Function Of Normalized Energy Research Articles

Analysis of Energy Distribution of Photoelectrons in Metals: Comparison with Experiment for Molybdenum

The energy distribution of photoelectrons, emitted from the surface of a metal has been analyzed on the basis of four models of absorption of a photon by an electron, including the ones, proposed by Fowler and DuBridge. In contrast to some earlier work the transmission coefficient as a function of normal energy has been accounted for. The experimental energy distribution, of photoelectrons for molybdenum is in better agreement with the theoretical (DuBridge, as modified herein) energy distribution corresponding to the enhancement of total (not normal) energy of an electron by the absorption of a photon, than that corresponding to the enhancement of normal energy. The theoretical results do not depend appreciably on the site of absorption of a photon by an electron (on the surface or inside the metal). The dependence of mean energy on frequency of radiation has also been discussed. The original derivation by DuBridge has been improved by discarding a couple of unjustified assumptions made by him.

A normalized energy function for fast transient stability assessment

New definitions of average angle centre and angle radius are proposed to develop a transient stability evaluation method which is fast and accurate for transient stability assessment. These two definitions are further developed to introduce two novel concepts, the normalized generators’ equations of motion and normalized energy function (NEF), which in turn allow the assessment of critical clearing time (CCT) of system contingencies in a new approach. Case studies on the 10-generator New England, 17-generator Iowa and 50-generator test power systems are reported to verify the validity of the normalized energy function method. The method is very fast requiring only almost 0.5 s for the stability evaluation of contingencies in the 50-generator test system.

An analytical formula and important parameters for low-energy ion sputtering

Sputtering yields for different ions and materials at low ion energies have a similar energy dependence. Due to this similarity, yield data can be characterized by a normalized energy function and two parameters for each ion target combination. One of these parameters is the threshold energy. An energy scaling can be based on this parameter. The other parameter is a multiplication factor. Both parameters depend mainly on the ion and target mass M1 and M2 and on the surface binding energy EB. An analytic expression for the normalized functions and both the parameters is given. This empirical relation also allows an estimate of unknown sputtering data, if M1, M2, and EB are noted. A physical interpretation of the empirical relation is given for the case M1≪M2, as in this case special collision processes which dominate the sputtering can be identified.

Spatially Dependent Energy Distributions for Electrons Drifting Through a Gas in a Uniform Electric Field

The steady-state distribution function is obtained for electrons initially emitted from a point source into a neutral gas and which subsequently drift under the influence of a uniform dc electric field while undergoing elastic collisions with the gas atoms. The usual approximations, regarding the distribution function as almost spherical in velocity space, and regarding the fractional energy gain or loss by an electron upon collision as small are retained. However, the terms in the Boltzmann transport equation involving spatial derivatives of the distribution, which are usually assumed small in comparison to the field and collision terms, are treated exactly. The distribution function is given as a sum of energy modes, each of which decay with distance from the source. The lowest of these modes is the far-distant distribution, while the higher ones, which decrease more rapidly with distance describe the decay of the initial source energy distribution. The complete distribution is obtained in terms of known functions in the case of an energy-independent collision frequency, whereas in the energy-independent cross-section case, only the lowest mode is obtained. The far-distant part of the distribution function is compared with the usual approximate expression which is obtained when the gradient terms are considered small and which is expressed as the density times a normalized energy function. It is shown, that when the gradient terms are correctly considered, the far-distant distribution in energy becomes position-dependent. Furthermore, the deviation from the approximate theory becomes larger, the further the electrons are off the geometrical axis. This position dependence is most important when the electron energy is large in comparison to thermal energies. The interpretation of Townsend method for the determination of the ratio of the diffusion coefficient to the mobility, $\frac{D}{\ensuremath{\mu}}$, is re-examined on the basis of this more exact theory. It is shown that the error in $\frac{D}{\ensuremath{\mu}}$ that results from using the conventional interpretation of this method under typical experimental conditions is never more than about 20%.