Alex Bogacz

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

Thomas Jefferson National Accelerator Facility

Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

Muons, Inc.

Alex Bogacz

Pulsed ‘Dogbone’ RLA for Muon Collider




Muons, Inc. RLA for Muons

‘Dogbone’ (Single Linac) RLA has advantages over the Double-Linac RLA ‘Racetrack’

FODO Optics is superior to Triplet focusing more passes are possible with the FODO scheme

Pulsed linac Optics…. proposed by Rol Johnson ....even larger number of passes is possible if the quadrupole focusing can be increased as the beam energy increases…..subject to a new SBIR with Muons Inc.




Muons, Inc.

E/2

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

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 profilethe droplets can be reduced in size according to the required energyboth charge signs can be made to follow a Figure-8 path (suppression of depolarization effects) Chuck Ankenbrandt




Muons, Inc.

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

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256.820


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248.6510

Mon Aug 28 09:18:21 2006 OptiM - MAIN: - D:\RLA explore\Dogbone_FODO\flat\Linac1.opt

0.5

0P

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phase adv. diminish uniformly in both planes

248.6510


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FODO

Triplet

FODO vs Triplet focusing ‘flat focusing' linac profile*

Bob Palmer*




Muons, Inc.

2-pass, 5-7 GeV

256.820


0.5

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256.820


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BETA_X BETA_Y DISP_X DISP_Yphase adv. drops much faster in the horizontal plane

FODO vs Triplet focusing ‘flat focusing' linac profile

248.6510


0.5

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Y

Q_X Q_Y

248.6510


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BETA_X BETA_Y DISP_X DISP_Yphase adv. diminish uniformly in both planes

FODO

Triplet




Muons, Inc.

3-pass, 7-9 GeV

256.820


0.5

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256.820


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BETA_X BETA_Y DISP_X DISP_Y no phase adv. in the horizontal plane

248.6510


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248.6510


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FODO

Triplet




Muons, Inc.

4-pass, 9-11 GeV248.6510


0.5

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Y

Q_X Q_Y

248.6510


900

50

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DIS

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FODO

Triplet


no phase adv. across linac- beam envelopes not confined




Muons, Inc.

5-pass, 11-13 GeV 248.6510


0.5

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Y

Q_X Q_Y

248.6510


900

50

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TA_X

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DIS

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BETA_X BETA_Y DISP_X DISP_Y phase adv. diminish uniformly in both planes

FODO

Triplet


no phase adv. Across the linac- beam envelopes not confined




Muons, Inc.

FODO

Triplet


6-pass, 13-15 GeV

248.6510


0.5

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Q_X Q_Y

248.6510


900

50

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no phase adv. Across the linac- beam envelopes not confined




Muons, Inc.

RLA requirements Simultaneous acceleration of both + - species

Manageable orbit separation at recirculation arcs

Beam dynamics challenges RLA Optics solutions Phase slippage in the linacs

Multi-pass linac optics

‘Droplet’ arc lattice Orbit separation - switchyard

7.5-pass Dogbone RLA - Linear Optics/Lattices designed

‘Dogbone’ RLA with FODO Focusing




Muons, Inc.

7.5 pass Ef

E0

= 13

4 GeV/pass32.5 GeV

2.5 GeV0.3 GeV

Dogbone RLA I

Possible RLA based Acceleration Scenario for MC

7 pass Ef

E0

= 23Dogbone RLA II

ILC Linac 103 GeV/pass

32.5 GeV

753.5 GeV




Muons, Inc. Possible RLA based Acceleration Scenario for MC

Low Energy RLA (2.5 GeV to 32.5 GeV)

7.5-pass ‘Dogbone’ RLA: Linac (4 GeV/pass ) + 7 droplet Arcs

SRF: 200-400 MHz

Top-to-injected energy ratio = 13

High Energy RLA (32.5 GeV to 753.5 GeV)

7-pass ‘Dogbone’ RLA: Linac (ILC 4000 m, 103 GeV/pass ) + 7 droplet Arcs

Tesla SRF: 1300 MHz, 25 MeV/m

Top-to-injected energy ratio =23

No injection at the middle of linac necessary Harold Kirk




Muons, Inc.

0 5000 1 104 1.5 104 2 104 2.5 104 3 10410

5

0

5

10

pass 0.5pass 1pass 2pass 3

s [cm]

RF

phas

e [d

eg]

b0 0 9.5 b1 0 4 b2 0 1 b3 0 0

Phase Slippage in the Linacs

Phase slippage of a semi-relativistic muon beam injected with the initial energy E0 and accelerated by E in a linac of length, L - assuming uniformly spaced RF cavities phased for a speed-of-light particle

RLA I (2.5 GeV to 32.5 GeV) RLA II (32.5 GeV to 753.5 GeV)

0 1 105 2 105 3 105 4 105 5 105

4

2

0

2

4

pass 1pass 2pass 3pass 4

s [cm]

RF

phas

e [d

eg]

b0 0 5 b1 0 1 b2 0 0.5 b3 0 0




Muons, Inc.

‘Pulsed’ vs ‘Fixed’ Dogbone RLA (8-pass)

4 GeV/pass

3 GeV

35 GeV

Quad pulse would assume 500 Hz cycle ramp with the top pole field of 1 Tesla.

Equivalent to: maximum quad gradient of Gmax =2 kGauss/cm (5 cm bore radius) ramped over = 10-3 sec from the initial gradient of G0 =0.1 kGauss/cm (required by 900 phase advance/cell FODO structure at 3 GeV). G8 =13 G0 = 1.3 kGauss/cm

These parameters are based on similar applications for ramping corrector magnets such as the new ones for the Fermilab Booster Synchrotron that have 1 kHz capability

-5-8

-2

500 + 250T 8× sec = 2×10 sec3×10

T 2×10




Muons, Inc.

‘Pulsed’ vs ‘Fixed’ Dogbone RLA (8-pass)

For simplicity, we consider a linear ramp according to the following formula:

A single bunch traveling with a speed of light along the Linac with quads ramped as above ‘sees’ the following quad gradient passing through i-th cell along the Linac (i = 1,…20)

where is the cell length and i defines the bunch position along the Linac.

For multiple passes through the Linac (the index n defines the pass number) the above formula can be generalized as follows:

where is the full Linac length and is the length of the lowest energy droplet arc. Here we also assume that the energy gain per linac is much larger than the injection energy.

max

00( )G GG t G t

max

00

celli

G GG G ic

25cell m

max0

0 12i

nlinac arc cell

G G nG G n ic

linac arc




Muons, Inc.

1-pass, 3-7 GeV

‘Pulsed’ vs ‘Fixed’ Dogbone RLA (8-pass) Pulsed

Fixed

5000

Fri Nov 16 16:22:24 2007 OptiM - MAIN: - M:\acc_phys\bogacz\Dogbone_pulsed\pulsed\Linac1.opt

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Muons, Inc.

8-pass, 28-32 GeV


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phase adv. diminishes down to 1800




Muons, Inc.

12-pass, 47-51 GeV


Fixed

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no phase adv. across the linac- beam envelopes not confined

phase adv. diminishes down to 1800




Muons, Inc. ‘Pulsed’ Dogbone ILC - example

max

00( )G GG t G t

T

1 12linac arc linacnT n i

c

4000linac m

200arc m

0

0.1

0.2

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0 5 10 15 20 25 30

31 10 sec

number of passes




Muons, Inc. Mirror-symmetric ‘Droplet’ Arc – Optics

16 cells2 cells 2 cells

600

Tue Jan 30 02:43:58 2007 OptiM - MAIN: - D:\ELIC\Figure-8\FODO\low_emitt\rec_in.opt

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Tue Jan 30 02:44:33 2007 OptiM - MAIN: - D:\ELIC\Figure-8\FODO\low_emitt\rec_in.opt

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Tue Jan 30 02:46:05 2007 OptiM - MAIN: - D:\ELIC\Figure-8\FODO\low_emitt\trans_in.opt

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Tue Jan 30 02:50:37 2007 OptiM - MAIN: - D:\ELIC\Figure-8\FODO\low_emitt\trans_out.opt

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

footprint

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septumspreader

dipole

dipole




Muons, Inc. Conclusions

‘Dogbone’ RLA – preferred configuration

better orbit separation for higher passes

offers symmetric solution for simultaneous acceleration of + and -

FODO lattice (900 deg. phase adv/cell) allows to accommodate large number of passes in the linac (8-pass RLA example)

uniform phase advance decrease in both planes

smaller variation of Twiss function – easier match to the Arcs

Pulsed linac Optics Dogbone RLA looks very encouraging…needs further studies...Increase from 8-pass (Fixed Optics) to 12-pass (Pulsed Optics) for 500 m long 4 GeV pass example

Muon Collider Acceleration Scheme with two Dogbone RLAsRLA I: 2.5-32 GeV

RLA II: 32-753 GeV

Alex Bogacz

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