Beam dynamics in high intensity cyclotrons including neighboring bunch effects: Model, implementation, and application

Space-charge effects, being one of the most significant collective effects, play an important role in high intensity cyclotrons. However, for cyclotrons with small turn separation, other existing effects are of equal importance. Interactions of radially neighboring bunches are also present, but their combined effects have not yet been investigated in any great detail. In this paper, a new particle in the cell-based self-consistent numerical simulation model is presented for the first time. The model covers neighboring bunch effects and is implemented in the three-dimensional object-oriented parallel code OPAL-cycl, a flavor of the OPAL framework. We discuss this model together with its implementation and validation. Simulation results are presented from the PSI 590 MeV ring cyclotron in the context of the ongoing high intensity upgrade program, which aims to provide a beam power of 1.8 MW (CW) at the target destination.

Figure 1

Comparison of calculated turn separation for centroid particles before (red line) and after (blue line) upgrade of the PSI ring cyclotron. The main cavity voltage is set to 0.735 and 0.9 MV for aluminum and copper, respectively, while the flattop is set to 11.2% of the main voltage.

Figure 2

Schematic plot of the top view of the three coordinates frames. The red curve is the orbit of bunch center, the blue area represents bunch shape, and the gray area is the hill region of the magnetic field.

Figure 3

The radial space-charge field $E_{\mathrm{sc}}(r)$ of the multiple Gaussian beams at the central beam region. The beams are truncated at 10% of their charge density and rms beam size is $r_{\mathrm{rms}}=1.0$ (mm). All graphs are on the same scale.

Figure 4

Radial eigenellipse of 2 MeV at the symmetric line of a magnet in the injector II cyclotron.

Figure 5

Tune diagram of injector II cyclotron, compared with FIXPO code.

Figure 6

The time consumption as a function of processors on Cray XT3, CSCS.

Figure 7

Top view of a 1 mA, 3 MeV coasting beam in PSI injector II in the local frame ${\mathbf{S}}_{\mathrm{local}}$ of PSI injector II. Up: turn 0, 5, 10. Down: turn 20, 30, 40. To compare with figures in Ref. 30, the beam’s transport direction is along the negative direction of the abscissa axis.

Figure 8

Comparison of the rms beam size in the transverse direction (left) and longitudinal direction (right) at the 112° azimuthal position of each turn in the PSI ring cyclotron.

Figure 9

Top view of 3 mA bunch distributions with 2°, 6°, and 10° initial phase widths at the initial position (top), turn 50 (middle), and 150 (bottom) in the local frame ${\mathbf{S}}_{\mathrm{local}}$ of the 112° azimuthal position of the PSI ring cyclotron.

Figure 10

Histogram of 3 mA bunch distributions with 2°, 6°, and 10° initial phase widths at initial position (left), turn 50 (middle), and 150 (right) in the PSI ring cyclotron.

Figure 11

Top view of 1 mA bunch distributions at the turn 130 in the local frame ${\mathbf{S}}_{\mathrm{local}}$ at the 112° azimuthal position of turn 130 in the PSI ring cyclotron. The results are obtained from single bunch (left), seven bunches (middle), and nine bunches (right) simulations, respectively.

Figure 12

Comparison of the histograms along the transversal direction in the local frame ${\mathbf{S}}_{\mathrm{local}}$ (left) and the energy spectra (right) of 1 mA beam at the 112° azimuthal position of turn 130 in the PSI ring cyclotron.