The effects of the highly damped modes in the energy and reaction rates in a plasma are discussed. These modes, with wavenumbers k ≫ k D , even being only weakly excited, with less than k B T per mode, make a significant contribution to the energy and screening in a plasma. When the de Broglie wavelength is much less than the distance of closest approach of thermal electrons, a classical analysis of the plasma can be made. It is assumed, in the classical analysis, withh → 0, that the energy of the fluctuationshω ≪ k B T .Using the fluctuation-dissipation theorem, the spectra of fluctuations with h = 0 is appreciably decreased. The decrease is mainly for the highly damped modes at high frequencies (∼ 0.5 − 3k B T ). Reaction rates are enhanced in a plasma due to the screening of the reacting ions. This is taken into account by the Salpeter factor, which assumes slow motion for the ions. The implication of including the highly damped modes (withh = 0) in the nuclear reaction rates in a plasma is discussed. Finally, the investigations presently done on these effects in particle simulations with the sheet model and the multiparticle quantum simulation code are described.

A stable, efficient algorithm to calculate numerically a Fresnel diffraction image, given any two-dimensional aperture or obstacle, is introduced. The algorithm predicts both the intensity and relative phase of the image. An alternate faster algorithm is presented for a limited class of apertures. Also examined are images formed from a variety of aperture shapes. Using this computational technique, plots on the complex plane are shown to give insight into Fresnel diffraction. With additional modifications to accept parameters from an experimental apparatus, the algorithms model Fresnel diffraction for laboratory situations. In addition, the algorithms are suitable for numerical implementation on personal computers. © 1996 American Institute of Physics.

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