I

Technical Discussion of the Recent Results from the National Ignition Facility

The Lawson criterion for ignition1,2 requires that the product Pτ exceeds a threshold value that depends on the plasma temperature. The central temperature of an ICF imploded capsule is roughly proportional to the capsule’s implosion velocity. The implosion velocity is limited to values below ~400 km/s to prevent hydrodynamic instabilities from breaking up the imploding shell. This constraint on the implosion velocity keeps the central temperature at ~5 keV. At such relatively low temperature, the onset of ignition requires3 a product Pτ exceeding ~30 Gbar-ns. Using the results of Betti et al.4 applied to NIC experiments, current implosions have achieved Pτ ~ 10-18 Gbar-ns5 and a temperature of 3-4 keV. The highest Pτ, ~18 Gbar-ns, is about half of the ignition requirement. Time-resolved measurements of the compressed core X-ray emission indicate that the confinement time τ is 100-150 ps, suggesting that pressures of 100-130 Gbar have been achieved.6 To achieve ignition-relevant Pτ ≥ 30 Gbar-ns, pressures exceeding 300 Gbar are required.

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1 J.D. Lawson, 1957, Proceedings of the Physical Society London B 70: 6.

2 R. Betti, P.Y. Chang, B.K. Spears, et al., 2010, Thermonuclear ignition in inertial confinement fusion and comparison with magnetic confinement, Physics of Plasmas 17: 058102.

3 Ibid.

4 Ibid.

5 S. Glenzer, D.A. Callahan, A.J. MacKinnon, et al., 2012, Cryogenic thermonuclear fuel implosions on the National Ignition Facility, Physics of Plasmas 19: 056318, and R. Betti, 2012, “Theory of Ignition and Hydroequivalence for Inertial Confinement Fusion, Overview Presentation,” OV5-3, 24th IAEA Fusion Energy Conference, October 7-12, San Diego, Calif.

6 Ibid.



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I Technical Discussion of the Recent Results from the National Ignition Facility The Lawson criterion for ignition1,2 requires that the product Pt exceeds a ­threshold value that depends on the plasma temperature. The central temperature of an ICF imploded capsule is roughly proportional to the capsule’s implosion velocity. The implosion velocity is limited to values below ~400 km/s to prevent hydrodynamic instabilities from breaking up the imploding shell. This constraint on the implosion velocity keeps the central temperature at ~5 keV. At such relatively low tempera- ture, the onset of ignition requires3 a product Pt exceeding ~30 Gbar-ns. Using the results of Betti et al.4 applied to NIC experiments, current implosions have achieved Pt ~ 10-18 Gbar-ns5 and a temperature of 3-4 keV. The highest Pt, ~18 Gbar-ns, is about half of the ignition requirement. Time-resolved measurements of the com- pressed core X-ray emission indicate that the confinement time t is 100-150 ps, suggesting that pressures of 100-130 Gbar have been achieved.6 To achieve ignition- relevant Pt ≥ 30 Gbar-ns, pressures exceeding 300 Gbar are required. 1  J.D.Lawson, 1957, Proceedings of the Physical Society London B 70: 6. 2  R. Betti, P.Y. Chang, B.K. Spears, et al., 2010, Thermonuclear ignition in inertial confinement fusion and comparison with magnetic confinement, Physics of Plasmas 17: 058102. 3  Ibid. 4  Ibid. 5  S. Glenzer, D.A. Callahan, A.J. MacKinnon, et al., 2012, Cryogenic thermonuclear fuel implosions on the National Ignition Facility, Physics of Plasmas 19: 056318, and R. Betti, 2012, “Theory of Ignition and Hydroequivalence for Inertial Confinement Fusion, Overview Presentation,” OV5-3, 24th IAEA Fusion Energy Conference, October 7-12, San Diego, Calif. 6  Ibid. 219

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220 An Assessment of the Prospects for Inertial Fusion Energy The compressed core of an ICF implosion consists of a central hot plasma (the hot spot) surrounded by a cold dense shell. The total areal density determines the hot spot confinement by the surrounding dense shell. The NIF indirect-drive point design target is intended to implode at low entropy to produce high areal densities. To date, the highest areal density measured in the experiments was 1.25 g/cm2 (shot N120321), about 20 percent below the design value of 1.5 g/cm2. The areal density of the central hot spot is another important parameter because it determines the capacity of the hot spot to slow down the 3.5-MeV fusion alpha particles required to trigger the ignition process. Hot spot areal densities up to ~70 mg/cm2 have been inferred from the measurements of the neutron yields, hot spot size, ion temperature, and burn duration. Such values of the hot spot areal densities are enough to slow down more than 50 percent of the alpha particles at the low temperatures (~3-4 keV) measured in the experiments but are not sufficient for ignition since alpha particles need to be slowed down at higher temperatures between 5 and 10 keV. At these high temperatures, the hot spot areal density needs to exceed ~200 mg/cm2 to stop the fusion alphas. The highest temperature achieved to date is ~4 keV, which is close to the ~5 keV required for the onset of ignition. However, in the experiments, the highest temperature and highest areal densities were not achieved on the same implosion. The temperature was ~3 keV in the highest areal density implosion to date. Together with the areal density, pressure, and temperature, the neutron yield is a critical parameter determining the performance of an implosion. A rough estimate of the expected neutron yield from the compression alone, without accounting for alpha particle heating, in the absence of nonuniformities—that is, a one-dimensional (1-D), or clean, implosion—can be obtained from a simple formula7 relating the yield to the measured areal density and ion temperature by Yn16 ≈ ρR0.56 (T/4.7 )4.7 MDT / 0.24, where the neutron yield, Yn16, is expressed in units of 1016, the areal density ρR is in g/cm2, the temperature T in keV, and the DT mass MDT in mg. A straightforward substitution of ρR = 1 g/cm2, T = 4 keV, and MDT = 0.17 mg leads to a compression 1-D yield of 3.3 × 1015 neutrons, about 4-8 times higher than currently measured in the experiments (4 - 9 × 1014). An overall performance parameter used by the LLNL group is the experimental ignition threshold factor (ITFx).8 The ITFx has been derived by fitting the results of hundreds of computer simulations of ignition targets to find a measurable 7  R. Betti, P.Y. Chang, B.K. Spears, et al., 2010, Thermonuclear ignition in inertial confinement fusion and comparison with magnetic confinement, Physics of Plasmas 17: 058102. 8  B. Spears, S. Glenzer, M.J. Edwards, et al., 2012, Performance metrics for inertial confinement fusion implosions: Aspects of the technical framework for measuring progress in the National Igni- tion Campaign, Physics of Plasmas 19: 056316.

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A pp e n d i x I 221 parameter indicative of the performance with respect to ignition. An implosion with ITFx = 1 has a 50 percent probability of ignition. It can be shown9 that the ITFx represents the third power of the Lawson criterion ITFx = [(Pt)/(Pt)ig]3, where (Pt)ig(T) is a function of temperature, representing the minimum product Pt required for ignition at a given temperature.10 For the indirect-drive point- design target with 0.17 mg of DT fuel, the ITFx can be expressed11 in terms of the measured areal density and neutron yield according to  ρR   Yn  2.3 16 ITFx ≈   1.5   0.32     Both the areal density and neutron yield are the so-called no-burn or no-alpha values as they are related solely to the hydrodynamic compression without account- ing for alpha particle energy deposition. To date, the highest value of the ITFx is about 0.1 from implosions, with areal densities and neutron yields in the range 0.8-1.2 g/cm2 and 5-8 × 1014 respectively.12 9  R. Betti, 2012, “Theory of Ignition and Hydroequivalence for Inertial Confinement Fusion, Over- view Presentation,” OV5-3, 24th IAEA Fusion Energy Conference, October 7-12, San Diego, Calif.; B. Spears, S. Glenzer, M.J. Edwards, et al., 2012, Performance metrics for inertial confinement fusion implosions: Aspects of the technical framework for measuring progress in the National Ignition Campaign, Physics of Plasmas 19: 056316. 10  R. Betti, P.Y. Chang, B.K. Spears, et al., 2010, Thermonuclear ignition in inertial confinement fusion and comparison with magnetic confinement, Physics of Plasmas 17: 058102; R. Betti, “Theory of Ignition and Hydroequivalence for Inertial Confinement Fusion, Overview Presentation,” OV5-3, 24th IAEA Fusion Energy Conference, October 7-12, San Diego, Calif. 11  B. Spears, S. Glenzer, M.J. Edwards, et al., 2012, Performance metrics for inertial confinement fusion implosions: Aspects of the technical framework for measuring progress in the National Igni- tion Campaign, Physics of Plasmas 19: 056316. 12  S. Glenzer, D.A. Callahan, A.J. MacKinnon, et al., 2012, Cryogenic thermonuclear fuel implosions on the National Ignition Facility, Physics of Plasmas 19: 056318; J. Edwards, et al., 2012, “Progress Towards Ignition on the National Ignition Facility,” MR1.00001, 54th Annual Meeting of the American Physical Society, Division of Plasma Physics, Philadelphia, Pa., October 29-November 2.