Contents of the Supplement B to Vol. 52 (2002)

Table of Contents

Contents of the Supplement B to Vol. 52 (2002)     

Mutual attraction of laser beams in plasmas: braided light

The energy loss of slow ions during grazing scattering from a LiF(100) surface as a function of the projectile atomic number Z1 is observed to show oscillations similar to those occurring in metals. A model of stopping of ions in an electron gas where screening is calculated from density functional theory reproduces well the experimental data. The same model gives good agreement with the energy loss obtained in transmission experiments performed with H and He projectiles. Analysis of these results allows us to gain new insights in the stopping of slow ions in ionic crystals.     

Ionization-induced electron trapping in ultrarelativistic plasma wakes

The onset of trapping of electrons born inside a highly relativistic, 3D beam-driven plasma wake is investigated. Trapping occurs in the transition regions of a Li plasma confined by He gas. Li plasma electrons support the wake, and higher ionization potential He atoms are ionized as the beam is focused by Li ions and can be trapped. As the wake amplitude is increased, the onset of trapping is observed. Some electrons gain up to 7.6 GeV in a 30.5 cm plasma. The experimentally inferred trapping threshold is at a wake amplitude of 36 GV/m, in good agreement with an analytical model and PIC simulations.     

Influence of the vacuum level upon the growth of carbon nanotubes on silicon carbide surface

We have investigated the influence of the vacuum level upon the growth of carbon nanotubes (CNTs) on 6H-SiC () surface.CNTs of about 160 nm in length were formed densely and uniformly on the 6H-SiC surface during annealing at 1700 °C in a high vacuum (∼10⁻² Pa). CNTs of about 1 μm in length were formed during annealing at 1700 °C in an ultra-high vacuum (∼10⁻⁷ Pa). However, CNTs were not formed and SiO₂ layers were formed on the SiC surface at 1700 °C in air. It is found that longer CNTs can grow up in an ultra-high vacuum, moreover, a little aligned and low-density graphite layers, or carbon nanofibers can also grow up.     

Origin of the Landau-Lifshitz hydrodynamic fluctuations in nonequilibrium systems and a new method for reducing the Boltzmann equation

The Landau-Lifshitz fluctuating fluxes in fluctuating hydrodynamics are derived from the deterministic Boltzmann equation with the aid of a reduction method developed by Fujisaka and Mori. Thus it is shown that the hydrodynamic fluctuations innonequilibrium systems are generated by the reduction of variables from the-space distribution function to its five momentum moments, i.e., the hydrodynamic variables. This differs from the Bixon-Zwanzig and Fox-Uhlenbeck theories, in which the Landau-Lifshitz fluctuating fluxes are derived from the molecular fluctuating force in thestochastic Boltzmann-Langevin equation, which is, however, negligible in nonequilibrium systems. Thus the present method improves the Chapman-Enskog reduction method so as to include the hydrodynamic fluctuations generated by the reduction of variables.Supported in part by the Scientific Research Fund of the Ministry of Education.     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.