SIMULATION OF : SIMULATION OF : H.O.M DAMPED CAVITIESH.O.M DAMPED CAVITIES

Grenoble - FRANCE

E.S.L.S Radio Frequency Meeting Aarhus, DENMARK – Sept 2005

TARGET OF SIMULATIONS AT E.S.R.F TARGET OF SIMULATIONS AT E.S.R.F

DEVELOPPING A PROTOTYPE OF NORMAL CONDUCTING CAVITY DEVELOPPING A PROTOTYPE OF NORMAL CONDUCTING CAVITY (at 352.2 MHz)(at 352.2 MHz)TO ATTENUATE TO ATTENUATE HHIGHER IGHER OORDER RDER MMODES WITH RIDGE WAVEGUIDE DAMPERS ODES WITH RIDGE WAVEGUIDE DAMPERS

INCLUDING FERRITEINCLUDING FERRITE

BASED ON R&D OF “EU PROJECT”

(NTHU)

SUMMARYSUMMARY

11-- OPTIMISATION OF THE BODY OPTIMISATION OF THE BODY ((Naked CavityNaked Cavity))

22-- OPTIMISATION OF THE FERRITE LOADED RIDGE WAVEGUIDEOPTIMISATION OF THE FERRITE LOADED RIDGE WAVEGUIDE

33-- SIMULATION OF THE GLOBAL CAVITY : BODY + 3 DAMPERS SIMULATION OF THE GLOBAL CAVITY : BODY + 3 DAMPERS

44-- COMPARISON : MAFIA / GDFIDL FOR SIMULATION OF COMPARISON : MAFIA / GDFIDL FOR SIMULATION OF THE BESSY II CAVITY THE BESSY II CAVITY (a design which doesn(a design which doesn´t use Ferrite)t use Ferrite)

1 - FIRST STEP : OPTIMIZATION OF THE BODY*- Superfish (2D) calculates Eigenvalues and main parameters of RF symmetrical cavities

74267426148.981148.9814984449844352.222352.222SUPERFISHScaled BESSY II Scaled BESSY II Cavity OptimisedCavity Optimised

6736142.447300353.5URMEL

[Dr H.Henke / Dr T.Weiland -

1984]LEP Model Cavity / LEP Model Cavity /

ESRF ESRF

52125212128.535128.5354055340553499.256499.256GDFIDL49534953128.147128.1473865138651499.726499.726SUPERFISH

48724872128.139128.1393801838018499.842499.842MAFIA[Dr F.Marhauser /

Bessy - 2000]BESSY II

66206620138.309138.3094786447864352.182352.182SUPERFISH

59025902128.196128.1964603946039352.078352.078SUPERFISHScaled BESSY II Scaled BESSY II Cavity Cavity Not OptimisedNot Optimised

76337633149.140149.1405118051180352.171352.171GDFIDL

RR(k Ohms)(k Ohms)

R/QR/Q(Ohms)(Ohms)QQ

ffRFRF(MHz)(MHz)

SIMULATION SIMULATION TOOLSTOOLSTYPE OF CAVITYTYPE OF CAVITY

- GDFIDL (3D) is used as Eigenvalue or Time domain solver for arbitrary RF structures

(** PERFECT BODY WITHOUT HOLE)

AA-- GDFIFL AS EIGENVALUE SOLVER FOR H.O.M STUDY OF THE BODYGDFIFL AS EIGENVALUE SOLVER FOR H.O.M STUDY OF THE BODY

GDFIDL is a Finite Difference solver for the Maxwell and Helmholz equations. Can be used as Eigenvalues or Time domain solver for arbitraries rf structures.

6490825361173.400-M-3

8418502311111.370-E-4

658694489896.9590-E-3

310940758865.4080-M-2

1355442533498.5240-M-1

149763351180352.1710-E-1

R/Q (Ω)

R(kΩ)

QFREQUENCY (MHz)

MODE TYPE

LIST OF THE MOST INFLUENTIALS LONGITUDINAL MODES TILL 1.3 GHz

Notations : m-E-n or m-H-n, m for azimuthal dependency, n as sequential index.Conditions : simulation of half cavity with electric or magnetic boundary for a meshing of 2 mm.

BB-- GDFIDL AS FINITE DIFFERENCES IN TIME DOMAIN SOLVER (FDTD) FOR TGDFIDL AS FINITE DIFFERENCES IN TIME DOMAIN SOLVER (FDTD) FOR THE BODYHE BODY

Conditions : Simulation on only 200 meters of half the cavity with magnetic boundary for a meshing of 2 mm. (No offset on transverse plane)

40x103

30

20

10

0

Impedance (O

hm

s)

1.6x109

1.41.21.00.80.60.4Frequency (Hz)

1494.71

352.234 MHz

497.474

896.5961110.45

1172.21

1316.30

1320.881464.97

864.575

1561.04 MHz

Remark : For modes which should have an high Q value,

the calculated impedance isn´t accurate

It´d require a longer wake length

FERRITEFERRITE

2 2 -- SECOND STEP : OPTIMIZATION OF SECOND STEP : OPTIMIZATION OF FERRITE LOADED RIDGE WAVEGUIDEFERRITE LOADED RIDGE WAVEGUIDE

WITH 3D SIMULATION SOFT : WITH 3D SIMULATION SOFT : High Frequency Structure Simulator (HFSSHigh Frequency Structure Simulator (HFSS®®))HFSS is based on a Finite Element Method with adaptive mesh refinement.

Eigenmodes of arbitrary RF strucutres are solved, including materials losses.

BASED ON DESIGN of N.T.H.U and BESSY

[P.Z Rao / F.Marhauser / E.Weihreter – 05/2004]

BASIC MODEL BASIC MODEL (Longitudinal cut)(Longitudinal cut)

VACUUMVACUUM

METALLIC METALLIC RIDGERIDGE

Waveguide part long enough to attenuate the fRF mode

P/Po = exp [ -(4.π.Z / λ).( 1-(λc / λ)2 )1/2 ]

Here, for : z = 0.25 m ⇒ P/Po ≈ 0.07

fc = 435 MHz

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

S11

1600140012001000800600Frequency (MHz)

AA-- BASIC FERRITE MODELBASIC FERRITE MODEL

fRF < fcRWG < f0M1

e = 6.350 mm

e = 3.175 mm

e = 1.5875 mm

fcRWG = 435 MHz

Effect induced by variation Effect induced by variation of Ferrite thickness (e)of Ferrite thickness (e)

No Ferrite Step

BB-- TAPERED FERRITE MODELTAPERED FERRITE MODEL

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

S11

1000900800700600500

Frequency (MHz)

BM - e = 6.350 mm

BM - e = 3.175 mm

BM - e = 1.5875 mm

TFM - e = 3 mmTFM - e = 6 mm

TFM - e = 12 mm

Effect induced by variation of Ferrite thickness (e) for Effect induced by variation of Ferrite thickness (e) for BBASIC ASIC MMODELODEL ((BMBM) and ) and TTAPERED APERED FFERRITE ERRITE MMODELODEL ((TFMTFM))

TFMTFM

CC-- TILE FERRITE MODELTILE FERRITE MODEL

NO STEP

TILES WITH PROGRESSIVE

THICKNESS

⇒ TO OBTAIN AN HOMOGENEOUS REPARTITION OF THE ABSORBED POWER

RESULTS OF SIMULATIONS TO COMPARE RESULTS OF SIMULATIONS TO COMPARE 3 TYPES OF FERRITE LOADED RIDGE 3 TYPES OF FERRITE LOADED RIDGE

WAVEGUIDE MODELSWAVEGUIDE MODELS0.80

0.75

0.70

0.65

0.60

0.55

0.50

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00

S11

1000900800700600500

Frequency (MHz)

BASIC MODEL - e = 1.5875 mm

TILE MODEL - e : 1 to 20 mm

TAPERED MODEL - e = 12 mm

EVOLUTION OF DENSITY POWER ABSORBED BY FERRITE EVOLUTION OF DENSITY POWER ABSORBED BY FERRITE FOR 3 MODELS : BASIC, TAPERED, TILEFOR 3 MODELS : BASIC, TAPERED, TILE

(FOR 1W INCIDENT)(FOR 1W INCIDENT)1.00

0.99

0.98

0.97

0.96

0.95

Abso

rbed P

ow

er

(W)

1000900800700600500

Frequency (MHz)

0.9998

TAPERED MODEL (e = 12mm)

BASIC MODEL (e = 1.5875 mm)

TILE MODEL (7 Tiles, e = 1/1.5/3/4/6/8/20)

3 3 -- THIRD STEP : THE GLOBAL CAVITY THIRD STEP : THE GLOBAL CAVITY - Body + 3 Dampers -

⇒ With GDFIDL only

VIEW OF THE WHOLE CAVITYVIEW OF THE WHOLE CAVITY

Including Ferrite

100x103

80

60

40

20

0

IMPE

DA

NCE (

Ohm

s)

3.0x109

2.82.62.42.22.01.81.61.41.21.00.80.60.4

FREQUENCY (Hz)

BODY + 3 DAMPERS : BASIC MODEL

BODY + 3 RIDGE WAVEGUIDES : WITHOUT FERRITEBODY + 3 DAMPERS : TILE MODEL

HOM max for 1A / 18 cavities (normalized)

HOM max for 500 mA / 18 cavities (normalized)

HOM max for 300 mA / 18 cavities (normalised)

FDTD SIMULATION WITH GDFIDL FOR FDTD SIMULATION WITH GDFIDL FOR THE GLOBAL CAVITY WITH 3 DAMPERSTHE GLOBAL CAVITY WITH 3 DAMPERS

For material properties at 500 MHz

Conditions : Simulation on 600 meters and 2 mm meshing. (No offset on transverse plane)

⇒ The TILE MODEL is a better absorber than

the BASIC one

25x103

20

15

10

5

0

IMPED

AN

CE (

Ohm

s)

2.2x109

2.12.01.91.81.71.61.51.41.31.21.11.00.9

FREQUENCY (Hz)

BODY + 3 DAMPERS : BASIC MODEL

BODY + 3 RIDGE WAVEGUIDES : WITHOUT FERRITEBODY + 3 DAMPERS : TILE MODEL

HOM max for 1A / 18 cavities

HOM max for 500 mA / 18 cavities

HOM max for 300 mA / 18 cavities

ZZOOOOMM ON BANDWITH : 0.9 to 2.2 GHzON BANDWITH : 0.9 to 2.2 GHz

GDFIDL ASGDFIDL AS EIGENVALUE SOLVER FOR EIGENVALUE SOLVER FOR THE GLOBAL CAVITYTHE GLOBAL CAVITY

R (k Ω)

R/Q (Ω)

Q

fRF (MHz)

Parameters

668868077426

145.130145.923148.981

460844664549844

345.584345.676*352.222

BODY + 3 DAMPERS :BASIC FERRITE

MODEL

BODY + 3 WAVEGUIDES :WITHOUT FERRITE

BODY

Study of the fundamental mode only - 2 mm meshing

*Remark Remark : Insertion of Ridge Waveguides had induced a huge shift on the fundamental frequency

120x103

100

80

60

40

20

0

ReZ

[Ω

]

3.0x1092.52.01.51.00.5Frequency [Hz]

MAFIA / F.Marhauser (BESSY) GDFIDL / V.Serrière (E.S.R.F)

4- COMPARISON MAFIA / GDFIDL FOR SIMULATION OF BESSY II CAVITY

(3 Circular Waveguides with Coaxial Transition DAMPERS)

- STRUCTURE WITHOUT ABSORBING MATERIALWITHOUT ABSORBING MATERIAL -

Wake on 400 meters and a 4 mm meshing

ZZOOOOMM ON BANDWITH : 0.6 to 1.2 GHzON BANDWITH : 0.6 to 1.2 GHz

ZZOOOOMM ON ON BANDWITH : 1.2 to 1.8 GHzON ON BANDWITH : 1.2 to 1.8 GHz

CONCLUSION ON SIMULATION TOOLS AND RESULTS

SIMULATIONS WITH 3 RF SIMULATION SOFTS HAS BEEN DONE : . SUPERFISHSUPERFISH : Perfect for optimisation of simple symmetrical Body . HFSSHFSS : Adapted for S parameters studies (even including absorbing materials) . GDFIDLGDFIDL : Usefull for H.O.M studies of complex Cavities even including ferrite

THE MAIN ELEMENTS OF THE CAVITY HAVE BEEN STUDIED GLOBALY : BODY, RIDGE, FERRITE

OPTIMISE THE “TILE” MODEL AGAIN TO ABSORB SUFFICIENTLY H.O.M WITHOUT THE FUNDAMENTAL ONE (by changing width and gap of the ridge and the length of the waveguide)

OBTAIN A FUNDAMENTAL MODE WITH A FREQUENCY CLOSER TO 352.2 MHz

THERMAL STUDY OF THE CAVITY

1) ASPECTS ALREADY DEALED WITH :

2) … POINTS TO DO :

…

STUDY OF TRANSVERSE H.O.M