# Presentation: 184024

## Theory and Simulations:

**Introduction and Plans**
- R.C. Fernow
- BNL
- Mutac Review
- BNL
- 29 April 2004

## Outline of MC simulation activities

-  design simulations for future muon-based facilities
- major focus is on beam dynamics
- 1) front end
- 		neutrino factory
- 		muon collider
-  	2) accelerators (S. Berg)
-  related simulation efforts in support of the experimental program
- targetry (R. Samulyak)
- MICE (K. Long)
- Muons Inc. (R. Johnson)

-  theory

## Theory and simulation committee

- H. Kirk (BNL)		Targetry coordinator
- D. Neuffer (FNAL)	Front end systems coordinator
- S. Berg (BNL) /		Acceleration coordinators
-    C. Johnstone (FNAL)
- A. Sessler (LBNL)	Theory coordinator
- M. Berz (MSU)
- E. Keil (CERN)
- R. Palmer (BNL)
- S. Koscielniak (TRIUMF)
- Major responsibilities
- planning to foster this work
- 	hold workshops
- 	advertise, interview, select postdocs for new positions

## Recent simulation workshops

- Ring coolers		UCLA		March 2003
- FFAG			KEK		July 2003
- Emittance exchange	FNAL		August 2003
- Targetry		BNL		September 2003
- FFAG			BNL		October 2003
- Ring coolers		Tucson		December 2003
- Emittance exchange	Riverside	January 2004
- Ring coolers		Mississippi	March 2004
- FFAG			TRIUMF	April 2004

## Code development

-  ongoing effort on simulation code development
-  front end
- 	ICOOL
- 	Geant (several varieties)
- 	COSY
- 	MARS
-  acceleration
- 	COSY
- 	private codes – optimization, cost estimates
-  targetry
- 	FronTier

## Ionization cooling rings

-  three families of ring coolers have been successfully simulated
-  all show significant 6D cooling
- 	tetra ring
- 	RFOFO ring
- 	dipole ring
-  ring with Li lens elements are under study
-  recent highlights
- 	RFOFO ring simulated with Geant
- 	dipole ring modeled with realistic fields
- 	dipole ring may be suitable for “table top” demonstration

## Tetra ring cooler

-  first cooling ring design by V. Balbekov, FNAL
-  only fully simulated with hard edge fields
-  drawbacks
-       large diameter, high B solenoids
-       field overlap at corners
-       injection space hurts performance

- (V. Balbekov, FNAL)

## RFOFO ring cooler (1)

-  designed by R. Palmer, BNL
-  first ring simulated with realistic fields
-  lattice has 12 identical cells, C = 33 m
-  focusing from 2. 8 T solenoids
-  bending from tipping the solenoids
-  wedge shaped LH2 absorbers
-  201 MHz RF, 12 MV/m
-  effects of windows, empty cells studied

- (R. Palmer, BNL)

## RFOFO ring cooler (2)

-  reference momentum is 203 MeV/c
-  minimum β┴ = 40 cm at wedge absorber
-  dispersion is 8 cm at wedge
-  closed orbit leaves the midplane
-  gives significant increase in muon density

## RFOFO ring cooler (3)

-  recently simulated with Geant
-  parameter tuning underway
-  needs better initial matching
-  current results ≈ ICOOL

- (Amit Klier, UC Riverside)

## Dipole ring cooler (1)

-  focusing from dipole body and edge angle, no solenoids
-  examined many designs
- weak focus
- strong focus (FFAG-like)
-  developed successful design algorithm
- 	design initial lattice using SYNCH
- 	parameter optimization with ICOOL (hard edge mode)
- 	realistic fields with TOSCA, ICOOL (multipole mode)

- (A. Garren, UCLA)

## Dipole ring cooler (2)

-  weak focusing ring
-  H2 gas filled, want βT small and constant
-  201 MHz
-  skew quads give transverse mixing

- (H. Kirk, BNL)

## Dipole ring cooler (3)

-  4 cell weak focus ring was simulated with realistic fields
-  B reverses sign between cells
-  realistic field gives similar lattice parameters ≈ SYNCH
-  dynamic aperture studies show
- 	realistic ≈ hard edge (in horizontal plane)
- 	realistic ≈ 1⁄2 hard edge (in vertical plane)

- (S. Kahn, BNL)

## Li lens cooling

-  present ring designs get εTN ~ 2 mm  (βT=40 cm, B=3 T)
-   we need εTN ~ 0.2 mm for a muon collider

- (Y. Fukui, UCLA)

-  preliminary ring modeling              gets εTN ~0.3 mm  (βT ~1 cm)
-  studying field overlap between solenoids and Li lens

- (V. Balbekov, FNAL)

-  linear channel had 35 x 2.6 m cells
-  Li lens: 13.5 cm long, 3 cm radius,
-        355  A/mm2, βT ~4 cm
-  matching between lenses is difficult
-  preliminary εTN ~ 0.5 mm

## Study 2a Front End

- objective: significant neutrino factory cost reduction from FS2
- major new elements
- (1) adiabatic RF bunching and phase rotation (D. Neuffer, FNAL)
- eliminate induction linacs
- (2) new linac front end with ATN = 30 mm acceptance (R. Palmer et al)
- (3) new simplified cooler design (R. Palmer)
- fewer components
- lower magnetic field

## New front end design

- overall configuration by R. Palmer

- (J. Gallardo, BNL)

## Realistic design

- Mawellian field from table of coils
- constant fields   periodic solenoids
- careful matching at transitions
- coils near the target moved radially for extra lifetime
- optimized collection profile
- radial constraint from tapered beam pipe
- RF windows in buncher
- discrete frequency buncher and rotator cavities
- cooler frequency exactly at 201.25 MHz
- Be coating over LiH absorbers
- new beam distribution using new B over target

## Field configuration

- front end uses 490 solenoids

- collection

- decay

- buncher

- rotator

- cooler

- 20 T at target

## Target

- 24 GeV protons on Hg jet
- jet at 100 mr from B axis, beam 67 mr from B axis
- particle creation using MARS (H. Kirk)

## Pion/muon collection

- 12.2 m taper from 20 T to 1.75 T
- improved collection design (K. Paul, U. Illinois)
- increased accepted  μ / p  by 13%

## Radiation

- • MARS calculations
-       of absorbed dose (H. Kirk)
- • peak deposition in SC coils
-       is ~ 1MGy/yr
- • no problem with SC lifetime

- (H. Kirk, BNL)

## Buncher

- 51 m long
- 31 cavities with 19 different frequencies (332232 MHz)
- gradients (0.9  9 MV/m)
- 51 bunches in train

## Rotator

- 54 m long
- 72 cavities with 18 different frequencies (232201 MHz)
- gradient 12.5 MV/m

- tapered

## Cooler design

- 100 m long alternating solenoid channel, BS = 2.8 T
- large, relatively flat β┴  ~ 70 cm
- use LiH absorbers as RF windows

## Cooler performance

- cooling increase μ density into accelerator acceptance by factor of ~2
- cools normalized transverse emittance by factor of ~2.4
- final εTN = 7 mm (equilibrium value for LiH is ~5 mm)

## Status of Study 2a

- current best result is  μ / p = 0.144 ± 0.007 into accelerator acceptance
- achieved approximately same performance as Study 2
- but this design gives muons of _both_ signs
- potential gain of a factor of 2 in neutrino flux
- there is still hope for further progress
- observed transverse cooling from the windows in the phase rotator
- can try different absorbers

## Future simulation plans

-    • complete Study 2a
-    • continue work on FFAG acceleration scenario
-                - design for electron demonstration model
-    • do preparation work for Study 3
- muon collider
-    • work on injection/extraction for ring coolers
-    • produce design for “table top” ring cooler
-    • use ring coolers in self-consistent front-end design