llrf preliminary design review 9-26-2005vojtech pacak/ron akre1 beam phase detector – pillbox...

9-26-2005 Vojtech Pacak/Ron Akre 1

LLRF Preliminary Design Review

BEAM PHASE DETECTOR – PILLBOX CAVITY

• Basic Requirements and Parameters

– Operating frequency: S-Band: f = 2856 MHz

– Loaded cavity bandwidth: 500 kHz Qo 2856/0.5 = 5700

– Power extracted from the cavity: 0.5 – 1 W

– Phase resolution: 0.03

– Charge of a single bunch: 0.1 – 1 nC

– Beam velocity, (v/c): = 1.0

– Axial space available: ~4” (~10 cm)

– Bore of the beam pipe: 0.87” i.e. r = 1.105 cm

• Superfish Simulation – 1” cavity

See Fig1 and Table 1.

– Cavity diameter: 3.27”

– Cavity height: 1.0”

– Unloaded Quality factor: Q = 12800

– Cavity Shunt Impedance R = V2p/2P = 1.5 M

– Transit Time Factor: T = 0.798

– Wake-loss parameter: k = 6.76x1011 V/C



Calculated Secondary Parameters – all values for a bunch charge 1 nC

– Voltage induced in the cavity by a relativistic charge q: Vq = 2 k.q ----------1352 Vp

– Energy stored in the cavity: Wq = (Vq/2) q ------6.76 x 10-7 J

– Power lost in the cavity: P = Wq/Q ---------0.95 W

– Peak voltage generated into 50 load for = 1, (Qe = Q): V50 = √(2x50xP) --9.7 Vp

Note:1) for a bunch charge 0.1 nC the deposited energy will be 100 times smaller and the induced voltage will be 10 times smaller

2) the above results were calculated for a critically coupled cavity; the output signal will depend on the output coupling coefficient , i.e. on the external Qe, see the graphs on Figs. 2 -5.

3) real cavity shunt impedance R will be 10 – 20% smaller



• Phase Signal Losses

– 14-bit ADC max signal: full scale output: 2.3 Vp-p or ~11 dBm

– Mixer Loss: 6 dB

– Chassis Losses: 2 dB

– Cable Losses: 8 dB

______________

Signal power needed for full scale ADC output: ~27 dBm or 0.5 W

• S/N Ratio

– ADC S/N Ratio: ~70 dB, (noise level ~ 260 V rms)

Available cavity output power and Vrms and S/N ratio at the ADC input for critical coupling:

1 nC bunch: ~1.0 W , ~1.1 Vrms , ~72 dB

0.1nC bunch: ~0.01 W , ~0.1 Vrms , ~52 dB

The above S/N ratio can further be increased by ~14 dB, (i.e. by a factor of 5), by averaging the output signal from the cavity – see Fig. 6.

• Phase Resolution

0.1nC bunch, S/N ratio after averaging 64 samples: 66 dB

– Phase signal resolution = 10-66/20 = 5 x 10 -4 radian ~= 0.03.

• Pillbox Cavity Test Model

– Simple mechanical model of the cavity is currently under construction, see Fig. 7.



90 V

79 V

1” pillbox cavityAxial Electric Field = 1000 V/m

z [cm]

r [c

m]

Fig. 1



2.856-GHz TM010 Short Pillbox Cavity Full, 1 inchProblem file: C:\LANL\MY_FILES\LCLS_PHASEDETECTORCAVITY\PH_DET_CAV_INCH_LCLS_FULL_BEAM_PIPE4_5CM.AF 7-23-2005 10:48:38-------------------------------------------------------------------------------Field normalization (NORM = 0): EZERO = 0.00100 MV/mFrequency = 2854.19710 MHz Relation between RF definition of the shunt impedanceBeta = 1.0000000 and the effective "linac shunt impedance definition”:

Transit-time factor = 0.7981844 R/Q = (r/Q)/(2T2)Stored energy = 1.90824E-09 JoulesUsing standard room-temperature copper. Data used for calculationSurface resistance = 13.93808 milliOhmNormal-conductor resistivity = 1.72410 microOhm-cmOperating temperature = 20.0000 CPower dissipation = 2673.3028 uWQ = 1.2801E+04 Shunt impedance = 3.3666E+01 MOhm/mRs*Q = 178.424 Ohm Z*T*T = 2.1449E+01 MOhm/mr/Q = 150.797 Ohm Wake loss parameter = 0.67608 V/pCWall segments:Segment Zend Rend Emax Power P/A dF/dZ dF/dR (cm) (cm) (MV/m) (uW) (uW/cm^2) (MHz/mm) (MHz/mm)---------------------------------------------------------------------------------------------- 3 -1.3000 1.1050 6.3341E-03 2.050 9.23E-02 0.000 5.237 4 -1.3000 4.0950 6.3279E-03 800.5 16.39 -3.041 0.000 5 1.3000 4.0950 3.3699E-07 1068. 15.97 0.000 -72.03 6 1.3000 1.1050 6.7441E-03 800.5 16.39 -3.041 0.000 7 4.5000 1.1050 6.7441E-03 2.077 9.35E-02 0.000 5.242 ---------------------------------------------------------------------------------------------- Total Dissipated Power 2673.

TABLE 1



Figs. 2 - 5



FIG. 6



FIG. 7

llrf preliminary design review 9-26-2005vojtech pacak/ron akre1 beam phase detector – pillbox...

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