5 inchesplasma shapes Let this last decade out into the wider margin of profiles and the tokamak can have considerably enhanced Î², transport barriers (regions where turbulence is suppressed), and self-generated bootstrap currents driven by the pressure gradient; these achievements should be exploited in advanced scenarios on ITER. (d) Compact stellarator (CS). Two features of stellaratorsâinherent steady-state operation of stellarators and the recent findings that high-Î² instabilities may be more benign than in tokamaksâ are clear potential advantages that may outweigh the added complexity of three-dimensional field configurations. The field is mainly produced by external coils. Courtesy of D.A. Spong, Oak Ridge National Laboratory. plasma in several ways but predominantly via small-scale plasma turbulence in the hot core. The typical time for energy to be lost, the energy confinement time, is more than 3 sec. ITER is projected to be firmly in the burning plasma regime, where the fusion self-heating exceeds the external heating. Ignition, where the self- heating is sufficient to supply all the energy to sustain the plasma and Q becomes infinite, may be approached but it is not an ITER goal. ITER has been designed by extrapolation from existing experiments. Key pro- cesses limit the performance, and these can be roughly split into four interrelated areas of research: â¢ Macroscopic stability and dynamics.â The fusion power increases roughly with the square of the plasma pressure. It is therefore desirable, in ITER and future fusion reactors, to maximize the plasma pressure. However, when the plasma pressure exceeds a critical value proportional to the magnetic pressure, macroscropic instabilities degrade or destroy the plasma. Some instabilities develop in hundreds of microseconds and smash the plasma
The Plasma Science of Magnetic Fusion 119 against the wall. Others that grow on a longer timescale change the magnetic topology into one where the field lines wander across some or all of the plasma. The loss of heat along the wandering field lines caused by the slower instabilities leads to undesirable cooling of the plasma. In large devices the faster instabilities damage the external structure. Research is focused on (1) trying to raise the critical pressure to attain better fusion performance, (2) understanding the limits so that they can be avoided, and (3) developing methods to control the slower instabilities. â¢ Cross-field transport from microscopic processes.â The free energy available from the large pressure and temperature gradients can drive a wide variety of small-scale microinstabilities and microturbulence in the plasma. The electric fields of this turbulence cause particle orbits to cross the magnetic field and transport heat and particles from the hot core to the colder edge much faster than the plasma transport induced by particle collisions. Reducing the plasma turbulence would decrease heat loss and allow for smaller burning plasmas. Research is focused on (1) understanding and predicting the turbulence, (2) elucidating the transport mechanisms for heat, particles, and momentum, and (3) finding regimes of low heat loss from the combination of collisional and turbulent processes. â¢ Boundary physics.â The edge of the plasma is a very complex region where the plasma transitions from the hot plasma core to a colder partially ion- ized plasma. Heat and particles are transported through the edge to the surrounding chamber walls or specialized high-heat-flux surfaces via vari- ous collisional, intermittent (bursty), and turbulent processes. To control the outflow, the outer shells of field lines are steered onto the specialized high-heat-flux surfaces. This is called the âdivertor.â The power onto the material surfaces in ITER is near the limit materials can stand without rapid erosion. Research is focused on (1) understanding the edge turbulence and transport, (2) controlling instabilities in the edge, and (3) spreading the heat loads over larger areas of material surfaces. â¢ Waveâparticle interactions.â Plasma waves carrying energy and momentum can propagate through magnetically confined plasmas. Ions or electrons moving at roughly the speed of the wave exchange energy and momentum with it. Radio frequency waves are launched into fusion plasmas to heat and drive currents by this waveâparticle interaction mechanism. Energetic particles, particularly alpha particles from fusion reactions in ITER, can impart energy to waves and destabilize them inside the plasma. Such insta- bilities may then eject the alpha particles from the plasma before they slow down and deposit their fusion energy in the plasma. Research is focused on (1) perfecting techniques to deliver heat and current to precise positions in the plasma with externally launched waves and (2) understanding and preventing the energetic particle instabilities.
120 Plasma Science In a fusion burning plasma, all the processes described above are closely inter- related: macroscopic instabilities change the magnetic configuration in which the cross-field transport, boundary, and waveâparticle effects take place; the cross-field transport, boundary, and waveâparticle heating effects (from both external sources and fusion-produced alpha particles) determine the internal pressure and magnetic field profiles; and so on. The scientific challenge in ITER will be to explore the exothermic fusion burning plasma regime in which plasma self-heating dominates the plasma dynamics. This highly nonlinear regime will probably lead to many new and exciting discoveries. Research on fusion burning plasmas will be focused on (1) determining how the large alpha particle component and heating changes the plasma behavior, (2) exploring plasma transport at the larger plasma scale rela- tive to microturbulence eddy scales, and (3) controlling the highly nonlinear and interconnected burning plasma regime. The success of the ITER burning plasma experiment depends on continuing to improve understanding and predictive capability. Such improvements would build on the scientific advances outlined in the section on recent progress and future op- portunities, later in this chapter. The required progress in these key areas will not be possible without a significant expansion of our plasma diagnostic capabilities. Quite simply, we cannot understand what we cannot measure. Existing theoretical models are not yet sufficient to accurately predict many aspects of burning plasma regimes. National initiatives focused on enhancing analytic theory, improving computational algorithms, and making dramatic improvements in the diagnostics deployed at existing facilities would make possible further breakthroughs in our understanding of the key burning plasma physics issues. Such initiatives would allow the United States to retain its leading role in plasma science within the international magnetic fusion program. ITER needs a deeper understanding of these key plasma physics issues; the party that comes to the ITER table with this expertise will have a strong position in the international magnetic fusion program for at least 15 years. Concept Improvement Is Important for ITER and Beyond At this time the tokamak is the logical choice of configuration in which to study burning plasmasâan essential step on the road to fusion power (see Burning Plasma for more details). The tokamak configuration has achieved the best overall fusion performance thus far and has been used in the design of ITER. However, it is clear that devices with considerably better performance are possible even though they have not yet been fully explored or perhaps even identified. The integrity and the insulating quality of the confining magnetic field may be improved by chang- ing the configuration to a modified (âadvanced tokamakâ) configuration or from a tokamak to something else. Principal among the alternatives are the tokamak variantsâspherical torus, stellarator, and reversed-field pinch (Figure 4.2 and
The Plasma Science of Magnetic Fusion 121 Table 4.1). The list also includes many other less-developed concept exploration ideas. These concept improvements must develop further during the ITER era and provide a basis for going beyond ITER to commercial fusion power. The goal is to be in a position to define an optimal fusion energy system for the post-ITER phase of magnetic fusion energy developmentâa demonstration electricity-producing power plant. Thus a key component of the U.S. fusion program, the importance of which this committee reaffirms, is the study of plasma confinement in tokamak variants and nontokamak magnetic confinement devices. While the fusion potential of a given concept is a complicated question, two TABLE 4.1â Characteristics of Major Magnetic Confinement Experimental Devices Around the World Year of Minor Magnetic Device Name Location First Plasma Radius (m) Field (T) Type of Device United States DIII-D San Diego, Calif. 1986 0.67 2.4 Comprehensive tokamak MST Madison, Wisc. 1988 0.52 0.5 Reversed-field pinch C-Mod Cambridge, Mass. 1991 0.22 8.0 High-magnetic-field tokamak NSTX Princeton, N.J. 1999 0.65 0.5 Spherical torus Foreign T-10 Russia 1975 0.35 3 Comprehensive tokamak JET U.K. 1983 1.25 3.4 Comprehensive tokamak FTU Italy 1989 0.30 8.0 High-magnetic-field tokamak JT-60U Japan 1990 1.00 4.0 Comprehensive tokamak ASDEX-U Germany 1991 0.50 3.9 Comprehensive tokamak Tore Supra France 1997 0.70 4.5 Superconducting tokamak MAST England 1998 0.65 0.6 Spherical torus LHD Japan 1998 0.60 3.0 Superconducting stellarator RFX-mod Italy 2004 0.47 0.7 Reversed-field pinch EAST China 2006 0.40 3.5 Superconducting tokamak Being built KSTAR South Korea 2008 0.50 3.5 Superconducting tokamak SST-1 India 2008 0.20 3.0 Superconducting tokamak NCSX Princeton, N.J. 2009 0.30 1.7 Compact stellarator JT-60SA Japan 2011 1.10 2.7 Superconducting tokamak W-7X Germany 2012 0.35 3.0 Superconducting stellarator World project ITER France 2016 2 5.3 Superconducting fusion burning tokamak NOTE: Plasma minor radius is half the width of the plasma in the horizontal midplane. Magnetic field strength is in tesla. Since fusion power is proportional to the fusion reaction rate integrated over the volume, the fusion potential is given approximately by the product of the square of plasma pressure Î² (Î² = nT/(B2/2Âµo)), the fourth power of the magnetic field B (in tesla), and the plasma volume (in cubic meters). Detailed parameters of these facilities and many other smaller devices are available from the following Web sites: â¢ U.S. facilities, at http://www.science.doe.gov/ofes/majorfacilities.shtml â¢ European facilities, at http://www.edfa.org/eu_fusion_programme/r-experimental_facilities.htm â¢ World Survey of Activities in Controlled Fusion Research, at http://nds121.iaea.org/physics/ â¢ http://www.fusion.org.uk/links/
122 Plasma Science simple considerations point to the direction of improvement. Raising the pressure limit for a given magnetic field and increasing the plasma volume increases the fu- sion power for a given cost of magnet coils (the parameter Î², the ratio of plasma pressure to magnetic pressure quantifies this). It is also desirable to reduce the turbulence so that the same confinement could be reached in a smaller device or with weaker field. Progress in demonstrating these advantages has been achieved over the past decade (Figure 4.3). Many magnetic confinement concepts are being pursued in the United States and worldwide (Table 4.1). At the present time, how- ever, the four concepts shown in Figure 4.2 are thought to offer the most significant potential advantages over the conventional tokamak. However, concept improvement has two other important roles. First, it gener- ates new ideas and regimes to be explored on ITER. Second, it enhances the under- standing of plasmas by broadening available plasma conditions and challenging the predictive models. Like all the areas discussed in this chapter, concept improvement would benefit greatly from a program to develop a new generation of diagnostic tools and predictive models. The critical long-term goal of the concept improvement program is to identify and develop a more efficient magnetic configuration for the post-ITER phase of magnetic fusion research. But, the burning plasma and concept improvement parts of the fusion program are not, of course, separate in a scientific sense. Indeed, over the past decade, U.S. leadership in a number of scientific areas has contributed significantly to making ITER smaller, more efficient, and less expensive. This was done by helping redefine ITERâs scientific goals, advocating significant science- driven changes in the engineering design, and by developing and pushing several modes of advanced tokamak operation pioneered in U.S. fusion experiments. The path beyond ITER to an optimal reactor is clearly predicated on understanding the basic plasma processes and thereby improving the science-based predictive capa- bility. The concept improvement program plays an important role in improving this capability both for specific concepts and for magnetic confinement in general. One reason for this is that innovative concepts explore a broader range of plasma conditions. Also, some basic plasma processes are best studied in a particular configuration, yet the knowledge gained has application in all. A good example is the reversed-field pinch, where three-dimensional magnetic reconnection and magnetic turbulence are prevalent and therefore easier to study. The United States is well positioned to continue to lead in scientific under- standing and innovation in magnetic fusion research. A balanced, forward-looking plan that focuses on further improving our predictive capability for the plasma physics processes that limit fusion reactor performance would naturally emphasize improved diagnostics, continued exploration of tokamak-variant and nontokamak configurations, and a healthy theory program. An innovation-focused plan would also make allowance for new discovery. Because the United States will not have to
The Plasma Science of Magnetic Fusion 123 FIGURE 4.3â Building a better magnetic bottle: examples of recent progress. In stellarators (three-dimensional magnetic configurations), large particle drifts across the magnetic field can cause significant heat and particle loss. Over the last 20 years, theoreticians have discovered three-dimensional configurations with effective sym- metries in the magnetic field strength. These have low drift losses. The deviation from symmetry is measured by the parameter Îµeff. Recent results from the Helically Symmetric Experiment (HSX) demonstrating the expected reduction in the electron diffusion in the low Îµeff quasi-helically symmetric (QHS) configuration are shown in diagram (a). SOURCE: Adapted from J.M. Canik and D.T. Anderson, Physical Review Letters 98: 085002 (2007). Â© 2007 by the American Physical Society. Diagram (b) displays results from many stellarator experiments show- ing increased confinement with smaller Îµeff. Also shown is the design value for the National Compact Stellarator Experiment (NCSX), which is under construction. SOURCE: Adapted from H. Yamada, J.H. Harris, A. Dinklage, E. Ascasibar, F. Sano, S. Okamura, J. Talmadge, U. Stroth, A. Kus, S. Murakami, M. Yokoyama, C.D. Beidler, V. Tribaldos, K.Y. Watanabe, and Y. Suzuki, âCharacterization of energy confinement in net-current free plasmas using the extended International Stellarator Database,â Nuclear Fusion 45: 1684-1693 (2005). Diagram (c) pres- ents data from the National Spherical Torus Experiment (NSTX) showing ion transport at the collisional levels (marked âneoclassicalâ) in discharges where turbulence is suppressed by sheared flows. SOURCE: Adapted from S.M. Kaye, R.E. Bell, D. Gates, B.P. LeBlanc, F.M. Levinton, J.E. Menard, D. Mueller, G. Rewoldt, S.A. Sab- bagh, W. Wang, and H. Yuh, âScaling of electron and ion transport in the high-power spherical torus NSTX,â Physical Review Letters 98: 175002 (2007). Â© 2007 by the American Physical Society. Diagram (d) shows that, as predicted by theory, NSTX achieves large values of current and pressure for given magnetic field strengths at the center of the plasmaâover 10 times the ratios expected in ITER. SOURCE: Adapted from S.M. Kaye et al., âProgress towards high performance plasmas in the National Spherical Torus Experiment (NSTX),â Nuclear Fusion 45: S168-S180 (2005).
124 Plasma Science shoulder a major fraction of the ITER cost, the country will be well positioned to lead the exploration of new plasma confinement and fusion science ideas that come to the fore over the next two decades. Examining Table 4.1 again, however, one observes that many other countries are developing a new generation of facilities, often employing scientific develop- ments that stem from older U.S. research. The United States played a more domi- nant role in magnetic fusion research when there were fewer players. It is clear, however, that with its present set of aging domestic facilities the United States is not well-positioned to lead in the many aspects of the science and technology that require either large powerful devices or the long pulses that superconducting magnets enable. Importance of This Research Magnetic fusion research has one primary goal: to develop a virtually unlim- ited, noncarbon, environment-friendly source of energy for the production of electricity. The potential of fusion is enormousâsee the first section in Chapter 1. Reactor system studies indicate that magnetic fusion could produce electricity at a cost (about 6 to 8 cents per kilowatt hour) commensurate with the likely cost of other baseload electricity-producing systems in the middle of the 21st century. Thus magnetic fusion could become a critically important contributor to the en- ergy security of the United States by the end of the 21st century. The primary goal of magnetic fusion research is important enough that it would be pursued even if it produced no other scientific benefit. However, magnetic fusion research does contribute to the national scientific enterprise in three ways that are not directly part of the primary goal: â¢ Plasma physics: Magnetic fusion relies upon and drives plasma science.â The most critical science for fusion is plasma physics. Thus the fusion research program has been the primary driver for development and support of plasma physics, a new discipline of physics, over the past 50 years. For example, in just the past decade fusion research has produced studies of laboratory magnetic reconnection; plasma and fluid dynamos; and mi- croturbulence. These processes have great importance in space and as- trophysical plasmas (see Chapter 5), and insight gained in the magnetic fusion program continues to be fruitful. The relatively large investment in developing computational methods for fusion is benefiting many areas of plasma research. This includes the direct use of fusion computer codes in other areas of plasma science. Similarly, new diagnostics developed in âSee http://aries.ucsd.edu/ARIES/DOCS for more information.
The Plasma Science of Magnetic Fusion 125 magnetic fusion have found application in areas such as low-temperature plasma science. â¢ Science: Fusion contributes to other sciences.â Fusion research continues to make important contributions to broader scientific pursuits. These include very significant contributions to the theoretical understanding of complex nonlinear systems. For example, fusion research has made fundamental contributions to the understanding of the onset of stochasticity, chaos, and nonlinear dynamics. These insights have important application in, for instance, meteorology and planetary science. Fusion research has also advanced atomic physics in two ways: by investigating and measuring the atomic processes in the low-temperature, partially ionized plasmas at the edge of fusion experiments and by providing a hot plasma environment to measure the properties of highly stripped atoms of relevance to astrophysi- cal plasmas. â¢ Workforce: The fusion program has trained many plasma scientists.â The chal- lenge and importance of fusion research has always been very attractive to students. It can be expected to have an even stronger draw over the next decade for both the United States and the rest of the world, as carbon-free energy becomes an increasingly important societal goal and ITER is being built. The fusion research program continues to train many young scientists who then move into other areas of plasma science such as space plasma physics, stockpile stewardship, inertial confinement fusion, and plasma processing of microprocessors. The NRC report An Assessment of the Department of Energyâs Office of Fusion Energy Sciences Program (2001) examines in more detail the linkage between fusion science and other areas of science. It identified a need to enhance those connec- tions and reduce the perceived isolation of the fusion community. In response to a recommendation in the report, two university-based fusion science centers have been established to form new links with the general physics community. NSFâs Physics Frontier Center at the University of Wisconsin, the Center for Magnetic Self-Organization, is also making explicit connections between fusion science, basic plasma science, and space and astrophysical plasma science. In the era of ITER, it will be increasingly important to enhance these connections so as to exploit the expertise of the wider scientific community for the benefit of fusion and to dis- seminate the insights and understandings gained in fusion. Recent Progress and Future Opportunities Since the achievement of significant deuterium-tritium fusion power in the mid-1990s (see Chapter 1), the magnetic fusion program has become focused on
126 Plasma Science solving key science issues and developing predictive capability. Significant progress has been made in a number of scientific areas, as described in the remainder of this section. Two factors have been instrumental in this progress: Plasma diagnostics has improved so that plasma properties at multiple spatial points and times are readily available and new theoretical models have been developed and implemented in computer codes. Examples of progress and opportunities in four areas will be dis- cussed: (1) macroscopic stability and dynamics; (2) microinstabilities, turbulence, and transport; (3) plasma boundary properties and control; and (4) waveâparticle interactions in fusion plasmas. Macroscopic Stability and Dynamics The first issue in magnetic confinement is to control the macroscopic stability of the plasma. The plasma is confined with strong magnetic fields that are gener- ated both by powerful magnets and by large currents flowing in the plasma itself (see Figure 4.1). The pressure expansion force of the plasma (typical pressures are a few atmospheres) is balanced by the magnetic forces. Small distortions from equi- librium grow when either the pressure or the current exceed stability limits. These distortions can grow on timescales as fast as tens of microseconds or as slow as seconds. Defects (distortions, aneurysms, and islands) form in the magnetic fields, bringing hot plasma into contact with relatively cool material surfaces and/or dilut- ing the hot central plasma with cool plasma from closer to the edges of the device. Boxes 4.1 and 4.2 describe two important examples of success in understanding, calculating, and suppressing important macroscopic instabilities. Advances in theory and computation have yielded an improved understanding of the stability boundaries in most situations. These theories are largely based on magnetohydrodynamicsâa fluid approximation to the plasma behavior. These cal- culations now incorporate the full geometric complexity of the plasma equilibrium. Although some kinetic and dissipative effects are being considered, more research is needed to improve the theoretical models. Thus precise quantitative theoretical predictions of stability boundaries are not yet possible. Nonetheless, by feeding the understanding into empirical models and fitting the data, ITERâs stability can be fairly precisely predicted. Opportunities in Macroscopic Stability and Dynamics Two goals motivate macroscopic instability research: to develop a precise quantitative predictive capability and to find regimes where the plasma param- eters exceed the normal limits set by instability thresholds and the plasma is con- trolled without deleterious effects. Recent progress suggests that these goals will largely be achievable in the next decade if advances in the theoretical models and
The Plasma Science of Magnetic Fusion 127 their computational implementation are forthcoming. Despite steady increases in computer power, simulating the fundamental kinetic plasma equations is very challenging, and rapid progress can often be made only through âreducedâ mod- els, typically hybrids of fluid and kinetic descriptions. In principle, such models average over short time and space scales to deduce tractable macroscopic equa- tions. Two aspects of the physics require development. The first is reduced hybrid magnetohydrodynamic (MHD) modeling, in which very low collisionality kinetic effects are included. Such modeling must include the nonlocal effect of long col- lision lengths of particles communicating plasma conditions long distances along magnetic field lines. The second physical effect that must be included in models is the interaction of the microinstabilities and turbulence with the macroinstabilities. This multiscale interaction will require interfacing fast-timescale microturbulence codes with macroinstability codes. Because it is relatively easy to identify growing instabilities, experimental sta- bility boundaries are well known. However, our understanding of the nonlinear evolution of instabilities is relatively primitive. For instance, in many cases it is not known when instabilities will grow explosively and when they will saturate at small amplitudes. Neither is it known when (nontearing) instability leads to nonlinear magnetic reconnection. Recent advances in diagnostic imaging make it possible to see details of the nonlinear structure. A comprehensive understanding of macroinstability physics is possible in the next decade if both the models and the diagnostics are improved. In many cases better understanding is likely to result in development of new control methods. Microinstabilities, Turbulence, and Transport The second major challenge for magnetic confinement is to improve the ther- mal insulation provided by the magnetic field. If energy diffused from the hot, central tokamak plasma to the relatively cool periphery via particle collisions alone, then the projected energy confinement time in ITER plasma would be hundreds of seconds, not three. However, this is not expected since at fusion temperatures energy diffusion across the magnetic field in a nearly collisionless magnetized plasma is dominated by small-scale microturbulence. This turbulence is driven by the strong gradients in plasma temperature, pressure, etc. Because the turbulent eddies are small (typically a centimeter or two in size), the random walk of particles and heat across the plasma is not catastrophicâbut it is problematic nonetheless. Details of the rate of energy transport vary, but larger magnetic fields result in smaller eddies and therefore smaller energy losses. If one could eliminate energy diffusion due to microturbulence, the payoff would be substantial. Energy trans- port via collisions alone would yield a burning plasma in a device whose linear dimensions are less than half the size of ITER. Controlling and perhaps reducing
128 Plasma Science BOX 4.1 Slowly Growing Magnetic Islands Magnetic islands are large-scale structures that break equilibrium symmetry so that magnetic field lines connect hot plasma regions to colder ones, degrading plasma energy confinement. These islands are created by a class of âtearingâ instabilities that grow on timescales of a few tenths of a second and connect the normally distinct magnetic surfaces. This is slow magnetic reconnection. In high-pressure plasmas, the saturated island width is measured via electron cyclotron emission (ECE) to be proportional to the plasma pressure. This scaling can impose an effective limit on the maximum pressure achievable in a tokamak since large islands can result in complete loss of plasma confinement. (a) Image of magnetic islands calculated in simulations. Field lines wrap around the green island surface as the surface itself wraps around the torus. (b) Comparison of theoretical predictions and the experimental measured island widthâthe good agreement is representative of the progress in understanding. SOURCE: Z. Chang, J.D. Callen, E.D. Fredrickson, R.V. Budny, C.C. Hegna, K.M. McGuire, M.C. Zarnstorff, and TFTR group, âObservation of nonlinear neoclassical pressure-gradient-driven tearing modes in TFTR,â Physical Review Letters 74: 4663 (1995). (c) Diagram of wave ray trajectories (red line) of high-power microwaves that are launched toward an absorption layer controlled in real time to be inside the island. (d) Data show- ing the shrinkage of the island width when microwaves are applied. Current driven by the waves replaces missing current and shrinks the island until it self-heals. This effective island healing has been demonstrated in several exist- ing devices, and near-term experiments will determine how to properly scale the physics of this technique to ITER plasmas. SOURCE: Adapted from R.J. (a) LaHaye, âNeoclassical tearing modes and their control,â Physics of Plasmas 13: 055501 (2006). (b)
The Plasma Science of Magnetic Fusion 129 (c) Threshold reached Island width (cm) Self -stabilization threshold (d) 2.2 2.4 2.6 2.8 3.0 3.2 Time (s) Microwave power on Island removed 4.1.1 D
130 Plasma Science BOX 4.2 Resistive Wall Modes At high plasma pressures, tokamak and spherical torus plasmas can develop instabilities that cause large- scale helical deformations of the equilibrium magnetic field. Close-fitting electrical conductors can slow the growth of such modes to the timescale of magnetic field penetration of the resistive wallâhence the name resistive wall mode (RWM). These modes grow sufficiently slowly that they can be controlled and suppressed. In tokamaks and spherical RWM Stable tori, spinning the plasma sufficiently fast past the conducting wall, combined with plasma dissipation, can completely stabilize Stable the mode. (a) Calculations and data showing stabil- ity with flow and instabil- ity without flow. Courtesy Unstable of General Atomics and Princeton Plasma Physics Laboratory. (b) Fast camera image revealing the global (a) helical deformation of the Unstable plasma during an RWM. These are in good agree- ment with reconstructions 4.2.1a (b)
The Plasma Science of Magnetic Fusion 131 of the plasma boundary from magnetic field measurements and calculated RWM eigenfunctions. SOURCE: S.A. Sabbagh, C. Sontag, J.M. Bialek, D.A. Gates, A.H. Glasser, J.E. Menard, W. Zhu, M.G. Bell, R.E. Bell, A. Bondeson, C.E. Bush, J.D. Callen, M.S. Chu, C.C. Hegna, S.M. Kaye, L.L. Lao, B.P. LeBlanc, Y.Q. Liu, R. Maingi, D. Mueller, K.C. Shaing, D. Stutman, K. Tritz, and C. Zhang, âResistive wall stabilized operation in rotating high beta NSTX plasmas, â Nuclear Fusion 46: 635 (2006). (c) Comparison of critical rotation speed for RWM stabilization and the measured critical value versus the plasma Î² (pressure). There is reasonable agreement with theoretical models, but the underlying plasma dissipation mechanisms are still under investigation. Additional understanding in critical rotation has been obtained using balanced beams at DIII-D. SOURCE: R.J. LaHaye, A. Bondeson, M.S. Chu, A.M. Garofalo, Y.Q. Liu, G.A. Navra- til, M. Okabayashi, H. Reimerdes, and E.J. Strait, âScaling of the critical plasma rotation for stabilization of the n = 1 resistive wall mode (ideal kink) in the DIII-D tokamak,â Nuclear Fusion 44: 1197 (2004). RWMs change the magnetic geometry of the plasma equilibrium and generate a torque that slows the plasma rotation. (d) Com- parison of the measured torque and theory. SOURCE: W. Zhu, S.A. Sabbagh, R.E. Bell, J.M. Bialek, M.G. Bell, B.P. LeBlanc, S.M. â² Kaye, F.M. Levinton, J.E. Menard, K.C. Sha- ing, A.C. Sontag, and H.Yuh, âObservation of plasma toroidal-momentum dissipation by neoclassical toroidal viscosity,â Physi- cal Review Letters 96: 225002 (2006). The stabilization of the RWM allows operation (c) at much higher pressure and fusion power than is otherwise achievable. For the low plasma rotation values expected on ITER, RWM stabilization may B.42c require active magnetic feedback control and is presently being prototyped on several devices. SOURCE: S.A. New Sabbagh, R.E. Bell, J.E. Menard, D.A. Gates, A.C. Sontag, J.M. Bialek, B.P. LeBlanc, F.M. Levinton, K. Tritz, and H. Yuh, âActive stabilization of the resistive-wall mode in high-beta, low-rotation plasmas,â Physical Review Letters 97: 045004 (2006). (d)
132 Plasma Science microturbulence in the new burning plasma regime of ITER will be central to the success of the project. Over the last decade, experiments and theory have shown that the small-scale turbulence that limits tokamak energy confinement (in most present conditions) is excited when the gradient of the logarithm of the ion temperature exceeds a specific threshold. The threshold depends in a complicated way on many local parameters: the geometry of the magnetic field, the gradients of density and velocity, and so forth. In most conditions, these quantities can be measured and the threshold can be numerically calculated. Indeed, a significant triumph of the last decade is the development of codes that can accurately solve the nonlinear, five-dimensional phase space (three-dimensional space and two-dimensional velocity) system of equations that describe electrostatic turbulence: the gyrokinetic equations. Further, unlike a decade ago, codes designed for this purpose are now in use at every large tokamak facility. For the high temperatures of interest, the turbulence-induced transport that occurs when the threshold is crossed is strong enough to force the local plasma temperature to remain close to the threshold. The overall energy confinement that results is well predicted by large-scale numerical turbulence simulations (Box 4.3). It is now clear that the limits imposed by the threshold model are at least partially surmountable. Under certain circumstances (particularly hollow current distributions and strong flow shear), regions of reduced turbulence called transport barriers develop spontaneously inside or at the edge of the plasma. In these regions the thermal insulation is very good, perhaps limited only by collisional processes, and the temperature gradients greatly exceed the usual threshold values. It has been shown experimentally that these regions of enhanced thermal insulation are associated with strong layers of flow shear and reduced turbulent fluctuations. In parallel with the work on transport barriers, it has become clear that weaker shear layers are generated by the turbulence itself, greatly reducing the energy losses that would occur in their absence (Box 4.4). This insight grew out of experimental, theoretical, and computational efforts and was a major success of the last decade of plasma science research in magnetic confinement fusion. Microturbulence in concept improvement devices can be quite different from the phenomenon in the tokamak. Fluctuations in the reversed-field pinch, for ex- ample, perturb the magnetic field significantly (Box 4.5). The perturbed magnetic field lines no longer isolate the plasma from the boundary, and charged particles traveling along the field lines can wander out of the device. The fundamental physics of this type of transport has been studied effectively in the reversed-field pinch, where ways to reduce its effects have been developed. Theory predicts that as many concepts improve and push to higher pressure (Î²), transport along chaotic magnetic field lines will play a larger role.
The Plasma Science of Magnetic Fusion 133 Opportunities in Microinstabilities, Turbulence, and Transport While progress in microinstability research has been strong over the last de- cade, maintaining the pace of this research in the next decade would likely require a refocused effort with clearer short-term objectives and even greater focus on comparisons of theory predictions (analytic and computational) with experimental data. Three scientific goals frame opportunities in this area. The first is to develop more accurate predictive models of the turbulence and transport, especially the electron dynamics, including the irreducible levels when mircoturbulence is absent. The second is to find, perhaps through a better understanding of transport barrier physics, regimes where turbulence and transport are reduced. The third goal is to advance the science of low-collisionality plasma turbulenceâturbulence with multiple scales in all dimensions of phase space. The computer codes for studying these problems are rapidly maturing. The principal needs for the next decade are in the areas of theory (to understand the nonlinear results) and diagnostics (to enable experiment/theory comparisons). All thrusts of magnetic confinement research, from ITER to innovative con- cepts, will benefit from improving the predictive understanding of microturbu- lence. Predictive models must include the ability to model four different spatiotem- poral scales simultaneously: fast electron dynamics; slower ion dynamics; longer wavelength, mesoscale plasma dynamics; and the slow evolution of bulk plasma (thermodynamic) properties that occurs on the transport timescale. This will re- quire the development of new reduced theoretical models of plasma behavior. Our understanding of the turbulence will be enormously enhanced when diagnostics capable of distinguishing fine levels of detail and measuring several plasma param- eters simultaneously can image the full cross section of the plasma. Such full-body diagnostics will reveal the global structure and the mesoscale correlations. Boundary Plasma Properties and Control In a magnetic confinement device, the bulk of the plasma is kept away from material structures for two distinct reasons. First, material structures act as a heat sink and cool the edge of the plasma. Hot charged particles exit the plasma and cold charged or neutral particles (some dislodged from the wall) enter the plasma. Sec- ond, hot plasma that comes into contact with material structures can melt, erode, or otherwise degrade these structures. Larger devices are generally more susceptible to this problem of material heating because the power per unit area increases with device size. The risks to plasma facing components also increase when the power is exhausted in short bursts and over small areas rather than continuously and smoothly over the entire plasma surface (Box 4.6). Because of its size, ITER will explore a new regime of boundary plasma physics in which the competing needs of
134 Plasma Science BOX 4.3 Science-Based Confinement Models Progress in the understanding of plasma turbulence has been substantial over the last decade. (a) In the mid-1990s, simulation-based transport models with no empirical parameters successfully predicted large dif- ferences in ion temperature, which empirical scaling laws cannot distinguish. The sharp difference in the gradi- ent in the central plasma was shown to be a consequence of the higher temperature at the plasma edge. This breakthrough focused attention on the plasma edge. Courtesy of D. Ernst, MIT. (b) Models of ion temperature gradient (ITG) turbulence were subsequently shown to be consistent with data from several experiments and configurations. Courtesy of J. Kinsey, General Atomics. (c) Recently, attention has shifted to direct comparisons of the fluctuations observed in experiment and simulations. Actual diagnostic views (left panel) are synthe- sized in numerical simulations (right panel). Courtesy of D. Ernst, MIT. (d) The predicted spectrumâs shape is in excellent agreement with the experimentally measured density fluctuations. The final panel also shows the broadening of the early focus on ITG turbulence to include trapped electron mode (TEM) turbulence. Courtesy of D. Ernst, MIT. NOTE: PCI, phase contrast imaging; AU, atomic units. the plasma and the plasma facing components come into conflict as never before. Indeed, ITER will press up against the material limits. In many devices (including ITER) the plasma in an edge layer, called the scrapeâoff layer, is steered along field lines into a cool region called the divertor. The field lines in the divertor direct the exhaust into solid plates that take some of
The Plasma Science of Magnetic Fusion 135 25 10.00 Model DIII-D Experiment JET 20 C-Mod GLF23 Predicted Wth (MJ) Supershot = 8.7% 1.00 (keV) 15 Pinj = 15 MW I p = 1.7 MA Ti 10 B = 4.5 T 0.10 5 L-Mode dre02219801c 50 H-mode Discharges 0 0.01 0 0.5 r/a 1.0 0.01 0.10 1.00 10.00 (a) (b) Experimental Wth (MJ) PCI Viewing Geometry Spectrum of Density Fluctuations Integration over parts of flux tube viewed by PCI due to Trapped Electron Modes 0.5 PCI laser chords 3 10 kÎ¸ [A.U.] 2 kr 0.4 (AU) 1 5 0 2 4 6 0.3 -1 Wavenumber [cm ] o o 65.8 145 PCI measurement Z [cm] 0 Region of flux 0.2 tube included Gyrokinetic 5 in integral Simulation 0.1 10 10 5 0 5 10 0 0.0 0 2 4 6 8 (Poloidal Projection) Wavenumber k R [cm -1 ] (c) (d) the power exiting the plasma. Atoms in the edgea, b, c, d fig B.4. 3 and the divertor radiate the rest of the power. It is desirable to maximize the radiation (without introducing too many neu- trals) and the effective area of the divertor plates. Much of the research in the last decade has been to design divertor configurations that accomplish this. One radical
136 Plasma Science BOX 4.4 Turbulence and Shear-Flow Generation An important element of understanding plasma turbulence is how it regulates itself and thereby saturates in amplitude. Turbulence in tokamaks can drive sheared flows that saturate or even suppress the turbulence, a kind of turbulent self-regulation. (a) Cartoon of poloidally symmetric flows found to be present and important in nonlinear simulations of tokamak turbulence. Several mechanisms for their generation have been identified theoretically. Radial oscillations of these poloidal flows, illustrated by the red and blue/purple opposing arrows, are predicted to help regulate the turbulence and determine the transport levels. (b) Configuration of the two- dimensional array of points imaged by the beam emission spectroscopy (BES) diagnostic developed in the last decade. This diagnostic has revealed the detailed structure and dynamics of plasma turbulent density fluctua- tions in a small region near the plasma boundary. SOURCE: G.R. McKee, McKee, R.J. Fonck, M. Jakubowski, K.H. Burrell, K. Hallatschek, R.A. Moyer, D.L. Rudakov, W. Nevins, G.D. Porter, and P. Schoch, âExperimental characterization of coherent, radially-sheared zonal flows in the DIII-D tokamak,â Physics of Plasmas 10: 1712 (2003). (c) Images of the fluctuations that are used to determine the amplitude, eddy size, correlation, and char- acteristic flow speeds of the density fluctuations. (d) Initial comparisons of the experimentally measured flow velocity fluctuation frequency spectrum show good agreement with predictions from simulation and theory. A focus of current research is to understand the conditions under which these shear layers form, the processes that limit their extent, and the lower limits on transport that can be achieved. In the next decade enhanced diagnostics could provide images and data from a larger fraction of the plasma to investigate spreading of turbulence from one region to another. SOURCES: X.Q. Xu, W.M. Nevins, R.H. Cohen, J.R. Myra, and P.B. Snyder, âDynamical simulations of boundary plasma turbulence in divertor geometry,â New Journal of Physics 4: 53 (2002) and K. Hallatschek and D. Biskamp, âTransport control by coherent zonal flows in the core/edge transitional regime,â Physical Review Letters 86: 1223 (2001). solution, flowing liquid lithium as a plasma facing component, is currently being explored on a small scale. Such a liquid wall may act like a sponge soaking up particles exiting from the plasma without returning any cold particles. This raises the possibility of hotter plasma edges and vastly improved plasma performance. In addition, the liquid lithium could allow self-healing of the plasma facing com- ponents after large transient heat-flux events.
The Plasma Science of Magnetic Fusion 137 (a) (b) (AU) (c) (d) Opportunities in Boundary Plasma Properties and Control The chief goal of research in boundary plasma properties is to find a stable regime where plasma and heat can be removed from the plasma and collected fig B.4.4 a,b,c,d without damage by material surfaces. It is also important that in such a regime the temperature at or near the edge be substantial. Progress toward this goal has been
138 Plasma Science BOX 4.5 Controlled Chaos Fluctuations in a plasma-confining magnetic field can cause magnetic field lines to wander chaotically through the plasma. Charged particles that follow the field lines will then also wander chaotically. Such magnetic chaos occurs in a toroidal laboratory plasma, the reversed-field pinch, as illustrated in the field line puncture plot (a) inferred from scaled computer modeling of the experiment. Each dot denotes a puncture of a field line with the plane, as lines wander in the radial direction (the horizontal axis) as they progress toroidally (the vertical axis). Recently, experimenters developed methods to decrease the drive for the chaos. Chaos is then largely eliminated (b) and magnetic islands become visible. Chaos develops when magnetic islands overlap. The extent of the overlap is measured by a parameter (inferred from experiment) shown in (c) that exceeds unity when nearby islands overlap. When chaos is controlled in the experiment (the blue curve), islands are mostly separated (or absent) over much of the plasma. The effect of chaos on transport of energy through the plasma is large. When chaos is present, energy transport in experiment (the thermal diffusivity) in (d) is large and in agreement with theory based on the chaos of (a). When chaos is suppressed, transport is greatly reduced, with a 10-fold enhancement in the confinement of energy in the plasma. Images courtesy of S.C. Prager, University of Wisconsin at Madison. (a) (b) Standard Improved 1.0 1.0 0.5 0.5 Toroidal angle / ï¿½ Toroidal angle / ï¿½ 0.0 0.0 -0.5 -0.5 -1.0 -1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Radius Radius B.4.5. a B.4.5.b
The Plasma Science of Magnetic Fusion 139 8 Overlap parameter 6 (c) 4 2 0 0.0 0.2 0.4 0.6 0.8 1.0 Radius 10000 Thermal diffusivity (m2/s) 1000 (d) 4.5.1 w 100 10 1 0.0 0.2 0.4 0.6 0.8 1.0 radius 4.5.1 z
140 Plasma Science BOX 4.6 Edge Pedestal and Stability Since turbulent energy transport limits the temperature gradient over most of the temperature profile, obtaining a transport barrier with high confinement near the plasma edge is crucial for ITER to reach burning conditions in the plasma center. While the edge barrier can be obtained, it is unstable above a critical pres- sure gradient. These instabilities, called edge localized modes (ELMs), deposit some fraction of the pedestal energy into the divertor or onto the wall in less than one thousandth of a second. (a) The desired ITER plasma temperature and density profiles with edge transport barrier. The key parameter for fusion performance is the temperature pedestal heightâhere it is about 5 kV. (b) Pressure limits in the pedestal. Instability occurs above the red line. Theory of the instability boundary is in reasonable agreement with the observations. SOURCE: P.B. Snyder, H.R. Wilson, J.R. Ferron, L.L. Lao, A.W. Leonard, D. Mossessian, M. Murakami, T.H. Osborne, A.D. Turnbull, and X.Q. Xu, âELMs and constraints on the H-mode pedestal: Peelingâballooning stability calculation and comparison with experiment,â Nuclear Fusion 44: 320 (2004). (c) Photograph and theoretical model of an unstable edge mode that has coalesced into singular plasma filaments aligned along and carrying a magnetic field line. The filaments erupt from the plasma carrying heat and particles. Such filaments have been observed in numerous experiments and some of their characteristics are in agreement with theory. SOURCES: A. Kirk, H.R. Wilson, G.F. Counsell, R. Akers, E. Arends, S.C. Cowley, J. Dowling, B. Lloyd, M. Price, and M. Walsh, âSpatial and temporal structure of edge-localized modes,â Physical Review Letters 92: 245002 (2004); R. Maingi, C.E. Bush, E.D. Fredrickson, D.A. Gates, S.M. Kaye, B.P. LeBlanc, J.E. Menard, H. Meyer, D. Mueller, N. Nishino, A.L. Roquemore, S.A. Sabbagh, K. Tritz, S.J. Zweben, M.G. Bell, R.E. Bell, T. Biewer, J.A. Boedo, D.W. Johnson, R. Kaita, H.W. Kugel, R.J. Maqueda, T. Munsat, R. Raman, V.A. Soukhanovskii, T. Stevenson, and D. Stutman, âH-mode pedestal, ELM and power threshold studies in NSTX,â Nuclear Fusion 45: 1066 (2005); M.E. Fenstermacher, T.H. Osborne, A.W. Leonard, P.B. Snyder, D.M. Thomas, J.A. Boedo, T.A. Casper, R.J. Groebner, M. Groth, M.A.H. Kempenaars, A. Loarte, G.R. McKee, W.M. Meyer, G. Saibene, M.A. VanZee- land, X.Q. Xu, L. Zeng, and the DIII-D Team, âStructure, stability and ELM dynamics of the H-mode pedestal in DIII-D,â Nuclear Fusion 45: 1493 (2005). (d) Nonlinear simulations of edge instability dynamics confirm the filamentation process, and such simulations are being used to better understand heat and particle transport in the nonlinear phase of the edge pressure collapse. If edge instabilities become too violent, large amounts of plasma energy are released rapidly, potentially damaging reactor components. Present experiments and model- ing are exploring ways to reduce or eliminate these instabilities while still retaining high confinement near the plasma edge. Extrapolating these techniques to ITER is an active area of research. SOURCE: P.B. Snyder, H.R. Wilson, and X.Q. Xu, âProgress in the peeling-ballooning model of edge localized modes: Numerical studies of nonlinear dynamics,â Physics of Plasmas 12: 056115 (2005). largely, though not entirely, empirical. The development from first principles of a reduced physics model capable of describing the full range of plasma boundary phenomena is an area of active research. This effort will also benefit (as do other areas) from diagnostic improvements. A new experiment, intermediate in scale between current U.S. facilities and ITER, could study boundary plasma science issues in conjunction with enabling fusion technology research (high-heat-flux components, development of materials that are resistant to damage from 14-MeV neutrons, and so on). Such an experiment would not focus on the science of burn- ing plasmas, but it could nonetheless accelerate progress toward an economically attractive fusion reactor.
The Plasma Science of Magnetic Fusion 141 (a) (b) (c) (d) WaveâParticle Interactions in Fusion Plasmas Hot magnetized plasma supportsB.4.6 variety of waves that can exchange fig a huge a,b,c,d energy and momentum with the plasma particles. The resonant particles, those moving almost at the speed of the wave, interact strongly with the wave. Stable waves launched from the edge of the plasma are used to heat the plasma and to drive current in the plasma. This is a well-developed technique and can be modeled with high accuracyâan example of the state of the art is given in Box 4.7. Resonant particles can cause waves to become unstableâBox 4.8 shows an example of such instability that can be driven by energetic particles.
142 Plasma Science BOX 4.7 Fast-Wave Heating High-power electromagnetic waves of tens of megahertz are commonly launched into fusion plasmas to heat the plasma and drive plasma current. (a) Diagram of a multichord phase contrast imaging technique developed in the last decade that measures the wave number of the wave-induced density fluctuations. (b) Numerical simulation of a high phase velocity wave, the fast wave (FW), that is launched from the right into a tokamak plasma. Simulations have become powerful enough to resolve the transformation of waves from one mode into another, a process known as mode conversion. Here the FW is predicted to mode-convert into two other waves with much shorter wavelength perpendicular to the confining magnetic field (IBW, ion Bernstein wave; ICW, ion cyclotron wave); shown is the real part of the parallel electric field (Re(E||)). (c) Data from the imaging technique that measures the expected launched (kR < 0) and reflected (kR > 0) low-k fast wave and the higher-k mode-converted (MC) waves. (d) Comparison of the experimental and theoretical profiles of the line-integrated density fluctuations showing agreement. High-k MC waves are predicted to be capable of gen- erating sheared plasma flows and could ultimately provide a powerful tool for efficiently controlling plasma microturbulence and therefore the fusion gain in burning plasmas. SOURCE: S.J. Wukitch, Y. Lin, A. Parisot, J.C. Wright, P.T. Bonoli, M. Porkolab, N. Basse, E. Edlund, A. Hubbard, L. Lin, A. Lynn, E. Marmar, D. Mossessian, P. Phillips, and G. Schilling, âIon cyclotron range of frequency mode conversion physics in Alcator C-Mod: Experimental measurements and modeling,â Physics Plasmas 12: 056104 (2005). NOTE: PCI, phase contrast imaging; R, radius. (b) (a)
The Plasma Science of Magnetic Fusion 143 1.0 MC Waves FW Ã± eL (AU) (c) 0.5 0 -10 -5 0 5 10 k R(cm -1) B.4.7.1 c (AU) (d)
144 Plasma Science BOX 4.8 Alpha-Particle-Driven Instabilities The 3.5-MeV alpha particles from deuterium-tritium fusion reactions are born with velocities just above the fastest characteristic macroscopic (AlfvÃ©n) wave speed of the plasma and are therefore capable of giving energy to the AlfvÃ©n waves, creating instabilities. These instabilities can threaten the reactor and the fusion burn by transporting alpha particles to reactor walls before they can heat the background plasma. (a) Triton (tritium nuclei) and alpha particle energy distribution functions were found to be consistent with theoretical expectation (from collisions, without instabilities). Courtesy of IOP Publishing Limited; S.S. Medley, R.V. Budny, D.K. Mansfield, M.H. Redi, A.L. Roquemore, R.K. Fisher, H.H. Duong, J.M. McChesney, P.B. Parks, M.P. Petrov, and N.N. Gorelenkov, Plasma Physics and Controlled Fusion 38: 1779 (1996); and R.K. Fisher, J.M. McChesney, P.B. Parks, H.H. Duong, S.S. Medley, A.L. Roquemore, D.K. Mansfield, R.V. Budny, M.P. Petrov, and R.E. Olson, âMeasurements of fast confined alphas on TFTR,â Physical Review Letters 75: 846 (1995). (b) The measured and predicted plasma electron heating through collisions with alphas. Reprinted with permission from G. Taylor, J.D. Strachan, R.V. Budny, and D.R. Ernst, âFusion heating in a deuterium-tritium tokamak plasma,â Physical Review Letters 76: 2722 (1996). Copyright 1996 by the American Physical Society. (c) Frequency versus time data from new density fluctuation diagnostics revealing a multitude of destabilized AlfvÃ©n wave eigenmodes that are not detectable by magnetic sensors outside the plasma. (d) Theoretical AlfvÃ©n eigenmode spectrum showing excellent agreement with data. Such waves could redistribute the alpha particles in advanced operat- ing modes proposed for ITER. (c) and (d) Reprinted with permission from R. Nazikian, H.L. Berk, R.V. Budny, K.H. Burrell, E.J. Doyle, R.J. Fonck, N.N. Gorelenkov, C. Holcomb, G.J. Kramer, R.J. Jayakumar, R.J. LaHaye, G.R. McKee, M.A. Makowski, W.A. Peebles, T.L. Rhodes, W.M. Solomon, E.J. Strait, M.A. VanZeeland, and L. Zeng, âMultitude of core-localized shear AlfvÃ©n waves in a high-temperature fusion plasma,â Physical Review Letters 96: 105006 (2006). Â© 2006 by the American Physical Society. (a)
The Plasma Science of Magnetic Fusion 145 (b) (c) (d)
146 Plasma Science Opportunities in WaveâParticle Interactions The goals of waveâparticle research in the next decade are twofold: first, to extend the modeling of launched wave excitation and propagation to three di- mensions and, second, to explore possible energetic-particle-driven instabilities in ITER. Calculations of the linear properties of the instabilities are rapidly becoming routine. The challenge now is to understand the nonlinear evolution and interac- tion of multiple unstable modes and their effect on fast-particle confinement. In particular, it is not clear whether the instabilities will benignly (perhaps benefi- cially) redistribute alpha particles or eject them to the reactor walls, potentially damaging the plasma facing components. Improved understanding of wave heating and fast-ion transport is needed to confidently predict the characteristics of the dominant heating sources in ITER burning plasmas. Conclusions and Recommendations FOR THIS TOPIC The U.S. decision to rejoin ITER is recent, and the magnetic fusion program is beginning to evolve into the burning plasma era. The present U.S. program was shaped in 1996 when a science-focused mission with three goals was adopted: (1) advance plasma science in pursuit of national science and technology goals; (2) develop fusion science, technology, and plasma confinement innovations as the central theme of the domestic program; and (3) pursue burning fusion energy science and technology as a partner in the international effort. These goals remain entirely pertinent since the central strategic questions that frame the future pro- gram are the following: â¢ What plasma science must be developed to maximize the scientific output of ITER? â¢ What science and enabling technology must be developed to move beyond ITER to fusion-generated electricity? The specific plasma science issues were discussed in the preceding section. Conclusion:â The scientific opportunities in magnetic fusion science are compelling, intellectually challenging, and a direct product of the scientific focus of the U.S. magnetic fusion program over the past decade. Realizing the promise of these opportunities and addressing new challenges will hinge on maintaining the focus on achieving three goals: (1) advancing plasma science, (2) ensuring concept improvement through innovation, and (3) pursuing burning plasma science. The science focus resulted in the growth of predictive capability, which now provides much of the direction for the program. This increasing capability to
The Plasma Science of Magnetic Fusion 147 predict and control the behavior of magnetically confined plasmas has begun to replace sometimes costly and time-consuming empirical approaches. For example, it has yielded a cheaper and more promising design for ITER. Organizing and structuring the program around key science issues requires a prioritization that is beyond this committeeâs mandate (this issue is addressed later in this section). However, the science dictates some opportunities and directions that should be part of the program. The key to recent and future progress on all three goals lies in better measure- ments and better models that will allow addressing and resolving new scientific challenges and opportunities as they arise. Recommendation:â DOE should undertake two broad initiatives that are essential for advancing all areas of magnetic fusion research: (1) A diagnostic initiative to develop and implement new diagnostics in magnetic fusion experiments. (2) A theory initiative to reinvigorate theory and develop the next generation of models. Both initiatives require additional resources in their respective areas. Recent advances inside and outside the magnetic fusion program have made possible diagnostics that can measure multiple physical quantities at many points inside the plasma simultaneously. A diagnostic initiative would lead to a new generation of diagnostics that would test the veracity of present predictive models (e.g., tractable reduced models such as hybrid fluid-kinetic models of macroscopic instabilities and the five-dimensional gyrokinetic models of microturbulence) and stimulate the growth of better models through a complementary theory ini- tiative. Specifically, a major new diagnostics initiative like that proposed by the communityâs Transport Task Force in its white paper is needed. The cost and scale of these diagnostics may exceed present levels, but so will the value of the information derived from the measurements. Taking advantage of this opportu- nity to significantly advance plasma measurements should be a key priority of the magnetic fusion program. Most of the advances in modeling plasmas originated from the development of tractable reduced models, helped by the astonishing increase in computational power. Addressing the fusion plasma science challenges will require new theory and models to extract further scientific gains from the next generation of computational modeling. The theory program needs to be reinvigorated, paying special attention to the support of theorists who are willing and able to engage with the experimental âThe white paper of the fusion communityâs Transport Task Force on the type of diagnostic initia- tive that is needed for microturbulence and anomalous transport is available at http://psfcwww2.psfc. mit.edu/ttf/transp_init_wht_paper_2003.pdf.
148 Plasma Science and simulation communities. The fusion programâs ability to evaluate new ideas for magnetic confinement depends critically on advancing predictive capability. It is the broad analytic aspects of theory that are the weakest in fusion plasma sci- ence today. Filling this critical void in the theory program should be a very high priority for the next decade. Theory has not only a direct impact but also plays a role in enabling the next generation of advances in computational simulation and modeling. The recent growth of large-scale computation in fusion research through the Scientific Discovery through Advanced Computing (SciDAC) initia- tives in concert with the DOE Office of Advanced Scientific Computing Research (OASCR) has been laudable. In FY06, for instance, the DOE Office of Fusion Energy Sciences (OFES) theory program was supported at about $25 million; the OFES contribution of $4 million to SciDAC was highly leveraged by OASCR to amount to a total investment of more than $10 million. Without these essential theory and diagnostic initiatives, large-scale computation would have only a limited impact on the magnetic fusion program. Moreover, the impact of computation would be greatly enhanced by stronger coupling to the theoretical and experimental com- ponents of the magnetic fusion program. It is the committeeâs opinion that new and continued investments in large-scale computation for fusion will achieve far better leverage if they are accompanied by investments to improve the underlying basis of analytic theory. Conclusion:â Participation in ITER remains the most effective path for ac- complishing the U.S. objective of studying a fusion burning plasma. Maxi- mizing the return on the U.S. investment in ITER will require the United States to maintain leadership in advancing key areas of plasma science and in ensuring concept improvement through increased scientific understand- ing. Without continuing leadership in these areas, the success of the ITER burning plasma experiments will be at some risk. The next large step in magnetic fusion research is to measure and explore the properties of burning plasmas. This step has been greatly facilitated by the U.S. decision to participate in ITER, which was recommended by the NRC Burning Plasma Assessment Committee. Significant research must continue in order to maximize ITERâs engineering and scientific success and to optimize its ultimate performance. Over the past decade, U.S. leadership in a number of scientific areas has contributed significantly to making ITER smaller, more efficient, and less expensive. This was achieved by redefining ITERâs scientific goals, advocating major changes in the engineering design, and by developing and pushing several advanced modes of tokamak operation. Many of these contributions to ITER came not from burning plasma research but from research formally classified as part of âNational Research Council, Burning Plasma: Bringing a Star to Earth, Washington, D.C.: The National Academies Press, 2004.
The Plasma Science of Magnetic Fusion 149 the pursuit of the programâs plasma science or concept improvement goals. The United States is projected to contribute $1.122 billion for its participation in the ITER construction project. To obtain an appropriate scientific benefit from this very substantial investment and to ensure ITERâs success, the United States would be wise to retain, and preferably grow, a strong domestic fusion science research program. Such a program is necessary to develop the understanding and predictive capability that is needed to extract critical information from ITER and to project beyond ITER to fusion power. Conclusion:â To ensure that the magnetic fusion program can progress be- yond ITER to electricity-producing fusion power, it is essential that research in concept improvement and innovation continue. To hasten fusion energy development, a demonstration reactor must follow the completion of the burning plasma research mission on ITER. This will require the definition and development of high-performance reactor configurations operat- ing at high plasma pressure (Î²) with controlled macroscopic instabilities, minimal microturbulence, and tolerable edge conditions. Research in concept improvement has shown that several configurations promise to yield improved predictive under- standing, new plasma regimes, and potentially superior reactor designs. Without continuing U.S. leadership in this area it is unlikely that improved configurations will be ready in time, and the era of fusion power will be delayed. Conclusion:â The U.S. fusion program lacks a clear vision for the next decade and has been slow to react to and evolve toward the developing burning- plasma, ITER era. While the scientific opportunities, the promising methodologies, and the pro- gram elements are clear, the detailed program structure is not. Although the ITER site was decided on only in mid-2005, the recent establishment of the U.S. Burning Plasma Organization is a positive step. However, the U.S. fusion program does not have a strategy for its evolution over time periods longer than the yearly budget cycles. In particular, it has not responded adequately to a program recommenda- tion of the Burning Plasma Assessment Committee: âA strategically balanced U.S. fusion program should be developed that includes U.S. participation in ITER, a strong domestic fusion science and technology portfolio, an integrated theory and simulation program, and support for plasma science. As the ITER project develops, a substantial augmentation in fusion science program funding will be required in addition to the direct financial commitment to ITER construction.â This recom- mendation has not yet been adequately addressed beyond participation in ITER. Also, the Energy Policy Act of 2005 calls for a plan for evolution into the burning plasma, ITER era and calls for its review by the National Research Council. The âFrom the report Burning Plasma, p. 6.
150 Plasma Science U.S. community has taken positive steps to organize itself for the burning-plasma era, most notably with the formation of the U.S. Burning Plasma Organization, a grassroots technical organization that is coordinating U.S. research activities in preparation for ITER. Although the scientific isolation of the magnetic fusion communityâboth from the rest of the physical sciences and from the rest of the plasma science communityâis decreasing, it is limiting progress and hindering the spread of knowledge and expertise developed in magnetic fusion to other areas. Including the community within a broader framework in the DOE Office of Science would have substantial intellectual benefits for the plasma science of magnetic fusion. The committee notes that the U.S. magnetic fusion science community has made several efforts to develop plans for the future, most recently in two reports of the Fusion Energy Science Advisory Committee: Scientific Challenges, Opportu- nities, and Priorities for the U.S. Fusion Energy Sciences Program (2005) and A Plan for the Development of Fusion Energy (2003). More work is needed. Recommendation:â The United States should develop, and periodically up- date, a strategy for moving aggressively into the fusion burning plasma era over the next 15 years. The strategy should lay out the main scientific issues to be addressed and provide guidance for the evolution of the national suite of facilities and other resources needed to address these issues. Such strategic planning should include 10 considerations. â¢ The critical strategic and scientific issues that need to be addressed over the next 15 years by the magnetic fusion community: (1) the plasma science needed to maximize the scientific output of ITER and (2) the science and enabling technology for going beyond ITERâto guide the development of a strategy. â¢ The importance of focusing on fewer scientific issues in greater depthâto compete effectively internationally. â¢ Development of fusion plasma science and, accordingly, predictive capabil- ity through initiatives in diagnostics and theory, with greater coupling to the continuing development and utilization of large-scale computationsâto maintain leadership in key scientific areas. â¢ Participation of the U.S. scientific community in setting the ITER scientific agenda and planning for U.S. involvement in ITER experimentsâto en- sure a strong scientific focus for ITER and significant involvement of U.S. scientists. âPlease see the following report for a comprehensive discussion of this issue: NRC, An Assessment of the Department of Energyâs Office of Fusion Energy Sciences Program, Washington, D.C.: National Academy Press, 2001. This report is also described in Appendix E of the current report.
The Plasma Science of Magnetic Fusion 151 â¢ Transformation of the present portfolio of aging U.S. facilities into a new portfolio designed to expeditiously address key fusion scientific issues, including a schedule for retiring some devices to make room for innova- tive new experimental facilities and resources neededâto rejuvenate the portfolio of U.S. experimental facilities. â¢ The desired degree of participation and timing of evolution toward fusion research program based on international collaborationâto take advantage of some overseas facilities that are more capable than present U.S.-sited facilities and to prepare for leading some key scientific experiments on ITER. â¢ The balance between the burning plasma program and the development of innovative regimes and devices that look beyond ITERâto be prepared for the fusion demonstration era that will follow ITER. â¢ Possible change in the structure of the fusion program from a focus on par- ticular experimental facilities, to a focus on science-oriented campaignsâ to better align the program with its scientific objectives. â¢ Rejuvenation of the U.S. fusion workforceâto address the impending de- mographic challenge and the need for a new generation of fusion scientists for the burning plasma era. â¢ Feasible budgetary scenarios for implementing this strategic plan over the next 10 to 15 yearsâto indicate how the fusion program should evolve to address its scientific goals over that period. There is a significant opportunity and an urgent need for the U.S. fusion pro- gram to develop a comprehensive, 15-year strategic plan. The plan would include 10 years of preparations for ITER construction, initial operation and scientific experiments, and the first 5 years (approximately) of ITER experimentation. While current fusion budget projections by DOE provide fully for U.S. partici- pation in the ITER construction project, in the most optimistic budget scenarios the domestic fusion research program (the program beyond that needed for ITER construction) is projected to grow only with inflation and the current partial (less than 50 percent) utilization of the major magnetic fusion research facilities is expected to continue. These projections make it difficult for the United States to close the growing gap between newer, more capable intermediate-scale facilities being built abroad and the aging U.S. facilities (Table 4.1). Until the strategic planning has been completed, it is not possible to predict how facilities may evolve or to determine appropriate budget levels. It is, however, clear from the earlier discussion in this section that the domestic fusion program must remain strong for ITER to be successful and for the eventual development of fusion power. This will require a robust level of support for the domestic fusion program.