1. 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

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

3. SPL

4. 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

5. 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
Time interval between bunches [ms] (tint) 16
~ 50/(n-1)
Bunch length [ns] 2
1 - 3

6. Accumulate and Compress Scenario

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

8. Smooth approx. - choosing No. of periods

9. Period geometry
Everything must add up for the ring

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

12. Basic Cell of the C0mpressor

13. Insertion for 3 Bunch Compressor

14. Compressor Lattice
Your Christmas Present!

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

16. Parameters of the Magnets of the Compressor

17. Magnet design

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

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)

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 :

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

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

24. The bunch and bucket at start of rotation

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!

26. Instability
Keil Schnell stability criterion:

27. 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

28. LHC parameters

29. 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
2. 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
14. The magnet aperture - the most expensive component
15. Calculating magnet stored energy
16. Resonant power supply design
D. RF
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

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