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The temperature in the sun’s interior is about 1 keV.At this temperature hydrogen atoms live for a million years before they fuse intohelium to release energy. What if we can make our own miniature sun on Earth? Wecan’t wait a million years, so we must increase the temperature to speed up the process.We can also increase the inertia in a head-on collision with heavier isotopes: deuterium (D) with one proton and one neutron, and tritium (T) with one proton and twoneutrons. The inertia has to overcome the electric repulsion of ions with like charges.For the sun, Hans Bethe invented the carbon cycle, in which protons can be made tofuse in a series of reactions involving carbon, each of which requires less energy.Better carbon cycles have been found since then, but no one has found a cycle that canwork on our time scales.
One might think that we could accelerate deuterons in aparticle accelerator and put a solid piece of tritium ice in the beam, but that won’t workbecause the deuterons lose more energy in off-angle scatters than they gain in head-onfusion collisions. There are two main ways to recover the energy from D–T fusioncollisions: magnetic confinement, and inertial fusion.10.2.1 Magnetic FusionBy trapping a plasma in a magnetic field, the ions and electrons are in thermalequilibrium with Maxwellian distributions, so that the energy gained or lost inelastic collisions is returned to the thermal distribution. Only a few collisions result10.2Fusion Energy357in fusion. The idea is to create a 50–50 % DT plasma at around 30 keV so that thereare enough high-energy ions in the tail of the distribution to fuse, generating morethan the energy used to create the plasma. Since the plasma is in thermal equilibrium, these are called thermonuclear reactions.
There are other nuclei besides Dand T that can be used; the principal reactions are:D þ T ! α þ n þ 17:6 MeVD þ D ! 3 He þ n þ 3:27 MeVD þ D ! T þ p þ 4:05 MeVD þ 3 He ! α þ p þ 18:34 MeVD þ 6 Li ! 2α þ 22:4 MeVp þ 7 Li ! 2α þ 17:2 MeVp þ 6 Li ! α þ 3 He þ 4:0 MeVp þ 11 B ! 3α þ 8:7 MeVHere p is a proton and n a neutron. The two D–D reactions occur with about equalprobability, but one of them yields a neutron.
Since thick shielding would be requiredto protect personnel from neutrons, aneutronic reactions are much preferred. Furthermore, neutrons not only require shielding but they also carry most of the energy,which must be captured as heat to be used in a steam turbine to produce electricity.The D–3He reaction is aneutronic, but 3He does not occur naturally. It is produced inthe first D–D reaction, which is neutronic.
The 6Li reactions use the 8 % isotope oflithium. The p-7Li reaction is aneutronic, but it occurs only 20 % of the time. Thisleaves the p-11B reaction, which is the best choice because it is entirely aneutronicand 7Li is a plentiful element. Though its reactivity is relatively low, p-11B has suchpromise that it is being pursued by a private enterprise. Charged products can, inprinciple at least, produce electricity without going through a Carnot cycle.Figure 10.1 shows the fusion probability for the various reactions. It is clear thatthe D–T reaction is by far the best. Shown in Fig.
10.2, the D–T reaction produces aneutron and a helium nucleus, or α-particle. The mass difference between the D + Tand the resulting α + n is converted into 17.6 MeV of energy by E ¼ Mc2. Most of theenergy is carried off by the 14-MeV neutron, while the 3.5-MeV α-particle is trappedin the magnetic field which confines the plasma. This confinement is far fromperfect, and the mean times for leakage of ions and of plasma energy are calledrespectively τp and τE. Neglecting the difference between τp and τE, we show inFig. 10.3 the required nτ product for breakeven and ignition. Breakeven occurs whenthe fusion energy produced is equal to that used in creating the plasma.
This is calledthe Lawson criterion. Ignition occurs when the α-particles are trapped in the B-fieldlong enough that they can maintain the plasma’s temperature without further input ofenergy. The Joint European Tokamak (JET) in England is, at the time of this writing,on the verge of achieving breakeven. The ITER tokamak in France (originally anacronym of International Thermonuclear Experimental Reactor), is designed toachieve ignition some years after it begins D–T operation in 2027.35810Plasma ApplicationsFig. 10.1 Reactivity ofvarious fusion collisionsvs.
ion temperatureFig. 10.2 Diagram of the D–T reactionFig. 10.3 The nτ product for D–T fusion, in units of cm3 s, vs. KTiThere are two principal ways to surpass the Lawson criterion: magnetic confinement and inertial confinement. In magnetic confinement, the minimum nτ inFig. 10.3 is achieved by holding a dense plasma in a magnetic field for a time τ. Ininertial confinement, a much denser plasma is held for a very short time by10.2Fusion Energy359compressing it with a laser or other pulsed power source. We consider magneticconfinement first.
Ions and electrons gyrate in Larmor orbits but are free to movealong lines of B. To trap them, one can use magnetic mirrors or cusps (see Figs. 2.7,2.8, and 2.14), or close the lines in a torus. Large mirror machines have been builtwith special devices to slow the loss of particles which scatter into the loss cone, butthese have not been as successful as tori. In a torus, the B-field lines must not closeon themselves but must randomly trace out magnetic surfaces. Instabilities thenarise, such as the gravitational instability in Sect. 6.7 and the drift-wave instabilityin Sect.
6.8. The former is driven by centrifugal force, and the latter by the pressuregradient which must exist somewhere in a confined plasma. An ion temperaturegradient instability has also been troublesome. These instabilities have beenbrought under control by shear in the magnetic field and other more subtlemeans, and it is now possible to satisfy the Lawson criterion.10.2.1.1Pinches and Pulsed PowerInertial confinement research began with pinches. These are plasmas created with apulsed current, whose B-field compresses the plasma to higher density until theplasma pressure is balanced by the magnetic field pressure. Figure 10.4 shows asimple z-pinch (zed-pinch in the U.K.), like the one described theoretically as earlyas 1934 by W.H. Bennett.
This type of pinch suffers from two instabilities: asausage instability, shown in Fig. 10.5, and a kink instability, shown in Fig. 10.6.In the sausage instability, if a bulge develops in a linear pinch, the B-field isweakened with the new field lines. The plasma pressure is then able to push thelines further out. The opposite case of a reduced radius neck developing in theplasma is shown in Fig. 10.5. In the kink instability (Fig.
10.6), a kink, or bend, inthe plasma will cause the B-field to be stronger on the inside of the curve than on theoutside, and the magnetic pressure difference will enhance the kink. By adding aDC magnetic field to the pinch, these instabilities can be slowed down, but suchpinches could not achieve confinement times adequate for fusion.In 1952 James Tuck at Los Alamos in the U.S. made a toroidal z-pinch called thePerhapsatron. To drive the current, the plasma was threaded through an iron coreand was the secondary winding of a transformer. This was one of the first toroidalexperiments.
In the U.K., a large toroidal “zed-pinch” called Zeta was built andexhibited at the 1958 Geneva conference, at which each nation showed what it hadbeen doing while fusion was a classified subject. Neutrons were observed from Zetawhich indicated that it had produced fusion reactions.
However, the DT reactionswere found to come from collisions on the wall, not the interior, much to the chagrinof my good friend Peter Thonemann.Z-pinch. The z-pinch is so simple that it was not easy to give up on them in spite oftheir unstable nature. One solution was to drive a current through an array ofhundreds of fine metal wires, as was done by T.W.L. Sanford et al. in 1995. Resultsfrom these and later wire array experiments are discussed in the context of a series36010Plasma ApplicationsFig. 10.4 A Z-pinch, or Bennett pinchFig.
10.5 Mechanismof a sausage instabilityFig. 10.6 Mechanismof a kink instabilityof distinct physical mechanisms by Malcolm Haines et al. in 2005. The wires notonly provided a hard core for the pinches, but they also stabilized the kinking inneighboring wires. Rayleigh–Taylor instabilities then made regular indentationsalong the linear plasmas.
Related experiments were done with imploding cylindrical liners. Though the main purpose of these experiments was to create X-rays, acapsule containing deuterium, struck by such implosions, could produce 1010 DDfusion neutrons. A very large experiment, the Z-machine, at Sandia in New Mexicoin the U.S., focused a number of these pinches onto a small wire-array targetenclosing a DD-filled capsule inside a hohlraum (defined later) to produce fusion.The power to the pinches was delivered through thick coaxial “cables” whichused demineralized (high resistivity) water as a dielectric between metal cylinders.Water has a high dielectric constant of 80. The power was stored in compactmegajoule capacitor banks.
The capacitors are charged in parallel, slowly, anddischarged in series, fast, in order to pulse-charge the water-dielectric coaxialcables in under 1 μs. This process is shown in Fig. 10.7.A spectacular discharge on the surface of the demineralized water tank in theZ-machine is shown in Fig. 10.8. Such discharges occur only at late time in normaloperation and do not affect the electrical energy delivered to the load during themain power pulse.10.2Fusion Energy361Fig. 10.7 Mechanism of charging and discharging a Marx bankFig.
10.8 The Z-machine at Sandia, NMSmaller pulsed-power systems at universities can deliver ~1 TW of power in100-ns pulses. A megajoule of energy is only the amount required to boil half a cupof water, but to deliver this energy in 100 ns takes a large machine. The Z-machine,along with high-power lasers, represent significant advances in technology, but theydo not directly relate to fusion energy. Electric power must be steady and36210Plasma Applicationscontinuously available, and this is difficult to supply with pulsed systems operatingat less than 10 Hz. The largest pulsed plasma machines carry out experiments a fewtimes a day at best.The equilibrium condition of a simple z-pinch such as that in Fig. 10.4 is given by∇ p ¼ JB;ð10:1Þwhere p is the plasma pressure, B ¼ Bθ θ^ , and J ¼ J z z^ .
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