202 FUSION turns out that the fraction of fuel that is burnt depends only on the confinement Inertial Confinement Fusion product pR and is given approximately by Φ ≈ pR / (Hb+ pR), where Hb≈ 7 g/cm2. Jürgen Meyer-ter-Vehn From this we learn that it requires pR ≡ Max-Planck-Institut für Quantenoptik, Garching, Germany 3 g/cm2 to burn 30% of the fuel. For R = 100 pm this gives p = 300 g/cm3 which is Stefano Atzeni 1500 times the solid density of DT. Centro Ricerche Frascati, Italy Such high compression is possible when one starts with a frozen fuel layer as shown in figure lb and keeps fuel entropy Rafael Ramis low during implosion by using temporally ETSI Aeronauticos, Madrid, Spain shaped driver pulses. The capsules for NIF and LMJ rely on such cryogenic design, Inertial confinement fusion (ICF) is an Basics of inertial confinement and a corresponding implosion simulation alternative way to achieving controlled In ICF fusion burn occurs in highly com is given in figure 1c. The main pulse gener thermonuclear fusion. The basic idea is to pressed deuterium-tritium (DT) fuel, ating an ablation pressure of some ignite and burn a few milligrams of deu heated to an ignition temperature of 108 K. 100 Mbar accelerates the shell to about terium-tritium fuel by means of high- In the standard scheme compression and 400 km/s, and most of the compression power laser or ion beam pulses. Two large heating is achieved by spherical implosion occurs only at the end, when the implod laser facilities are presently under con of small capsules containing the fuel (fig ing fuel stagnates in the centre. At this struction which should demonstrate with ure la). A short pulse of radiation (laser, time the pressure reaches about 200 Gbar in the next 5 to 10 years the feasibility of ion beam, or X-ray radiation) is used to and is higher than in the centre of the sun. single micro-explosions. These are the ablate the outer layer of the capsule and to Driving all the fuel to ignition tempera National Ignition Facility (NIF) in implode the inner part, driven by the abla ture (volume ignition) requires much Livermore, US and the Laser Megajoule tion pressure like a spherical rocket. The drive energy and therefore degrades the (LMJ) in Bordeaux, France. The latter will energy yield of the ignited capsule (up to energy gain, which is the ratio of fusion be described later in this issue (see André some 100 MJ) can be contained in a reac energy yield to the energy invested for and Decroisette, chapter 5.3) tor vessel. For civilian energy production ignition. For power reactors one needs It should be noted that ICF has the scheme implies pulsed operation with target gains in the range of 50 -100. One emerged from the neighbourhood of a few miicro-explosions per second. way to obtain such high gains is to ignite nuclear weapons research, and significant In contrast to magnetic confinement only a central hot spot in the fuel from parts of ICF research had been classified fusion (MCF), inertial confinement where a burn wave then propagates into until recently. This changed in 1994 when involves no magnetic fields to contain the surrounding colder DT that has been declassification took place in the US which fuel, but relies exclusively on mass inertia. compressed at much lower energy costs opened the door for international collabo The imploded fuel of density p and radius (hot spot ignition). The hot spot forms all ration in this field for the first time. Still, R keeps together inertially for a small time by itself during implosion from the DT both the NIF and the LMJ project are part interval tcon ≈ R/cs, where cs ≈ 108cm/s is vapour filling the hollow interior initially. of so-called ‘stockpile stewardship pro the sound velocity of the igniting fuel. For Gains calculated for the NIF capsule grammes’ in the US and France, serving to a typical R = 100 pm this time is 100 ps. In and a potential reactor capsule are plotted maintain the stockpile of thermonuclear order to burn a significant portion of the versus beam energy in figure 2. Notice the weapons in these countries under the con fuel in such a short time one has to com sharp onset of the gain curves, jumping ditions of the comprehensive test ban press it to high densities so that the fusion from negligible gain to high values at treaty. Detailed information on NIF con reactions occur more rapidly. The time for some ignition energy. This is because cerning energy applications as well as a fusion reaction is given by tfus = most of the gain stems from burning the stockpile stewardship can be found on the µ /
Symmetry and stability Compression of the fusion fuel and cre ation of a central hot spot with a radius as small as 1/50-1/30 of the initial target Fig 1 a Principle of spherical implosion driven by external radiation. 1 b Sector of a cryogenic capsule. radius requires a high degree of spherical 1c Flow diagram of an x-ray driven implosion (one-dimensional simulation using NIF parameters) symmetry during implosion. The chal-
2.2 Inertial Confinement Fusion Meyer-ter-Vehn, Atzeni, Ramis Europhysics News November/December 1998 FUSION 203 shown convincingly that RTI always grows less than classically. The actual growth rate can be described by y = [ ak / (1 + kL) ]1/2 - βkva, where L is a mea sure of the thickness of the unstable layer, va is the ablation velocity, and β ≈ 1.5 - 3 depends on material, heating mechanism and details of the flow. Apparently, strong ablation (occurring for implosions driven by lasers or thermal X-rays, but not by ion beams) stabilizes RTI for small wave lengths. The growth rate of the most dan gerous modes with wavelengths compara ble to the thickness of the shell is typically reduced by a factor of 2-3. This feature is now well established by both measure ments and numerical simulations. Also, much progress has recently been made in analytical understanding. Denoting the perturbations by mode Fig 2 Target gain versus laser energy for two cases of x-ray drive. Left shaded area refers to the NIF design with numbers l ≈ 2πR/λ, corresponding to 300 eV hohlraum radiation leading to 400 km/s implosion velocity. Right shaded area right is for a larger, reactor spherical harmonics, the relevant RTI sized capsule with 225 eV and 300 km/s.The shaded regions mark the ignition uncertainty due to non-uniformities: modes at the outer surface seeded by tar the left-hand edges correspond to perfectly uniform implosions while the right-hand edges correspond to capsules get defects and early irradiation imprint with surface roughness of 50-100 nm. These capsules will operate at sufficiently high energies (black points) to become independent of the non-uniformities. Lines of 10% and 15% coupling efficiency from laser to x-ray energy lie in the range of l ≈ 10-500. They couple absorbed by the capsule are shown and also lines of constant fusion output (from J. Lindl, Phys. Plasmas 2,3933 1995) to the inner surface of the shell, smoothed by a factor exp(-l∆R/R), where they sum lenge is to keep the relative non-uniformi sion). Increasing AR makes the shell more up to the deformations caused by irradia ty of the driving pressure below 1%. robust, but implies also higher driving tion asymmetries and seed the inner RTI Another crucial difficulty is due to pressure (and therefore higher beam with relevant modes between l ≈ 8-30. Rayleigh-Taylor instability (RTI), which power) to drive the shell to the required Significant insight has been obtained by has been the single most studied topic in velocity. comparing implosion experiments with ICF. As illustrated in figure 3a, it first According to the classical RTI theory, a computer simulations. An example of a 2D occurs at the outer surface of the shell (the small perturbation with wavelength A at simulation of a stagnating shell with a ablation layer) where the tenuous, beam- an unstable surface grows exponentially dominant l ≈ 8 perturbation is given in heated plasma accelerates the shell with the rate y = (ka)I/2, where k = 2π/λ figure 3b, showing ignition despite the inwards, and later at the inner surface, and a is the acceleration. As the amplitude strong deformation of the hot spot. More when decelerated by the less dense, hot becomes comparable to A, the pace of recent 3D computations at higher resolu central material. The former process may growth slows, but then different wave tion confirm these results. Presently, the lead to rupture of the shell, while the latter lengths couple nonlinearly, giving rise to a most advanced 3D codes correctly predict mixes hot and cold fuel, thus hindering turbulent mixing layer of depth h, which the experimentally observed neutron formation of the hot spot. In fact, ignition grows in time as h ≈ 0.07 at1. These basic yields. This is a crucial test because neu with a MJ driver requires the implosion of results, when applied to the unstable abla tron yield is highly sensitive to RTI a very thin shell having an in-flight- tion front, would render ICF practically growth and mixing. Based on these aspect-ratio of R/AR ~ 40 (ratio of shell impossible. Fortunately, experiments per results, it is now believed that the RTI radius to shell thickness during implo- formed over the last two decades have problem can be solved by keeping irradia-
Fig 3 Rayleigh-Taylor instabilities in the implosion of an ICF shell. 3a Radius versus time flow chart of an imploding shell, where unstable layers are Indicated by the thick grey lines. The Inserts show the deformations of the shell caused by Instabilities. 3b Central ignition of a reactor-sized fusion target (from S. Atzeni, Laser & Particle Beams 9 1991). Density and ion temperature maps obtained from 2D simulation clearly show that despite the growing shell deformation (upper row) the central hot spot first self-heats and then propagates to the whole fuel. The target has an initial radius of 2 mm and is directly irradiated by a laser pulse of 1.6 MJ, imposing a perturbation with peak-to-valley
amplitude of 0.7%. The computed fusion yield exceeds 100 MJ News 1998 November/December Europhysics 204 FUSION tion asymmetries below 1 - 2% and by heat the interior of the gold casing to a which will be built in the near future, is developing capsules with a surface rough temperature of T = 300 eV. This gives a described in chapter 5.3. The advantage of ness of less than too nm. radiation flux of σT4 ≈ 1015 W/cm2, just lasers is that one can easily generate puls enough to drive the capsule to ignition. es much shorter and focus them to spots Direct and indirect drive Apparently, such hohlraum targets are much smaller than that finally needed for Presently, there are two paths to achieving quite flexible concerning irradiation ICF. This makes it possible to reach an uniform irradiation. Firstly, the direct geometry. For heavy ion beams, they may intensity of 1015 W/cm2 which is already drive approach, where a large number of be the only target option. relevant for ICF studies with small lasers, overlapping beams is shone directly on Also for NIF and LMJ, hohlraum targets much below the MJ level. Over the last 30 the fusion capsule, and secondly, the indi will be used in the first operation phase. years most ICF-related experiments on rect drive approach, where one converts They look similar to the design in figure 4, laser-plasma interaction, on hohlraum the beam energy into X-rays which then but with laser beams entering through heating, on ablative acceleration of matter drive the capsule implosion. At present, windows near the axis and X-ray conver and Rayleigh-Taylor instability have been direct drive is thought to be possible only sion taking place on the inner surface of performed with such lasers, as have cap with lasers. Significant progress has been the gold casing. The coupling efficiency sule implosions, which have demonstrated made to reduce the spatial and temporal between incident beam and X-ray energy 600 times compression and 1014 fusion coherence of the laser light which causes absorbed by the capsule is in the range of neutrons from single implosions. Recently, interference speckles on the target that 10 -15% according to simulations and the leading machines have been NOVA in seed the Rayleigh-Taylor instability. scaled experiments. The parameters of Livermore, GEKKO-XII in Osaka and Different smoothing techniques have been both figures 1 and 2 refer to NIF; the 1.2 MJ OMEGA in Rochester. In Europe laser developed where one splits the laser beam laser pulse of the NIF design results in fusion research has been carried out with into many beamlets and then randomizes 167 kj absorbed by the capsule and leads PHEBUS in Limeil near Paris, VULCAN in the phases. Direct drive laser ICF will to a yield of 16 MJ. This implies a target Oxford, UK, ASTERIX in Garching, ABC in depend crucially on these methods. gain of 15. Coupling efficiencies for heavy Frascati and some other machines, in par Quite different is the indirect drive ion beam targets critically depend on final ticular in Russia. approach, using so-called hohlraum tar beam focussing and the converter mass gets. In simple terms, the idea is to enclose which is determined by the focal radius Heavy ion accelerators the fusion capsule in a casing (the and the ion stopping range. This is still an For power stations generating inertial hohlraum) which is heated with ion or area of active research, and coupling effi fusion energy (IFE), drivers having high laser beams like an oven. As a result the ciencies of 10 -15% are expected for reac- repetition rate (10 Hz) and high driver capsule is bathed in highly isotropic tor-sized targets, driven by 10 MJ pulses. efficiency are needed. Heavy ion accelera hohlraum radiation so that it ablates and tors are leading candidates in this respect. implodes very symmetrically. An example Lasers Driver efficiencies of 20 - 30 % are expect of a hohlraum target is shown in figure 4, High-power lasers represent the leading ed, relaxing the need for high target gain. it was designed during a recent study on driver option to demonstrate ignition and Also, accelerators can deliver the pulses at heavy ion beam fusion. The ion beams are high target gain in single shot experi rates of up to 100 Hz, which could possibly stopped in the converter elements which ments. The Laser Megajoule ignition laser, serve several reactor cavities. Two types of heavy ion systems have been considered; induction linacs at LBL Berkeley and RF linacs combined with storage rings and buncher units at GSI Darmstadt in Germany. All this work is still at an early development stage, but will certainly gain momentum as soon as ignition is demon strated with lasers. The main disadvantage, which has impeded heavy ion driven ICF in the past, is the relatively high cost of accelerators, particularly for medium-sized test facili ties. However, the cost scaling is favourable for large units such as power stations. When compared to competing laser drivers for IFE, such as KrF-lasers and diode-pumped glass lasers, which may also reach acceptable levels of effi ciency and repetition rate, it is the proven durability and reliability of accelerators that distinguish heavy ion drivers.
Light ion beams and X-rays Pulsed power technology provides another option for low-cost drivers. It may be used to produce either intense light ion beam Fig 4 Perspective view of a hohlraum target driven by heavy ion beams (from R. Ramis et al., Proc. 12th Int. pulses or X-ray pulses by Z-pinch implo
Europhysics News November/December 1998 Symp. on Heavy Ion Inertial Fusion, eds. I. Hofmann et al., Heidelberg, Sept. 24-27,1997) sions. Pulsed power machines have proven FUSION 205
Fig 5 The design of the heavy ion driven ICF reactor HIBALL 1 reactor chamber, 2 INPORT blanket, 3 final focusing quadrupole magnets, 4 rotatable top shield, 5 coolant exit, 6 primary pump, 7 heat exchanger, 8 secondary coolant pump, 9 steam generator, 10 w ater intank, 11 steam exit, 12 high-pressure turbine, 13 low pressure turbine, 14 electricity generators, 15 condenser and water preheater, 16 beam lines, 17 target transport line, 18 target factory, 19 reactor containment, 20 machine building. (Badger et al. report KfK-3202, vol. 1 and 2, Kernforschungszentrum Karlsruhe, 1981) very useful for ICF physics experiments designed with protected first walls, which proof-of-principle phase of ICF, the IFE and may even succeed in single-shot cap may turn out to be a critical advantage. reactor phase will require mass produc sule ignition, but it is difficult to see how Also, for the single-shot facilities, present tion of such targets at low cost (a few euro to make them IFE drivers, satisfying the ly of interest, complex reactor issues like cents per target). Certainly, one has to requirements of high repetition rate and repetitive operation, pellet injection, learn from single target ignition about the long-life operation. Solutions for this have remote handling, and many others, do not options available. been proposed but need to be studied. have to be solved. Nevertheless, a number Light ion beam pulses are generated in of design studies have been performed to Problems still to be solved diodes, used to discharge up to a few MJ obtain a comprehensive view of IFE reac The scientific and technological basis has of energy from capacitor banks with cath tors and to understand the interdepen been developed to ignite and burn micro ode electrons insulated by a magnetic field dence of parameters. One of the most fusion targets by means of MJ laser pulses and ions extracted from an anode plasma. complete studies was the HIBALL study, a In scaled experiments, implosions with By properly shaping these diodes, design of a heavy ion driven IFE reactor. high convergence ratio and neutron yields focussed proton beams depositing 10 - Figure 5 shows the HIBALL reactor block. have been achieved, showing close agree 1000 TW/g into target material have been In the HIBALL chamber, the first metallic ment between experiment and multidi demonstrated. Future light ion beam dri wall is protected from the target X-rays, mensional simulations. The crucial prob vers for ICF will accelerate Li or C beams ions and neutrons by an array of porous lem of symmetry and stability is in two-stage diodes up to some tens of SiC tubes through which liquid PbLi is approached along two lines, direct drive MeV. Targets would be foam-filled spheri flowing and wetting the outer surface. using laser smoothing techniques and cal hohlraums. IFE and MFE reactors have many prob indirect drive using gas-filled hohlraums. A new version of X-ray production by lems in common. This is evident for ques For further reading, we refer to the review means of pulsed power is Z-pinch implo tions concerning, for example, breeding by J. Lindl Phys. Plasmas 2 3933 (1995). sion of cylindrical wire arrays, which turn blankets and other components exposed Still missing is the actual demonstra out to be much more stable than solid to high heat and neutron fluxes. A less evi tion of target ignition and high gain, but liner implosion and lead to significant dent example of synergy is the production this is expected to happen within the next conversion into X-rays. Recent work at the and repetitive injection of cryogenic fuel 10 years using the laser facilities NIF and Sandia laboratories has demonstrated pellets into the reaction chamber. Though Megajoule. In case of success, ICF 200 TW /1.8 MJ of X-ray pulses from the DT-ice pellets used for refuelling in research will move on to develop reactors 20 MA discharges performed on the Z MFE are less structured than IFE targets, for inertial fusion energy. The search for machine (K. Matzen Phys. Plasmas 4 1519, the pneumatic techniques developed in the most suitable reactor driver having 1997). There are plans for a larger facility MFE of accelerating them to high velocity first of all high efficiency and repetition capable of ICF capsule ignition. without heating will certainly become of rate will then become the main focus. interest for IFE reactor development. Presently, heavy ion beams appear to be Reactor design Target manufacturing is a critical issue the most promising candidates, but also An important feature of IFE reactors is for IFE. Methods of producing capsules KrF lasers and diode-pumped glass lasers that driver and reactor chamber are sepa with the required smoothness of surfaces may meet the efficiency and repetition rated from each other and can therefore and layer interfaces, including the cryo requirements. Some of the reactor issues be developed independently. Another spe genic DT layer, have been developed. also apply for magnetic fusion and may
cific point is that fusion chambers can be While this is sufficient for the single-shot be solved jointly. Europhysics News November/December 1998