The distribution function at low energy, u

The time evolution of high-energy electron distribution in an electron-beam-generated argon plasma is calculated. The distribution is derived for energy values above the threshold value of the first excited state (11.56 eV) from a reduced Boltzmann equation with no electron-neutral and electron-electron collisions. This equation can be numerically solved with a continuous source term taking account of all the new plasma electrons produced over the total energy range by primary electrons. As a result, the distribution reaches a steady state within a very short time tau s and its shape is pressure independent for a given current density, and a given energy of the beam, the evolution time tau s being inversely proportional to the pressure. Moreover, the energy distributions for given beam energy and pressure are in the same ratio as the primary-electron currents. An analytical approximation for the distribution tail is given as a function of the beam parameters (energy and current) and may be used for an electron-beam-generated Ar plasma as soon as these parameters are known. The branching ratios for energy deposition with electron-beam energy ranging between 103 and 106 eV is calculated. The relative influence of primary and secondary electrons is also discussed.

The flowing afterglow of an Ar-N2 mixed gas plasma gives rise to the recombination of nitrogen atoms according to the reaction N(4S)+N(4S)+(Ar-N2)KB(V') to N2(B3 pi g,v')+(Ar-N2) N2(B3 pi g,v') to N2(A3 Sigma uv")+hv (first positive system). Quantitative optical spectroscopy measurements of the emission spectra of the N2(B3 pi g-A3 Sigma u) transition have allowed determination of the total KB and individual KB(v') rates of atomic nitrogen recombination into excited N2 molecules in the B3 pi g state with upper vibrational levels v' between 1 and 12. The active nitrogen atoms are produced by dissociation of N2 molecules in a surface-wave-induced microwave discharge (2450 MHz) sustained in an open-ended dielectric tube. The discharge is operated at atmospheric pressure and the absorbed microwave power is about 200 W for a 5 cm discharge length.

We address the problem of the definition of the finite-volume correlation length. First, we study the large-N limit of the N -vector model, and we show the existence of several constraints on the definition if regularity of the finite-size scaling functions and correct anomalous behaviour above the upper critical dimension are required. Then, we study in detail a model in which the zero mode in prohibited. Such a model is a generalization of the fixed-magnetization Ising model which is equivalent to the lattice gas. Also in this case, we find that the finite-volume correlation length must satisfy appropriate constraints in order to obtain regular finite-size scaling functions, and, above the upper critical dimension, an anomalous scaling behaviour. The large-N results are confirmed by a one-loop calculation in the lattice φ 4 theory.