A Semi Analytical Investigation of the Paracial Ray Equation

Abstract

A new common procedure for solving paraxial ray equation of acharge particle going thiough a pure magnetic field has been introduced.The-prlsented approach ii nrainly concem with using power seriesmethod usually ,."a to solve differential equations of special forms. Inorder to rnake the power series method applicable for solving equationsof soft of paraxial ray equation, the domain of solution, the axialcoordinate where the magnetic field exist, are descretized into severalsubdomains, such that-magnetic field can consider to be flxedthroughout each of these subdomains. computer has been adopted to beu n,uin tool for execution i, order to make prqsent technique of apractical impoftance. The outputs of this procedure are conlpared rvithsome of the available conespondence anall'tical equations' The resultsclearly shorvn that the neu'technigue have an accurate results and hasthe i.op..ry of analytical proce{ure. Anyrvay, the algorithnr ofpr.r.nt.d method are formulated to a subroutine written in Fortrarr-77iungrog" rvhich nray used to replace any of the subroutines that work,n,ith ,rumerical ntethods in the well knorvn software. Hott'ever, oneu'ould not face the nurlerical errors any more.