nufact’05 24-june-2005 h. schönauer cern the typical approaches to muon acceleration at higher...

NUFACT’05 24-June-2005H. Schönauer

CERN

The typical approaches to Muon acceleration at higher

energies:

• Recirculating linacs

• Scaling FFAG’s : constant tune, non-isochronous

• Non-scaling FFAG’s in various variants, most are weakly

non-isochronous:

Current investigations try to reduce RF phase slip

An Isochronous 10-20GeV Muon Ring with Constant Tunes, Operating Above Transition H.O. Schönauer, CERN


CERN

FFAG Family

Scaling FFAG’s

fRF ~ 10 MHz

non-isochronous Constant tune Japan’s Neutrino Factory

Non-scaling FFAG’s

fRF ~ 200 MHz

non-isochronous, operating around transition

Varying tune,

Linear lattice

Off-bucket acceleration

Mainstream


fRF ~ 200 MHz

Isochronous, operating at transition

Varying tune

non-linear lattice

On-crest acceleration

GHR


fRF ~ 200 MHz

Isochronous, operating above transition : locally non-isochronous

Constant tune

non-linear lattice

In-bucket acceleration

HOS


CERN

Periodic Half-Cell

B (hom., 4T)

-b (hom.)

D1 m

F1.2 m

Small kF, kD Values <0.1 m-2 -> max. Field < 2T

O0 2m

O24 m

O3 0.5 m

O1 0.5 m

66 Cells make C=1250 m (fits inside JPARC Ring)

In order to keep the tunes constant, the kF, kD values have to be constant

the gradients are prop. B,

For lin. Dispersion -> Quads are pure sextupoles


CERN

Strategy for Lattice Design

40 45 50 55 60 65

0.04

0.02

0.02

0.04

The following is a starting assumption for the orbit at the entrance of the cell (O0). Here a (initially linear) Dx= -0.31m is assumed. Abscissa is Brho for 10 -20 GeV in Tm.

This gives a ToF error as you expect it (in ps/cell):

40 45 50 55 60 65

5

5

10

15


CERN

Calculate numerically a non-linear correction to this entrance orbits to make ToF =const. Adding this to the linear orbit dependence of the 1st plot gives anon-linear dispersion at the entrance:

40 45 50 55 60 65

0.02

0.04

0.06

0.08

0.1

40 45 50 55 60 65

0.05

0.1

0.15

0.2

0.25

0.3

0.35

With this orbit dependence, one obtains the ToF error as a function of Brho in ps:

Strategy for Lattice Design II


CERN

Strategy for Lattice Design III

0 0.020.040.060.08 0.1 0.12

0.1

0

0.1

0.2

The inverse homogenous bendingmay have a curved entrance face to adjustthe closing angle. Alternatively, one may add a correction to the F magnet.

Both approaches spoil the focusing structure and upset the tune constancy…

Are two focusing elements per half cell not enough..?

G.H. Rees’ lattice cell offers three …


CERN

bd(-) BF(±) BD (+) BF(±) bd(-)

O 0.5 0.5 0.5 0.5 O

0.45 0.62 1.26 0.62 0.45

0.5 Normal cell (3º, 6.4 m) 0.5

2.4 Insertion cell (3º, 10.2 m) 2.4

Four superperiods, each of 20 normal & 10 insertion cells

New and old ring circumferences: 920.0 and 1254.6 m

Present GHR Scheme


CERN

bd(-) BF(±) BD (+) BF(±) bd(-)

O 0.5 0.5 0.5 0.5 O

0.45 0.62 1.26 0.62 0.45

2.4 Periodic cell (2.92º, 10.2 m) 2.4

123 Periods, Circumference = 1254.6 m

Periodic Cell Derived from Earlier GHR Scheme


CERN

Periodic Cell as Seen by BeamOptics

2.92

All Combined-Function Magnets are Rectangular

bD bF bdbFbd


CERN

0.5 1 1.5 2 2.5

0.15

0.1

0.05

0.05

0.1

0.15

Orbits 8 – 20 GeV

0.5 1 1.5 2 2.5

-0.2

-0.15

-0.1

-0.05

0.05

0.1

8

10

20 GeV

bd bF bDo oO

Rotation by /123


CERN

Focusing Parameters 8 – 20 GeV

5 10 15 20

-0.4

-0.2

0.2

0.4

kD

kd

kF

8 GeV 10 GeV 20 GeV


CERN

Focusing Parameters

10 33.7 0.159 0.427 0.25511. 37. 0.179 0.446 0.26311.8 39.5 0.199 0.458 0.26312.5 42. 0.219 0.468 0.2613.3 44.5 0.239 0.476 0.25514. 47.1 0.259 0.482 0.24814.8 49.6 0.279 0.487 0.2415.5 52.1 0.299 0.49 0.22916.3 54.6 0.319 0.49 0.21617. 57.1 0.339 0.488 0.217.8 59.6 0.359 0.483 0.18118.5 62.1 0.379 0.473 0.15719.3 64.6 0.399 0.453 0.12420. 67.1 0.419 0.395 0.0524

T [GeV] B [Tm] kd kF kD [m-2]


CERN

Tune Variation 8 – 20 GHz

22.2 22.4 22.6 22.8 23

10.2

10.4

10.6

10.8

11


CERN

10 0.1998 0. 42.66 0.337311. 0. 137.6 0.364711.75 0.001614 49.32 0.384612.5 0.3047 37.65 0.400913.25 0.02882 32.81 0.411314. 0.2094 29.32 0.425314.75 0.8608 26.51 0.441915.5 0.9745 24.91 0.45316.25 1.049 23.63 0.463417. 1.042 22.59 0.47317.75 1.016 21.65 0.48318.5 0.9861 20.75 0.49419.25 0.9489 19.81 0.507520. 0.8671 18.38 0.5328

T [GeV] ToF [ps] t Dx [m]


CERN

Lattice Functions at 10 GeV and 20 GeV

10 GeV 20 GeV

0 2 4 6 8 10 s m

0

5

10

15

20

b m D m

0 2 4 6 8 10 s m

5

10

15

20

b m D m


CERN

RF Issues

t

revst

revsrevsy ffE

eVhff

1

cos1800

cos2 0

For 200 MHz RF (h=800) and 750 MV we have

One synchrotron period during acceleration for gamma-t ~20 …

Bucket height:

sts f

Eh

eV

p

dp 20

cos2

0

nufact’05 24-june-2005 h. schönauer cern the typical approaches to muon acceleration at higher...

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