Adiabatic buncher + ( ) Rotator (David Neuffer)

1. Adiabatic buncher and () Rotator Exploration & OptimizationDavid Neuffer(FNAL), Alexey Poklonskiy (FNAL, MSU, SPSU)

2. Adiabatic buncher + () Rotator (David Neuffer) • Drift (90m), •  decay, • Beam develops  correlation • Buncher (60m) (~333Mhz200MHz, 04.8MV/m) • Forms beam into string of bunches •  Rotation(~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)

3. Longitudinal Motion (2D simulations) Bunch Drift   E rotate Cool   System would capture both signs(+, -)

4. Research Directions PROBLEM: Many possible variations and optimizations (some done by D.Neuffer, R.Palmer, R.Fernow, J.Gallardo, …) • Shorter bunch trains (into ring cooler) • Longer bunch trains (more ’s) • Different final frequencies 200MHz (FNAL)  88 MHz (CERN)  ~44MHz (JNF) SOLUTION: Develop simulation model for optimization PROBLEM:Calculate cost/performance optima for neutrino factory • SOLUTION: Perform optimization on various parameters: • longitudinal emittance •  survival rate • 6D simulation, transverse focusing and matching into cooler • final cost (depends on length, number of different frequencies and voltages of cavities in buncher, etc.)

5. Intentions • 1. Use COSY Infinity code (M. Berz, K. Makino, et al.) • ability to compute maps to arbitrary order • own programming language allows building complicatedoptimization scenarios with human interaction • internal optimization routines and interface to add more • provides differential algebra framework which could significantly simplify use of gradient optimization methods • (additional) perform testing of the way COSY handle large amounts of data, beams with large momentum and time coordinates range Problem: use of Taylor series leads to tricky way of handling beams with large coordinate spread (need to split large beam into smaller parts and track them separately)

6. Intentions • 2. Perform simulations of currently existing variants of buncher parameters and compare results with those obtained by another codes • 3. Develop and apply optimization procedure: • Develop some strict or heuristic map-based method • Use control theory approach

7. Current Status • Model of buncher was written in COSY Infinity • Simulations of particle dynamics in buncher with different orders and different initial distributions were performed • Comparisons with previous simulations (Neuffer’s code, ICOOL) shows good agreement (starting from 5th order) • Some memory limitations in COSY were found and corrected • Currently programming algorithm of buncher optimization

8. Some 2D Simulation Results (t-E) 6th order, using Gaussian initial distr, narrow

9. Some 2D Simulation Results (t-E) 6th order, using Gaussian initial distr, wide

10. Some 2D Simulation Results (t-E) 5th order, using initial distr from MARS, wide

11. Future Plans • Finish programming and perform linear optimization of longitudinal motion in buncher • Study transverse focusing • Add phase rotator and perform complete system optimization • Use control theory for optimization