Adiabatic buncher and (  ) Rotator Exploration & Optimization David Neuffer(FNAL), Alexey Poklonskiy (FNAL, MSU, SPSU)

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)

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

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.)

Intentions 1. Use COSY Infinity code (M. Berz, K. Makino, et al.) ability to compute maps to arbitrary order own programming language allows building complicated optimization 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)

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: 1.Develop some strict or heuristic map-based method 2.Use control theory approach

Current Status 1.Model of buncher was written in COSY Infinity 2.Simulations of particle dynamics in buncher with different orders and different initial distributions were performed 3.Comparisons with previous simulations (Neuffer’s code, ICOOL) shows good agreement (starting from 5 th order) 4.Some memory limitations in COSY were found and corrected 5.Currently programming algorithm of buncher optimization

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

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

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

1.Finish programming and perform linear optimization of longitudinal motion in buncher 2.Study transverse focusing 3.Add phase rotator and perform complete system optimization 4.Use control theory for optimization Future Plans