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A.Poklonskiy (SPbSU, MSU), D.Neuffer (FNAL) C.Johnstone (FNAL), M.Berz (MSU), K.Makino (MSU)

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Exploring and optimizing Adiabatic Buncher and Phase Rotator for Neutrino Factory in COSY Infinity

A.Poklonskiy (SPbSU, MSU), D.Neuffer (FNAL)

C.Johnstone (FNAL), M.Berz (MSU), K.Makino (MSU)

Goal:

- Build neutrino factory to study different neutrino-related things and/or muon collider… to collide
Problems:

- Muons are short-living particles compact lattice, fast beam gymnastics
- Muons are produced with large initial momentum spread cooling
- Energy spread is large energy spread reduction before cooling
- Some desired beam manipulations requires new types of field configuration development of such new elements
- All these small muons production rate (<0.2) and…PRICE!

- Improve from baseline:
- Collection
- Induction Linac “high-frequency” buncher

- Cooling
- Linear Cooling Ring Coolers

- Acceleration
- RLA “non-scaling FFAG”

- Collection

– e– + ne +

+ e+ + n + e

and/or

The Neutrino Factory and Muon Collider Collaboration

http://www.cap.bnl.gov/mumu/mu_home_page.html

- Drift (90m)
- decay, beam develops correlation

- Buncher (60m) (~333Mhz200MHz, 04.8MV/m)
- Forms beam into string of bunches

- Rotator (~12m)(~200MHz, 10 MV/m)
- Lines bunches into equal energies

- Cooler (~50m long)(~200 MHz)
- Fixed frequency transverse cooling system

- Replaces Induction Linacs with
- medium-frequency RF (~200MHz)

Buncher

Drift

(E) rotator

Cooler

System would capture both signs(+, -)

- Drift
- Length LD

- Buncher
- Length LB
- RF Gradients EB
- Final RF frequency RF (LD, LB, RF: (LD + LB) (1/) = RF)

- Phase Rotator
- Length LR
- Vernier offset, spacing NR, V
- RF gradients ER

- Shorter bunch trains (for ring cooler, more ’s lost)?
- Longer bunch trains (more ’s survived)?
- Different final frequencies? (200,88,44Mhz)
- Number of different RF frequencies and gradients in buncher and rotator (60…10)?
- Different central energies (200MeV, 280MeV, optimal)?
- Matching into cooling channel, accelerator
- Transverse focusing (150m B=1.25T solenoidal field or…)?
- Mixed buncher-rotator?
- Cost/perfomance optimum?

OPTIMIZATION IS NEEDED

- COSY Infinitycode (M. Berz,K. Makino, et al.)
- Where M – map of the equations of motion (flow), obtained as a set of DA – vectors (Taylor expansions of final coordinates in terms of initial coordinates)
- uses DA methods to compute maps toarbitrary order
- own programming language allows complicatedoptimization scenarios writing
- internal optimization routines and interface to add more
- provides DA framework which could significantly simplify use of gradient optimization methods
- model is simple now, but much more complicated in future and COSY has large library of standard lattice elements

Use ofTaylor seriesleads to tricky way of handling beams with large coordinate spread (and that is exactly the case) Relative coordinates should be < 0.5 (empirical fact)

synchronous particle

equations in deviations from synchronous particle

nonlinear oscillator

COSY Infinity uses similar coordinates

- Existence of stable regions, where we have oscillatory motion and unstable regions, and, therefore existence of separatrix (depends on frequency, RF gradient, synch. phase, etc… ). Stable area is called the “bucket”.

- Use central energies as centres of boxes, use RF period as ranges for the box
- Add “jumping” between intervals after each step. We change buckets and particles could be lost in one bucket and re-captured in another

- 50 central energies x 60 RF cavities in Buncher = 300 maps…
- We are using DA arithmetic, everything is a DA-vector, including elementary functions (sin), so we need relatively high expansion order. Use 2 times more intervals + 5th orderleads to natural advantage in buncher… maybe.
- Use COSY’s ability to generate parameter-dependent maps with ease and special law of bunches central energies distribution (smaller energies tends to be closer to each other)
40-50 maps 12-15 maps

Potential calculation time reduction. Implementing.

- 6000 particles, 50 central energies, 70 RFs
- 1st order: 0 hrs 10 min
- 7th order: 8 hrs some mins

OPTIMIZATION?

- Model is implemented in COSY Infinity and checked for consistency with other codes
- Some removal of the obstacles is done
- Brute-force optimization still seems to be infeasible. Looking for some more sophisticated method.

- Should longitudinal motion be studied separately, or should it be included on the very early stages?
- Are there any map-dependent criterias which could be used for map-based optimization?

- From synchronism condition one could derive following relation for kinetic energies of synch particles:

- From the rotator concept one could derive amount of energy gained by n-th synchronous particle in RF
- So for final energy n-th particle has after the rotator consists of m RFs we have

- The idea of the whole structure is to reduce overall beam energy spread and to put particles energies around some central energy. So we have general objective function:
- First, we can set and get

- For calculating we can use particle’s energies distribution

- n energy particles %
- ----------------------------------------------
- -12 963.96 1023 17.050000
- -11 510.85 692 11.533333
- -10 374.64 537 8.950000
- -9 302.98 412 6.866667
- …

- Model of buncher and phase rotator was written inCOSY Infinity
- Simulations of particle dynamics in lattice with different orders and different initial distributions were performed
- Comparisons with previous simulations (David Neuffer’s code, ICOOL, others) shows good agreement
- Several variations of lattice parameters were studied
- Model of lattice optimization using control theory is proposed
- Model of central energies distribution is developed. Some results for parameters have been obtained

- Finish central energies optimizations, try changing more parameters, check optimized parameters for whole distribution (COSY, ICOOL?)
- Develop some criteria for simultaneous optimization of central energies and energies of all paritcles in a beam or use control theory approach for the whole longitudinal motion optimization
- Study transverse motion and particles loss because of decay and aperture, final emittance cut
- Different lattices for different cooling sections/targets/whatever proposed (project is on R&D status)