Slowing Down of Neutrons in Infinite Homogeneous Media

We have derived from the Boltzmann equation a new integral equation governing the slowing down of neutrons in a homogeneous mixture of atoms. The new equation reflects a view of the neutrons as propagating down the energy scale, whereas the Boltzmann equation expresses a collision balance. Unlike the Boltzmann equation the new equation lends itself to approximate solution by iteration and to the construction of an accurate variational principle for p, the resonance escape probability. Some numerical results are given

Resonance capture of neutrons in infinite homogeneous media

In a previous paper, a variational principle was introduced for 1 - p, the capture probability for neutrons slowing down in a homogeneous medium of infinite extent. In the present paper, the variational principle is used together with simple but accurate trial functions to obtain expressions for (i) corrections to the commonly used 'narrow resonance' formula for capture and (ii) interference effects in the capture of neutrons by closely spaced resonances

Time-dependent collision cascades

We use the linearized Boltzmann equation to discuss the time dependence of atomic collision cascades. The atoms are presumed to interact via a power-law potential, the power being denoted (-2/a). We wish to ascertain whether the equation, and/or certain special solutions, show striking changes in behavior at certain special values of a. We find a value of a which distinguishes energy-conserving cascades from anomalous cascades, and another which signals the failure of the linear approximation. Scaling, and also the emergence of similarity solutions, are discussed

Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling

The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $\rho(t)$ is studied using an expansion in $\rho$; in particular, in the limit $\gamma\rightarrow0^+$, the singularities in the expansion coefficients are analyzed to predict the asymptotic dependence of the electric field on the linear growth rate $\gamma$. Generically $|E_k|\sim \gamma^{5/2}$, as $\gamma\rightarrow0^+$, but in the limit of infinite ion mass or for instabilities in reflection-symmetric systems due to real eigenvalues the more familiar trapping scaling $|E_k|\sim \gamma^{2}$ is predicted.Comment: 13 pages (Latex/RevTex), 4 postscript encapsulated figures which are included using the utility "uufiles". They should be automatically included with the text when it is downloaded. Figures also available in hard copy from the authors ([email protected]

Spectral representations for the memory kernel characterizing self-diffusion

Approximate spectral representations are developed for the memory kernel which characterizes self-diffusion. These spectral representations are based upon approximate eigenfunctions constructed via the Rayleigh variational principle. A heuristic model is developed first in an effort to provide physical insight into the nature of the approximations employed, and then a number of specific trial functions are examined. These trial functions include sums of identical one- and two-particle functions as well as linear combinations of hydrodynamical variables. The results from these spectral representations indicate that the long-time behavior of the memory kernel (and thereby of the momentum autocorrelation function) is sensitive to the long-range effects of the interparticle potential. In addition, the equivalence of most of these spectral representations to specific low-order perturbation approximations is demonstrated.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45130/1/10955_2005_Article_BF01026732.pd

Aspects of Fokker-Planck transport

We apply to a simple example, taken from neutron thermalization, techniques we have been using in the study of Fokker-Planck transport of test particles. The example from neutron physics concerns the divergence of the series expressing diffusion length as a function of absorber concentration. In both cases, analytic continuation, and matched asymptotic expansion play a role

Aspects of Fokker-Planck transport

We apply to a simple example, taken from neutron thermalization, techniques we have been using in the study of Fokker-Planck transport of test particles. The example from neutron physics concerns the divergence of the series expressing diffusion length as a function of absorber concentration. In both cases, analytic continuation, and matched asymptotic expansion play a role