SRF CAVITY GEOMETRY OPTIMIZATION FOR THE ILC WITH MINIMIZED SURFACE E.M. FIELDS AND

SUPERIOR BANDWIDTH

The Cockcroft Institute of Accelerator Science and Technology, Daresbury WA4 4AD, UK.School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK.

N. Juntong, R.M. Jones, V.F. Khan and I.R.R. Shinton

Particle Accelerator Conference, PAC’09, Vancouver, Canada, 4th - 8th May 2009

Acknowledgements We have benefited from discussions at the weekly Manchester Electrodynamics

and Wakefields (MEW) meeting held at Cockcroft Institute, where these results were first presented. N.J. is in receipt of a joint support from the Royal Thai Government

and the Thai Synchrotron Light Research Institute.

The ILC main linac baseline design uses a TESLA [1] cavity geometry operating in a π phase advance per cell and aims at an accelerating gradient of 31.5 MV/m. In the quest for

higher gradients Ichiro [2], Re-entrant [3], LL [4,5] and LSF [6] designs are aiming at gradients higher than 50 MV/m. The goal of each design is to minimize the ratio of surface

electric field to accelerating field (Es/Ea) and surface magnetic field to accelerating field (Bs/Ea). The fractional bandwidth (kc) of the monopole mode is also an important quantity. The

fractional mode separation of the next nearest neighbour to the π mode is

(where N=9) and this factor provides an additional figure of merit.

INTRODUCTION

The resonant frequency of this optimized cell varied linearly with respect to the equator elliptical parameter B with a slope of 2.79 MHz per mm for a given iris elliptical bn value as

displayed in Fig. 3 (left).

A 1 mm increase of the iris radius results in an increase of: the cell to cell coupling constant (kc) of approximately 12-13%, the surface electric field Es/Ea by 2% and the surface

magnetic field Bs/Ea by approximately 1.3% for a given set of fixed parameters an, bn, and Req. This is displayed in Fig. 3 (right). These observations enabled us to quickly establish the

optimum iris radius.

NLSF 9-CELLS CAVITY PROPERTIES

SUMMARY and FUTURE WORK The NLSF cavity was optimized based upon the LL, TESLA and

LSF cavity designs. The NLSF cavity has an improved surface field in that Bs/Ea is reduced by 8.5% compared to TESLA and Es/Ea is 13% superior to that of the LL design. It also has a 26.5% wider monopole bandwidth compared to the LSF design (hence giving it an improved tolerance on a cell-to-cell errors). An analysis of the transverse modes

indicated that dipole modes in the first three bands have large R/Q values and can impart significant momentum kicks to the beam. The R/Q value at a phase advance per cell of π/9 is particularly severe in

this respect. However, appropriate modification of the HOM damping couplers will ensure these modes are adequately suppressed.

REFERENCES[1] The TESLA Conceptual Design Report.[2] T. Saeki et al., EPAC06, MOPLS087.[3] V. Shemelin, PAC05, p.3748.[4] J. Sekutowicz et al., JLAB TN-02-023, 2002.[5] J. Sekutowicz et al., PAC05, p.3342.[6] Z. Li, C. Adolphsen, LINAC08, THP038.[7] www.ansoft.com/products/hf/hfss/[8] To be submitted to SRF2009.

Iris radius (mm) Bandwidth (MHz)

30 (LL, ICHIRO) 19.7

30 (LSF) 16.7

31 18.3

32 (NLSF) 20.7

33 23.2

35 (TESLA) 24.3

We initially investigated the infinite periodic series of the NLSF standard mid-cell geometries in which the brillouin diagram is obtained using the eigenmode module of HFSS v11. The brillouin diagram in Fig. 5 was obtained from simulations performed on a 9

cell cavity consisting of NLSF standard mid-cells. The modes in the 3rd, 5th and 6th dipole bands have a low group velocity and thus there is the potential for modes to be trapped.

The largest R/Q is located at a π/9 phase advance per cell in the 3rd dipole band. The R/Qs located at a 5π/9 phase advance per cell in the 2nd dipole band and at a 6π/9 phase advance per cell in the 1st dipole band are also high. A similar behavior is also observed in

the LSF design [6].

PARAMETERISATION

Table 1: Monopole bandwidth versus different iris radius.

The 32 mm iris radius was chosen for NLSF as it is the optimum design based on a trade-off among the three figure of merit, kc, Es/Ea and Bs/Ea, as displayed in Fig. 2. The NLSF cell

has surface fields Bs/Ea 8.5% lower than the TESLA, Es/Ea 13% lower than the LL and a monopole bandwidth 26.5% wider than the LSF. The cell profiles, along with surface fields,

are presented in Fig. 6.

NLSF STANDARD MID-CELL PROPERTIES

Future work [8] includes an optimization of the monopole mode for a full 9 cell cavity (including end cells) and an analysis of the HOMs excited.

The cell length is half the operating wavelength (Lc = 115.304 mm). The equator radius (Req) is chosen to be equal that of the LL design. The parameters Lc, Req, Ri, an and A are fixed, simplifying the problem to optimizing the elliptical cavity parameters bn and B in term of the operating

frequency (1.3 GHz) and the optimum surface e.m. fields. By varying the geometrical parameters modeled in Fig. 1 we minimize Es/Ea, Bs/Ea and maximize kc. In order to obtain a final design there is a trade-off in these three parameters. All simulations of e.m. fields were made using

HFSS v11 [7].

DESIGN ALGORITHM

Figure 3: Frequency change versus ΔB. Dependence of the three figures of merit versus iris radius is also illustrated.

Figure 1: Cell geometry of a NLSF standard mid-cell.

Figure 2: Three figures of merit, Bs/Ea, Es/Ea, kc, of NLSF design (design #10) compared with the other designs. Design #4-#6 used Ri=30 mm, design #7-#8

used Ri=31 mm, design #9-#10 used Ri=32 mm, design #11-#12 used Ri=33 mm and design #13 use Ri=35 mm with an=10.5 mm.

Parameter Unit TESLA LL ICHIRO LSF-1 LSF-2 LSF-3 LSF-4 LSF-5 LSF-6 LSF-7 LSF-8 LSF-9 LSF-10

Riris mm 35 30 30 30 30 30 31 31 32 32 33 33 35

Req mm 103.3 98.58 98.14 98.14 98.58 100 98.14 98.58 98.14 98.58 98.14 98.58 98.14

A mm 42 50.052 50.052 47.152 47.152 47.152 47.152 47.152 47.152 47.152 47.152 47.152 47.152

B mm 42 36.5 34.222 30.35 33 41.45 30.1 32.7 28.65 31.35 27.2 29.8 25.5

a mm 12 7.6 7.6 10.5 10.5 10.5 10.5 10.5 10.5 10.5 10.5 10.5 10.5

b mm 19 10 9.945 20.15 19 17.2 16.5 15.5 16.5 15.5 16.5 15.5 12.5

fs (fπ) GHz 1.301161.3000

81.30040

1.30000

1.29998

1.30002

1.30012

1.30000

1.30002

1.30023

1.30006

1.30003

1.29998

Bandwidth MHz 24.32 19.74 19.82 17.25 16.92 16.23 18.52 18.17 20.86 20.50 23.38 22.98 27.34

kcc % 1.89 1.53 1.54 1.34 1.31 1.26 1.43 1.41 1.62 1.59 1.81 1.78 2.19

Epeak/Eacc - 2.18 2.42 2.37 2.07 2.06 2.07 2.09 2.12 2.12 2.11 2.16 2.18 2.27

Bpeak/EaccmT/(MV/

m)4.18 3.64 3.62 3.78 3.75 3.76 3.81 3.79 3.86 3.83 3.91 3.88 4.00

Parameter Unit TESLA LL ICHIRO NLSF

fs (fπ) GHz 1.301161.3000

81.30040

1.30023

Bandwidth MHz 24.32 19.74 19.82 20.50

kcc % 1.89 1.53 1.54 1.59

Epeak/Eacc - 2.18 2.42 2.37 2.11

Bpeak/EaccmT/(MV/

m)4.18 3.64 3.62 3.83

2

2

2/9/8 4/

N

kc

Table 2: NLSF standard mid-cell properties compared to other designs.

TH5PFP045

Figure 6: Cavity profiles (top left), surface electric field ratio (top right) and surface magnetic field

ratio (bottom right) compared to the TESLA (black), LL (blue) and NLSF (red) designs. Here s is the coordinate along the surface of the cavity.

Figure 5: Dipole mode R/Q’s for a nine-cell NLSF cavity.Figure 4: Brillouin diagram of a NLSF cavity. Cells subjected to an infinite periodic structure are indicated by the lines. The points indicate the cavity

eigenfrequencies.