The physics of thermonuclear ignition in inertial confinement fusion (ICF) is presented in the familiar frame of a Lawson-type criterion. The product of the plasma pressure and confinement time Pτ for ICF is cast in terms of measurable parameters and its value is estimated for cryogenic implosions. An overall ignition parameter χ including pressure, confinement time, and temperature is derived to complement the product Pτ. A metric for performance assessment should include both χ and Pτ. The ignition parameter and the product Pτ are compared between inertial and magnetic-confinement fusion. It is found that cryogenic implosions on OMEGA [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] have achieved Pτ∼1.5 atm s comparable to large tokamaks such as the Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)] where Pτ∼1 atm s. Since OMEGA implosions are relatively cold (T∼2 keV), their overall ignition parameter χ∼0.02–0.03 is ∼5× lower than in JET (χ∼0.13), where the average temperature is about 10 keV.

X-ray 1-3 and radio 4-6 observations of the supernova remnant Cassiopeia A reveal the presence of magnetic fields about 100 times stronger than those in the surrounding interstellar medium. Field coincident with the outer shock probably arises through a nonlinear feedback process involving cosmic rays 2,7,8 . The origin of the large magnetic field in the interior of the remnant is less clear but it is presumably stretched and amplified by turbulent motions. Turbulence may be generated by hydrodynamic instability at the contact discontinuity between the supernova ejecta and the circumstellar gas 9 . However, optical observations of Cassiopeia A indicate that the ejecta are interacting with a highly inhomogeneous, dense circumstellar cloud bank formed before the supernova explosion 10-12 . Here we investigate the possibility that turbulent amplification is induced when the outer shock overtakes dense clumps in the ambient medium 13-15 . We report laboratory experiments that indicate the magnetic field is amplified when the shock interacts with a plastic grid. We show that our experimental results can explain the observed synchrotron emission in the interior of the remnant. The experiment also provides a laboratory example of magnetic field amplification by turbulence in plasmas, a physical process thought to occur in many astrophysical phenomena.High-resolution X-ray images and radio polarization maps of Cassiopeia A show two distinct strong magnetic field regions [3][4][5][6]12 . Narrow X-ray filaments, a fraction of a parsec in width, are observed at the outer shock rim at a radius of about 2.5 pc. These structures are produced by synchrotron radiation from ultrarelativistic electrons (with teraelectronvolt energy) and can be explained by magnetic fields of the order of 100 µG or more 2,3 . The interior of the remnant contains a disordered shell (about 0.5 pc in width at a radius of 1.7 pc) of radio synchrotron emission by gigaelectronvolt electrons 4 . The inferred magnetic field in these radio knots is a few milligauss, about 100 times higher than expected from the standard shock compression of the interstellar medium 15 . Optical observations of Cassiopeia A show the presence of both rapidly moving (5,000-9,000 km s −1 ) and essentially stationary dense knots. Although the moving knots themselves have a high velocity, their overall pattern is nearly stationary 10 . This led to the suggestion 10 that a dense pre-existing inhomogeneous stationary cloud bank could be present. New rapidly moving knots predominantly appear at a position broadly coincident with the shell of bright radio emission 6 . Sizes of the observed small-scale features within the shell range from 0.01 to 0.1 pc arranged in larger patterns extending to 0.5-2 pc (ref. 16). Interaction between the ejecta and the cloud bank may excite the turbulence that amplifies the magnetic field and makes Cassiopeia A an exceptionally bright radio source 4 . The interaction is akin to the Rayleigh-Taylor instability otherwise proposed as a source of turbulenc...

A multidimensional measurable criterion for central ignition of inertial-confinement-fusion capsules is derived. The criterion accounts for the effects of implosion nonuniformities and depends on three measurable parameters: the neutron-averaged total areal density (rhoR(n)(tot)), the ion temperature (T(n)), and the yield over clean (YOC=ratio of the measured neutron yield to the predicted one-dimensional yield). The YOC measures the implosion uniformity. The criterion can be approximated by chi=(rhoR(n)(tot))(0.8) x (T(n)/4.7)(1.7)YOC(mu)>1 (where rhoR is in g cm(-2), T in keV, and mu approximately 0.4-0.5) and can be used to assess the performance of cryogenic implosions on the NIF and OMEGA. Cryogenic implosions on OMEGA have achieved chi approximately 0.02-0.03.

We summarize recent additions and improvements to the high energy density physics capabilities in FLASH, highlighting new non-ideal magnetohydrodynamic (MHD) capabilities. We then describe 3D Cartesian and 2D cylindrical FLASH MHD simulations that have helped to design and analyze experiments conducted at the Vulcan laser facility. In these experiments, a laser illuminates a carbon rod target placed in a gas-filled chamber. A magnetic field diagnostic (called a Bdot) employing three very small induction coils is used to measure all three components of the magnetic field at a chosen point in space. The simulations have revealed that many fascinating physical processes occur in the experiments. These include megagauss magnetic fields generated by the interaction of the laser with the target via the Biermann battery mechanism, which are advected outward by the vaporized target material but decrease in strength due to expansion and resistivity; magnetic fields generated by an outward expanding shock via the Biermann battery mechanism; and a breakout shock that overtakes the first wave, the contact discontinuity between the target material and the gas, and then the initial expanding shock. Finally, we discuss the validation and predictive science we have done for this experiment with FLASH.