Incompressible turbulent flows are investigated in the framework of ideal magnetohydrodynamics. All the field quantities vary with only two spatial dimensions. Equilibrium canonical distributions are determined in a phase space whose co-ordinates are the real and imaginary parts of the Fourier coefficients for the field variables. In the geometry considered, the magnetic field and fluid velocity have variable x and y components, and all field quantities are independent of z. Three constants of the motion are found (one of them new) which survive the truncation in Fourier space and permit the construction of canonical distributions with three independent temperatures. Spectral densities are calculated. One of the more novel physical effects is the appearance of macroscopic structures involving long wavelength, self-generated, magnetic fields (‘magnetic islands’) for a wide range of initial parameters. Current filaments show a tendency toward consolidation in much the same way that vorticity filaments do in the guiding-centre plasma case. In the presence of finite dissipation, energy cascades to higher wavenumbers can be accompanied by vector potential cascades to lower wavenumbers, in much the same way as, in the fluid dynamic (Navier-Stokes) case, energy cascades to lower wavenumbers accompany enstrophy cascades to higher wavenumbers. It is suggested that the techniques may be relevant to theories of the magnetic dynamo problem and to the generation of megagauss magnetic fields when pellets are irradiated by lasers.

Continuing work in the design of shock ignition targets is described. Because of reduced implosion velocity requirements, low target adiabats, and efficient drive by short wavelength lasers, these targets produce high gain (> 100) at laser energies well below 1 megajoule. Effects of hydrodynamic instabilities like Rayleigh-Taylor or Richtmyer-Meshkov are greatly reduced in these low-aspect ratio targets. Of particular interest is the optimum ratio of ignitor to compression pulse energy. A simple pellet model and simulation-derived coupling coefficients are used to analyze optimal fuel assembly, and determine that shock ignition allows enough control to create theoretically optimum assemblies. The effects on target design due to constraints on the compression and ignitor pulse intensities are also considered and addressed. Significant sensitivity is observed from low-mode perturbations because of large convergence ratios, but a more powerful ignitor can mitigate this.

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The turbulent behavior of a two-dimensional dynamics of electrostatic drift-wave turbulence, proposed by Hasegawa and Mima, is explored analytically and numerically. A dual-cascade hypothesis leads to modal potential spectra which vary as k−14/3 at lower k and k−6 at higher k.