Design considerations for astorage ring resonant cavity

beam position monitor /tilt monitor for SPX

Glenn DeckerOctober 1, 2010

ASD Seminar

The Monolith

Dave Bowman: Open the pod bay doors, HAL.

HAL: I’m sorry, Dave. I’m afraid I can’t do that.

Dave Bowman: What’s the problem?

HAL: I think you know what the problem is just as

well as I do.

Dave Bowman: What are you talking about, HAL?

HAL: This mission is too important for me to

allow you to jeopardize it.

h

w

d

x

y

z

(0,0,0)

fmnp =c

2 [ mw( )

2+ n

h( )2 p

d( )2

+ ]

fmn0 =c

2 [ mw( )

2 nh( )

2+ ]

1/2

1/2

Ez = Ez0 sin(mπx/w) sin(nπy/h)

Bx = Bx0 sin(mπx/w) cos(nπy/h)

By = By0 cos(mπx/w) sin(nπy/h)

Pillbox TM modes p = 0;independent of z:

Rectangular Cavity Modes

E

B

h

w

Second Lowest Mode 120

dx

y

z

Ez = E0 sin(πx/w) sin(2πy/h)

Bx = Bx0 sin(πx/w) cos(2πy/h)

By = By0 cos(πx/w) sin(2πy/h)

f120 = 5.63 GHz

E

B

e-

VerticalBPM / TiltMonitor

= 2 * SPX frequency

h=w

h = w = 5.95343 cm

(w,h) = (4.39486,6.69288) cmf210-f120 = f120-f110 = 1.55 GHz,Maximum mode separation

5 10 15 20

h(cm)

10

15

5

Choice of Transverse

f120 = f210 ; degeneracy

h = 5.32491 cmasymptote

w = 2.66246 cmasymptote

Cavity Dimensions

f120[w,h] = 5.63 GHz

w(cm)

ModeFrequency

(GHz)

110 4.08

120 5.63

210 7.18

130 7.54

220 8.16

230 9.57

140 9.59

310 10.47

320 11.17

240 11.26

150 11.71

330 12.24

(w, h) = (4.4, 6.7) cmf210 - f120 = f120 - f110 = 1.55 GHz,

Maximum mode separation

BPM / Tilt Mode

110*

210

4.08 GHz 5.63 GHz

120**

7.18 GHz

220**

8.16 GHz

310*

130* 140**

7.54 GHz 9.59 GHz

10.47 GHz

320**

11.17 GHz

230

9.57 GHz

150*

11.71 GHz

240**

11.26 GHz

330*

12.24 GHz

Pillbox Mode Symmetries

*Beam-driven modes;

w=4.4 cm

h=6.7cm

x

y

** Vertical BPM-like Modes:

Bx(h/2+δy) = - Bx(h/2-δy),

Bx(h/2+δy) = Bx(h/2-δy).

(0,0)

Bx(y=h/2) = 0

Bx(y=h/2) non-zero

Output

e-

Waveguides(Cutoff Freq. between modes110 and 120)

e-

OutputWaveguides

(Cutoff Freq. between modes 110 and 120)

e-

e-

E

BE

B

EB

Top View

Front ViewSide

EB

RFRF

Two-sided Waveguide Couplers

View

TE10

x

y

Orthographic Projection

E

B

B

E

B

B

E

Fields

Total energy stored in cavity with peak longitudinal field D:

Voltage, Energy

Bunching Factor Untilted Beam

Bunching Factor Tilted Beam

The energy deposited into mode TMmn0 by a point charge q is q2

Loss Factor

(0,0,0)

Cavity width a (cm)Cavity depth d (cm)

10

20

5

10

d

(0,0,0)

Cavity height b (cm)

5 10

20

0 / y2(m-3)

8E48E4

Loss Factor

Peak at (a, b, d) = (w, h, d) = (5.33, 6.15, 1.98) cm

Loss Factor, BPM

Loss Factor, Tilt Monitor

Power deposited into mode TM120 including bunching factor and resonant enhancment:

Results

Q

LOM, HOM Power

Mafia Model

Mafia Model, Bx at top of Cavity,

t = 33 ps

TM110

TM130

TM310

TM330?

????

1.25 mm 2.5 mm

Mafia Model, Ey in External Waveguide

t = 33 ps

TM120

TM140

TM320?

TM340?

????

1.25 mm 2.5 mm

e-

e-

E

BE

B

EB

Top View

Front View Side

EB

View

TE10

LOMH-Loops,

To ProcessingElectronics

Top TopLoop Loop

BottomLoop

BottomLoop

E-probe

HeavyCoupling E

B

B

E

B

B

E

LOM Loop Couplers

Top Loop

Bottom Loop

0

180

Modes 110, 130, 150, etc.

Short

Modes 120, 140, 160, etc.

Terminated

Reflected

SuitableDelay

Broadband Hybrid

Odd LOM / HOM Damping Scheme

3 - 15 Ghz

(also 310, 510, etc.)

Input CablesPhase Matched

Waveguide Tee (H-Plane)

http://www.sunist.org/shared%20documents/References/TeeGSG.pdf

Ez Surface Charge Density

E

BE

B

EB

BE

EB

BE

TM120

Cavity Mode

TE10

Waveguide Mode

EB

BE

EB

B

E

E

B

BE

EB

B

E

Waveguide Ring

Resonator

E

B

TM110

Cavity Mode

Waveguide Ring

Resonator

E

B

B

E

B

E

BE

BE

To WaveguideTermination

e-

e-

Front View

Side View

Top View

WaveguideH-Plane TeeWR-187

Low Order ModeWaveguide TerminationScheme

BroadbandLoad

E-Field Lines

Summary

● A C-band cavity beam position / tilt monitor design concept has been completed.

● Dimensions are 4.4 cm wide by 6.7 cm high to maximize LOM / HOM mode separation (a bit wider will improve signal strength).

● Operating frequency is 5.63 GHz = 2 * SPX crab cavity frequency.● Output waveguide prevents strongly beam-driven LOM, HOM modes from

getting to processing electronics.● Sensitivity amounts to -47 dBm = 30 microradians = 360 nanometers (with

24 bunches, 102 mA total stored beam current, 5 mm cavity depth).● LOM power deposited at 4.08 GHz is 300 watts, scales with cavity depth.

● Mafia simulations support design concept, sensitivity to mode TM140 is strongest. Everything coupled to output waveguide scales with vertical position / tilt.

● LOM, HOM mode damping scheme using waveguide appears feasible.