Progress in the design of a damped an tapered accelerating structure for CLIC Jean-Yves Raguin CERN AB/RF

The Tapered Damped Structure 2p/3 travelling-wave mode, 150 cells – Av. Acc. Grad. of 150 MV/m Strong damping Each cell coupled to four rectangular identical waveguides Cutoff frequency of the fundamental waveguide mode between the p-mode frequency of the fundamental passband and the lowest frequency of the first dipole band Trapped fundamental mode whereas the E-M energy of the higher modes propagates out of the cells and is absorbed by SiC loads terminating the waveguides Light detuning Linear variation of the irises radius from 2.25 mm at the head of the structure to 1.75 mm at the end, each cell being tuned to have the same fundamental frequencies Dipole frequency spread (5.4 %) which contributes to a further reduction of the transverse wakefields Demonstrated suppression of the transverse wakefields by two orders of magnitude within 0.67 ns (time between two consecutive bunches) on a 15 GHz-scaled version (ASSET experiment)

Accelerating mode: electric field magnitude (Log) SiC load Dipole mode: Poynting vector

Performance limits and peak surface electric fields L= 50 cm Pin/section = 248 MW h = 23.8 %

Temperature increase for the middle cell of the TDS with Pulsed surface heating Temperature increase for the middle cell of the TDS with = 150 MV/m and tp=130ns Due to the configuration of the cell-waveguide coupling iris (3.3 mm wide) the local magnetic field is too high, leading to excessive maximum temperature rise

Design of a new 2p /3 damped and tapered structure Criteria to design new CLIC damped accelerating structure Solutions To prevent electric breakdown, low peak surface electric field To prevent excessive pulse heating, low peak surface magnetic field Good damping of higher order modes and, in particular, of the first and second dipole modes Use of an elliptical profile for irises Appropriate profile of the cells wall Damping of higher order modes by coupling each cell to four T-cross waveguides

Topology of the cell and of the damping waveguides

Field pattern of the first two waveguide modes Fundamental mode Damping for the first dipole band Second mode Damping for the second dipole band Electric field Electric field Perfect Elec. wall Perfect Mag. wall Magnetic field Magnetic field

First cell Iris thickness: 0.55 mm Q=3744 with s = 5.80.107 Mhos/m (Cu) R’/Q= 24.5 kW /m vg/c = 8.1 % fcutoff,TE10-e = 32.1 GHz Epeak / Eacc = 2.55 Hpeak / Eacc = 4.50 mA/V 3.0 mm 5.25 mm

Hsurf/Eacc (mA/V) on the walls of the first cell

Last cell Iris thickness: 1.00 mm Q=3373 with s = 5.80.107 Mhos/m (Cu) R’/Q= 30.0 kW /m vg/c = 2.6 % fcutoff,TE10-e = 32.4 GHz Epeak / Eacc = 1.75 Hpeak / Eacc = 4.38 mA/V 3.0 mm 5.25 mm

For 84 cells (L= 28 cm) Epeak=400 MV/m Pin/section = 130 MW h = 26.1 % DT=154 K DT=120 K

Transverse wakefields analysis First cell Middle cell Last cell Real part of the transverse impedance vs. frequency computed with GdfidL for the first, middle and last cells Transverse wakefields |W t | = 90 V/pC/mm/m at the 2nd bunch Q dip,first= 52 Q dip,middle= 51 Q dip,last= 44 Dfdip /f dip,first = 3.3 %

THERE IS ROOM FOR IMPROVEMENT…

Design of a damped structure - b d = 110 deg. Working at a lower phase advance allows to decrease Epeak / Eacc Decrease iris thickness along the structure Increase the coupling cell- waveguide along the structure for better damping

First cell Iris thickness: 0.80 mm Q=3387 with s = 5.80.107 Mhos/m (Cu) R’/Q= 24.1 kW /m vg/c = 7.7 % fcutoff,TE10-e = 32.3 GHz Epeak / Eacc = 2.21 Hpeak / Eacc = 4.50 mA/V 3.0 mm 5.25 mm

Last cell Iris thickness: 0.55 mm Q=3365 with s = 5.80.107 Mhos/m (Cu) R’/Q= 33.2 kW /m vg/c = 3.8 % fcutoff,TE10-e = 32.3 GHz Epeak / Eacc = 2.00 Hpeak / Eacc = 4.17 mA/V 3.2 mm 5.32 mm

For 83 cells (L= 25.4 cm) Epeak=355 MV/m Pin/section = 128 MW h = 24.8 % DT=122 K DT=122 K

Transverse wakefields analysis First cell Middle cell Last cell Real part of the transverse impedance vs. frequency computed with GdfidL for the first, middle and last cells Transverse wakefields |W t | = 58 V/pC/mm/m at the 2nd bunch Q dip,first= 53 Q dip,middle= 31 Q dip,last= 24 Dfdip /f dip,first = 4.9 %

There is room for improvement (2)…

Design of a damped structure - b d = 110 deg. (2) First cell Iris thickness: 0.80 mm 2.0 mm 3.867 mm Q=3266 with s = 5.51.107 Mhos/m (Cu) R’/Q= 24.0 kW /m vg/c = 7.6 % fcutoff,TE10-e = 32.3 GHz Epeak / Eacc = 2.20 Hpeak / Eacc = 4.51 mA/V 3.0 mm 5.25 mm

Last cell Iris thickness: 0.55 mm Q=3252 with s = 5.51.107 Mhos/m (Cu) R’/Q= 32.5 kW /m vg/c = 3.8 % fcutoff,TE10-e = 32.3 GHz Epeak / Eacc = 1.95 Hpeak / Eacc = 4.10 mA/V 3.2 mm 5.32 mm

For 83 cells (L= 25.4 cm) Epeak=355 MV/m Pin/section = 130 MW h = 24.4 % DT=119 K DT=128 K

For 77 cells (L= 23.5 cm) Epeak=348 MV/m Pin/section = 125 MW h = 23.8 % DT=121 K DT=122 K

Transverse wakefields analysis 83-cell structure First cell Middle cell Last cell Real part of the transverse impedance vs. frequency computed with GdfidL for the first, middle and last cells Transverse wakefields |W t | = 45 V/pC/mm/m at the 2nd bunch Q dip,first= 43 Q dip,middle= 27 Q dip,last= 21 Df dip/f dip,first = 5.4 %

Shall we dare to lower the accelerating gradient?…

Average accelerating gradient of 125 MV/m For 75 cells (L= 22.9 cm) Epeak< 300 MV/m Pin/section = 89 MW h = 27.2 % DT=88 K DT=87 K with the same beam current…

Investigation of new materials Conclusions Design of copper structure with average accelerating gradient of 150 MV/m, peak surface electric field lower that 300 MV/m and maximum temperature rise lower than 100 K seems unrealistic – would lead to smaller iris radius Copper structure with average accelerating gradient of 125 MV/m, peak surface electric field lower that 300 MV/m and maximum temperature rise lower than 100 K seems feasible Investigation of new materials Design of the latest structure with molybdenum irises – calls for a reassessment of the fundamental mode characteristics Material for the cell outer walls which would solve the pulsed surface heating problem? Transverse wakefields suppression Need for tuning the dipole frequencies