Elena Benedetto, CERN 16/12/08 Beam stability in the SPL-based accumulator: issues and planned studies Elena Benedetto, CERN 16/12/08 EUROn WP2 joint with IDS Target kickoff meeting, 15-17/12/08 at CERN

Beam stability in the SPL-based accumulator: issues and studies Why? What? How? Many thanks to M. Aiba, R. Garoby, M. Martini, M. Meddahi, E. Metral, for introducing me to the subject. The work they have done (with many other people) is the starting point of my studies. Elena Benedetto

Why and What(1/3)? Motivations Proposed CERN SPL based Proton Driver → R.Garoby (see M.Martini’s talk) Accumulator ring Isochronous (h=0), no RF, 400ms, beam frozen longitud. to preserve Dp/p 6 bunches, 120ns bunch length Compressor ring rapid phase rotation in ~36ms, strong RF, large slippage factor h ~2ns bunch length @ extraction to the Target → M.Aiba, CERN-AB-2008-060 BI Instabilities may arise in the accumulator, with t<400ms No synchrotron motion to stabilize Collective effects studies done in the past, for a different scenario, via analytical estimations → R.Cappi, J.Gareyte, E.Metral, D.Mohl, CERN/PS 2000-069 (AE) They will be repeated for the designed new machine via analytical estimations AND simulations. Elena Benedetto

What(2/3)? Impedances in a machine: EM interactions of the beam with the environment → wake-fields Impedance = Fourier transform of the wake-field Can induce beam instabilities: single bunch and coupled bunch In the transverse and longitudinal plane 2b A bunch passing offset through a discontinuity (e.g. RF cavity) leaves behind itself a wake-field which interacts with the subsequent bunches Courtesy G.Rumolo If the head of a bunch is displaced with respect of the pipe axis, via interaction with the conducting wall, it generate a wake filed that affects the tail,… in our case (h=0) no mixing between head-tail to help stabilizing! Elena Benedetto

What(3/3)? Impedances in a machine: EM interactions of the beam with the environment → wake-fields Resistive wall (beam pipe, kickers, collimators,…) Single-bunch Coupled-bunch “Broad-band” impedance “Resonators” (RF cavities, kickers,…) The effects (instabilities) induced by wake-fields are intensity dependent Elena Benedetto

How(1/3)? Impedances in a machine: EM interactions of the beam with the environment → wake-fields Resistive wall (beam pipe, kickers, collimators,…) “Broad-band” impedance “Resonators” (RF cavities, kickers,…) In the longitudinal plane: if h0 the rise time goes to → CAREFUL! high order terms h~a=a0+a1(Dp/p) +… may become important! → estimated via analytical formula → study of instability threshold and/or rise-time gives the allowed impedance in the machine → such components must be carefully designed to keep the impedance as small as possible Elena Benedetto

How(2/3)? The HEADTAIL code The analytical estimations will be supported by a simulation campaign. The HEADTAIL code: Macroparticle simulations, the bunch is sliced and interacts slice-by-slice with the wake-fields. Developed at CERN, in 2002 (G.Rumolo (G.R.), F.Zimmermann, CERN-SL-Note-2002-036-AP) Studies of beam interactions w. electron-cloud and w. broad-band wake-fields, in 2004-’06 (G.R., E.Benedetto, F.Zimmermann) Upgraded to study a large variety of wake fields (broad-band, resistive-wall, kickers,...) and single-bunch instabilities, in 2007-’08 (G.R., D.Quatraro, E.Metral, B.Salvant) In the near future will be included multi-bunches capabilities (G.R., E.Metral) Localized impedance source Courtesy G.Rumolo Elena Benedetto

How(3/3)? Plans HEADTAIL already contains (almost) all the tools needed for the beam stability study in the accumulator Evaluate the expected machine impedance → (to be put in the code) …and the allowed one! Eventually propose cures: Introduce non-linear elements (sextupoles, octupoles) to stabilize Relax the constraint h=0 → CAREFUL! Need RF cavities → they will increase impedance Carefully design machine elements … 3 or 1 bunches option(?) Elena Benedetto

Thanks for your attention!

Slides from R.Garoby and M.Aiba Back-up material Slides from R.Garoby and M.Aiba

n FACTORY: SPL-based proton driver (1/4) from M. Aiba An HP-SPL based 5 GeV – 4 MW proton driver has been designed (HP-SPL + 2 fixed energy rings (accumulator & compressor) Feasibility Study of Accumulator and Compressor for the 6-bunches SPL based Proton Driver R.G. @ ETH Zurich 18/11/2008 R.G. 11 R.G. 11 2 December, 2008

n FACTORY: SPL-based proton driver (2/4) Accumulator [120 ns pulses - 95 ns gaps] Accumulation Duration = 400 ms Compression t = 0 ms t = 12 ms t = 24 ms t = 36 ms etc. until t = 84 ms SPL beam [42 bunches - 33 gaps] Compressor [120 ns bunch - V(h=3) = 4 MV] Target [2 ns bunches – 5 times] R.G. 12 R.G. 12 2 December, 2008

n FACTORY: SPL-based proton driver (4/4) from M. Aiba R.G. 13 R.G. 13 2 December, 2008

Accumulation scenarios M.Aiba # bunches # acc. turns/time (ms) # ppb (end of acc.) Acc. circum. (m) Acc. bunch length (ns) 6 400 / ~400 1.67E+13 318.5 120 3 740 / ~460 3.33E+13 185.8 1 1920 / ~1200 1.00E+14 Use the same accumulator for 1 and 3 bunches options No big tolerance to change the accumulator circumference, especially in 1 bunch and 3 bunches Transverse S.C. would not be an issue because of long bunch length in accumulator and the kinetic energy of 5 GeV Longitudinal S.C. could be managed by making the bunch in good shape (linear slope at both ends, parabolic with compensation RF for 1 bunch) Details are in CERN-AB-2008-060 and CERN-AB-Note-2008-048 Elena Benedetto

Alternative choice Accumulator with barrier bucket conserve dP/P M.Aiba Accumulator with barrier bucket conserve dP/P have h~0.06 or more(?) but have larger impedance with barrier RF cavity would be technically challenging to realize rather short barrier length (~20 ns) cost barrier RF cavity Elena Benedetto