1 Muons, Inc. Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008 Dejan Trbojevic...

Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008 11Muons, Inc.

Dejan Trbojevic

Work with the Muons Inc.

FFAG – Type Multipass Arcs for RLA’s


FFAG – Type Multipass Arcs for RLA’s:

Introduction:

Present design of the muon RLA’s

A short introduciotn to the non-scaling FFAG

Problems:

Matching of the circular non-scaling FFAG to the straight linac.

Time of flight adjustments for each pass.

Goals:

Try to make four or five times in muon energy by either a race track or dog-

bone acceleration with a single arc (2.5-10 GeV or 10-40 GeV).

Match the betatron and dispersion functions from the arc to the linac.

Design a chicane to adjust the time of flight for different energy passes.


‘Racetrack’ vs ‘Dogbone’ RLA (both + and - species )

E/2

E

better orbit separation at linac’s end ~ energy difference between consecutive passes (2E)

allows both charges to traverse the Linac in the same direction (more uniform focusing profile

the droplets can be reduced in size according to the required energy

both charge signs can be made to follow a Figure-8 path (suppression of depolarization effects) Chuck Ankenbrandt

From Alex Bogacz:


1-pass, 3-5 GeV

phase adv. drops much faster in the horizontal plane

256.820

Mon Aug 28 23:36:36 2006 OptiM - MAIN: - D:\RLA explore\Dogbone_Triplet\flat\Linac1.opt

0.5

0P

HA

SE

_X

&Y

Q_X Q_Y

256.820

Mon Aug 28 23:35:11 2006 OptiM - MAIN: - D:\RLA explore\Dogbone_Triplet\flat\Linac1.opt

60

0

50

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]

BETA_X BETA_Y DISP_X DISP_Y

Triplet

FODO vs Triplet focusing ‘flat focusing' linac profile*

From Alex Bogacz:

256.82 meters


From CYCLOTRONS to FFAG’s:


Presently runs at 590 MeVwith energy on target of 1.2 MW2 mA in CW mode

Upgrade to 1.8 MW at the beam energy of 590 MeV

PSI – (Paul Scherrer Institute)CYCLOTRON 4.5 meter outer orbitCompared to TRIUMF 7.6 m


The first SCALING FFAG

r~60-100 cm

rsin(/sin(r

MURA-KRS-6 Phys.Rev. 103, 1837 (1956)November 12, 1954K. R. Symon: The FFAG SYNCHROTRON – MARK I

k

oo r

rBB

This is why FFAG had lost:


Many scaling FFAG’s have been built:latest complex at KURRI-Kyoto Japan


Proton driven reactor:latest complex at KURRI-Kyoto Japan


First current in KURRI’s FFAG


Non-scaling FFAG concept

Orbit offsets are proportional to the dispersion function:

x = Dx p/p

To reduce the orbit offsets to ±4 cm range, for momentum range of p/p ~ ± 50 % the dispersion function Dx has to be of the order

of:

Dx ~ 4 cm / 0.5 = 8 cm

The size and dependence of the dispersion function is best presented in the normalized space and by the H function:

= Dx /x and = D’x x + x Dx x

with H:

H = 2 + 2


The minimum emittance lattice:The minimum emittance lattice requires reduction of the function H:

The normalized dispersion amplitude corresponds to the <H>1/2

Conditions are for the minimum of the betatron function bx and dispersion function Dx to have small values at the middle of the dipole (combined function dipole makes it even smaller).

minLd15

Dxmin=Ld/24


D. Trbojevic E.D. Courant, and A. Garren, September 30, 1999, Montauk, Long IslandHigh Energy Muon Collider Workshop

Our first publication:

Lee Teng: 1956 Non-scaling FFAG proposal at the conference


Lattice got simplified with smaller number of magnets: just two kinds


Muon acceleration

Basic Properties of the non-scaling FFAG

- Extremely strong focusing with small dispersion function. - large energy acceptance.- tunes variation- very small orbit offsets-small magnets-linear magnetic field


Basic Properties of the Non-Scaling FFAG

A . Particle orbits B. Lattice


Scaling FFAG – Non scaling FFAG

Scaling FFAG properties:• Zero chromaticity.• Orbits parallel for different

p/p• Relatively large

circumference.• Relatively large physical

aperture (80 cm – 120 cm).• RF - large aperture• Tunes are fixed for all

energies.• Negative momentum

compaction.• B =Bo(r/ro)k non-linear field

Non-Scaling FFAG properties:• Chromaticity is changing.• Orbits are not parallel.• Relatively small

circumference.• Relatively small physical

aperture (0.50 cm – 10 cm).• RF - smaller aperture.• Tunes move 0.4-0.1 in basic

cell.• Momentum compaction

changes.• B = Bo+x Go linear field

B = Bo+r GoB =Bo(r/ro)k


EMMA: first non-scaling FFAG


EMMA: first non-scaling FFAG Two already built magnets:

EMMA’s cavity:


EMMA: first non-scaling FFAG: six cells on a girder


Design of the arcs – from the densely populated FODO cells for the 2.5 -> 10 GeV muons

N=142 cellsL=1.9 mLBD=0.9 mLQF=0.6 m

For the: p/p=+-60%BBD=1.64 TBQF =-1.09 TGF=20.8 T/mGD=-10.2 T/m

r=42.9

4 m

85.9

m


x max=69.7 mm

x min= -35.1 mm

1.9 m

0.3 m 1.08 m

FODO cell for the p/p=+-60 % -> 2.5 - 10 GeV

Single arc cells

35.1 mm

LBD = 1.08 m , LQF=0.6 m


FODO cell for the p/p=+-60 % -> 2.5 - 10 GeV


The matching cell lengthis: L=3 * 1.9 m = 5.7 m

Matching cell – geometrical constraint - arc to linac


Matching cell to the non-scaling FFAG arcs


Non scaling FFA arcs with matching cells without linac

Orbits from 2.5 – 10 GeV

through the matching cells and arcs:


Non scaling FFAG arcs with matching cells without linac

Betatron Functions from 2.5 – 10 GeV



Non scaling FFA arcs with matching cells without linac

Dispersion from 2.5 – 10 GeV



The linac – Betatron Function dependence on energy


Matching cell with linac – arc to linac

Orbits magnified 100 timesFrom 2.5 GeV- 10GeV


Multipass Linac - racetrack FFAG

Chicane

Chicane

Chicane Chicane

Non-scaling FFAG arc

20 Cavities

20 Cavities

Non-scaling FFAG arc


Multipass Linac with combined function triplets

Details of the orbits withChicanes:


Path length difference from the arc cells=0.55m for arc)


Details of the chicane calculations:

...!42

1~cos~,cos

1,1

cos

122

422

pklL

L

pc

B

BlLLLl

o

oo

Lo

L

Lo /L=cos


Details of the Chicane

CAVITY TRIPLET


Phil Meads: IEEE Transactions on Nuclear Science, Vol. NS-30, No. 4, August 1983


Analytical formulae from the combined function magnet:

p_max

p_min

LINAC


New matching cell

f

f

d

l o

xmax

xmin

amax

umin

umax

do

dmin

dmax

fmin

fmax

fo

d

d

d

amin

Df

Ff

F

cfo

Dd

Dd

D

cdo

eB

p

eB

p

eB

p

eB

p

eB

p

eB

p

minmin

maxmax

minmin

maxmax

Input parameters are:xmax and xmin from the arc NS-FFAGpmax, po, and pmin, Dx, x, y,

Unknowns: BD , BF , fo , do , and lo

To be matched to the input parameters of the linac: x, y, x,y


Analytical formulae from the combined function magnet:


Matching Cell - @ zero dispersion end

d

dmax

dmin

am

ax am

in

dmin

dmax

do

min

minmin

sinsin d

do

do

d a

max

maxmax

sinsin d

do

do

d a

dodo

do

dddo

au

a

minminmin

minminmin

tan

sin

sin

maxmaxmax

maxmaxmax

tan

sin

sin

ddoo

dodo

dd

au

a

um

ax

um

in

l o


Matching Cell @ entrance

pmin

pmax

po

xm

ax

xm

in

a max

a min

fmax

fo

fmin

fmax

fmin

fo

fo

f

f

fo u

sinsinmax

max

max

fo

f

f

fo u

sinsinmin

min

min

fo

fffou

sin

sin maxmaxmax

fofo

ffu

sin

sin minminmin

um

axu

min

fmin-

fo

fo- fmax

w

j

fo

f

ffo

w

sinsinmax

max

fo

f

fof

j

sinsinmin

min

l o

umax=amax+lo tan(fo-fmax)

umin=amin+lo tan(fmin-fo)

fmax

max

maxmaxmax

max

sin

sinf

fo

ffoffo

ffo

x

wx

fo

fo

foff

fof

x

jx

sin

sin1 min

minmin

minmin

fo- fmax= do- dmax

fmin- fo= dmin- do


A solution for zero offsets at the end

f

f

d

l o

xfp

+xfp-

Xd+

umin

umax

do

dmin

dmax

fmin

fmax

fo

d

d

d

Xd-

low p-

high p+

po

F/2

D/2

oppff

fff G

B

xn

oddd

d

odp ppnnn

nX /411

22

offf

f

ofp ppnnn

nX /411

22

oppdd

dpdod G

B

Xn

dddo

dd

dddpd

nA

AXx

sinh1tan

cosh

fffo

ff

fffpf

nA

AXx

sin1tan

cos

xd+=0

xd-=0

0

tan1sinh

1cosh

cosh

cosh

ff

food

do

dd

ddpfpdpd

dddpd

nl

n

XXXx

AXx


p>pcent orbits matched to linac -> zero dispersion for each

momentum

p=pcent

p=pmax


Orbits matched to linac -> zero dispersion for each momentum

10 GeV

2.5 GeV

FFAG cell Matching cell

Linac


Conclusions:

• A solution of the non-scaling FFAG arcs with RLA’s looks very good.

• This multiple pass linac is designed by the triplet combined function dipoles cells.

• Time of flight adjustments is necessary due to 0.6 m delay for the lowest energy pass through the arc. A details of chicane design has to be studied.

• Initial matching between the two arcs and linac for any energy without orbit offsets in the linac !

• The simulation of acceleration with many particles is already set-up by the PTC (Polymorphic Tracking Code).

Thanks to Muon Inc. for the support

1 Muons, Inc. Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008 Dejan Trbojevic...

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