rf design of normal conducting deflecting cavity...rf design of normal conducting deflecting cavity...

RF Design of Normal Conducting Deflecting Cavity

Valery Dolgashev (SLAC), Geoff Waldschmidt, Ali Nassiri

(Argonne National Laboratory, Advanced Photon Source)

48th ICFA Advanced Beam Dynamics Workshop on Future Light Sources March 1-5, 2010

SLAC National Accelerator LaboratoryMenlo Park, California

Deflecting Cavity RF Design and Analysis G. Waldschmidt 8/23/07 2

Motivation


Simplified ConfigurationRF source

Hybrid

1st and 2nd structures 3rd and 4th structures

Klystron

Storage ring

Undulator

HybridHybrid


Outline• Design considerations• Thermal stability• Wakefield damping • Cavity pulsing• X-band deflector


Design requirements for APS deflecting cavity, assuming 4 cavities in the system

Frequency 2.815 GHzDeflecting Voltage 2 MV per structureAvailable power 4 MW per structureRepetition rate ~1000 Hz

The main constraints on the rf design are set by high average power loss in the cavity and heavy wakefield damping.


Design Considerations• Available power ~ 25 MW for whole system• Large aperture radius ≥ 21 mm => Low shunt

impedance• Pulsed heating < 100o C => maximum surface

magnetic field < 300 kA/m for 4 us pulse• Maximum surface electric fields < 100 MV/m• No field amplification on edges of input coupler =>

“Fat lip” coupler• Heavy loading of LOM / HOM’s• High average power operation

“Do no harm” – the set of the transverse cavities should not degrade existing operation modes of the APS ring


Evolution of the Deflecting Cavity Design

(a) 9-cell symmetric cavity with center-fed input coupler and no wakefield damping

(b) 9-cell with wakefield damping and external loads

(c) 9-cell with heavy wakefield damping and internal loads

(d) 3-cell with heavy wakefield damping and internal loads

Input coupler not shown


dampingwaveguides

input waveguide

beam axisz

y

x

3-Cell deflector fed from middle cell, 2 MeV vertical kick with 2.83 MW of input rf power

Surface electric fields for 2 MeV transverse kick. Maximum surface electric fields is 60 MV/m.

Surface magnetic fields for 2 MeV transverse kick. Maximum surface magnetic fields 240 kA/m.


3 cell deflector fed from end cell, transverse kick 2 MeV, input power 2.86 MW

Surface electric fields for 2 MeV kick, maximum fields 60.5 MV/m

Surface magnetic fields for 2 MeV kick, maximum fields 240 kA/m

232 mm

With an “end-cell coupling” the loaded Q of the next-to-working mode is reduced from 11.2·103 to 4.6·103 for critically coupled

cavity and can be reduced more for over-coupled cavity.


Deflecting Cavity with Damping Waveguides and Loads

Beam axis

HOM load in rectangular waveguide

LOM-HOM loads in ridged waveguides

Input coupler


Deflecting Cavity ParametersFrequency 2.815 GHz

Cavity Length ~23 cm

Deflecting Voltage 2 MVPeak Power 2.86 MWWorking mode Qo 12000Rt / Q 117Beam pipe aperture radius 21 mmIris radius 22 mmPhase advance per cell π

Structure length w/o beam pipes

11.17 cm

Iris thickness 18 mmDuty Factor 0.147%Kick / (Power) 1/2 1.19 MeV/MW1/2


-20

-15

-10

-5

0

5

10

15

20

-120 -80 -40 0 40 80 120

ExHy

Elec

tric

Fiel

d [M

V/m

], M

agne

tic F

ield

* Z

o [M

V/m

]

z [mm]

Transverse Electric and Magnetic Fields on Axis

Transverse electric and magnetic fields on axis vs. z for 2MeV transverse kick

EyHx


High Average Power Operation


Iris Optimization• Large >21 mm radius aperture necessary to avoid radiation heating• Klystron pulse width reduced to 1.3 μs to reduce thermal load => duty

factor is 0.147%. • Cavity iris thickened to 18 mm to reduce peak thermal gradients and

increase cooling efficiency.

T12R22: 0.94 MW/m2 T15R23: 0.83 MW/m2 T18R24: 0.68 MW/m2

Elliptical iris with thickness of 18 mm and radius of 22 mm was chosen, for which peak power density was reduced by ~30% while reducing shunt impedance by ~15%

T Iris thickness (mm)R Iris radius (mm)≡≡ “Peak” power density on cavity’s iris surface

Example: Optimization of iris thickness


High Average Power Operation – Thermal Stability

• Cavity will deform due to the rf losses and the deformed cavity may change field profile and result in increased losses.

• Deflecting field profile will be perturbed and may require additional power in order to maintain prescribed deflecting voltage. If this continues, the cavity will absorb more and more heat and exceed material stress limits.

• π-mode in the cavity is “backward standing wave” and it may be more susceptible to rf thermal issues.

We need to show that the cavity is thermally stable.


RF / Thermal Flowchart with ANSYS

Start of rf / thermal analysis

Deformed cavity

Self-contained analysis performed entirely in ANSYS

Loop continues until power level converges

Undeformed cavity


Multi-Pass Magnetic Field DistortionMinimal field distortion after 43 iterations

Black: Original Field MagnitudeRed: Deformed Cavity Field Magnitude

Original / deformed fields are nearly identical


Multi-Pass Frequency Shift

Frequency Shift

100

125

150

175

200

225

250

275

0 10 20 30 40 50

Iteration

Freq

uenc

y (k

Hz)

Slater MethodSlater: End CellSlater: Center CellAnsys HF

Maximum frequency shift from iteration-to-iteration is 2.4 kHz

Frequency converges after the third iteration Frequency shift

shown for a full end / center cell

Study done on the most recent slightly modified geometry


Multi-Pass Power Loss

Power Loss

2086

2088

2090

2092

2094

2096

2098

0 10 20 30 40 50

Iteration

Pow

er

Maximum power variation from iteration-to-iteration is 10.0 W

43 iterations simulated

Study done on the most recent slightly modified geometry


Wakefield Damping


• LOM / HOM monopole and HOM dipole modes were analyzed using the frequency-domain finite-element code HFSS up to 5-6 GHz.

• MAFIA and GdFidL time-domain wakefield solvers were used to evaluate the monopole and dipole mode impedances and compare with HFSS as a verification.

• GdfidL parallel simulations calculated mode impedances > 12 GHz with λ/10 resolution in the high permittivity (εr = 30) damping material.

Low-Order-Modes/ Higher- Order-Mode analysis

3-cell structure was adopted since the heavily-loaded 9-cell cavity could not be adequately damped for beam stability.


• Mode coupling from cavity to damping waveguide was optimized to increase the damping of HOM / LOM’s and reject the operating mode (while keeping thermal issues under control)

• Monopole and horizontal dipole modes are heavily damped with a loaded Q of less than 200 for the majority of modes.

• Vertical dipole modes are not easily damped since their frequency and field configurations may be close to the operating mode.

• Ridge waveguide has been integrated into the design to improve damping of the vertical modes.

LOM/HOM Damping Considerations


Suppression of Long-Range Wakes

x

Monopole wake Horizontal wake


Monopole Modes

2022 MHz1956 MHz

Ql ~ 130

ls P

VR2

2

=


Horizontal Dipole Modes

Ql ~ 20

2620 MHz

2663 MHz

2

2

2 ol

rrt rkP

VR o==


Vertical Dipole Modes

2827 MHz

2815 MHz

2827 MHz mode has a large Rt/Q and is damped minimally. It is the greatest HOM contributor to the vertical long range wake

28272815

2

2

2 ol

rrt rkP

VR o==


Z-Impedance with Inter-Cavity-Coupling Effects

o HFSS GdFidl

fp*RS < 0.8 MOhm-GHz2022 MHz

1956 MHz

Monopole Impedance


Horizontal Transverse -Impedance with Inter-Cavity-Coupling Effects

2.5 MOhm/m

o HFSS GdFidl 2620 MHz


2.5 MOhm/m

o HFSS GdFidl

2815 MHz 2827 MHz

2930 MHz

Vertical Transverse Impedance with Inter-Cavity-Coupling Effects


LOM/HOM Damper Loads – Simplified Model

Load X Center

Load X Outer

Load Y


(W)

Beam Induced Damper Load

130 mA maximum beam current, 24 singlets fill pattern generates greatest damper losses

Loss factor:Mafia: 7.802*1011

GdFidl: 7.82*1011Total losses due to monopole modes is 2.03 kW


Cavity Pulsing

• Critically matched coupler requires ~2.8 MW peak power pulsed at 1 kHz rep rate for a 2 MeV kick of the 16 mA bunch.

• Net deflecting voltage must be reduced below 13 kV for the following 86 mA bunch train (while cavity is emptying).

• Variations in cavity Q due to manufacturing or contamination creates a voltage differential• Overcouple cavity to reduce fill time constant• Reverse klystron phase to empty cavity more

quickly


Pulse Shape and Approximate Timing Diagram

16 mA enters Cav. #1 (Sector 6)

Cavity power

86 mA enters Cav. #1

Red: Ideal square inputBlack: 100 ns ramp

Timing pictorial in APS SR

Klystron power (100 ns ramp)

Duty factor 0.147%

t = 0

Vt = 0.2 MV

Ql ~ 6000 for critically coupled input coupler


Deflecting Voltage Differential for 86 mA Bunch

7.1=β

P=3.0 MW

Peak input power at cavity

1%2%3%4%5%

All cavities have Q’s ranging from Qu = 12,000 ± 600. Cavities optimally positioned based on Q’s.

Single cavity in cavity set #2 with Q 1-5% lower than nominal value (12,000)

Net difference in deflecting voltage between cavity set #1 and cavity set #2


APS Deflector Summary

• The deflecting cavity design has evolved to satisfy strict requirements in beam stability and high average power losses.

• A 3-cell standing wave structure will produce 2 MeV kick with ~2.86 MW input power for a critically coupled cavity.

• Four structures will produce a 4 MeV initial kick and a 4 MeV recovery kick.

• A single, commercially available 25 MW klystron is sufficient. • A set of two structures will occupy less then 50 cm of beam space.• Low-order and high-order modes are heavily loaded by six ridged and

four rectangular waveguides with internal loads. • Cavity power coupling has been characterized for various parameters

affecting parasitic voltage kicks to the beam.

Deflecting Cavity RF Design and Analysis G. Waldschmidt 8/23/07

X-band Deflector


6 cell SW 11.424 GHz deflector


Periodic cell of Pi standing wave deflector,0.25 MW/cell, deflecting gradient 26 MV/m

Maximum surface electric fields 105 MV/m.Maximum surface magnetic fields 410 kA/m,Pulse heating 23 deg. C for 100 ns pulse.

a = 6 mmt = 2 mm, round irisQ=7,792


Waveguide coupler for 6 cell SW X-band deflector,

1.5 MW of input power, deflection 2 MeV

Maximum surface electric fields ~105 MV/m.Maximum surface magnetic fields ~420 kA/m,Pulse heating 24 deg. C for 100 ns pulse.


Parameters of 6 cell X-band SW deflectorFrequency 11.424 GHz

Beam pipe diameter 10 mmOne cell length 13.121 mmPhase advance per cell π

One cell kick 0.34 MeV/Sqrt(0.25 MW)Structure kick (6 cells) 1 MeV/Sqrt(375 kW)Unloaded Q 7800Loaded Q 3800Maximum Electric field 53 MV/m / Sqrt(375 kW)Maximum Magnetic field 210 (kA/m) / Sqrt(375 kW)Structure length (with beam pipes) 12 cmNear mode separation 13.6 MHz


Summary of RF Power Considerations for X-band option

41

• SLAC 11 GHz XL-4 klystron can produce 50 MW of power at 120 Hz repetition rate and pulse length 2 μs. We expect that with some development a modified klystron can work in low power mode ~5 MW at 1 kHz repetition rate.

• A pair of 6-cell deflectors bracketing one undulator will need about 1 MW, so one such klystron is capable of powering 5 (~20 with SLED) “short x-ray pulse” stations at ~1 kHz repletion rate.

• For 1kHz operation, average power loss in 6 cell deflector would be manageable 200 W.

• With lower beam energy (say for SPEAR III) the deflectors could be driven by commercial 100 kW klystrons, like CPI’s VKX-7876E .

rf design of normal conducting deflecting cavity...rf design of normal conducting deflecting cavity...

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