Beam Dynamics of Low Energy Muon Acceleration

Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

Thomas Jefferson National Accelerator Facility

NuFact’05, INFN Frascati, June 24, 2005

Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration

Beam Dynamics of Low Energy Muon Acceleration

Alex BogaczJefferson Lab

7-th International Workshop on Neutrino Factories and Superbeams, LNF Frascati, June 24, 2005





Overview

FFAG acceleration below 5 GeV not cost effective ‘Dogbone’ RLA (3.5-pass) scheme based on 200MHz SRF

Pre-accelerator (273 MeV/c – 1.5 GeV) based on solenoid focusing Main Linac (1 GeV/pass) based on triplet focusing Three ‘droplet’ arcs with horizontal multi-pass separation

Longitudinal phase-space compression in the arcs (M45 and off-crest RF)

M45 and off-crest RF linac accelerationLarge (2) transverse acceptance

Lattices – linear optics, tracking studies, emittance preservation multi-pass linac opticstracking studies





Muon Acceleration Complex

Linear pre-accelerator (273 MeV/c – 1.5 GeV)

‘Dogbone’ 3.5-pass RLA (1.5 – 5 GeV)

5 – 10 GeV FFAG

10 – 20 GeV FFAG





‘Dogbone’ RLA (3.5-pass) scheme

Linear pre-accelerator (273 MeV/c – 1.5 GeV) - solenoid focusing

Main Linac (1 GeV/pass) - triplet focusing Single magnet horizontal multi-pass separation

3 Arcs based on the same strength of bending magnets (~ 1 Tesla)





Initial beam emittance/acceptance

after the cooling channel at 273 MeV/c

Study IIa rms A = (2.5)2

normalized emittance: x/y mmrad 4.8 30

longitudinal emittance: l

(l = p z/mc)

momentum spread: p/p

bunch length: z

mm

mm

270.07176

1500.17442





Beam Parameters

Study IIa

Final energy GeV 5Number of bunches per pulse 89Number of particles per per pulse 31012

Bunch/accelerating frequency MHz 200/200Average repetition rate Hz 15Average beam power kW 144




Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration Pre-accelerator– Longitudinal

dynamics

100 0 100

0.2

0

0.2

Phase [deg]

Dp/

p

0 50 100 150 200 250 3000

0.5

1

1.5

2

s [m]

Ener

gy [G

eV]

longitudinal acceptance, bucket height

energy profile along the linac

p/p=0.17or =93 (200MHz)




Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration Pre-accelerator– Longitudinal

acceptance

100 50 0 50

0.2

0.1

0

0.1

0.2

fi [deg]

Dp/

p

Phase space contours initial, half-way through and at the end of acceleration – contours defined for particles at 2.5 (95% of particles contained inside)




Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration Linear Pre-accelerator – Longitudinal

dynamics, tracking

25-25 S [cm] View at the lattice beginning

200

-200

dP/P

* 1

000,

25-25 S [cm] View at the element 275

200

-200

dP/P

* 1

000,

25-25 S [cm] View at the lattice end

200

-200

dP/P

* 1

000,

3020

Fri Dec 03 11:22:15 2004 OptiM - MAIN: - D:\Study 2A\PreLinac\Linac_sol.opt

250

30-9

0

Bet

atro

n si

ze X

&Y

[cm

]

Ang

le[d

eg][-

90,+

90]

a b Angle[deg]





sol

1 +cos(kL) sin(kL) sin(kL) 1 - cos(kL)2 k 2 k

k sin(kL) 1 +cos(kL) 1 - cos(kL) sin(kL)k4 2 4 2=

sin(kL) 1 - cos(kL) 1 +cos(kL) sin(kL)2 k 2 k

1 -cos(kL) sin(kL) k sin(kL) 1 +cos(kL)k4 2 4 2

M

‘soft-edge’ solenoid model

Zero aperture solenoid - ideal linear solenoid transfer matrix:

0k = eB /pcLarmour wave number:





‘soft-edge’ solenoid – edge effectNon-zero aperture - correction due to the finite length of the edge :

It decreases the solenoid total focusing – via the effective length of:

It introduces axially symmetric edge focusing at each solenoid end:

axially symmetric quadrupole

22 2

edge z 0-

1 k a= B (s) ds B L2 8 0k = eB /pc

z

0 -

1L = B (s) dsB

0 00

M edgeedge

edge

1 0 0 01 0 0

=1 0

0 1

M M M Msoft sol edge sol edge=




Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration ‘soft-edge’ solenoid – nonlinear

effectsNonlinear focusing term F ~ O(r2) follows from the scalar potential:

Scalar potential in a solenoid

Solenoid B-fields

(r,z) = 0 Bz zz

Bzd

d

2 z2 r24

2zBz

d

d

2

z 2 z2 3 r2 12

3zBz

d

d

3

8 z4 24 z2 r2 3 r4192

Bz(r,z) = Bz 2zBz

d

d

2

r2

4

Br(r,z) = r2

zBz

d

d

r3

16 3zBz

d

d

3




Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration ‘soft-edge’ solenoid – nonlinear

effects

In tracking simulations the first nonlinear focusing term, F ~ O(r2) is also included:

Nonliner focusing at r = 20 cm for 1 m long solenoid with 25 cm aperture radius

aL

rpceB

LdsBrdsBpce

F 31

2221 22

022

22

22 2/ 4, 0.8

20.07

2 3L r r a

B dsF r rF aLB ds




Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration Linear Pre-accelerator – transverse

emittance

63.9529227.065

Tue Feb 15 10:29:00 2005 OptiM - MAIN: - D:\Study 2A\PreLinac\Linac_sol.opt

0.05

0

11.9

101

0

Em

ittan

ce[c

m]

Xm

ax&Ym

ax[c

m]

Emit_X Emit_Y Xmax Ymax

3020

Tue Feb 15 10:30:19 2005 OptiM - MAIN: - D:\Study 2A\PreLinac\Linac_sol.opt

20

0.09

0

Inte

nsity

dP/P

Intensity dP/P





Main Linac - multi-pass Optics

Focusing compromise strategy

focusing optimized for the half-pass (1.5-2 GeV) - 900 phase advance per cell

Uniform focusing restored in the second half of the first full-pass (2.5-3 GeV)




Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration Main Linac - Multi-pass Optics (lower

passes)

900

Fri Dec 03 12:46:02 2004 OptiM - MAIN: - D:\Study 2A\Linacs\Linac_05.opt

300

50

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]

BETA_X BETA_Y DISP_X DISP_Y

1890

Fri Dec 03 12:47:40 2004 OptiM - MAIN: - D:\Study 2A\Linacs\Linac1.opt

300

50

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]


1.5-2 GeV

2-3 GeV




Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration Main Linac - Multi-pass Optics (higher

passes )3-4 GeV

4-5 GeV

1890


300

50

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]


1890


300

50

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]





Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration Main Linac - Multi-pass phase

advance slip

3-4 GeV

2-3 GeV

1890

Fri Jun 24 12:14:19 2005 OptiM - MAIN: - D:\Study 2A\Linacs\Linac1.opt

0.5

0P

HA

SE

_X&

Y

Q_X Q_Y

1890

Fri Jun 24 12:17:19 2005 OptiM - MAIN: - D:\Study 2A\Linacs\Linac2.opt

0.5

0P

HA

SE

_X&

Y

Q_X Q_Y




Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration Main Linac - the half-pass (1.5-2 GeV)

longitudinal tracking

900

Fri Dec 03 13:11:43 2004 OptiM - MAIN: - D:\Study 2A\Linacs\Linac_05.opt

300

50

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]


25-25 S [cm] View at the lattice beginning

200

-200

dP/P

* 1

000,


200

-200

dP/P

* 1

000,




Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration Main Linac - transverse emittance

(tracking)

900

Tue Feb 15 10:07:08 2005 OptiM - MAIN: - D:\Study 2A\Linacs\Linac_05.opt

0.05

0

80

Em

ittan

ce[c

m]

Xm

ax&Ym

ax[c

m]


the half-pass 1.5-2 GeV





Arc Optics - beam transport choices

Principle of uniform focusing periodicity (900) – cancellation of chromatic effects

Single dipole (horizontal) separation of multi-pass beams in RLA No need to maintain achromatic Spreaders/Recombiners

Compact Spreaders/Recombiners – minimized emittance dilution

SC dipoles and quads (triplets) in RLA (1 Tesla dipoles/1 Tesla quads)

Requirement of high periodicity and ‘smooth’ transition between different kinds of optics, linac-spreader-arc-recombiner-linac




Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration ‘Droplet’ return (600 out - 3000 in - 600

out)

arc footprint

300000

Sat Apr 10 02:25:41 200410

000

-100

00

1-1

Y1 Y2 Y3 Y4





Droplet arc – Optics building blocks inward and outward cells, missing dipole cell

90

Fri Dec 03 13:23:10 2004 OptiM - MAIN: - D:\Study 2A\Droplette\A_out.opt

300

3-3

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]

BETA_X BETA_Y DISP_X DISP_Y 90

Fri Dec 03 13:24:34 2004 OptiM - MAIN: - D:\Study 2A\Droplette\A_out.opt

300

3-3

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]


90

Fri Dec 03 13:27:09 2004 OptiM - MAIN: - D:\Study 2A\Droplette\L_out.opt

300

3-3

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]

BETA_X BETA_Y DISP_X DISP_Y 4536

Fri Dec 03 13:33:34 2004 OptiM - MAIN: - D:\Study 2A\Droplette\SprTr.opt

300

3-3

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]






Chromatic properties of the periodic cell

p/p=0.07




Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration Droplet Arc Optics (Spreader and

Transition) - Arc 1

127.650

Fri Dec 03 13:40:25 2004 OptiM - MAIN: - D:\Study 2A\Droplette\halfArc.opt

300

3-3

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]


Dipoles:

L[cm] B[kG]150 7.8

Quads:L[cm] G[kG/cm]

D 68 -0.32F 125 0.32





Arc 1 – Longitudinal dynamics (tracking)


200

-200

dP/P

* 1

000,


80-8

0dP

/P *

100

0,

193.50

Fri Dec 03 13:54:04 2004 OptiM - MAIN: - D:\Study 2A\Arcs\Arc.opt

300

5-5

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]






Arc 1 – Transverse emittance (tracking)


200

-200

dP/P

* 1

000,


80-8

0dP

/P *

100

0,

255.30

Tue Feb 15 10:54:52 2005 OptiM - MAIN: - D:\Study 2A\Droplette\Arc.opt

0.2

0

50

Em

ittan

ce[c

m]

Xm

ax&Ym

ax[c

m]






Arc 2 – Optics

256.50

Fri Jun 24 13:01:46 2005 OptiM - MAIN: - D:\Study 2A\Arcs\Arc2.opt

300

5-5

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]






SummaryLattice for 3.5-pass, 5 GeV, RLA based on 200MHz SRF - linear optics

Pre-accelerator, three styles of cryo-modules

Proof-of-principle Arc optics lattice - further longitudinal compression in the Arcs, with M56 ~ 3 m

multi-pass linac optics

compact Spr/Rec

matched periodicity (betatron phase advance per cell) between linacs and Arcs

Future work…Emittance preservation scheme - nonlinear corrections in the Arcs

Chromatic corrections in the Arcs to effectively restore longitudinal space linearity (via three families of sextupoles)

Emittance preservation checked independently by ICOOL

Documents

Beam Dynamics of Low Energy Muon Acceleration