1. LLRF Preliminary Design Review 9-26-2005Vojtech Pacak/Ron Akre1 BEAM PHASE DETECTOR – PILLBOX CAVITY Basic Requirements and Parameters – Operating frequency: S-Band: f = 2856 MHz – Loaded cavity bandwidth:  500 kHz  Q o  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 = V 2 p /2P = 1.5 M  – Transit Time Factor:T = 0.798 – Wake-loss parameter:k = 6.76x10 11 V/C

2. LLRF Preliminary Design Review 9-26-2005Vojtech Pacak/Ron Akre2 Calculated Secondary Parameters – all values for a bunch charge 1 nC – Voltage induced in the cavity by a relativistic charge q:V q = 2 k.q ----------1352 V p – Energy stored in the cavity:W q = (V q /2) q ------6.76 x 10 -7 J – Power lost in the cavity:P =  W q /Q ---------0.95 W – Peak voltage generated into 50  load for  = 1, (Q e = Q):V 50 = √(2x50xP) --9.7 V p 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 Q e, see the graphs on Figs. 2 -5. 3) real cavity shunt impedance R will be 10 – 20% smaller

3. LLRF Preliminary Design Review 9-26-2005Vojtech Pacak/Ron Akre3 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.

4. LLRF Preliminary Design Review 9-26-2005Vojtech Pacak/Ron Akre4 90 V 79 V 1” pillbox cavity Axial Electric Field = 1000 V/m z [cm ] r [cm] Fig. 1

5. LLRF Preliminary Design Review 9-26-2005Vojtech Pacak/Ron Akre5 2.856-GHz TM010 Short Pillbox Cavity Full, 1 inch Problem file: C:\LANL\MY_FILES\LCLS_PHASEDETECTOR CAVITY\PH_DET_CAV_INCH_LCLS_FULL_BEAM_PIPE4_5CM.AF 7-23-2005 10:48:38 ------------------------------------------------------------------------------- Field normalization (NORM = 0): EZERO = 0.00100 MV/m Frequency = 2854.19710 MHzRelation between RF definition of the shunt impedance Beta = 1.0000000and the effective "linac shunt impedance definition”: Transit-time factor = 0.7981844 R/Q = (r/Q)/(2T 2 ) Stored energy = 1.90824E-09 Joules Using standard room-temperature copper. Data used for calculation Surface resistance = 13.93808 milliOhm Normal-conductor resistivity = 1.72410 microOhm-cm Operating temperature = 20.0000 C Power dissipation = 2673.3028 uW Q = 1.2801E+04 Shunt impedance = 3.3666E+01 MOhm/m Rs*Q = 178.424 Ohm Z*T*T = 2.1449E+01 MOhm/m r/Q = 150.797 Ohm Wake loss parameter = 0.67608 V/pC Wall 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

6. LLRF Preliminary Design Review 9-26-2005Vojtech Pacak/Ron Akre6 Figs. 2 - 5

7. LLRF Preliminary Design Review 9-26-2005Vojtech Pacak/Ron Akre7 FIG. 6

8. LLRF Preliminary Design Review 9-26-2005Vojtech Pacak/Ron Akre8 FIG. 7