Beam focusing characteristic of an elliptical solenoid magnet in the presence of space charge

Development of microwave ion source and low energy beam transport system for high current cyclotron

“…This can not be achieved with axisymmetric solenoids. We have carried out detail beam dynamics simulations [10] and planned to add an elliptical solenoid before the inflector for matching the beam to the inflector entrance.…”

Self-consistent space charge dominated beam dynamics in a spiral inflector

“…(10) gives the self-potential in terms of optical coordinates u and h. The expression for the self-field of a rotated beam in the case of a linearly coupled system is also discussed in references [26,27] and in our recent work [28] in context of elliptical solenoid. The equations of motion associated with the Hamiltonian described in Eq.…”

Transport characteristics of a Glaser magnet for an axisymmetric and non-axisymmetric space charge dominated beam

“…28 and 29 and in our recent work in context of elliptical solenoid. 30 The space charge potential u S ðx; y; sÞ in the laboratory coordinate system is quadratic in x and y. It generates a coupled linear space charge force whose coefficients are functions of the transverse beam sizesr x ðsÞ andr y ðsÞ in the rotated frame and the tilt angle hðsÞ which changes as a function of the axial distance s. At any axial location s the beam sizesr x ðsÞ andr y ðsÞ in the rotated frame can be obtained from the beam sizes r x ðsÞ and r y ðsÞ in the laboratory frame, which are basically related to elements of the beam matrix r, i.e., r 11 and r 33 .…”