BENCHMARKING THE BEAM LONGITUDINAL DYNAMICS CODE

The relatively recent Beam Longitudinal Dynamics code BLonD has already been applied to a wide range of studies for all present CERN synchrotrons. Its application area ranges from studies of RF manipulations, over single and multi-bunch interactions with impedance, to the action of feedback loops and RF noise. In this paper, we present benchmarks and comparisons with measurements, theory, or other codes, which have increased greatly the trust in the code. Tests related to bunch-to-bucket transfer, feedback loops, diffusion due to noise injection, as well as collective effects, are presented. INTRODUCTION The CERN BLonD code [1] has been developed by a group of developers for about two years now. Despite this short development time, it can model single or multi-bunch longitudinal dynamics in multi-harmonic RF systems, with beam-based feedback loops, RF phase noise injection, and (multi-turn) intensity effects due to machine impedance and/or space charge. Similarly vast is the range of applications the code has been used for already. Benchmarks against theoretical predictions, comparisons with measurement data, and other particle tracking codes have greatly increased trust in the code, and thus also trust in predictions given by BLonD for beam behaviour after upgrades or in future machines. In this paper, we present a few selected benchmark and comparison studies. BENCHMARKS & COMPARISONS Bunch-to-Bucket Transfer A good test case for RF manipulations is the bunch-tobucket transfer between the PS and the SPS. After arrival to flat top in the PS, the bunch distribution can be reconstructed using phase-space tomography [2] in a stationary RF bucket at 10 MHz. Bunches are then split twice into two bunches each, using the harmonics 20 MHz and 40 MHz. Then, the bunches are rotated in phase space using a sudden increase in the 40 MHz and 80 MHz voltages. These short bunches are subsequently extracted and injected into the SPS buckets, which are dominated by 200 MHz and have a higher-order component of 800 MHz in bunch-shortening mode. Starting from the reconstructed distributions, we have compared the bunch length at PS extraction and the transmission after the start of the SPS ramp between measurements, simulations using BLonD, and simulations performed in 2012 [3] with the former ESME [4] code. The results using two different RF voltages for the bunch rotation are summarised in Fig. 1. ∗ helga.timko@cern.ch Figure 1: Code-to-code comparison and benchmark with experimental data for the PS-SPS bunch-to-bucket transfer at different RF voltages used for the bunch rotation prior to PS extraction. Simulations with both codes reproduce reasonably well the measurement data and the observation that, using a higher rotation voltage, a better transmission and shorter bunch length can be achieved. The discrepancy between simulations and measurements is attributed to the fact that simulations use a single reconstructed particle distribution, while measurements are averaged over many bunches and many cycles with non-negligible bunch-to-bunch and shotto-shot variations. Comparing results obtained with BLonD and ESME starting from the same bunch distribution, the values obtained for transmission and bunch length agree within 1-2 %, see Table 1. This small difference is probably due to the ESME tracking being based on real time and the BLonD tracking based on number of turns, which can result in ±1 turn difference in extraction time between ESME vs. BLonD, and given the rotation, the bunch length (and with it the transmission) is very sensitive to extraction time.