# Presentation: 320532

## Realistic Fields for a Ring Cooler

- Steve Kahn
- 2 July 2002
- NuFact’02 Meeting

## Ring Cooler Geometry

## Sketch of Dipole Magnet

**Pole face is shaped to achieve required gradient**

**The design of the wedge magnet is from P. Schwandt (dated 30 Jan 01).**
- It has been revised.

## Saturation in Dipole Magnet

- Figure shows the permeability for the vertical midplane of the magnet.
- <10 on inner edge of the aperture.

## By on and off the Vertical Symmetry Plane

- Figure shows two curves:
- Ideal Field:
- 2D field from shaped iron pole and effective yoke width.
- Calculate index=0.473
- 3D Field Calculation
- Calculation using TOSCA
- Gives index=0.47

## Dipole Field along Reference Path

- Figure 4:  Field components for a path displaced 10 cm vertically from the reference path

- Figure 3:  By along central reference path.

## Avoiding a 3D Map

- The 2D part of a long accelerator magnet is traditionally parameterized by Fourier harmonics.
- A generalization of the traverse field that takes into account the s dependence of the field has the form:

## Transverse Harmonics as a Function of s

- Calculated along the reference path

## Dipole Field Description

- The harmonic description is currently in Muc_Geant.
- I have calculated harmonics of B(s) and Br(s) at positions along a reference path through the dipole magnet at 7 different radii using the TOSCA program.
- I have fit the previous formula (2 transparencies ago) to parameterize K(s) as:
- Kn(s) = a[tanh((z-zo)/)–tanh((z+zo)/)]  for each n
- The parameters for K(s) come from a combined fit of Br and B
- The fits for the *Dipole *and *Sextupole* components look reasonably good.  The fit to the *Quadrupole *component is not that stable.
- Note the difference in the Br and B for zo for the quadrupole fit.
- Since the harmonics are power series r the field at large radius will be less reliable.  This can be seen in the field for r>14 cm.
- This may be a serious problem since tracks at large radius may be lost by *incorrect* fields.
- I am investigating if there is a better parameterization than the harmonic series.

## Previous Comments on Long Solenoid Magnet made at Shelter Island

- The end plate effectively separates the solenoid field from the dipole.
- Radial fields are present only in the vicinity of the end plate.
- The end plate takes about 40 cm of longitudinal space.
- Actually I have the solenoid end plate and the dipole field clamp overlapping in space!
- We need to determine reasonable amounts of allowable space

- Dipole Magnet Starts

- End Plate

- Dipole End Clamp

## Long Solenoid Magnet

**Long Solenoid Magnet**

**coil**

**Thick Flux Return  **

**Vanadium Permadur End Plate**

**Supplemental Inner Coil**

**We have added an inner coil on end plates to reduce *****no field *****region**

## Fields in Long Solenoid

- Comparison of Bz with and without supplemental inner coil

- Axial and radial field components along long solenoid

##  Short Solenoid Magnet

## Short Solenoid Fields

## Ideal Short Solenoid Field Flip Magnet

- Top figure shows Valeri’s design for the short field flip solenoid.
- The lower figure shows the field and dispersion for that magnet.
- This form of the field assumes that there is a Neumann condition at the end of the magnet.
- The field will continue ~2 T forever.

- Bz on axis

## Short Solenoid Fields From Opera2D

- Field with iron covering ends

- Field with aperture for muons

- This forces field to be sort of parallel to axis

- How critical is it to have this field plateau?

## Fields in Geant

**B****s**

**B****y**

**G****y**

- The figures shows the field components along the reference path in one quadrant of the ring.
- Bs and By are in kgauss and Gy is in kgauss/cm
- This field description is from the muc_geant and there is a provision to write this out for ICOOL

## Current Status:  Travels 3.5 Revolutions when RF is turned on

- Track is lost with REALISTIC field after 3.6 turns

- Track  goes > 19 turns in HARD EDGE field

- Tracking on axis  with the RF and Absorbers

## Comparison of Field Along Tracks

- The figures at the left show the field seen by *on axis*  traversing first octant of ring.
- There are differences at the ends of the short and long solenoids as expected.
- There is By in the center of the Short Field Flip solenoid for the *realistic muon* since its does not have zero displacement at that point.
- This is an indication that the ring would have to be *tuned *for the realistic fields.

## Tracking With a Realistic Beam

- I have shown how the reference particle looks with the *Realistic Fields *and with the *Hardedge Field.*  As an exercise, I would like to look at the *Hardedge Field* case with realistic muon bunch with the following parameters:
***x **= ****y **= 4 cm*.
***Px** = ****Py** = 32 MeV/c.*
***E** = 18 MeV.*
***ct** = 9 cm.  *
*There is also an energy-momentum correlation. *
- Use newer RF cavity times, phases, and frequency.  These still are not perfectly optimized, but they are better than previously available.

## Properly Phased (?) with RF and Absorbers

- Transmissions and emittances calculated for GEANT hard-edge Model.
- The GEANT model has high residual losses after first turn which are not understood.

## ICOOL Models for Comparison

- On the right are the results of the Rick Fernow’s ICOOL model of the Balbekov Ring.
- It uses the *hard-edge field* model.
- It shows ~50% transmission
- It shows a significant 6D emittance cooling.
- I have made my own ICOOL model using the *on-axis *realistic fields that I have shown.
- The initial attempt shows significant losses.
- This was done the day before I left for England and needs still to be worked on.