Modeling the Upper, Middle, & Lower NF linac in G4beamline Kevin B. Beard, Muons,Inc. & Alex Bogacz, Jefferson Lab LEMC2009 workshop 8-12 Jun 2009 Muons, Inc.

Neutrino Factory ~ 25 GeV LEMC2009 workshop 8-12 Jun 2009 Muons, Inc.

Muon Collider ~ 1.5 TeV LEMC2009 workshop 8-12 Jun 2009 Muons, Inc.

pre-accelerator linac - not very relativistic Morteza Aslaninejad, Cristian Bontoiu Jürgen Pozimski, Ajit Kurup Imperial College, London, UK 0.6 GeV/pass 3.6 GeV 0.9 GeV 244 MeV 146 m 79 m 2 GeV/pass 264 m 12.6 GeV Mm = 105.658 MeV Etotal: 244 MeV → 900 MeV P: 220 MeV/c → 894 MeV/c KE: 138 MeV → 794 MeV εTN ~ 40,000 mm-mr Δp/p ~ 17% Δφ ~ +/- 102o RF Muons, Inc.

Why another simulation? OptiM – fast, interactive, design, matrix based 0th order design tool, symplectic soft edge solenoids, very good at tuning (free) GPT – good at tracking ($) G4beamline – tracking, Geant4 particle decays & interactions, energy depositions, showers, etc., not so good at tuning (free & open source) http://g4beamline.muonsinc.com LEMC2009 workshop 8-12 Jun 2009 Muons, Inc.

Linear Pre-accelerator – 244 MeV to 909 MeV 6 short cryos 15 MV/m 8 medium cryos 17 MV/m 11 long cryos 1.1 Tesla solenoid 1.4 Tesla solenoid 2.4 Tesla solenoid Transverse acceptance (normalized): (2.5)2= 30 mm rad Longitudinal acceptance: (2.5)2 pz/mc= 150 mm 8m 3m 5m Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

Solenoid Model (Superfish) outer coil shield inner coil ‘Soft-edge’ Solenoid

Two-cell cavity (201 MHz) – COMSOL Morteza Aslaninejad Cristian Bontoiu Jürgen Pozimski

Field maps single RF cell solenoid Ez Bz double RF cell Ez Bx,By LEMC2009 workshop 8-12 Jun 2009 Muons, Inc. MAG, Aug 31, 2010

g4beamline 2.02 valve assembly conductor RF cell counterwound solenoid & flux return shield RF cell LEMC2009 workshop 8-12 Jun 2009 Muons, Inc. MAG, Aug 10, 2010

g4beamline 2.08 LEMC2009 workshop 8-12 Jun 2009 Muons, Inc.

LEMC2009 workshop 8-12 Jun 2009 Aug 31, 2010 Muons, Inc.

Simple Phasing via spreadsheet 0ₒ≡on crest L=2λ c=λf z=cβt Ez(z,t) ≈ qEzo cos(2πf t + φ) cos(π z/L) +L/2 ΔE ≈ ∫ Ez(z,z/cβ) dz -L/2 ΔE ≈ -2qEzo L cos(π/ 2β) cos(φ) β2/(π (1-β2) ΔE ≈ -2qEzo L cos(π/ 2β) cos(φ) β2/(π (1-β2) Ti ≈ Ti-1+ (zi - zi-1)/(cβi-1) LEMC2009 workshop 8-12 Jun 2009 Aug 31, 2010 Muons, Inc. Muons, Inc. ΔE ≈ ∫ Ez(z,z/cβ) dz Ez(z,t) ≈ qEzo cos(2πf t + φ) cos(π z/L) Ti ≈ Ti-1+ (zi - zi-1)/(cβi-1)

Linac parameters Muons, Inc.

phases partially adjusted Longitudinal phases partially adjusted phases from spreadsheet LEMC2009 workshop 8-12 Jun 2009 Muons, Inc.

Comparison of GPT, OptiM, g4beamline KE[MeV] z[cm] G4beamline w/adj. φ's OptiM G4beamline w/OptiM's φ's KE[MeV] LEMC2009 workshop 8-12 Jun 2009 z[cm] Muons, Inc.

Ez Ez LEMC2009 workshop 8-12 Jun 2009 Muons, Inc.

LEMC2009 workshop 8-12 Jun 2009 Sep 14, 2010 Muons, Inc.

Fine tuning is still in progress Synchrotron motion Pz ~ oncrest ~ 1 synch period LEMC2009 workshop 8-12 Jun 2009 t t Muons, Inc. G4beamline model is working well and in general agreement with other simulations Essential step toward our long term goal of complete end-to-end simulations Fine tuning is still in progress Will soon begin particle interactions with the hardware

Transverse motion GPT G4beamline y[m] LEMC2009 workshop 8-12 Jun 2009 z[m] z[m] Muons, Inc.

G4beamline improvements from this work: fieldmap timeOffset fixed (simple bug fix) pillbox autoTune being added (tune for max,min ΔE or Δt rather than assume Δv=0) LEMC2009 workshop 8-12 Jun 2009 Muons, Inc.

Linac – near term plans optical rematch of linac to cooling channel greatly improve RF phasing capability of G4beamline optical rematch of linac to cooling channel optimize longitudinal and transverse acceptance determine energy deposition in components prepare the transfer line to RLA I

LEMC2009 workshop 8-12 Jun 2009 Sep 14, 2010 Muons, Inc.