Drift momentum

Here A(t) denotes the vector potential of the laser field, p = (p1,p2) the final electron momenta, and k the drift momentum of the first electron in between ionization and recollision. The binding potential V of the first electron and the electron-electron interaction Vi2 enter (4.4) through their form factors... 

Charge carriers in a semiconductor are always in random thermal motion with an average thermal speed, given by the equipartion relation of classical thermodynamics as m v /2 = 3KT/2. As a result of this random thermal motion, carriers diffuse from regions of higher concentration. Applying an electric field superposes a drift of carriers on this random thermal motion. Carriers are accelerated by the electric field but lose momentum to collisions with impurities or phonons, ie, quantized lattice vibrations. This results in a drift speed, which is proportional to the electric field = p E where E is the electric field in volts per cm and is the electron s mobility in units of cm /Vs. 

In the fluid model the momentum balance is replaced by the drift-diffusion approximation, where the particle flux F consists of a diffusion term (caused by density gradients) and a drift term (caused by the electric field ) ... 

The fluid model is a description of the RF discharge in terms of averaged quantities [268, 269]. Balance equations for particle, momentum, and/or energy density are solved consistently with the Poisson equation for the electric field. Fluxes described by drift and diffusion terms may replace the momentum balance. In most cases, for the electrons both the particle density and the energy are incorporated, whereas for the ions only the densities are calculated. If the balance equation for the averaged electron energy is incorporated, the electron transport coefficients and the ionization, attachment, and excitation rates can be handled as functions of the electron temperature instead of the local electric field. 

In reality, the slip velocity may not be neglected (except perhaps in a microgravity environment). A drift flux model has therefore been introduced (Zuber and Findlay, 1965) which is an improvement of the homogeneous model. In the drift flux model for one-dimensional two-phase flow, equations of continuity, momentum, and energy are written for the mixture (in three equations). In addition, another continuity equation for one phase is also written, usually for the gas phase. To allow a slip velocity to take place between the two phases, a drift velocity, uGJ, or a diffusion velocity, uGM (gas velocity relative to the velocity of center of mass), is defined as... 

Thus, for Knudsen cosine scattering, / = 1, and for specular reflection, / = 0. Equation (59) may be solved for the drift velocity of the scattered molecule to give Uf = (1 - f)ut. The viscous force transmitted to the wall during gas collisions is the product of the number of collisions per second and the momentum change per collision,... 

Bhaga (B3) determined the fluid motion in wakes using hydrogen bubble tracers. Closed wakes were shown to contain a toroidal vortex with its core in the horizontal plane where the wake has its widest cross section. The core diameter is about 70% of the maximum wake diameter, similar to a Hill s spherical vortex. When the base of the fluid particle is indented, the toroidal motion extends into the indentation. Liquid within the closed wake moves considerably more slowly relative to the drop or bubble than the terminal velocity Uj, If a skirt forms, the basic toroidal motion in the wake is still present (see Fig. 8.5), but the strength of the vortex is reduced. Momentum considerations require that there be a velocity defect behind closed wakes and this accounts for the tail observed by some workers (S5). Crabtree and Bridgwater (C8) and Bhaga (B3) measured the velocity decay and drift in the far wake region. 

Consider a gas, near ambient pressure and temperature, forced by a small pressure gradient to flow through the channels of a packed bed of powder. At room temperature, a gas molecule can be adsorbed on a solid surface for an extremely short time but not less than the time required for one vibrational cycle or about 10 sec. When the adsorbed molecule leaves the surface it will, on the average, have a zero velocity component in the direction of flow. After undergoing one or several gas-phase collisions it will soon acquire a drift velocity equal to the linear flow velocity. These collisions and corresponding momentum exchanges will occur within one,... 

Several studies have been made of the behaviour of low energy positrons in gases under the influence of a static electric field e. The broad aim of this work has been to study the diffusion and drift of positrons in order to understand better the behaviour of the momentum transfer and annihilation cross sections at very low energies. The theoretical background has been given in section 6.1, and the diffusion equation with an... 

As shown in Figure 6.18, electron drift velocities below e/p = 1 Td (= 1017 V cm2) are at least four times larger than those for positrons. Bose, Paul and Tsai (1981) attributed this difference to higher momentum transfer cross sections for positrons than for electrons at very low (i.e. 

Fig. 11.2. Spatial distribution of the radiation as a function of the laser strength parameter ao. The peak of each emission lobe depends on the backward contribution. The lobes are centered at an angle tan 1(p /px) 2/ao in the plane of the polarization, with a width of 2/ao- p andp, are, respectively, the electron momentum perpendicular and parallel to the laser propagation axis. As ao is increased, the ponderomotive drift of the electron trajectory in the forward direction grows significantly, and the spatial distribution becomes more and more collimated...

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