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

Compact high current proton cyclotron and associated beam dynamics

“…Simulations performed on the beam matching indicate that for better beam transmission and less emittance growth through spiral inflector, one needs convergent phase ellipses with different orientations in the two transverse planes [14]. Thus to match an axisymmetric beam from the ion source to the entrance of the spiral inflector we have also planned to used an elliptical solenoid at a suitable location between the second solenoid and inflector.…”

“…Details of design and optimization procedure of a spiral inflector are discussed in ref. [14,15]. Here we will discuss only important parameters and results of beam dynamics simulation.…”

“…We have obtained differential equations for the beam envelopes u m and h m in the u and h directions assuming particle trajectories to remain very close to the axis. The paraxial equations of motion of a particle of charge q and mass m in the self and applied fields in a spiral inflector can be written as [14]…”

“…To obtain ϕ s (u, h, s), it is needed to have a new coordinate system (u t , h t , s) rotated by an angle θ with respect to the optical coordinate system where the motions become uncoupled. At this position the space charge potential can be easily calculated assuming a uniform density beam and then can be transformed to the original coordinate system [14] as…”