Alex Bogacz

Operated by JSA for the U.S. Department of Energy

Thomas Jefferson National Accelerator Facility

Alex Bogacz 1

Alex Bogacz

Recirculating Linac

Acceleration End-to-end

Simulation

NuFact'09, Chicago, IL, July 24, 2009



Alex Bogacz 2

Linac and RLAs - Goals

0.6 GeV/pass3.6 GeV

0.9 GeV244 MeV

146 m

79 m

2 GeV/pass

264 m

12.6 GeV


IDS Goals:

Define beamlines/lattices for all components

Resolve physical interferences, beamline crossings etc

Error sensitivity analysis

End-to-end simulation (machine acceptance)

Component count and costing



Alex Bogacz 3

RLA Acceleration - Status

Presently completed lattices

Linear pre-accelerator – solenoid focusing

4.5 pass Dogbone RLA × 2 (RLA I + RLA II)

Optimized multi-pass linac optics (bisected - quad profile along the linac)

Droplet return arcs (4) matched to the linacs

Transfer lines between the components – injection chicanes

Droplet arcs crossing – Double achromat Optics design

Chromatic corrections with sextupoles at Spr/Rec junctions

Error analysis for the Arc lattices (proof-or-principle)

Magnet misalignment tolerance – DIMAD Monte Carlo Simulation

Focusing errors tolerance – betatron mismatch sensitivity

Piece-wise end-to-end simulation with OptiM (pre-accelerator + RLA I)




Alex Bogacz 4

Linac-RLA Acceptance


Initial phase-space after the cooling channel at 220 MeV/c

ISS/IDS rmsA = (2.5)2

normalized emittance: x/y mmrad 4.8 30

longitudinal emittance: l

lp z/mc)

momentum spread: p/p

bunch length: z

mm

mm

24

0.07

165

150

0.17

412

x,y = 2.74 m

x,y = -0.356

= 2.08

20-20 X [cm] View at the lattice beginning

80

-80

X`[

mra

d]

40-40 S [cm] View at the lattice beginning

18

0-1

80

dP

/P *

10

00

,



Alex Bogacz 5NuFact'09, Chicago, IL, July 24, 2009

Linear Pre-accelerator – 244 MeV to 909 MeV

6 short cryos

15 MV/m

8 medium cryos

17 MV/m

11 long cryos

17 MV/m

1.1 Tesla solenoid 1.4 Tesla solenoid 2.4 Tesla solenoid

1460

Tue Feb 12 12:50:16 2008 OptiM - MAIN: - M:\casa\acc_phys\bogacz\IDS\PreLinac\Linac_sol.opt

30

0

30

0

Siz

e_

X[c

m]

Siz

e_

Y[c

m]

Ax_bet Ay_bet Ax_disp Ay_disp

Transverse acceptance (normalized): (2.5)2= 30 mm rad

Longitudinal acceptance: (2.5)2 pz/mc= 150 mm




‘Soft-edge’ Solenoid

Non-zero aperture - correction due to the finite length of the edge :

It introduces axially symmetric edge focusing at each solenoid end:

Hard edge solenoid:

22 2

edge z 0

-

1 k a= B (s) ds B L

2 80k = eB /pc

0 0

0

M edgeedge

edge

1 0 0 0

1 0 0=

1 0

0 1

sol

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

2 k 2 kk 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 k1 - cos(kL) sin(kL) k sin(kL) 1 +cos(kL)

k4 2 4 2

M

a <<L

M M M Msoft sol edge sol edge=

a L




‘Soft-edge’ Solenoid – Nonlinear Effects

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

Solenoid B-fields

Nonlinear focusing included in particle tracking

(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) = r

2

zBz

d

d

r3

16 3zBz

d

d

3




Linear Pre-accelerator – 244 MeV to 909 MeV

1460

Tue Feb 12 12:50:16 2008 OptiM - MAIN: - M:\casa\acc_phys\bogacz\IDS\PreLinac\Linac_sol.opt

30

0

30

0

Siz

e_

X[c

m]

Siz

e_

Y[c

m]

Ax_bet Ay_bet Ax_disp Ay_disp

Transverse acceptance (normalized): (2.5)2= 30 mm rad

Longitudinal acceptance: (2.5)2 pz/mc= 150 mm

40-40 S [cm] View at the lattice end

18

0-1

80

dP

/P *

10

00

,


18

0-1

80

dP

/P *

10

00

,



Alex Bogacz 9

Multi-pass Linac Optics – Bisected Linac

1-pass, 1200-1800 MeV

‘half pass’ , 900-1200 MeV initial phase adv/cell 90 deg. scaling quads with energy

mirror symmetric quads in the linac

39.91030

Fri Jan 23 14:33:20 2009 OptiM - MAIN: - N:\bogacz\IDS\Linacs_bisect\Linac05.opt

15

0

50

BE

TA_

X&

Y[m

]

DIS

P_

X&

Y[m

]

BETA_X BETA_Y DISP_X DISP_Y

78.91030


15

0

50

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]


quad gradient

quad gradient





Injection/Extraction Chicane

660

Tue Mar 18 13:50:11 2008 OptiM - MAIN: - D:\IDS\Arcs\double_chicane3.opt

20

0

0.5

-0.5

BE

TA_

X&

Y[m

]

DIS

P_

X&

Y[m

]


1.5 GeV

0.9 GeV



Alex Bogacz 11

Pre-accelerator–Chicane–Linac Matching

216.9120

Wed Jun 11 00:32:07 2008 OptiM - MAIN: - D:\IDS\PreLinac\Linac_sol_chicane_1.opt

30

0

0.5

-0.5

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]


= 2×10-5





Pre-accelerator–Chicane–Linac Matching

216.9120

Wed Jun 11 00:32:07 2008 OptiM - MAIN: - D:\IDS\PreLinac\Linac_sol_chicane_1.opt

30

0

0.5

-0.5

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]


= 2×10-5

8-8 X [cm] View at the lattice end

40

-40

X`[

mra

d]




Injection-to–Linac – Chromatic Corrections


40

-40

X`[

mra

d]


40

-40

X`[

mra

d]


40

-40

X`[

mra

d]

uncorrected one family of sextupoles two families of sextupoles

660

Tue Mar 18 13:50:11 2008 OptiM - MAIN: - D:\IDS\Arcs\double_chicane3.opt

20

0

0.5

-0.5

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]


[ / ] 0.2 0.03 50 0.3 [ / ]sext

pG kGauss cm S D kGauss cm

p

xy = 1800 xy = 1800xy = 1800 xy = 1800




Linac ½-to-Arc1 – Beta Match

E =1.2 GeV

720

Wed Jun 11 11:53:06 2008 OptiM - MAIN: - D:\IDS\Arcs\Arc1.opt

15

0

3-3

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]


Already matched ‘by design’

900 phase adv/cell maintained across the ‘junction’

No chromatic corrections needed

36.91030


15

0

50

BE

TA_

X&

Y[m

]

DIS

P_

X&

Y[m

]





Linac1-to-Arc2 – Chromatic Compensation

E =1.8 GeV

720

Wed Jun 11 14:08:34 2008 OptiM - MAIN: - D:\IDS\Arcs\Arc2_match.opt

15

0

3-3

BE

TA_

X&

Y[m

]

DIS

P_

X&

Y[m

]


‘Matching quads’ are invoked

No 900 phase adv/cell maintained across the ‘junction’

Chromatic corrections needed – two pairs of sextupoles

36.91030

Wed Jun 11 13:14:37 2008 OptiM - MAIN: - D:\IDS\Linacs_short\Linac1_fudg.opt

150

3-3

BETA

_X&Y

[m]

DISP

_X&Y

[m]





Linac1-to-Arc2 - Chromatic Corrections

30-30 X [cm] View at the lattice beginning

80

-80

X`[

mra

d]


80

-80

X`[

mra

d]


80

-80

X`[

mra

d]

initial uncorrected two families of sextupoles

36.91030

Wed Jun 11 13:14:37 2008 OptiM - MAIN: - D:\IDS\Linacs_short\Linac1_fudg.opt

150

3-3

BETA

_X&Y

[m]

DISP

_X&Y

[m]

BETA_X BETA_Y DISP_X DISP_Y 720

Wed Jun 11 14:08:34 2008 OptiM - MAIN: - D:\IDS\Arcs\Arc2_match.opt

15

0

3-3

BE

TA_

X&

Y[m

]

DIS

P_

X&

Y[m

]





1300

Tue Jun 10 21:14:41 2008 OptiM - MAIN: - D:\IDS\Arcs\Arc1.opt

15

0

3-3

BE

TA_

X&

Y[m

]

DIS

P_

X&

Y[m

]


10 cells in2 cells out

2 cells out

footprint

-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

0 2000 4000 6000 8000 10000

z [cm]

x [cm]

(out = in and out = -in , matched to the linacs)

transition

transition

E =1.2 GeV

40-40 S [cm] View at the lattice end

30

0-3

00

dP

/P *

10

00

,


300

-300

dP/P

* 1

000,

Mirror-symmetric ‘Droplet’ Arc – Optics



Alex Bogacz 18

Adiabatic compression in the RLA off-crest acceleration in the

linac + non zero momentum compaction in the arcs (M56~6 m)

Longitudinal Compression in the RLA

20 0 200.9

1

Recirculator entrance

20 0 200.9

1

Arc1 exit

20 0 200.9

1

Arc2 exit

20 0 200.9

1

Arc3 exit

20 0 200.9

1

Arc4 exit

20 0 200.9

1

Recirculator exit




Alex Bogacz 19

Summary

Presently completed Lattices:

Pre-accelerator (244 MeV-0.9) + injection double chicane

RLA I (0.9-3.6 GeV) and RLA II (3.6-12.6 GeV)

4.5 pass linac

Droplet Arcs1-4

Chromaticity correction with sextupoles validated via tracking

Piece-wise end-to-end simulation with OptiM (transport code)

Solenoid linac

Injection chicane

RLA I

Still to do… end-to-end simulation with fringe fields (sol. & rf cav.)


Documents

Alex Bogacz