| Abstract: | Approximate equations are derived for a narrow (paraxial) electron beam with a three-dimensional axis; these equations generalize
the familiar equations 1] to the case in which the field of the charge in the beam is important. A class of beams is distinguished
for which the problem reduces to ordinary differential equations.
The paraxial approximation for a narrow beam of electron trajectories in a given field is well known for the case in which
the characteristic dimension L* of the irregularities is much greater than a*, the characteristic width of the beam. The field of a three-dimensional beam can be included in the equations 1] if the
beam density ρ is nonuniform over lengths L*. The self-field of the beam was not actually taken into account in1]. In this paper we attempt to remedy this deficiency,
with partial success for an axisymmetric beam with a rectilinear axis 2].
Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 5, pp. 3–10, 1968. |
