A Possibility of Constant Energy Extraction at ATF2 Kalinin Accelerator Science
Wilkens, John, Features Writer has reference to this Academic Journal, PHwiki organized this Journal A Possibility of Constant Energy Extraction at ATF2 Kalinin Accelerator Science in addition to Technology Centre Daresbury Laboratory Warrington UK FONT Meeting 19 April 2007 Ox as long as d Beam energy oscillations of a few take place at the KEK ATF. The amplitude in addition to phase at the extraction turn r in addition to omly fluctuates extraction by extraction. The energy jitter causes a position/angle jitter in the Diagnostic section of the Extraction Line. To have jitter reduced, an energy stabilisation approach is proposed that is constant energy extraction done at the turn where the oscillation passes zero. Improvement by factor of 10 can be obtained even when the extraction is done with uncertainty up to several turns. For a three-bunch ATF mode, oscillation measurement results are given. An extraction set-up based on a turn-by-turn BPM in addition to a digital processor is proposed. A set of signal processing algorithms is discussed. ENERGY OSCILLATION Investigating energy oscillations of three bunches, we discovered that bunches oscillate together, as a solid structure. So, as long as this mode a fine method of energy stabilisation can be suggested based on that circumstance that floating number of the extraction turn makes no difference to ATF2 experiments. Continuously monitoring the energy oscillation, it is possible to pick up the turn where the oscillation passes the energy equilibrium value, in addition to on the next turn execute the extraction.
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An energy oscillation manifests itself as a horizontal oscillation in the non-zero dispersion Damping Ring arcs. For dispersion 0.1m in addition to energy deviation the oscillation amplitude is 20m. To measure horizontal oscillation, we used a BPM connected to a pair of the upper button electrodes of the arc pickup. A sum-difference Jitter BPM processor  was used. In one shot, the sum in addition to difference multi-turn arrays were recorded by the oscilloscope. The sampling interval was 0.2ns, the memory length was about 300 turns. The arrays were transferred to a computer where bunch selection in addition to intensity normalisation was done prior to oscillation analysis. The BPM was calibrated against the orbit DR BPMs. Figure 1. Synchrotron oscillations of three bunches. The oscillation envelope is unstable. The oscillation amplitude in addition to the phase on the last turn r in addition to omly fluctuate extraction by extraction. Figure 2. Synchrotron (left) in addition to betatron (right) spectra. To see relative phases of the bunches, oscillation difference spectra were calculated. The peak of height about 28m is the spectrum of the first bunch oscillation. The spectrum of each bunch is shown in the vicinity of horizontal betatron tune. The noise-like betatron oscillations are a few m.
The processor is shown below the dashed line. With processor OFF (or disconnected), the CM is transparent, in addition to the thyratron is triggered in routine way by the start signal ST delayed by the number of turns in the TD2R in addition to by some number of buckets in the TD2B.  THE EXTRACTION SET-UP The processor is triggered by the same ST. The processor either leaves the CM transparent, if no oscillation has been detected, or closes the CM to cut the TD2R, if oscillation was detected. In the last case the processor keeping monitoring the oscillation, picks up the turn where the oscillation has come to zero or got the opposite sign, in addition to generates EXTRACT which through an additional TD2E, the CM in addition to TD2B triggers the thyratron. The extraction occurs at the later turn where is the oscillation period. SIGNAL PROCESSING One bunch is monitored. It can be single bunch or one bunch from two or three spaced by 1/3 of circumference. On each turn, starting with the injection turn, the bunch BPM signal is sampled by the ADC in addition to stacked in the Memory of the length M. The ADC is triggered by pulses manufactured from the beam signal in the BPM. To cut pulses from other bunches, the gate G is used clocked by revolution frequency. So, on each next turn, a single bunch array is available in the Memory, with its first element recorded last. The processing is done in the DSP. It starts with the ST. The DSP works using its built-in clock. The turn-by-turn time is established by a counter clocked by revolution frequency. The counter is triggered by ST.
The processing has three stages: First, the DSP reads the array from the Memory, calculates the oscillation amplitude A in addition to compares it to the established threshold a. If the DSP keeps the CM transparent as long as the TD2R signal in addition to waits as long as the next ST. If the DSP cuts the TD2R. Next, with oscillation detected, the DSP calculates the number of the turn where the oscillation is expected to pass zero. Finally, the DSP starting with the turn where n is a few turns in addition to , reads on each turn the array in addition to calculates the sine phase At the turn where comes to zero or gets opposite sign, the DSP sends EXTRACT in addition to waits as long as the next ST. Take the ST turn number in addition to where 1 turn=0.46s. Then the first stage is to be finished within turns, or 130s. The second stage is to be finished within turns, or 20 s ( as long as n=4 turns). The calculation of the phase is to be done within 0.46 s. ALGORITHMS The algorithm set below is designed to be fast. However, more investigation is necessary to see whether calculating resources of fastest 16bit DSPs (8 parallel channels, clock 1GHz, up to 4G of elementary operation per second, cache memory) are sufficient as long as this set of algorithms applied to arrays of the length, say, M = 256. For the oscillation tune take Q as an integer closest to Assume Q is known. On the first stage, after reading the signal array the DSP first calculates the reverse average signal intensity necessary as long as normalisation. Then the array is calculated: (1) where the elements in addition to are the signals from the button electrodes 1 in addition to 2 respectively. The sum in (1) is the average dc offset.
Next, to enhance the accuracy of Fourier trans as long as mation, a suitable window is applied to (1). A dc offset generated by the window is subtracted. Finally, (2) Now using single term of Fourier Interpolation polynomial, the oscillation amplitude A in addition to a refined value of Q can be calculated by applying a known dichotomy algorithm. Initial term coefficients are: (3) where k = 1, 0, +1. Final dichotomy gives the refined value in addition to values in addition to . The oscillation amplitude A is calculated as (4) where [mm] is the BPM scale coefficient. On the second stage, the turn is calculated. Use (5) that interpolates the reverse time samples in (2). Calculate a pair of values in addition to as long as , say, Comparing with in addition to taking into account the signs enable to overcome phase ambiguity in addition to find the oscillation phase in addition to then the turn as (6) On the third stage, calculating (2) as long as the turns the turn-by-turn sine phase in the vicinity of zero can be calculated simply as (7) SUMMARY Constant energy extraction improving the beam quality, is possible at the KEK ATF2 in the three-bunch mode. The stabilisation energy set-up is based on a turn-by-turn BPM in addition to a signal digital processor that executes the extraction on the turn where the energy oscillation passes zero. Unlike classical feedback stabilisation method, this approach does not require longitudinal kicker. ACKNOWLEDEMENTS I am grateful to Dr P. Burrows a leader of the FONT Project, as long as his support of this work. I am thankful to T. Naito as long as useful discussion in addition to in as long as mation in addition to to Dr G. Christian in addition to Dr G. White as long as their help in beam measurements.
REFERENCES  S. Araki et al, Proposal of the Next Incarnation of Accelerator Test Facility at KEK as long as the International Linear Collider, PAC05, p.847.  T. Naito et al, Observation of the Longitudinal Beam Oscillation at ATF DR, KEK Preprint 2003-73, October 2003.  Ross, B. Meller, Detection in addition to Feedback of Synchrotron Oscillations in the ATF Damping Ring, ATF Report ATF-04-06, 22 January 2005.  D. Teytelman et al, Design in addition to Accelerator Tests of Gproto Bunch-by-Bunch Signal Processor, EPAC 2006.  A. Kalinin, A Digital-Oscilloscope-Based BPM as long as High Rate Bunch-by-Bunch Measurement (A Jitter BPM), FONT Collaboration Meeting 23 September 2005, http://hepwww.ph.qmul.ac.uk/~white/FONT  T. Naito et al, Timing System as long as Multi-Bunch/Multi-Train Operation at ATF-DR, KEK Preprint 99-144, November 1999, A.  A. Kalinin, A Single Bunch BPM as long as ATF Feed Forward, FONT Collaboration Meeting 28 October 2005, http://hepwww.ph.qmul.ac.uk/~white/FONT
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