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Theplasma was instead lost in bursts called ELMs (Edge Localized Modes), a namewhich suggests that these were not well understood. The H-mode density is a factor2–3 above previous values, now called the L (low)-mode. Other large tokamakshave also produced the H-mode, and now they all operate with it.ELMs are thought to be “peeling-ballooning” modes driven by the large bootstrap current caused by the sharp pressure gradient in the thin pedestal layer.Peeling is a form of the kink mode.
Ballooning is a bubbling out of the plasmainto a weaker field, where extrusion can grow more easily. The pedestal raises the βof the plasma, and thus the fusion power, which increases as β2. The H-mode was anentirely unanticipated gift of nature. The conditions can be adjusted so that theselarge outward bursts of plasma are replaced by a stream of small bursts, calledgrassy ELMs. Even better, it is possible eliminate ELMs altogether.
This has beenachieved in the ASDEX Upgrade in Germany and the DIII-D in the U.S. withneutral beams counter-injected relative to the plasma current. Figure 10.37 showsthe ELM activity as seen by the oscillations in the deuterium α-line Dα. As thepower is raised, the tokamak goes from the L-mode into the H-mode. At first, thereare ELMs, but a long period ELM-free H-mode ensues. The average density,however, is low in the ELM-free mode, as seen in Fig. 10.38. Apparently, theradial flux at high density cannot be transported to the open field lines leading to thedivertor without ELMs.Fig.
10.36 The H-mode barrier10.2Fusion Energy379Fig. 10.37 An ELM-free discharge in ASDEX-U [Suttrop et al., Plasma Phys. Control. Fusion45, 1399 (2003)]Fig. 10.38 Density increase from ELM-free to ELMy H-mode with counter- and co-injection inASDEX-U [Suttrop et al., loc. cit.]D-Shapes and DivertorsA toroidal plasma suffers from instabilities and other particle loss mechanisms thatdo not occur in cylinders. Since these effects are caused by the fact that one side ofthe plasma is closer to the major axis than the other, we can increase the volume ofthe plasma harmlessly by making the tokamak taller rather than wider.
This has ledto tokamaks with D-shaped cross sections, which are now commonly adopted. Anexample is shown in Fig. 10.39. At the top and bottom of the plasma there are“divertors”, which capture the plasma exhaust. The confined part of the plasma is38010Plasma ApplicationsFig. 10.39 Diagram of aD-shaped tokamak (fromGeneral Atomics, SanDiego, California)enclosed by the last closed flux surface, called the Scrape Off Layer.
The surfacesoutside of that capture the escaping plasma and lead it into the divertors, where hightemperature materials and heavy cooling condense the hot plasma. Figure 10.40shows the elongated chamber of the JET tokamak in England, which has beenoperating since 1983. Figure 10.41 shows a water-cooled divertor designed for afuture tokamak.The Density LimitIn assembling data from numerous tokamaks, M. Greenwald found that theiraverage plasma density always fell below a hard limit which was proportional tothe power input.
This is shown in Fig. 10.42. It was thought that as the power wasraised, the wall was bombarded by escaping ions, thus releasing high-Z impuritiesnear the boundary. These would radiate and cool the plasma, increasing theresistivity there and thus changing the current profile into an unstable form.However, the density limit does not depend on the impurity level or the power. Ifthe density is slowly raised in the H-mode until it reaches the limit, the H-modedisrupts unstably into the L-mode.
If the density is allowed fall slowly, it decays atthe rate that keeps the discharge at marginal stability. The density limit is not wellunderstood.10.2Fusion Energy381Fig. 10.40 Diagram of the JET tokamak in the U.K. [J. Wesson, Tokamaks, Oxford SciencePublications (1987), p 658]Fig.
10.41 Diagram of adivertor. CFC is a carbonfiber compositeHeating and Current DriveThere are four main ways to heat a fusion plasma: ion-cyclotron resonance heating(ICRH). electron-cyclotron resonance heating (ECRH), lower-hybrid resonance38210Plasma ApplicationsFig. 10.42 The Greenwalddensity limit in tokamaks[M. Greenwald et al., Nucl.Fusion 28, 2199 (1988)]heating (LHRH), and neutral beam injection (NBI). In ICRH and LHRH, internalantennas are placed near the wall to excite ion cyclotron and lower hybrid waves,respectively. The wave energy is damped preferentially into ion energy. Thoughuseful in experiments, such antennas would not survive in a reactor.
These threewaves are of quite disparate frequencies. For instance, at B0 ¼ 3T andn ¼ 1 1020 m3, fci is 1.1 MHz, fLH is 230 MHz, and fce is 84 GHz. ECRH,being in the microwave range, can be carried in waveguides and injected with ahorn without requiring an internal antenna.ECRH power, of order 100 GHz, is produced by gyrotrons, which produceelectron cyclotron radiation by injecting an electron beam to gyrate in a strongmagnetic field. A picture of a gyrotron is shown in Fig.
10.43. The magnet is at thebottom, and the top part collects the depleted beam. A bank of these, at 170 GHzand 1 MW, will be used in ITER. As shown in Problem 4.47, the cyclotronresonance can be reached only from the inside of the torus, where space in thecentral column is at a premium. For this reason, ECRH is often applied at 2ωc.Large tokamaks are mainly heated by the injection of neutral atoms (NBI) whichcan penetrate into the interior of the plasma before being ionized. These atoms musttherefore have a large injection energy, typically hundreds of keV. For instance, theJT-60U tokamak in Japan has developed a 500-keV, 22-A ion source for an injector.To make a neutral beam one can start with a positive ion and add an electron, orstart with a negative ion and strip an electron, which is easier.
Neutral beaminjectors typically start with negative deuterium ions (D), which are then passedthrough a gas such as lithium or cesium to be turned into neutrals. Neutral beamscan be injected radially or, usually, tangentially in the same direction as thetokamak current.Figure 10.44 shows the DIII-D tokamak at General Atomic in San Diego,California. The two large cylinders on the left are the neutral beam injectors.
Abeam dump on the far side captures the un-ionized beam. Neutral beam injectorstend to be larger than the tokamak itself and to dominate the laboratory. When10.2Fusion Energy383Fig. 10.43 A largegyrotron [ITER.org]neutral beams are injected in the direction of the tokamak current, they contribute tothat current when ionized. Varying the angle of injection affords a way to controlthe current profile. This is called non-inductive current drive, since it is steady-stateand does not involve pulsing a transformer.Electron cyclotron current drive is another way to achieve steady-state operationof a tokamak. To do this, waves at a frequency corresponding to ωc somewhere inthe interior of the plasma are injected from the inside of the torus.
We can useFig. 4.36 if we add a line representing the injected ω. If an X-wave is sent in fromthe outside of the torus, ω lies to the right, and the whole diagram moves to the righttowards ω as ωp increases. The wave will meet the cutoff at ωR and be reflected. Butif the wave is injected from inside the torus, where ωc is larger than ωL, it can travelto the radius where ω ¼ ωc and give electron cyclotron current drive with itsz component. The space in the central column very limited, and the need to injectfrom the inside is problematic.38410Plasma ApplicationsFig. 10.44 The DIII-D tokamak in the U.S.DisruptionsTokamaks are subject to catastrophic events known as disruptions.
There are manypossible causes for this loss of confinement, but it is a global instability that causes athermal quench—a sudden cooling of the plasma. The resistivity then increases, andthe toroidal voltage can then accelerate electron runaways to MeVs. Large “halo”currents flow poloidally, partly in the plasma and partly in the wall. Large J B forcesare induced in the walls as J decreases. The D-shaped plasma “falls” vertically, asshown in Fig.
10.45. It is sometimes possible to anticipate a disruption when oscillations appear in Mirnov pickup coils near the edge. In that case, the disruption can beprevented by injection of a neutral gas such as He or Ne through a fast valve. It is clearthat disruptions must be avoided in a reactor, and this can be done by operating thetokamak below its maximum power. With superconducting magnets, tokamaks canrun almost steady state.
The EAST (Experimental Advanced Superconducting Tokamak) in China can run pulses as long as 1000 s without disrupting.10.2.1.6Spheromaks and Spherical TokamaksWhen the aspect ratio of a tokamak is reduce to the order of unity, the machinebecomes a spherical tokamak. If the central column is removed and the plasma isinjected, it forms a self-organized structure called a spheromak.
A smoke ring is anexample of a self-organized structure. Instabilities, especially the kink instabilities,are suppressed at low aspect ratios, probably because of the short connection lengthbetween good and bad curvature regions.10.2Fusion Energy385Fig. 10.45 Vertical motion of the plasma during a tokamak disruption [R. S. Granetz et al., Nucl.Fusion 36, 545 (1996)]Fig. 10.46 Drawing of aspherical tokamak showingthe regions of good and badcurvature of one field line[from F.F. Chen, AnIndispensable Truth(Springer, 2011), p. 376;adapted from original byS.
Prager, Univ. ofWisconsin]A diagram of the NSTX spherical tokamak experiment at Princeton is shown inFig. 10.46. A more compact machine, the MegAmpere Spherical Tokamak MASTis shown in Fig. 10.47. START (Small Tight Aspect Ratio Tokamak), a predecessorof MAST, achieved a beta of 40 %, an order of magnitude higher than the “Troyonlimit” for ordinary tokamaks.38610Plasma ApplicationsFig. 10.47 The MASTspherical tokamak [CulhamCentre for Fusion Energy,U.K.]Fig. 10.48 Diagram of aspheromak [Univ. ofWashington, College ofEngineering]A diagram of a spheromak is shown in Fig. 10.48. A toroidal current creates anentirely poloidal B-field, and there is no central core.
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