Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 1 COURSE SUMMARY A Design Study of a Compressor ring for A Neutrino Factory MT 2009 E. J. N. Wilson LECTURE 17

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 2 Putting “it” together  The SPS Design Committee get down to business (1971)

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 3 SPL

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 4 SPL Output Parameters – for the neutrino factory Ion speciesH-H- Kinetic energy5GeV Mean current during the pulse40mA Mean beam power4MW Pulse repetition rate50Hz Pulse duration0.4ms Bunch frequency352.2MHz Duty cycle during the pulse62 (5/8)% rms transverse emittances0.4  mm mrad Longitudinal rms emittance0.3  deg MeV Length535m

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 5 Neutrino Factory Demands ParameterBasic valueRange Beam energy [GeV] Burst repetition rate [Hz]50? Number of bunches per burst (n)41 – 6 ? Total duration of the burst [  s] ~ Time interval between bunches [  s] (t int ) 16~ 50/(n-1) Bunch length [ns] Specifications (from R. Palmer’s conclusion at ISS meeting in RAL on Thursday 27, April 2006)

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 6 Accumulate and Compress Scenario

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 7 Space charge Q shift  Radial force equals rate of change of momentum

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 8 Smooth approx. - choosing No. of periods

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 9 Period geometry  Everything must add up for the ring

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 10 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

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 11

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 12 Basic Cell of the C0mpressor

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 13 Insertion for 3 Bunch Compressor

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 14 Compressor Lattice  Your Christmas Present!

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 15 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

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 16 Parameters of the Magnets of the Compressor

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 17 Magnet design

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 18 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

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 19 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)

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 20 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 :

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 21 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

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 22  This is a biased rigid pendulum  For small amplitudes  Synchrotron frequency  Synchrotron “tune” Synchrotron motion (continued)

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 23

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 24 The bunch and bucket at start of rotation

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 25 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!

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 26 Instability  Keil Schnell stability criterion:

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 27 Some parameters of accumulator and compressor Table 6: Main parameters of the accumulator and compressor for a neutrino factory RingParameter6 bunches case Accumulato r Circumference [m]318.5 Nb. of accumulation turns400 Type of magnetsNC CompressorCircumference [m]314.2 Nb. of compression turns36 RF voltage on h=3 (MV]4 Transition gamma2.3 Type of magnetsSC Interval between bunches [  s] 12

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 28 LHC parameters

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 29 ORGANISATION OF DESIGN 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 Choose a lattice 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 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 The magnet aperture - the most expensive component 15. Calculating magnet stored energy 16. Resonant power supply design D. RF 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 1. Keep a parameter list

Lecture17(Course Summary).PPT - E. Wilson - 3/3/ Slide 30 THE “MOMENT OF TRUTH”  Adams, waiting for the first beam in the SPS, asks his team if they have remembered everything.