Can Stripline Beam Position Monitors Work in the

Can Stripline Beam Position Monitors Work in the CLIC Drive Beam? Steve Smith 5 March 2010

CLIC Drive Beam BPMs • Requirements – Transverse Resolution < 2 microns – Temporal Resolution < 10 ns • Bandwidth > 20 MHz – Absolute accuracy < 20 microns – Must survive • even un-anticipated beam modes – Wakefields < TBD • Potential Solutions: – Striplines – Buttons – resonant cavities – Detect dipole modes in other structures? CLIC Steve Smith March 2010

Stripline BPM • Are stripline BPMs feasible? – Resolution – Temporal Response – Wakefields • Even if feasible – Are Stripline BPMs the best choice? – Probably not, if cavity BPMs work • Stripline BPM: – Basis of Operation – Parameters – Algorithm CLIC Steve Smith March 2010

Stripline BPM • A short bunch with charge Q • Traversing a BPM Stripline – With Impedance Z – length L – And angular coverage f • Produces an impulse doublet CLIC Steve Smith March 2010

Stripline BPM • Algorithm: – Measure amplitudes on 4 strips • Resolution: Given: R = 11. 5 mm and sy < 2 mm Requires s. V/Vpeak = 1/6000 12 effective bits • Small difference in big numbers • Calibration is crucial! CLIC Steve Smith March 2010

Stripline BPMs • Limitations of conventional striplines • 12 GHz bunch spacing – lowest frequency intentionally provided in beam spectrum – Above waveguide propagation cutoff – TE 11 ~ 7. 6 GHz for 23 mm aperture – Non-local signals above cutoff – At 12 GHz we’re intentionally propagating >100 MW • Try lower frequency – Below waveguide cutoff – Signal are local below cutoff – How much signal is needed? – How much signal is present? – Try Fbpm = 2 GHz – Main beam doesn’t see 2 GHz CLIC Steve Smith March 2010

Stripline Parameters • • • Diameter 23 mm Stripline length 38 mm Width: 10% of circumference Impedance 50 Ohm Transfer response: – Peaks at 2 GHz (+ 6 & 10 GHz) – Nulls at 4, 8, 12 GHz (!) CLIC Steve Smith March 2010

Processing • Filter to ~ 20 MHz Bandwidth around 2 GHz • Downmix to some convenient IF • Digitize with fast, high Neff ADC – E. g. 120 Msample/sec, 12 effective bits • Chose convenient Intermediate frequency FIF ~ 30 MHz – or 90 or 120 MHz) – Assume noise figure ~14 d. B – Including • cable, filter and mixer losses • amplifier NF • ADC noise • Single-bunch resolution sy < 2 microns for Q > 100 p. C • Need 10 m. A of current modulation at BPM processing frequency to achieve 2 micron resolution • Beam current: 100 A – 10 -4 modulation is sufficient for BPM – Noise or driven modulation CLIC Steve Smith March 2010

Natural Charge Variation • Tolerance to charge variation is ~ 10 -3 • Assume spectrum is white noise (flat in frequency) – (consider other noise models later) • How much of this fluctuation is in BPM processing Bandwidth? CLIC Steve Smith March 2010

Study Beam Current Noise • Noise Density Models – White Noise • Power ~ independent of frequency • No correlation between charge of adjacent bunches – Brownian Noise • P~ 1/f 2 • Random walk – “Pink” noise • P ~ 1/f • “flicker noise” • Consequences of bunche-interleaving (frequency multiplication) • White noise – Bunch interleaving only increases frequencies – Doesn’t change power distribution • Brownian & Pink Noise: – Study CLIC Steve Smith March 2010

• • • Brownian Noise Assume Power spectral density of Charge in Drive Beam Linac is P ~ 1/f 2 Re-map bunch number through Delay Loop, and Combiner Rings What is noise and its spectrum? CLIC Steve Smith March 2010

Brownian Noise • Spectrum is 500 MHz and harmonics, scaling like 1/f 2 – Why? – Interleaving of 24 segments of 120 bunches each modulates low-frequency noise to multiples of 500 MHz – In approximation that current ~ constant across 120 bunch segment, spectrum would be purely harmonics of 500 MHz. • Harmonics fall off like 1/f 2 – Due to our choice of noise spectrum • 1/f 2 in this case CLIC Steve Smith March 2010

Pink Noise • • Important features do not depend on noise model Example: Pink Noise – P ~ 1/f – More high frequency components than Brownian – Now spectral lines fall off at 1/f – “interleaving” of segments not so obvious due to larger high-frequency components than Brownian – Low frequencies still up-converted to 500 MHz and harmonics CLIC Steve Smith March 2010

Impact on BPM design • • • Low-frequency noise in DBL gets upconverted to N x 500 MHz Perhaps make striplines longer Propose to peak response peak at. 5 GHz. Reduces coupling at 2 GHz by sin(60 o) = 0. 866 Increases coupling at 500 MHz to ½ that at peak of response Choice of operation at 0. 5, 1. 0, 1. 5, 2. 0 GHz CLIC Steve Smith March 2010

Drive Beam Charge Feedback? • Will charge feedback work too well? – Wipe out charge noise on which BPM operates? • CLIC operation mostly cares about low frequency noise • Structure fill time smoothes out high frequencies • Bunch spacing = 2 GHz bunch spacing – don’t care about frequencies at harmonics of bunch spacing – For frequencies F = N x 2 GHz – Either make feedback not “too good” at high frequencies – Or inject signal into feedback to create desired modulation CLIC Steve Smith March 2010

Induce Charge modulation? • If natural bunch-bunch charge variation is insufficient for BPM signal • Can we intentionally modulate beam charge by 10 -4 ? – At 2 GHz? • Modulate drive beam at 10 -4 in drive beam linac – 4 cycles/2880 bunches = 4/5. 76 ms = 0. 69 MHz – Frequency multiplying / bunch interleaving translates this modulation to 2 GHz. • Every bunch in the main beam sees the same drive since bunch spacing is 2 GHz. • Plus temporal filtering by – PETS fill time of 1 -2 ns – Accelerating cavity fill time of ~ 50 ns • If we need better resolution: – increase modulation – otherwise reduce modulation amplitude CLIC Steve Smith March 2010

Intentional Charge Modulation CLIC Steve Smith March 2010

Single Bunch Response • What happens if a single bunch of full charge traverses this BPM? • Transient is too big for dynamic range • Not too big for damage threshold • Need programmable attenuator in signal path to support this mode. CLIC Steve Smith March 2010

Bunch trains • Bunch train response • Common-mode power during train – ~4 k. W – at 12 GHz and harmonics • Average power at 100 Hz rep rate ~100 m. W • What if delay loop and/or combiner rings are turned off? – E. g. for commissioning, debugging • Current drops by factor of up to 24 • Does resolution go down? – No, signal at 2 GHz increases – from ~ 10 m. A to up to 2000 m. A • Resolution improves when commissioning(!) • Need programmable attenuators in signal path CLIC Steve Smith March 2010

Bunch Train Leading/Trailing Transients • Attenuator takes care of single bunch/non-standard fill patterns • What about the turn-on / turn-off transients of the nominal fill pattern? • Simulate 4 -ns ramp up/down • A few-ns ramp-up adequately limits transients • >10 ns ramp-up anticipated for beam-loading compensation • What about details of beam-loading compensation? CLIC Steve Smith March 2010

TBD • Does beam-loading compensation scheme produce too much 2 GHz at beginning of train? – Fill starts halfway full, then bunches dropped to other end of train – Spectrum may be very interesting – Need to get fill pattern, study • Coupling to ~10 k. W of TM 01 mode RF power at 12 GHz? – May need improved rejection of 12 GHz in upstream end of striplines • Must do a full simulation of stripline for all modes • How does response non-linearity affect steering algorithm? – Striplines integrate over beam charge distribution with non-uniform weight CLIC Steve Smith March 2010

Revised Stripline Parameters • • • Diameter 23 mm Stripline length 50 mm Width: 10% of circumference Impedance 50 Ohm Again stripline response has null at 12 GHz CLIC Steve Smith March 2010

Wakefields • Dipole wake: • W 1 = 35 m. V/p. C/mm 2 – integrated over 1 BPM – Low Q • Comparable to pair of choke cavities at end of PETS CLIC Steve Smith March 2010

Summary • As far as we can tell conventional stripline BPM can work – On local signals – Below waveguide cutoff • Can achieve required resolution • Should have accuracy of typical BPM of this diameter • But it would work on charge variation in drive beam to get signal • There exist multiple possible processing frequencies • Must pay attention to source of charge modulation which provides signal for BPM – Bunch charge variation? – Intentional modulation in drive beam linac • Low amplitude ~10 -4 level • Impress modulation at low frequency < MHz • Bunch interleaving upconverts modulation frequency CLIC Steve Smith March 2010

Alternatives • Dedicated cavity? – Dipole cavity BPMs measure offset directly • not small difference of big numbers – Don’t need much coupling to achieve resolution requirements • Therefore doesn’t require much wakefield • Calibration simpler than stripline • Works at bunch rate fundamental – Rather than on noise, modulation • Incidental use of feature already present in PETS? – Choke cavities can be tweaked for dipole mode at 12 Ghz • But Igor keeps finding ways the position signal gets contaminated: – mode conversion of fundamental mode, – Fabrication tolerances • If there is a robust solution, this would be very sweet! CLIC Steve Smith March 2010