K.A. Brown (M. Sivertz) Collider Accelerator Department, BNL Development of micro-bunching beams and application to rare K decay experiments K.A. Brown (M. Sivertz) Collider Accelerator Department, BNL (M. Tomizawa) JPARC Project, KEK

Outline Physics Motivations Parameters from KOPIO Micro-bunching at BNL AGS Micro-bunching at J-PARC Re-bucketing at RHIC (bunch compression) Re-bucketing at J-PARC Summary

Separating signal from background Microbunching is crucial to the measurement of the kaon momentum which allows for the kinematic suppression of backgrounds by transforming to the kaon rest frame. Make cuts on the pion energy and the difference in photon energies in the kaon rest frame.

Physics Motivation: Microbunch Separation Microbunch separation determined by the length of time required to clear out kaons from the previous microbunch. Difference in time-of-flight between high momentum and low momentum kaons is ~30 nsec => 40nsec (25MHz) Signal efficiency drops when neighboring microbunch too close

Physics Motivation: Microbunch Width Fully reconstructs the neutral Kaon in KL  p0 n n measuring the Kaon momentum by time-of-flight. Start when proton beam hits the target End at the decay time and decay point reconstructed from the two photons. Timing uncertainty due to microbunch width should not dominate the measurement of the kaon momentum; requires RMS width < 300ps (of course the optimal width depends on the detector geometry)

Physics Motivation: Interbunch Extinction Effects of Interbunch Kaons KL  p0 p0 events, shifted in time Kinematic cuts are used to reduce background due to KL  p0 p0 When KL does not come from the microbunch, incorrect kinematic fit does not allow for good rejection. Panels show effect of KL production at varying interbunch times. P*(p) E*(g1) – E*(g2) Signal and p0 p0

Physics Motivation: Intensity KOPIO had planned to study the very rare decay KL  p0 n n which has a BR = 3x10-11. The goal was to collect ~100 events with a S/B > 2/1. This requires more than 1.5 x1014 decays and for cleanliness we wanted ~0.5 decay/spill in the decay region. Optimization of duty factor and running time indicates 100Tp/spill. Total integrated # protons to achieve the experiment goals was ~ 7 – 9 x 1020. Final value depended on inefficiencies.

KOPIO Beam requirements Spill length with 100TP of ~3 seconds. Number of KL decays per microbunch: 3.57 Yields ~0.5 KL decay in 10 < Z < 14 meters Both are a flat optimum Variation of intensity between microbunches only impacts total run time (duty factor) Microbunch rms < 300psec (goal 200psec) Number of protons outside microbunches < 10-3 inside microbunches ( +/- 2 nsec)

Time Structure of Beam AGS Cycle Spill Structure 0 sec 2.3 sec 5.3 sec Injection and acceleration AGS Cycle Spill Structure 0 sec 2.3 sec 5.3 sec Extraction Start of Cycle 40 ns between microbunches 200 ps RMS Microbunch width End of Spill and Cycle mbunch spacing structure Start of Spill Proton intensity Time

BNL AGS: Micro-bunched slow extraction Empty buckets generate energy modulation of debunched beam Higher cavity voltage and/or smaller DP/P  shorter bunches Need ~200 ps bunches every 40 ns Frequency 200 ps 40 ns Time Extraction resonance Debunched beam

Microbunching the AGS Beam Extracted particles 25 MHz fundamental + 100 MHz harmonic Simulation of the extraction process for 25+100 MHz RF cavities. Impose a high frequency longitudinal oscillation on the beam. Slowly bring the beam into resonance (82/3) with RF. Beam is forced through the narrow phase region between the RF buckets. Adding the 100MHz harmonic cavity sharpens up the phase region in resonance. Extraction Region

Test Beam Results: Microbunch Width 93 MHz cavity at 22 kV gave s = 217 ps. Microbunch time, in ns Simulation 93 MHz cavity at 22 kV gave s = 240 ps. Microbunch time, in ns Data

Test Beam Results: Interbunch Extinction 4.5 MHz cavity at 130 kV gave e = 8 (+/- 6) x 10-6 Microbunch time, in ns Data Interbunch events Microbunch time, in ns Simulation 4.5 MHz cavity at 130 kV gave e = 1.7 (+/- 0.9) x 10-3. Interbunch events

Microbunch Beams at J-PARC

50GeV Synchrotron (Main Ring) •Imaginary Transition g • High Gradient Magnetic Alloy loaded RF cavity • Small Loss Slow Extraction Scheme • Both Side Fast Extraction for Neutrino and Abort line • hands on maintenance scheme for small radiation exposure •Injection Energy 3GeV •Output Energy 30GeV (slow) 40GeV (fast) 50GeV (Phase II) •Circumference 1567.5m •Beam Power 0.75MW (Phase II) Particles 3.3x1014 ppp •Repetition 0.3Hz •Harmonic 9 •Bunch Number 8 •Nominal Tune (22.4, 20.8) RF abort C2 E3 neutrino D3 M3 M2 E1c BT Collimators D2 Injection D1 Slow extraction M1 E2 Ring Collimators Injection dump C1

J-PARC Slow Extraction •Dispersion free @LSS horizontal chromaticity Qx’=~0 separatrix is independent of momentum •Bump orbit is moved during extraction (dynamic bump) small angular spread @ ESS fixed bump dynamic bump

Microbunch beams at J-PARC Microbunch technique developed for AGS Will NOT work for J-PARC, without some modifications. Large chromaticity extraction Alternatives? Bunched beam slow extraction. Bunch Compression using Re-bucketing (RHIC) Bunch Compression using chicanes (ERL technique) External Superconducting RF cavity (LEP, KEKB, CESR) followed by series of bend magnets: basic idea is to give bunch a time dependent momentum distribution. Different path lengths for different momenta will compress bunch.

Re-bucketing at RHIC Basic Idea: Lengthen the bunch by placing on the unstable fixed point Rotate elongated bunch to upright (high in dE, short in dt) Turn on higher harmonic RF with voltage matched to dE of the elongated bunch. What does it look like?

Re-bucketing in RHIC

Tomographic reconstruction of re-bucketing in RHIC

Re-bucketing at J-PARC The basic method needs simulation studies to develop further: Debunch 1.7 MHz beam to DC (continuous distribution in time) This is the hard part! Beam loading goes as 1/RF Voltage Rebunch ~25 MHz Debunch/rebunch at high intensity = beam loading compensation in the 25 MHz system must be very good. Re-bucket at ~200 MHz End product is shorter bunches (~5 nsec) with 25 MHz spacing. Finally, need to develop slow extraction of this bunched beam, that will further reduce bunch widths by another factor of 4 (or so). To get to 200 psec requires more thinking..

Re-bucketing at J-PARC: Problems De-bunching: beam loading is inversely proportional to RF voltage. As RF volts are decreased, instabilities become greater. CERN: problem was too significant = use bunch splitting BNL: h=6 to h=12 for high intensity = use bunch splitting 25 MHz bunched beam extraction at high intensity. Debunched beams have lower peak current, avoid instabilities BNL experience: coherent effects become significant. Bunches are still too long.

External Chicane for Bunch Compression Imposed Time dependent momentum distribution Differences in Time of flight compresses bunch. Superconducting RF Cavity Series of Sector Bends

External Chicane for Bunch Compression To get even a 100 to 200 psec compression requires a very long system of magnets! Clever techniques can reduce the size, but only by relatively small factors. It can work very well as an “after-burner” system, to get another 50 to 100 psec in compression.

kinematic suppression of background Summary For rare K-decay experiments, very short bunched beams provide: kinematic suppression of background momentum resolution via time of flight Short bunched beams from J-PARC are feasible. RF phase displacement technique, as developed at BNL, is still the best option, but requires some modifications Re-bucketing, as done at RHIC, will require addition of two (and possibly a third) RF systems at J-PARC. Most difficult problem for J-PARC will be beam loading compensation for the RF systems. It must be very good, to keep intra-bunch extinction low.

Supplemental Material

Overview of AGS Slow Extraction

J-PARC Slow Extraction •3.3x1014 protons per pulse(15uA) full beam power : 750kW @50GeV

Microwave instability seen at KEK Instabilities Microwave instability Longitudinal Space Charge Below transition, longitudinal space charge opposes the effect of the RF voltage, perturbing longitudinal phase space (Good thing!) Microwave instability seen at KEK

Instabilities As seen at CERN PS e-p instability As bunch lengths get very short and peak beam currents get high, the probability of higher mode interactions with electrons increases. V. Danilov et al, LANL, proceedings of the 1999 Particle Accelerator Conference, New York, 1999 R. Cappi, et al, proceedings of the 2001 Particle Accelerator Conference, Chigago As seen at CERN PS

Instabilities Transverse space charge Main effect is on the betatron tune. Two components, the incoherent tune shift ( effectively the tune spread) and the coherent tune, or the change in the frequencies of the beam centroid. Will change as beam is extracted and average current decreases. A tune shift during extraction and a change in the tune spread during extraction will affect the bunching and possibly the intra-bunch extinction (needs simulations). Resistive wall ? Well known not to be a problem when g<gtr.

AGS performance for g-2 operation 6 single bunch transfers from Booster Peak intensity reached: 72  1012 ppp Bunch area: 3 eVs at injection 10 eVs at extraction Intensity for g-2 ops: 50-60  1012 ppp Strong space charge effects during accumulation in AGS Dilution needed for beam stability 2 seconds Peak current Intensity 40 A 5 x 1013 protons

Longitudinal Phase Space Dilution at Injection A key parameter is peak beam current. Bunch Dilution using 93 MHz VHF cavity

High Intensity Slow Extraction 70 TP Slow extracted beam observations. Vertical Chromaticity is kept positive after transition.

Slow Extraction Dynamics A particle with a magnetic rigidity Br receives (thin lens) kicks by a sextupole of length L,

Slow Extraction Dynamics h stable X unstable

Slow Extraction Dynamics Unstable region Stable region Distrib. Of particles Extraction Methods: Move particles into resonance by changing betatron tune of particle distribution (AGS). Increase particle amplitudes until encounters the unstable region (RF knockout method).

K0PI0 Experiment

Spill and Ripple

Spill and Ripple

Spill and Ripple

Spill and Ripple