A Design Study of a Compressor ring for LECTURE 17 COURSE SUMMARY A Design Study of a Compressor ring for A Neutrino Factory MT 2009 E. J. N. Wilson

Putting “it” together The SPS Design Committee get down to business (1971)

SPL

SPL Output Parameters – for the neutrino factory Ion species H- Kinetic energy 5 GeV Mean current during the pulse 40 mA Mean beam power 4 MW Pulse repetition rate 50 Hz Pulse duration 0.4 ms Bunch frequency 352.2 MHz Duty cycle during the pulse 62 (5/8) % rms transverse emittances p mm mrad Longitudinal rms emittance 0.3 p deg MeV Length 535 m

Neutrino Factory Demands Specifications (from R. Palmer’s conclusion at ISS meeting in RAL on Thursday 27, April 2006) Parameter Basic value Range Beam energy [GeV] 10 5 - 15 Burst repetition rate [Hz] 50 ? Number of bunches per burst (n) 4 1 – 6 ? Total duration of the burst [ms] ~ 50 40 - 60 Time interval between bunches [ms] (tint) 16 ~ 50/(n-1) Bunch length [ns] 2 1 - 3

Accumulate and Compress Scenario

Space charge Q shift Radial force equals rate of change of momentum

Smooth approx. - choosing No. of periods

Period geometry Everything must add up for the ring

Phase advance per cell The beta at the F quadrupole which defines the scale of the apertures goes through a minimum at about 70 deg/cell. Other considerations which might lead to close to 90 degrees per cell are Sensitivity to closed orbit errors Ease of locating correctors Schemes for correcting the chromaticity in the arcs without exciting resonances

Basic Cell of the C0mpressor

Insertion for 3 Bunch Compressor

Compressor Lattice Your Christmas Present!

Correction of chromaticity Parabolic field of a 6 pole is really a gradient which rises linearly with x If x is the product of momentum error and dispersion The effect of all this extra focusing cancels chromaticity Because gradient is opposite in v plane we must have two sets of opposite polarity at F and D quads where betas are different

Parameters of the Magnets of the Compressor

Magnet design

Various coil and yoke designs ''C' Core: Easy access Less rigid ‘H core’: Symmetric; More rigid; Access problems. ''Window Frame' High quality field; Major access problems Insulation thickness

RF Cavity constraint is Voltage per meter and MW of power (Shunt impedance and Q) pressure from need to provide a good acceleration rate or large bucket (e.g. for bunch rotation)

Rf frequency (injection) At injection, in order to use the Keil Schnell criterion to combat instabilites we must have enough voltage to reach a threshold value of :

Rf frequency(in collision)) When colliding bunches, we want a short bunch either: or: If h is small, the bucket area must be much bigger Hence But check synchrotron wave number < 0.1

Synchrotron motion (continued) This is a biased rigid pendulum For small amplitudes Synchrotron frequency Synchrotron “tune”

The bunch and bucket at start of rotation

Intensity and impedance Local enlargement in the beam tube which can resonate like a cavity Voltage experienced has same form as the current which excites it Impedance Relates force on particles to the Fourier component of the beam current which excites the force. A complex quantity - REAL if the voltage and current are in phase - IMAGINARY if 90 degrees or "i" between voltage and current (L = +, C = –) - different from r.f. wave by 90 degrees!

Instability Keil Schnell stability criterion:

Some parameters of accumulator and compressor Table 6: Main parameters of the accumulator and compressor for a neutrino factory Ring Parameter 6 bunches case Accumulator Circumference [m] 318.5 Nb. of accumulation turns 400 Type of magnets NC Compressor 314.2 Nb. of compression turns 36 RF voltage on h=3 (MV] 4 Transition gamma 2.3 SC Interval between bunches [ms] 12

LHC parameters

ORGANISATION OF DESIGN 1. Keep a parameter list A. Lattice Working Group Rossbach ,J. and Schmüser, P. (1992). Basic course on accelerator optics. Proceedings of the 1986 CERN Accelerator School, Jycaskyla, Finland, CERN 87-1 http://doc.cern.ch/yellowrep/2005/2005-012/p55.pdf 2. Choose a lattice http://doc.cern.ch/yellowrep/2005/2005-012/p55.pdf 3. Decide phase advance per cell 4. Calculate beta max and min 5. Decide period geometry 6. Calculate beta max and min 7. Calculate dispersion 8. Calculate transition energy B. Errors and corrections http://preprints.cern.ch/cgi-bin/setlink?base=cernrep&categ=Yellow_Report&id=95-06_v1 9. Identify sources of orbit distortion 10. Correction of chromaticity 11. Effect of errors 12. Identify sources of orbit distortion 13. Acceptance required C. Magnet and power supply http://preprints.cern.ch/cgi-bin/setlink?base=cernrep&categ=Yellow_Report&id=92-05 14. The magnet aperture - the most expensive component 15. Calculating magnet stored energy 16. Resonant power supply design D. RF http://preprints.cern.ch/cernrep/2005/2005-003/2005-003.html 17. RF Cavity tuning (frequency swing) 18. Choice of RF frequency (scaling) 19. Choice of RF voltage (injection) 20. Bucket size for capture and acceleration E. Collective effects 21. Instability thresholds http://doc.cern.ch/yellowrep/2005/2005-012/p139.pdf

THE “MOMENT OF TRUTH” Adams, waiting for the first beam in the SPS, asks his team if they have remembered everything.