Electric fields collisions

In diffusion charging, particles are charged by unipolar ions (ions having the same sign) in the absence of an applied electric field. Collisions of ions and particles occur as a result of random thermal motion of the ions, the brownian motion of the particles being generally neglected. 

When ions move under equilibrium conditions in a gas and an external electric field, the energy gained from the electric field E between collisions is lost to the gas upon collision so that the ions move with a constant drift speed v = KE. The mobility K of ions of charge e in a gas of density N is given in tenns of the collision integral by the Chapman-Enskog fomuila [2]... 

It is helpful to distinguish three different types of problem to which Newton s laws of motion may be applied. In the simplest case, no force acts on each particle between collisions. From one collision to the next, the position of the particle thus changes by v,5f, where v, is the (constant) velocity and 6t is the time between collisions. In the second situation, the particle experiences a constant force between collisions. An example of this type of motion would be that of a charged particle moving in tr uniform electric field. In the third case, the force on the particle depends on its position relative to the other particles. Here the motion is often very difficult, if not impossible, to describe analytically, due to the coupled nature of the particles motions. 

If the electrodes are moved closer together, the positive column begins to shorten as it moves through the Faraday dark space because the ions and electrons within it have a shorter distance through which to diffuse. Near the cathode, however, the electric-field gradient becomes steeper and electrons from the cathode are accelerated more quickly. Thus atom excitation through collision with electrons occurs nearer and nearer to the cathode, and the cathode glow moves down toward the electrode. 

The multiple energetic collisions cause molecules to break apart, eventually to form only atoms, both charged and neutral. Insertion of sample molecules into a plasma discharge, which has an applied high-frequency electric field, causes the molecules to be rapidly broken down into electronically excited ions for all of the original component atoms. 

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. 

The collision terms may be simplified by using the condition that mjM is very small this leads to the Lorentz approximation. If there were no electric field, the equilibrium situation would be one in which the mean kinetic energy of the electrons would be equal to that of the... 

For collision frequencies large compared with the frequency of the electric field, the current remains in phase with the electric field in the reverse case, the current is 90° out of phase. The in-phase component of the current gives rise to an energy loss from the field (Joule heating loss) microscopically, this is seen to be due to the energy transferred from the electrons to the atoms upon collision. 

Fig. 4.1. The La line of the H atom and its structure in the constant electric field (a) and the rotational structure of the vibrational transition (b). Wavy arrows show collision-induced transitions, thick horizontal arrows indicate the optical transitions that mutually interfere.

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