Electron velocity

This frequency is a measure of the vibration rate of the electrons relative to the ions which are considered stationary. Eor tme plasma behavior, plasma frequency, COp, must exceed the particle-coUision rate, This plays a central role in the interactions of electromagnetic waves with plasmas. The frequencies of electron plasma waves depend on the plasma frequency and the thermal electron velocity. They propagate in plasmas because the presence of the plasma oscillation at any one point is communicated to nearby regions by the thermal motion. The frequencies of ion plasma waves, also called ion acoustic or plasma sound waves, depend on the electron and ion temperatures as well as on the ion mass. Both electron and ion waves, ie, electrostatic waves, are longitudinal in nature that is, they consist of compressions and rarefactions (areas of lower density, eg, the area between two compression waves) along the direction of motion. 

Fig. 6. Schematic energy levels of a soHd as a function of interatomic distance where the vertical line represents the equiUbrium spacing (68). A band of states obeying Fermi distribution is required by the PauH principle. High electron velocities and equivalent temperatures exist in conductors even when the...

The field, of strength E, is assumed in the z-direction the charge of the electron is e no magnetic field effects are considered, since the electron velocities are assumed small compared with the velocity of light.26 The Boltzmann equation is thus... 

Since the potential energy of the electrons in the ffee-electron gas is assumed to be zero, all the energy of the mobile electrons is kinetic. The electron velocity mf at the Fermi level E is given by... 

There are several other methods which have been used in the experimental determination of electron impact ionization cross sections. Nottingham and Bell76,77 developed a method specifically for the purpose of accurately determining the absolute electron impact ionization cross section of mercury. A semicircular electron velocity analyzer included in their design ensured that very high energy resolution was possible since only electrons of the required velocity emerged from the analyzer into the ionization chamber. Other aspects of the experiment are similar to the condenser plate method. 

In these equations, e and m are respectively the electron charge and mass, v is the electron velocity at energy E, e is the base of natural logarithm, and 6max is the maximum transferable energy. 

Note that Eq. (8.1) is remarkably independent of electron velocity. The stopping power -dE Idx = v-1(-dE /dt) does depend on velocity, but Frohlich and Platzman preferred not to use the stopping power due to a lack of knowledge of the actual tortuous path. Taking s = 80, ir = 5, d = 3.3A, and x = 10-11 s for water at 20°, they computed -dE /dt 1013 s-1, which is about three orders of magnitude less than that for excitation and ionization at higher energies. 

In the joint presence of an electric field E and a magnetic field B in a medium, the stationary electron velocity can be written as... 

B. Low-Energy Electron Emission in Fast Heavy-Ion-Atom Collisions 1. Longitudinal Electron Velocity Distributions... 

More details of the emission of ultralow- and low-energy electrons from fast heavy ion-atom collisions may be seen in the doubly differential cross sections as functions of the longitudinal electron velocity for increasing transverse electron velocity. Examples considered in this chapter include singly ionizing... 

Figure 10. Double differential cross sections (ddcs = Avj

Examination of the Fermi-Dirac distribution function Eq. (2.41) shows that the condition for applicability of the ideal-gas distribution to electron velocities is... 

The electron therefore has about 2 percent probability of penetrating the barrier. However, if it is considered that the electron oscillates with a wavelength of about 2 bohr radii (a0 = 5.3 x 1(Anm), the electron velocity calculated from its momentum p = h/X = mv, corresponds to h/2mao. It therefore collides h/2ma times per second (i.e. 1.3 x 1017) with the barrier and penetrates after 1(A15 seconds, and moves freely through the crystal. 

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