A Precise Beam Dynamics Model of the Psi Injector 2

The Injector 2 at Paul Scherrer Institut (PSI) is a 72 MeV separate sector cyclotron producing a high intensity proton beam up to 3 mA CW, which is subsequently injected to the 590 MeV Ring Cyclotron. The injection energy of the pre-bunched beam is 870 keV at an intensity of 10 to 11 mA. In this paper we describe initial conditions for the Injector 2 to obtain a matched beam with space charge that is coupled in the transverse-longitudinal plane. The precise beam dynamics model is based on the OPAL (Object Oriented Parallel Accelerator Library) simulation code, a tool for charged-particle optics calculations in large accelerator structures and beam lines including 3D space charge. INTRODUCTION The Injector 2 (see Figure 1) is a high intensity proton cyclotron producing high quality beam reaching 72 MeV that is then injected into the 590 MeV Ring cyclotron. It is composed of four sector magnets and accelerating cavities. The injection energy is 870 keV with 2π mm × mrad beam emittance and a dc current of 11 mA. The accelerator operates at a frequency of 50.63 MHz . Figure 1: PSI Injector 2. The better understanding of space charge effects in isochronous cyclotrons, such as the Injector 2, is still of great interest. Due to space charge forces combined with radial and longitudinal coupled motion, a stationary compact beam is developed within the first several turns of the injector and remains quasi stationary until extraction. Currently, there is no self-consistent theory/model, to match a bunched beams with non-linear space charge in cyclotrons, hence we have to rely on numerical methods. For this purpose, we use open source code OPAL [1]. In the first stage ∗ [email protected] of this research the stationary initial distribution with space charge based on theoretical model Baumgarten [2, 3] is found. INITIAL CONDITIONS Tune Diagram and Accelerated Equilibrium Orbit The calculations for the tunes νr and νz , as shown in Figure 2, matching well the Injector 2 design values. In this calculation we used measured mid-plane fields. The Accelerated Equilibrium Orbit (AEO) is shown in Figure 3. Figure 2: Tune diagram for Injector 2. Figure 3: AEO of Injector 2. Initial Matched Distribution with Linear Space Charge Forces We obtained a matched sigma-matrix σ for given emittances iteratively using the linearized model as described in [2, 3]. MOPWO057 Proceedings of IPAC2013, Shanghai, China ISBN 978-3-95450-122-9 1020 C op yr ig ht c ○ 20 13 by JA C oW — cc C re at iv e C om m on sA tt ri bu tio n 3. 0 (C C -B Y3. 0) 04 Hadron Accelerators A13 Cyclotrons The decoupling transformation of the ”symplex” (i.e. ”Hamiltonian matrix”) is S = σγ0 , where γ0 being the symplectic unit matrix [3]. The decoupling results are in S′ = RSR−1. N random vectors ψk are generated with independent variables of Gaussian distribution. We then scale with the corresponding variances given by the root of the diagonal elements of σ0. The covariance matrix of the produced random vectors σ0 = −Sγ0 followed by inverse transformation S = R−1S′R, gives the desired correlated distribution