EMMA Magnet Design Ben Shepherd Magnetics and Radiation Sources Group ASTeC STFC Daresbury...

EMMA Magnet Design

Ben ShepherdMagnetics and Radiation Sources Group

ASTeCSTFC Daresbury Laboratory

EMMA Magnet Design – Ben Shepherd FFAG 2007 - Grenoble, April 12-17 2007

Overview

Introduction – the EMMA lattice EMMA magnets – ‘interesting’ aspects 3D modelling Current status Next steps


ERLP and EMMA

EMMA will be an FFAG addon to the Energy Recovery Linac Prototype (ERLP) project at Daresbury

EMMA: 10MeV 20MeV

ERLP is in the early stages of commissioning – the photoinjector gun is being commissioned and the booster linac is about to be installed

Ready by the end of 2007…?


The EMMA Ring

21 cells, each has:

2x D magnet2x F magnet

84 magnets in main ring

+ injection

+ extraction

6m


EMMA Cell Layout

FD D

Cavity

15 MeV Reference orbit centreline

ClockwiseBeam

Inside of ring

Outside of ring

Magnet Reference OffsetsD = 34.048 mmF = 7.514 mm

Geometry consisting of 42 identical(ish) straight line segments of length 394.481 mm

Long drift 210.000 mm

F Quad 58.782 mm

Short drift 50.000 mm

D Quad 75.699 mm

Magnet Yoke LengthsD = 65 mmF = 55 mm

Circumference = 16.568m


Magnet Challenges

‘Combined function’ magnets Dipole and quadrupole fields

Independent field and gradient adjustment Movable off-centre quads used

Very thin magnets Yoke length of same order as inscribed radius ‘End effects’ dominate the field distribution Full 3D modelling required from the outset

Large aperture + offset Good field region (0.1%) must be very wide

Close to other components Field leakage into long straight should be minimised

Close to each other Extremely small gap between magnets F & D fields interact

Full 3D modelling and prototyping essential!


F magnet

D magnet

http://www.cst.com/

Modelling carried out using CST EM Studio

Combined modelwith ‘realistic’ steel –B-H curve provided by Tesla

also produce Microwave Studio


F Magnet


D Magnet

Smaller horizontal aperture – but further out – so more challenging!

Smaller horizontal aperture – but further out – so more challenging!


Reduction of gradient with yoke length (F)

2D model gradient only reached by extending the magnet longitudinally by a factor of 3.

However, end effects are dominant, and the integrated gradient is larger than in the hard-edge model.


Field Clamps

Tracking studies suggest that field clamps are needed

Reduce the amount of field leaking into the long straight

Symmetric or asymmetric? Occupy space and increase

power demand


0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

-250 -200 -150 -100 -50 0 50 100 150 200 250

none

symmetric

asymmetric

clamp plate position

Field Clamps

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

-250 -200 -150 -100 -50 0 50 100 150 200 250

z / mm

fiel

d /

T

no clamp plate

symmetric clamp plate

asymmetric clamp plate

clamp plate position

`

F magnet

D magnet

Field at clamp reduced by ~80%in each case

Difference between asymmetric and symmetric windows is negligible


-300 -200 - 100 0 100 200z / mm

-0.004

-0.002

0

0.002

gx'

/T/

mm

Adjusted gradient on central trajectory

-200 -150 -100 - 50 0 50 100z / mm

-50

-40

-30

-20

-10

0

x/

mm

Trajectories through both magnets; gradient evaluated at =3.88°

— QBD— QBF— added— combined

-300 -200 - 100 0 100 200z / mm

-0.004

-0.002

0

0.002g

x'/

T/m

m

Adjusted gradient on central trajectory

max difference ~0.25T/m (5%)

Plot of absolute x gradient

Differences between separate and combined models

F

D


Shape Optimisation

Two variables tangent point chamfer size

Optimise in terms of normalised integrated gradient quality

integrate vertical field along z

differentiate w.r.t x

normalise to value at centre of vac chamber

0.1% region


Tangent point variation

QBD – tangent point 10mm tangent point 48mm

hyperbolic region

tangent region

poleprofile

inscribed radius

QBF Pole Shape

10

12

14

16

18

20

22

24

30 35 40 45 50 55 60

X / mm

Y /

mm

hyperbola

16

20

11


No chamfer 10mm chamfer

size of chamfer

Variation of chamfer on pole ends

Angle can be adjusted too – 45° used up to now

OPERA-3D results suggest that a chamfer of up to 5mm has negligible effect on field quality


Magnet Apertures

F magnet D magnet

Beam stay clear apertures highlighted

F: -28.2…13.8mm (42 mm)D: -41.6…-17.3mm (24.3 mm)


2D Modelling of F Magnet

Using OPERA 2D (Neil Marks):

0.02% over required good gradient region


3D Modelling

In OPERA 3D (Takeichiro Yokoi)



11mm

pole shape

gradient quality

+5%

-5%



14mm

pole shape

gradient quality

+5%

-5%



15mm

pole shape

gradient quality

+5%

-5%



16mm

pole shape

gradient quality

+5%

-5%



20mm

pole shape

gradient quality

+5%

-5%



28mm

pole shape

gradient quality

+5%

-5%


Optimal result (OPERA-3D)

Tangent point at 11mm Good field region: ±26mm


3D Field Effects

Transverse gradient strength changes as the integration region is expanded

‘End effects’ are dominant over full range

z


Pole Shape - Alternatives

Optimisation done so far in terms of ‘hyperbolic section’ and ‘tangent section’

‘End effects’ mean that the field profile is different to a long magnet

Maybe try a slightly different pole shape? Difficult to set parameters for a ‘free’ curve Quadratic section? Polynomial approximation of hyperbola? Try to guess optimal shape from ‘constant integrated

gradient’ contours

What tweaks to the pole shape are

required to make the gradient more

uniform?

What tweaks to the pole shape are

required to make the gradient more

uniform?


Future Work

Complete yoke shape optimisation Include field clamp plates Model both magnets together

Finalise current-turns in combined model Build and test prototypes

Requests for quotes were sent out last week Comparison of codes

CST & OPERA results must agree Interface: magnet codes tracking codes


Conclusions

EMMA Magnets: design is “nearly finished” Good gradient region should be improved Pole shapes could be tweaked further

Prototypes are in the process of being ordered Tests from these will validate 3D codes

Acknowledgements: Takeichiro Yokoi Neil Marks Neil Bliss

EMMA Magnet Design Ben Shepherd Magnetics and Radiation Sources Group ASTeC STFC Daresbury...

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