Strict Kinetic Treatment of the Electron Response to Spatial Field Disturbances in Nonequilibrium Plasmas

In generalization of former approaches for the simplified solution of the inhomogeneous electron Boltzmann equation a higher order solution technique has been developed. This technique is based on a multi-term expansion of the electron velocity distribution function and allows a strict study of the electron kinetics in plasmas acted upon by space-dependent electric fields. This solution technique is used to investigate the response of the plasma electrons to spatially limited disturbances of the electric field in weakly ionized plasmas of helium and mercury. By solving the kinetic equation with increasing order of the multi-term expansion the convergent solution of the kinetic problem and thus the strict spatial behaviour of the velocity distribution and of significant macroscopic properties of the electrons has been determined and analysed. Furthermore, the impact of higher order terms of the expansion has been revealed and the falsification of the velocity distribution and of related macroscopic properties has been evaluated when instead of the multi-term solution the simpler two-term solution of the kinetic equation is used.     

A critical exponent in a degenerate parabolic equation

We consider positive solutions of the Cauchy problem in $\mathbb{R\,}^n$ for the equation $$u_t=u^p\,\Delta u+u^q,\quad p\geq1,\; q\geq 1$$\nopagenumbers\end and show that concerning global solvability, the number q = p + 1 appears as a critical growth exponent. Copyright © 2002 John Wiley & Sons, Ltd.     

Montecarlo and boltzmann calculations of electron energy distributions in RF fields

Summary Detailed comparisons between Montecarlo and Boltzmann calculations of electron energy distributions in gases acted upon by RF fields are presented. Attention is turned to model gases of special theoretical interest but various calculations have also been made for real gases such as pure CO and He−CO mixtures. The analysis has shown that large discrepancies exist between energy distributions obtained with the two mentioned techniques under conditions of particular physical interest. The discrepancies are found to be the consequence of the two-term approximation and are expected to disappear if an appropriate multiterm solution of the Boltzmann equation is adopted.     

Interaction of atomic hydrogen with metal surfaces

Received: 23 March 1998/Accepted: 21 August 1998     

Fundamentals of a Technique for Determining Electron Distribution Functions by Multi-Term Even-Order Expansion in Legendre Polynomials. 2. Comprehensive Investigation of a Model Plasma

Applying the new technique for finding the converged solution of the Boltzmann equation in a weakly ionized plasma, which was developed in the first part of this paper, a comprehensive study of the electron velocity distribution function for a model plasma with elastic and exciting collisions is performed by solving the Boltzmann equation with increasing order of approximation. The purpose of this investigation is that of calculating the isotropic distribution f₀, the first contribution f₁ to the anisotropy of the velocity distribution, the important macroscopic quantities and, more generally, that of studying the total anisotropy as well as the changes of all these quantities when the approximation degree is enlarged beyond the 2 terms of the conventional Lorentz approximation. By varying some parameters of the model plasma, that is the electric field strength, the magnitude of the excitation cross section and the excitation threshold, the main features of plasmas in inert as well as molecular gases are modelled and the impact of these parameters on the mentioned quantities is analysed. Some of the converged results are compared with results of corresponding Monte Carlo simulations. The approximation degree required to find the converged values of isotropic distribution, main macroscopic quantities and electron distribution in the velocity space (and thus its real anisotropy) is estimated by solving the Boltzmann equation over wide parameter ranges.     

Mikrowellendiagnostik der Rauschtemperatur im Stickstoffplasma der Schwachstromsäule

This paper covers the calculation and measurement of the noise temperature for a stationary and axial homogeneous column plasma of a nitrogen discharge. The calculations are based on an electron energy distribution function which was obtained by the solution of the Boltzmann equation for a nitrogen plasma. In the low current column of this plasma the noise temperature was measured, using a Dicke-radiometer. The comparison between the calculated and measured values of the noise temperature shows a good agreement in the considered parameter region. Using a Maxwellian distribution, which was fitted to the real nitrogen plasma by the aid of the formulation of an energy balance for the electrons, the noise temperature was additionally determined in a approximate way and compared to the first calculations.     

Effect of the orientation of substituents on the chemical shifts of 13C. IV—13C NMR spectra of N,N-diisopropylamides and -thioamides

N,N-diisopropylamides and -thioamides show hindered rotation around the N? CH bonds, and the presence of mixtures of conformational isomers can be demonstrated at temperatures below 273 K in solution. ¹H and ¹³C NMR spectra of these conformers are measured and assigned. The ¹³C data serve to study through-space effects on ¹³C chemical shifts, which strongly depend on the conformations of the isopropyl groups. For amides, a through-space shielding of the N-methine carbons is found to exist only for conformers in which the methine hydrogen atom is spatially close to the oxygen atom. Chemical shift differences between amides and thioamides can be rationalized in terms of through-bond and through-space contributions, and serve for a better understanding of the shift differences in N,N-dialkylamides and -thioamides.     

Experimental determination of the total reaction cross section of the stellar nuclear reaction 16O + 16O

The total reaction cross section for ¹⁶O + ¹⁶O has been measured at six energies between E_c.m. = 6.8 and 11.9 MeV. Cross sections for the production of protons, alphas, neutrons, deuterons, ³¹S, ³⁰P, ¹²C(g.s.) + ²⁰Ne(g.s.) and the relative γ-yield were obtained with a variety of experimental methods. No ³H or ³He were found. All cross sections are normalized to ¹⁶O + ¹⁶O elastic scattering at θ_c.m. = 90°, which was measured separately with high precision between E_c.m. = 7.3 and 14.4 MeV. The elastic scattering and relative γ-yield of ¹²C + ¹²C were measured between E_c.m. = 3.9 and 7.5 MeV. The elastic scattering and neutron yield of ¹²C + ¹⁶O were measured between E_c.m. = 5.4 and 10.1 MeV.     

γγ Angular correlations perturbed by randomly reorienting hyperfine fields

The stochastic model of Blume for time-dependent hyperfine interactions is extended to randomly reorienting fields on the base of the work of Lynden-Bell. Two limiting cases are considered, the so-called diffusion and the strong collision model. Formulas are given for the perturbation factors of the angular correlation function which are valid for any fluctuation rate. Numerical calculations for the nuclear spinI=5/2 are presented.