# Presentation: 660646

## “Shielding” Demonstrationin a Simplified RFOFO Cell

- Amit Klier
- UC Riverside

## Outline

- The Guggenheim RFOFO (a reminder)
- The Simplified RFOFO cell
- “Shielding” results from Poisson-Superfish

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## The idea: change the geometry

- The RFOFO Ring

- Turn this

- into this

- Injection/extraction – not a problem!
- Less heating of the absorbers
- Tapering possible – more efficient cooling
- BUT
- Massive, expensive
- Magnetic shielding may be necessary

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## Some geometric manipulations

- P

**** = Atan(P/2**r**)

- r

- “peel off”

- Rotate by angle 

- original RFOFO field map volume

- Collapse to one layer

- 

- For each point x,y,z  r,,y

- 

- rotate By, B
- Br not affected

- y

- 

- stretch ~ 1/cos 

- squeeze ~ cos 

- Read **B** from field map –

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## Results

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## The problem

- The geometric manipulations I did are nice as an exercise, but:
- Not Maxwellian
- Influence of adjacent cells (above, below) not taken into account
- For a complete simulation:
- Simulate the actual geometry
- Try to shield the “rings”

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## Moving forward in small steps

- First small step was to simulate “shielding” in a very simplified model cell (presented here)
- Next steps will include a full simulation of a “Guggenheim” without any shielding
- Next: more realistic shielding, forces, etc.

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## The simplified RFOFO cell

- The RFOFO cell:

- Simplified version:
- Cancel solenoid tilting
-  cylindrical symmetry
- Cut in half (at field flip)
- Boundary conditions:
- Bz = 0 at edges
- Br = 0 at r = 0
- “Shielding”:
**B**  surface (i.e. Bz = 0)
- at r = Rshield

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## Fields from Poisson-Superfish:No shielding

- r

- z

- solenoid

- half-
- absorber

- RF cavities

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## Shielding at r = 1.5 m

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## Shielding at r = 1.2 m

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## Shielding at r = 1.0 m

- “worst case”

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## Back to no shielding

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## Strength of B field at r = 0

- For the comparison
- I normalized the currents
- to match Bz maximum
- at r = 0 without shielding

| Shielding | Current (A/mm2) |
| --- | --- |
| none | 53.00 |
| 1.5 m | 51.66 |
| 1.2 m | 48.18 |
| 1.0 m | 42.47 |

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## Comparing no shielding and“worst case” (normalized) at r = 0

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## Comparing no shielding and“worst case” (norm.) at r = 10 cm

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## Comparing no shielding and“worst case” (norm.) at r = 20 cm

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006

## Conclusion

- Shielding affects the magnetic field very little around the beam
- This demonstration is only the beginning

- A. Klier - RFOFO Guggenheim

- KEK, January 26 2006