Dragan Toprek

Theory of the central ion trajectory in the spiral inflector

Abstract This paper presents the analytical and numerical theory of the central ion trajectory through the spiral inflector. Analytical expressions for the equations which describe the central ion trajectory are derived.

Some optical properties of the spiral inflector

Abstract This paper compares some optical properties of different spiral inflectors using the program CASINO. The electric field distribution in the inflectors has been numerically calculated from an electric potential map produced by the program RELAX3D. The magnetic field is assumed to be constant. We have also made an effort to minimize the inflector fringe field using the RELAX3D program.

Design of the central region in the Gustaf Werner cyclotron at the Uppsala university

This paper describes the design of the central region in the Gustaf Werner cyclotron for h ¼ 1; 2 and 3 modes of acceleration. The electric field distribution in the inflector and in the four acceleration gaps has been numerically calculated from an electric potential map produced by the program RELAX3D. The geometry of the central region has been tested with the computations of orbits carried out by means of the computer code CYCLONE. The optical properties of the spiral inflector and the central region were studied by using the programs CASINO and CYCLONE, respectively. r 2002 Elsevier Science B.V. All rights reserved.

Space charge effect in the spiral inflector

Abstract This paper presents the analytical and numerical theory of the space charge effects in the beam in the spiral inflector. It considers a simplified model of a “straight” cylindrical beam by using a uniform particle distribution. Numerical results represented in this paper are obtained by using a modified version of the program CASINO.

Centering of the ion trajectory in the cyclotron

Abstract In this paper we present the theory of the horizontal motion ions through the acceleration gap in the case of a static magnetic field and time-varying electric field. It also describes the motion of the center of the ion trajectory through the acceleration gap and also during the acceleration process. The result also describes analytically the angle through which the ion passed (so called “flying angle”) between two acceleration gaps. That angle can be measured from the center of the ion trajectory or from the center of the cyclotron. The analysis shows that the “flying angle” of the ions measured in these two reference systems is not same. Namely, the “flying angle” of the ion measured from the center of its trajectory is bigger than in the case when the “flying angle” is measured from the center of the cyclotron. It shows that difference between “flying angle” in these two reference systems becomes less and less during acceleration process.

Design of the central region for axial injection in the VINCY cyclotron

Abstract This paper describes the design of the central region for h = 1, h = 2 and h = 4 modes of acceleration in the VINCY cyclotron. The result which is worth reported in that the central region is unique and compatible with the three above mentioned harmonic modes of operation. Only one spiral type inflector will be used. The central region is designed to operate with two external ion sources: (a) an ECR ion source with the maximum extraction voltage of 25 kV for heavy ions, and (b) a multicusp ion source with the maximum extraction voltage of 30 kV for H− and D− ions. Heavy ions will be accelerated by the second and fourth harmonics, D− ions by the second harmonic and H− ions by the first harmonic of the RF field. The central region is equipped with an axial injection system. The electric field distribution in the inflector and in the four acceleration gaps has been numerically calculated from an electric potential map produced by the program RELAX3D. The geometry of the central region has been tested with the computations of orbits carried out by means of the computer code CYCLONE. The optical properties of the spiral inflector and the central region were studied by using the programs CASINO and CYCLONE respectively. We have also made an effort to minimize the inflector fringe field using the RELAX3D program.

Beam orbit simulation in the central region of the RIKEN AVF cyclotron

Abstract This paper describes the modification design of the central region for h =2 mode of acceleration in the RIKEN AVF cyclotron. we made a small modification to the electrode shape in the central region for optimization of the beam transmission. The central region is equipped with an axial injection system. The spiral type inflector is used for axial injection. The electric field distribution in the inflector and in four acceleration gaps has been numerically calculated from an electric potential map produced by the program RELAX3D. The magnetic field is measured. The geometry of the central region has been tested with the computations of orbits carried out by means of the computer code CYCLONE. The optical properties of the spiral inflector and the central region are studied by using the program CASINO and CYCLONE, respectively. We have also made an effort to minimize the inflector fringe field effects using the RELAX3D program.

Design of the central region in the Warsaw K-160 cyclotron

This paper describes the design of the central region for h=2 and 3 modes of acceleration in the Warsaw K-160 cyclotron. The central region is unique and compatible with the two above-mentioned harmonic modes of operation. Only one spiral type inflector will be used. The electric field distribution in the inflector and in the four acceleration gaps has been numerically calculated from an electric potential map produced by the program RELAX3D. The geometry of the central region has been tested with the computations of orbits carried out by means of the computer code CYCLONE. The optical properties of the spiral inflector and the central region were studied by using the programs CASINO and CYCLONE, respectively.

Effects of Magnet Errors in the ILC 14 mrad Extraction Line

The ILC baseline extraction line is designed for 14 mrad horizontal crossing angle between e{sup +} and e{sup -} colliding beams at Interaction Point (IP). The extraction optics in the Interaction Region (IR) includes a detector integrated dipole field (anti-DID) to reduce orbit perturbation caused by the detector solenoid and minimize detector background. This paper presents a study of random field and alignment errors in the extraction magnets, compensation of the induced orbit perturbation, and effects of errors on extraction beam power loss. The results are obtained for the baseline ILC energy of 500 GeV center-of-mass and three options of beam parameters.

Comment on “Theory of the central ion trajectory in the spiral inflector”

In Refs. [1–4] the theory of ion trajectory through a spiral inflector was studied in a very detailed way, but some mathematical details as to how the differential equation of ion motion can be solved are still missing. In Ref. [5] these mathematical details are presented, but the careful reader will notice a mathematical inconsistency which can be the source of the wrong conclusion that an analytical solution of the central ion trajectory through the spiral inflector is not unique. As the author of Ref. [5] I feel a need and responsibility to eliminate that mathematical inconsistency. In Ref. [5] the differential equation of the projection of the ion trajectory into the x–y plane, Eq. (25), is not solved correctly from the mathematical point of view, but its parametric solutions (Eqs. (36a) and (36b)) are correct. We will try to solve again Eq. (25), but now in a consistent way from the mathematical point of view. We will use the same symbols as Ref. [5] with the same meanings. 2. Correct solution of the differential equation