# Presentation: 693002

## Simulating the RFOFO Ring with Geant

- Amit Klier
- University of California, Riverside
- Muon Collaboration Meeting
-  Riverside, January 2004

## OUTLINE

- Basics - geometry and magnetic field
- Setting the parameters
- Reference orbit and the clock
- Single particles in the ring
- “Cooling” with an Ideal Absorber
- Acceptance and RF parameters
- Cooling of a beam
- With/without muon decay
- Comparing to other results

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Basic ingredients

- Simulation software                        data-driven Geant v3.21 (R. Raja)
- Geometry from B. Palmer, R. Fernow, V. Balbekov (MC-Note 264)
- Realistic magnetic field maps – external (R. Godang, S. Bracker: MC-Note 271)

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## The ring geometry

- 33 m circumference
- 12 cells (2.75m):
- LH2 wedge absorber –
- 	opening angle **110°**,
- 	pointing upwards
- 	no windows
- 6 RF cavities –
- 	28.75 cm long,
- 	acceptance radius 25 cm
- 2 tilted solenoids
- 	inner/outer r = 77/88 cm
- 	tilt angle ±3°
- 	(only for display here)

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## A view of a single cell

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## 3-D view of the RFOFO ring

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Setting the ring parameters

- The reference orbit
- Run without RF acceleration or absorbers
- Find a closed orbit (periodic in cells)
- Start at the middle of the wedge absorber –
- 	symmetry plane
- One of 2 point in which pT vanishes
- 	(with no RF and absorber)

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## With only magnetic field turned on

- The ring shows stability for initial pz’s
- in the range ~165–260 MeV/c
- The strategy:
- Find closed orbits for various initial Pz
- 	x and y dependence  dispersion functions
- Set the clock – determine RF cavity entry times (the clock’s rotation frequency should be an integer  RF frequency)
- 	 Then RF cavities and absorbers can be turned on

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Closed orbits in a single cell

- Solid line – the reference orbit

- 270 MeV

- 250 MeV

- 227 MeV

- E = 200 MeV

- 200 MeV

- 227 MeV

- 250 MeV

- E = 270 MeV

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Dispersion functions at the center of the wedge

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Setting the clock

- RF frequency: f = 201.25 MHz
- Set the entry times of the RF cavities
- pz=200.96 MeV/c (E227 MeV)
- 	 the 25th harmonic
- (actually, ~201.26 MHz was the closest I could get)

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Turn on RF and LH2 absorber

- Use an “ideal” absorber
- no multiple scattering, straggling
- Simplified RF acceleration field:
- In the cavity volume (cavity coordinates): Ex=Ey=0,
- Ez=G·sin[(t-tent)+ent]
- (G=13.5 MV/m, ent=-13° for the single-particle simulation)
- Inject muons at 5 initial points in each phase space coordinate
- central value, ±1,2 (Gaussian beam from MC-264)

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Perfect absorber – perfect cooling

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Slide 14

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Introducing “realistic” absorbers..

- Turn on all processes (except muon decay)
- 	Looks like a big mess!
- But only a few particles
- are shown here!
- High statistics are needed
- to simulate cooling –
- 		a beam

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## The beam

- Gaussian distributions (from MC-264):
- x = y = 4.25 cm
- px = py = 30 MeV/c
- z = 7 cm (cT = 8 cm in the Note)
- pz = 22.5 MeV/c (E = 20 MeV in the Note)
- To find the best acceptance:
**400 muons**, no decay, ideal absorber
- Count the number of muons after 6 ring turns (“stable”)
- For cooling simulation:
**1600 muons**, w/ & w/o decay, “realistic” absorber

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Finding the best acceptance using ideal absorber

- ent ~ -2o

- maximum @ ~14 MV/m

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Simulating beam cooling with a “realistic” absorber

- A Gaussian beam of **1600** muons was generated with all physics processes on
- The same beam without muon decay –performance cross-check
- Emittance calculation (similar to ECALC9)
- Slightly different cuts;
- No transverse amplitude–momentum correlation (L calculated only from E-t covariance matrix)

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## The beam in 15 turns (no muon decay)

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Cooling performance:transmission, 2-D emittances

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Cooling performance:6-D emittance, merit factor

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Performance after 10 turns –comparison to other simulations

|  | ICOOL (MC-239) | Balbekov (MC-264) | Geant (current) |
| --- | --- | --- | --- |
| Transmission, no decay (%) | 61 | 70 | 64 |
| Transmission with decay (%) | 50 | 56 | 51 |
| Merit factor | 50 | 55 | ~40 |

- Possible reason for lower merit factor: smaller initial beam (longitudinal)

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Why do we see the jump in longitudinal emittance? (first few turns)

- Simulating RFOFO with GEANT

- Jan. 28, 2004

## Conclusions

- Geant performance shows good agreement with other simulations (ICOOL, Balbekov)
- lower merit factor maybe due to different initial beam
- To be done:
- Use “standard” ECALC9 to calculate emittance
- More realistic ring – absorber windows, injection, etc.
- Geant-Simulate other cooling rings (e.g. Kirk-Garren)
- 	– with R. Godang, S. Kahn, EE working group
- MC-Note in preparation, to be published soon...

- Simulating RFOFO with GEANT

- Jan. 28, 2004