1. Beam Dynamics in the ESS Linac Under the Influence of Monopole and Dipole HOMs A.Farricker 1, R.M.Jones 1, R.Ainsworth 2 and S.Molloy 3 1 The University of Manchester, UK and Cockcroft Institute, UK 2 John Adams Institute, UK 3 ESS, Lund, Sweden The European Spallation Source (ESS) The ESS linac is currently under construction in Lund, Sweden, upon completion it will be the worlds most powerful next generation neutron source. It is designed to accelerate a proton beam up to an energy of 2 GeV, with a beam power of 5 MW, which is then collided with a target to produce high neutron flux via spallattion. The accelerator makes use of both normal conducting (NC) and superconducting (SC) technology, with the low energy stages being NC (orange) and the higher energy stages using three families of SC cavity (blue) [2]. Beam losses in a high power linac such as ESS must be minimised, as such understanding the causes of beam loss in the accelerator is very important. Here we investigate the implications of monopole and dipole modes on the beam dynamics, in particular the emittance dilution from the SC section of the linac. Investigating HOMs With a Drift-Kick-Drift Model When a bunch reaches a cavity it induces a voltage in all of the allowed modes in a cavity: The voltage inside the cavity decays according to: We treat each bunch as a point like charge and each cavity as an instantaneous impulse/kick at the centre of a cavity, this changes the energy of the bunch which in turn results in a time arrival error at the next cavity given by: Differences in energy are caused by both RF errors and by interactions with the HOMs already present in the cavities, these are described by: These kicks are applied sequentially along the length of the linac, we measure their effect by comparing the bunch train emittance without any of these effects. This is implemented numerically in Python [1]. Effects of Same Order Modes (SOMs) 90mA 75mA Design-62.5mA RF Errors One SOM was included in each cavity (the closest in frequency to the fundamental). In the case of high Q the size of the emittance growth exceeds that due to RF errors alone, making it the limiting factor in performance. The Q’s are expected are on the order of 10 6 which is in the region where the growth seen including SOMs is comparable to that from RF errors. To confirm the Q’s lie in this region further simulations need to be carried out as it is anticipated that the input coupler will reduce the Q to the level of 10 6. Alignment Tolerances In the left hand plot uniformly distributed alignment errors are applied. For large offsets, the expected quadratic behaviour is observed. However in the region of the iris very little is seen except statistical noise. The limiting factor on alignment tolerances is due to transverse kicks from the fundamental (right hand plot), due to an angular offset from the beam axis. In the plot to the right it can be seen that it is extremely significant in comparison to that from dipole modes. This ultimately leads ESS to set alignment tolerances at +/- 0.5mm or +/- 1mrad at 1m References 1. R.Ainsworth Nucl.Instrum.Methods Phys.Res.,Sect. A, 734 (2014) 95-100 2. C.Darve etal, Proceedings of SRF2013,Paris,France MOP004 3. M.Schuh etal, Phys.Rev.ST Accel.Beams 14,051001 (2011) Final Remarks. If Homs lie near to machine lines they are a concern, however ESS requires at least a 5MHz separation for all modes below the beam pipe cut-off frequency. For Q’s greater than 10 6 SOMs begin to be the dominant cause a growth in emittance that exceeds that caused by RF error and become the dominating factor, these SOMs now require carful consideration. The alignment tolerances for the cavities are limited by transverse kicks from the accelerating mode. Effects of HOMs Near Machine Lines A single mode in one particular high beta cavity is shifted to lie exactly on the nearest machine line. The growth observed under these conditions is significant and can be up 6 times the initial value is observed (left plot). The emittance dilution observed approximately follows the R/Q ‘s variation with beta as would be expected and is therefore heavily dependent on the position of this cavity in the linac. Growth at the levels seen would compromise the operability of the machine. This data highlights the implications of modes lying close to machine lines and how detailed studies are critical to the design process. This highlights the key reason ESS requires all HOMs (below the beam pipe cut off frequency) to be at least 5 MHz away from any machine lines and have rejected designs on these grounds. Parameter (Unit)Value Beam Power (MW)5 Beam Current (mA)62.5 Linac Energy (GeV)2 Beam Pulse Length (ms)2.86 Repetition Rate (Hz)14 Number of Spoke Cavities26 Number of Medium Beta Cavities36 Number of High Beta Cavities84 R/Q