The magnetic analogue method as used in the study of a cyclotron central region

Collective ion acceleration with electron rings

The potential distribution in cyclotron‐type gaps with liner (outer electrodes at ground potential) is determined via Schwarz‐Christoffel transformation, as well as by computer analysis (relaxation method) First‐order focusing formulas for both static, as well as time‐varying, potentials are derived In addition exact calculations were carried out by direct numerical integration of the equations of motion with a computer program The numerical data permitted an accurate evaluation of the validity of the analytical approximation, as well as further improvement of the theoretical formulas Focusing relations are presented in a generalized form which shows the scaling laws and is readily applicable to different types of particles, energies, or lens geometries As an example, the theory is applied to the axial motion of ions in a cyclotron

First-order theory of electrical focusing in cyclotron-type two-dimensional lenses with static and time-varying potentials.

Orbit dynamics in the central region have been studied with the aim of optimizing the design for beam quality and RF phase acceptance. Axial ion motion near the centre is dominated by the strong phase dependent RF electric forces at the dee gaps; the consequent restriction of the phase acceptance to ions lagging the RF voltage peak can be lifted both by using an asymmetric dee gap geometry and by the addition of third harmonic to the RF fundamental. A transition from six- to three-sector magnet geometry at the centre to increase the axial focusing was also tried, but was found to give rise to unacceptable ±9° phase oscillations if the dee gap were oriented to avoid the usual gap crossing resonance. Other effects producing coherent radial oscillations, such as first harmonic magnetic field components and dee-voltage asymmetries, have been assigned tight tolerances. The proposed design also makes possible near perfect centring for ions of all phases. Numerical orbit tracking has shown that a beam with the emittance of the external ion source can be accelerated to 20 MeV within 0.25 ? in. mrad for an RF phase band at least 25° wide: in the absence of inflationary effects at higher energies this would yield a 500 MeV beam with ±600 keV energy resolution.

Central Region Orbit Dynamics in the TRIUMF Cyclotron

A METHOD of computer solution is described for three-dimensional magnetostatic boundary value problems for isotropic piecewise homogeneous media, based on a finite-difference approximation of the variational and integral forms of Maxwell's equations in the vector potential. The method is illustrated by solving the problem on the influence of a cube with fixed permeability on an external homogeneous field.

Numerical simulation of linear magnetostatic fields

Computer Solutions for Three-Dimensional Electromagnetic Field Geometries

In connection with the University of Maryland electron ring accelerator project, possibilities of forming the electron ring in a cusped magnetic field were investigated. The results of numerical calculations as well as analytic theory are presented. In order to reduce ripples in cylindrically rotating beams, and maximum phase space acceptance, a special way of winding coils and use of ferro-magnetic material is proposed.

On Formation of an Electron Ring in a Cusped Magnetic Field

The isochronous cyclotron at the University of Maryland has been designed to allow computer control of all machine operations in a manner which permits unique operational flexibility. Digital control lines, 16 bits wide, run from various devices in the laboratory to a central multiplexer unit. From there, they are routed to either the operator's console or to a computer data bus. The data bus is attached to a small control computer which will be interfaced to an on-line IBM 360/44, and it will be capable of reading and setting machine controls as well as communicating with the machine operator. The software of the control computer will consist of a highly simplified time sharing system which will coordinate the execution of several independent software modules called 'tasks'. Each task will pertain to a particular control function, and the operating system will 'time share' among several tasks, allowing them to run concurrently. It is intended that this system will greatly simplify normal operations, allowing the operator greater freedom from menial chores.

D. Nelson

Papers

Computer Solutions for Three-Dimensional Electromagnetic Field Geometries

On Formation of an Electron Ring in a Cusped Magnetic Field

Computer Control for the Maryland Cyclotron