Accession Number : AD0710407

Title :   CONVOLUTION ANALYSIS OF ELECTRON IMPACT EXPERIMENTS,

Corporate Author : MCDONNELL DOUGLAS ASTRONAUTICS CO ST LOUIS MO EASTERN DIV

Personal Author(s) : Cowperthwaite,Ronald L. ; Myers,Howard

Report Date : 01 JUL 1970

Pagination or Media Count : 41

Abstract : Electron impact experiments are analyzed from the standpoint of the influence of the electron beam energy distribution on the measurements. A generalized electron energy distribution function is formulated. Special cases of this distribution function yield analytical representations of operational electron guns. The energy distribution of the gun is found to strongly affect the salient features of the cross section. A procedure is thence developed for unfolding the true cross section from impact measurements by removing the distortion of the electron beam. Comparisons with measured data are presented. The response function for a simple retarded gun is derived. The unfolding equation is found to be a first order differential equation. This is in strong contrast to the simple accelerated electron gun which gives an algebraic equation for the unfolding equation. The stability of the integration, with respect to errors in the initial value, is evaluated. The solution is found to be exponentially unstable when forward integration is used, and exponentially stable when backward integration is used. An important practical consequence of the backward integration stability is that it permits estimating the initial value of the true cross section with the folded cross section. (Author)

Descriptors :   (*ELECTRON BEAMS, RESOLUTION), ELECTRON GUNS, PARTIAL DIFFERENTIAL EQUATIONS, INTEGRAL EQUATIONS, NUMERICAL INTEGRATION

Subject Categories : Particle Accelerators
      Nuclear Physics & Elementary Particle Physics

Distribution Statement : APPROVED FOR PUBLIC RELEASE