Dynamics of electrons in a half-space with cylindrical electro-static field

Motion of electrons in a half space with cylindrical electro-static field, which is associated with electron emission devices, is investigated. The eq uation of motion is given as a nonlinear ordinary differential equation of the second order, Statistical behavior of electrons exhibits a dilatational invariance property of the system. An approximate formula of absorbed poin ts distribution of the electrons is given by the solution of a Fredholm int egral equation of the second kind. Since its kernel function is [0, 1) char acteristrics function, we give its finite sum expression using the properti es of B-spline, which is the iterated kernel function of its Neumann series solution.