Impedance of the CLIC-DRs: What we know so far and what else we need to study…. E. Koukovini-Platia M. Barnes, A. Grudiev, N. Mounet, Y. Papaphilippou, G. Rumolo

Updated list of parameters with the new lattice design at 3 TeV From Y. Papaphilippou, G. Rumolo, CLIC‘09  Advantages: DA increased, magnet strength reduced to reasonable, reduced IBS  Relative to collective effects (main changes): Higher energy, larger horizontal emittance (good) Longer circumference (bad) With combined function magnets

New update of the lattice design at 3 TeV From Y. Papaphilippou  Lattice has been redesigned to reduce the space charge effect (ring circumference shortened). However, higher order cavities will also help in this sense (simulations foreseen)  The 1 GHz option has been considered because: it is better for the RF design (less impedance) it could relieve constraints due to e-cloud, ions, coupled-bunch instabilities,... 1 GHz option

SINGLE BUNCH: INSTABILITIES Longitudinal The Boussard criterion (including in the formula the suppression factor (b/  z ) 2 ) would give a maximum normalized impedance value of ≈0.7 to 1.8  Transverse The TMCI threshold is given by the formula below for resonator impedance The CLIC-DRs are in short bunch regime, and the formula translates into a tolerable impedance value of ≈12 M  /m if  r =2  x 5 GHz From CLIC‘09

Remarks Longitudinal The given threshold value of 1  refers to the normalized longitudinal impedance, i.e. the impedance divided by the ratio between the frequency and the revolution frequency (e.g. being  r =0.7 MHz, the tolerable impedance at 100 MHz could be in principle 1*(100/0.7)≈150  ) The formula comes from a coasting beam formula applied to a bunched beam (with a correction factor). But the CLIC DR bunches are very short! The formula also mainly applies to the low frequency part of the impedance, so that the stability against possible higher frequency peaks should be investigated in further detail. Transverse Here we have a short bunch formula that should correctly give an estimation of the order of magnitude of the transverse impedance The transverse impedance should include the contribution of the resistive wall, because the single bunch part is not negligible for these short bunches!

Transverse stability checked with HEADTAIL Used a broad-band resonator model with  r =5 GHz and Q=1 Looked for the instability threshold in R T for nominal bunch intensity and assuming an axisymmetric impedance source (i.e. same impedance effect in x and y, which is usually not true!) Start with 0 chromaticity, but study with positive values of chromaticity are underway Should we consider a lower threshold than that for TMCI? Maybe there’s already emittance growth for lower values of impedance (e.g. due to the interplay of space charge and impedance) H Instability threshold (TMCI) V Instability threshold (TMCI) Tune shift, mode 0 Mode -1 (?) QsQs QsQs Tune shift, mode 0 See Eirini’s talk

Impedance of the kickers (M. Barnes) Choice to go for stripline kickers to reduce the (longitudinal) impedance at high frequencies Tapered kicker results in significant impedance reduction above ~100MHz, with a residual high peak at around this frequency This peak seems to have an amplitude way below the longitudinal impedance threshold, however HEADTAIL simulations could be helpful since we are in a very short bunch regime (but wakes needed) Transverse impedance is maybe a more serious issue? We would need wakes and impedances to calculate the effect on the beam.

Scaling of NLC DR RF cavity NLC DR RF cavity parametersCLIC DR RF Frequency: f[GHz] Shunt impedance: R [MΩ] (~ 1/√f) Unloaded Q-factor: Q 0 (~ 1/√f) Aperture radius: r [mm] (~ 1/f) Max. Gap voltage: V g [kV] Gradient: [MV/m] G ~ V g /4r444 HOM (σ z =3.3mm) Total loss factor: k l [V/pC] (~ f) Fundamental loss factor: k 0 l [V/pC] (~ f) HOM loss factor: k || l [V/pC] (~ f) Transverse HOM kick factor: k T t [V/pC/m] (~ f 2 ) From PAC 2001, Chicago AN RF CAVITY FOR THE NLC DAMPING RINGS R.A. Rimmer, et al., LBNL, Berkeley, CA 94720, USA From PAC 1995, Collective effects in the NLC DR designs T. Raubenheimer, et al., A. Grudiev

Impedance estimate in DR, PDR Calculated RF cavity parameters HOMNLC DRCLIC DRCLIC PDR Frequency: f[GHz] Number of cavities: N = V rf /V g 2 (3) Total HOM loss factor: k || l * N [V/pC] Long. HOM energy loss per turn per bunch [μJ]: ΔU = k || l * N * eN e Incoherent long. HOM loss power [kW]: P || incoh = ΔU * N b f/h Coherent long. HOM loss power [kW]: P || coh ~ P || incoh *Q HOM *f/f HOM ( if the mode frequency f HOM is a harmonic of 2 GHz) Careful Design of HOM damping is needed Total HOM kick factor: k T t * N [V/pC/m] Tran. HOM energy loss per turn per bunch [μJ]: ΔU = k T t * 2πf/c * N * eN e 2 * d 2 (d – orbit deviation, 10mm assumed) Tran. HOM loss power is not an issue: < [kW] A. Grudiev ⇒ We can use for our HEADTAIL simulations the information about the details of the HOMs from the reference on the previous page ⇒ The Q will depend on the efficiency of the HOM absorbers, so we should specify a Q such that the rise time of the instability is in the order of the damping time ⇒ Alexej calculated that 10M  /m translate into a kick factor of about 6 x 10 4 V/pC/m (i.e. only 10 times larger than the one from the cavities!)

Some techniques to fight electron cloud cause impedance sources: – Surface coating with low SEY materials (Cu, NEG, TiN, a-C) – Non-smooth surfaces (natural roughness, grooves) – Clearing electrodes – NEG coating to have good vacuum From S. Suetsugu From T. Demma Electron cloud and good vacuum against ion instabilities (from the LER 2010 Workshop)

Resistive wall in the CLIC-DR regime N. Mounet Pipe cross- section: Layers of coating materials can significantly increase the resistive wall impedance at high frequency – Coating especially needed in the low gap wigglers (question mark about the electron ring, as NEG is not proved to pump at low temperatures) – Low conductivity, thin layer coatings (NEG, a-C) – Rough surfaces (not taken into account so far)

General Resistive Wall Impedance: Different Regimes Vertical impedance in the wigglers (3 TeV option, pipe made of copper without coating) Note: all the impedances and wakes presented have been multiplied by the beta functions of the elements over the mean beta, and the Yokoya factors for the wigglers Low frequency or “inductive-bypass” regime “Classic thick-wall” regime High frequency regime N. Mounet

Resistive Wall Impedance: Various options for the pipe Vertical impedance in the wigglers (3 TeV option) for different materials  Coating is “transparent” up to ~10 GHz  But at higher frequencies some narrow peaks appear!!  So we zoom for frequencies above 10 GHz  N. Mounet

Resistive Wall Impedance: Various options for the pipe Vertical impedance in the wigglers (3 TeV option) for different materials: zoom at high frequency  Above 10 GHz the impact of coating is quite significant.  Relaxation time (as taken from graphite) does not seem to make a large difference on the main peak N. Mounet Resonance peak of ≈1M  /m at almost 1THz

... Bunch length Bunch to bunch Bunch train In terms of wake field, we find The presence of coatings strongly enhances the wake field on the scale of a bunch length (and even bunch-to-bunch) The single bunch instability threshold should be evaluated, as well as the impact on the coupled bunch instability This will lower the transverse impedance budget for the DRs

Resistive wall: what is pending … Because of the unprecedented frequency range, few issues remain to be addressed to give more reliable impedance and wake estimations Properties of the coating material – Measure or calculate ,  and  – Ac conductivity (relaxation time) – Anomalous skin effect (breaking of Ohm’s law in high frequency) Yokoya’s factors, applicable in the classical resistive wall regime, could be not valid at high frequency (and the wiggler chambers are flat)  underway! Surface roughness could play a significant role in the frequency range in which we are interested Influence of temperature (wigglers are cold, better for Cu but worse for a-C?) Effects of curvature, especially in the wigglers

Work plans Data-base of the known contributions to the CLIC-DR impedance – Transverse – Longitudinal Contributions till now – Resistive wall with and without coating – HOMs – Longitudinal impedance of stripline kickers What else can be included – Instrumentation (e.g. BPMs, do we have a design?) – Clearing electrodes if there is a plan to have them We need the short- and long-range wake fields associated to these impedances in order to assess the global effect on the beam – Single bunch studies – Coupled bunch