FACET Optics Design

FACET Optics Design

Yuri Nosochkov

May 17, 2011

Outline

* Parameter specifications* Sector-20 including future upgrade option* Upgrade of Sector-10 compressor chicane* Adjustments in Sector-19 and e+ production line* Bunch length compression* Particle tracking* Tolerances* Tuning

Specified parameters at IP

Energy 23 GeV

Charge per bunch 2·1010 (3.2 nC) e- or e+

Bunch length ≤ 25 m with full compression

Spot size at IP ≤ 20 m round

Momentum dispersion at IP ≤ 10-4 m

Momentum spread 4% full width with full compression

Longitudinal space for experiment2 m between last FF quad and IP,

~25 m after IP

Linac modifications

Add positron chicane in Sector-10 and adjust quad focusing

Adjust focusing in Sector-19 and e+ production line

FACET optics in Sector-20: chicane, Final Focus and experiment line

* Sector-20 requires a bending system with R56 = 4 mm for final compression of bunch length.

* Chicane bending optics is used because it is compatible with an upgrade option of simultaneous transport of e- and e+ bunches using separate e- and e+ chicanes.

* The present proposal includes only one chicane for e- (or e+) transport. The second e+ chicane can be added in the future upgrade. However its baseline optics must be designed now since the two chicanes share some of the constraints.

* The upgrade e+ chicane is designed for 52.7 mm longer path length required for correct longitudinal positions of the drive (e-) and witness (e+) bunches in wakefield plasma experiment.

Sector-20 chicane scheme

e-

e+

e-

e+e+ upgrade

e-

IP

R56 = 4 mm

R56 = 4 mm, s = 52.7 mm

Shared FFShared Linac

64 m

x = y

= 0

sailboatchicane

Focusing in linac and e-/e+ chicanes

* FACET optics is designed to be compatible with simultaneous transport of e- and e+ bunches in the future upgrade option.

* In this case, the e- and e+ beams will share most of the 2 km quadrupole Linac optics and have separate paths in the Sector-10 and Sector-20 upgrade chicanes.

* In the shared parts of Linac and Sector-20 the e- and e+ transfer matrices are related: Mx(e-) = My(e+), My(e-) = Mx(e+), thus resulting in the matching condition for beta functions: x(e-) = y(e+), y(e-) = x(e+).

* The e- and e+ chicanes must therefore provide a match to these beta conditions. One convenient way to obtain an automatic beta match is to use the above matrix condition in the e- and e+ chicanes as well. This solution is used in the FACET design. Without the above matrix condition, the chicanes would have to be rematched anytime the incoming beta functions are changed.

Sec-10 Sec-20

Shared e-/e+ Shared e-/e+ Shared e-/e+

FF

e-e-

e+ e+ upgrade

* The present proposal includes one (lower) chicane for either electron or positron transport.

* The 2nd (upper) chicane for positrons can be added in the future for simultaneous running of e- and e+ bunches.

Sector-20 layout

e-

e+ upgrade

IPDump

FinalFocus

Experimentalarea

Bends (in red), quads (blue), sextupoles (green), wiggler (pink)

Sector-20 optics functions

* The Sector-20 optics provides a small round spot at IP with zero dispersion, R56 = 4 mm, and it is compatible with the future e+ chicane.

* Incoming emittance and IP -functions: x/y = 50/5 m·rad, x/y = 1.5/15 cm.

IP

Chicane FF

Dump

* The upgrade optics of e- and e+ chicanes provide:

Mx(e-) = My(e+), My(e-) = Mx(e+), R56 = 4 mm, zero IP dispersion, 52.7 mm longer path length for e+, geometric separation between e- and e+ lines.

* IP beta and incoming emittance:x = y = 6 cm, x = y = 25 m·rad.

Coupled emittance and equal X&Y beta at IP simplify e- and e+ matching in the shared FF for the same round spot at IP.

Sector-20 upgrade optics

IP IP

e- chicanee+ chicane

FFFF

Sextupole correction

Limited space in Sector-20 does not allow for a dedicated IP chromatic correction. 8 sextupoles on 6 power supplies are included symmetrically in Sector-20 chicane. They minimize chromatic growth, IP 2nd order dispersion, and T566 compression term. At present, the sextupoles are divided into 3 families and their strengths are obtained empirically by minimizing IP spot size in tracking simulations.

W-function

2nd orderdispersion

Without sextupoles With sextupoles

IP IP

T566 = 258 mm T566 = 87 mm

Sector-20 magnets

BENDS

NAME Qty L(m) BL (kGm)

B1EP 2 1.0630 17.3294B2E 2 1.8249 25.1717B3E 2 0.5287 7.8412B5D36 1 0.9779 10.7408

B2P 2 1.0630 17.3294B3P 2 1.0630 17.3294B4P 2 0.8400 13.3224B5P 4 0.5080 8.0569B6P 2 1.4220 22.5530

WIGGLER BENDS

NAME Qty L(m) BL (kGm)

WIG1E 2 0.2440 1.9180WIG2E 1 0.4880 3.8360

WIG1P 2 0.2440 1.9180WIG2P 1 0.4880 3.8360

QUADRUPOLES

NAME Qty L(m) GL (kG)

Q1E 2 0.5962 316.988Q2E 2 1.0000 363.429Q3E 4 0.7142 276.761Q4E 6 0.7142 255.699Q5E 2 0.4284 131.223Q6E 1 0.3100 200.059QFF1 1 0.4609 75.095QFF2 3 0.4609 160.040QFF4 2 0.7142 214.695QFF5 1 2.0260 630.552QFF6 1 0.7142 419.716QS1 1 1.0000 245.182QS2 1 1.0000 174.118

Q1P 2 0.8394 535.279Q2P 2 0.7341 451.580Q3P 2 0.1068 33.429Q4P 2 1.1463 467.769Q5P 4 0.4086 440.995Q6P 1 0.6254 228.619

SEXTUPOLES

NAME Qty L(m) G2L (kG/m)

S1E 2 0.2500 1841.27S2E 2 0.7620 12861.30S3E 4 0.2500 2013.89

S1P 2 0.2500 5713.70S2P 4 0.2500 7464.83S3P 2 0.2500 2466.54

This proposal: 7 bends, 3 wiggler bends, 27 quads, 8 sextupoles in Sector-20

Upgrade (in blue):+ 12 bends, 3 wiggler bends, 13 quads, 8 sextupoles

Mostly existing SLAC magnets

Existing correctors and BPMs

new

new

new

Sector-20 linear optics beam size

(mm)

Linear optics rms beam size (without radiation and non-linear effects) assuming = 50/5 m-rad and E = 1%.

IP

Optics functions and beam size at monitors (1)

Optics functions and beam size at monitors (2)

Upgrade of Sector-10 chicane

* New e+ chicane will be installed mirror symmetrically with respect to the existing e- chicane in Sector-10 to provide the positron bunch compression.

* Two new bends will be made for the 1st and last positions in the chicane. They require a very good field quality because of large e-/e+ trajectory offsets, and will have a special pole face angle for focusing adjustment.

* The existing outer bends will be moved to inner positions in the e+ chicane since they meet the field and aperture requirements at these positions.

* Two new quad corrector magnets will be made

for the positron chicane.

e-

Existing chicane

e+

e-

New chicane

Sector-10 chicane optics

Concept of the new 1st / last bends

e+

e-

New chicane

* Using the existing design for e- and e+ chicanes would not provide a beta match for both beams to the shared Linac because the chicane matrices do not satisfy to Mx(e-) = My(e+), My(e-) = Mx(e+). This mismatch can create a large -beat downstream of the chicane for one of the beams.

* 2 focusing strengths in the chicanes are needed to suppress the -beat.

* The adopted solution is to use the chicane quad correctors as one focusing strength and adjust edge focusing in the new outer bends by using a special angle at the pole face where beams are separated.

Large beam offsets (±89.7 mm) in the new bend require tight field tolerances, but comparable to the existing bend tolerances.

The matched Sector-10 chicane (using the chicane quad correctors and special pole face angle in the new bends) reduces the downstream -beat for the e+ beam from 90% to below 3% (when e- beam is exactly matched).

Residual-beat downstream of Sector-10

Chicane

beat for e+ beat canceled

With existing chicane design With matched chicane optics

Chicane

functions in Sector-10 chicanes

Field tolerances in the new Sector-10 chicanes should satisfy the existing chicane specifications and must be compatible with the existing bend field quality. This requires that x functions for e- and e+ beams are comparable to electron x function in the existing chicane (or lower). This is achieved by quadrupole strength adjustment in the adjacent Sectors 10 and 11 and further improved by inserting an extra quad upstream of the chicane.

Existing beta

x(e-) x(e+)

Reduced beta

x(e-)

x(e+)

With extra quad

x(e-)

x(e+)

Optics match in Sector-19

• 6 quad strengths in Sector-19 are used for match to FACET optics. Two other quads cannot be used because they provide a fixed kick for e+ production line.

• The e+ production line optics is matched to the new larger functions in Sector-19 using 6 quadrupole families.

Q190701 e+ target

Existing

with FACET

Sector-19 Sector-20 Sector-19 FACET

e+ target

IP

e+ productio

n

FACETSector-19

Optics match in e+ production line

Existing and dispersion Matched to FACET

Q190701 target

The match keeps a small beam spot at the production target

Production line Production line

Bunch compression in linac

Bunch length compression is achieved through manipulation of beam energy spread and bunch length along the Linac using momentum compaction of bending systems and optimization of RF accelerating phase.

DR

Sec-10 Sec-20

Illustration of bunch length compression in the Linac

Bunch length compression at IP

• Bunch compression from damping ring to FACET IP is optimized using LiTrack code (by K. Bane).• Gaussian fit sigma: ~20 m.• However, the short bunch has a large energy spread which generates chromatic growth of X/Y beam size at IP. This effect is reduced using sextupoles.

LiTrack simulation at IP

* ELEGANT tracking in Sector-20 with ISR, without errors.

* Incoming beam at entrance into Sector-20: E = 23 GeV, x / y = 50 / 5

m·rad, Gaussian X-Y spread with = , longitudinal spread from LiTrack simulation.

ELEGANT tracking with ISR:Transverse IP size

X Y

* ELEGANT tracking in Sector-20 with ISR and CSR, without errors.

* CSR increases horizontal beam size from 11.3 m to 14.1 m.

ELEGANT tracking with ISR and CSR: Transverse IP size

X

Y

X Y

* ELEGANT tracking in Sector-20 with ISR and CSR, without errors.

* Bunch length at IP = 18.8 m.

ELEGANT tracking with ISR and CSR:Bunch length

Zp/p

Tuning of IP beta functions

Compensation of optics errors and achieving optimal beam parameters require the optics capability for tuning.

IP beta functions can be varied using strength adjustment in four FF quads.The available range for quad strengths will need to be verified.

Tuning of longitudinal position of IP waist

Each quad family in Sector-20 chicane has a main power supply. In addition, there is a boost power supply which allows separate adjustment for the quads on the left and right sides in the chicane within 10% range.

Large shift of IP waist using four FF quads

Small shift of IP waist using four chicane quads on right hand side

Tuning knob for IP dispersion

Linear tuning knob for IP dispersion using 5 chicane quads and 3 FF quads.

Some residual distortions: /* < 10%, Dx' < 50 rad.

Tuning of R56 in Sector-20

R56 in Sector-20 can varied using adjustment of five chicane quadrupoles.The available range for quad strengths will need to be verified.

IP match to plasma

• The IP beta functions need to be matched to the extremely strong plasma focusing for minimal beta beating in the plasma.• With unequal x and y IP beta, only one plane can be matched exactly.• A more appropriate option is to minimize beta beating in both planes.• The “match” is achieved by optimizing * value and IP waist position.

Power supply jitter tolerances

Magnet

Name (Qty)Tolerance, I/I rms

Magnet Name (Qty)

Tolerance, I/I rms

Magnet Name (Qty)

Tolerance, I/I rms

Chicane-10 bend (4)

5.0·10-4 Q4E (6) 2.4·10-4 S1EL (1) 3.9·10-2

Chicane-10 quad (2)

5.0·10-2 Q5E (2) 7.5·10-3 S1ER (1) 2.5·10-2

B1E (2) 2.0·10-4 Q6E (1) 3.9·10-3 S2EL (1) 1.5·10-2

B2E (2) 1.6·10-4 QFF1 (1) 5.0·10-3 S2ER (1) 1.2·10-2

B3E (2) 6.6·10-4 QFF2 (3) 1.0·10-3 S3EL (2) 1.0·10-1

Q1E (2) 1.0·10-2 QFF4 (2) 1.1·10-4 S3ER (2) 9.0·10-2

Q2E (2) 6.6·10-4 QFF5 (1) 3.5·10-4

Q3E (4) 1.4·10-4 QFF6 (1) 8.2·10-4

• Tolerances for the new Sector-10 chicane are set to the existing chicane tolerances.• Tolerances for Sector-20 are determined in DIMAD tracking simulations and correspond to 2% growth of beam core rms IP size relative to ideal beam size with ISR and appropriate model of large energy spread. These errors are assumed uncorrectable.

Multipole field tolerances in the new bends

* New 1st / last bends in Sectors 10 and 20 have large horizontal offsets of e- and e+ trajectories (±89.7 mm and ±11.7 mm) which lead to tight tolerances on multipole field content. The additional challenge is due to the special pole face angle in Sector-10 bend which naturally

increases the multipole field near the pointing bend end.

* Tolerances were estimated in DIMAD tracking simulations

including the FACET upgrade option and assuming the orbit

is corrected.

* Sector-10 new bends: tolerances Bn/B0 are specified at X = 10 cm based on 2% emittance growth from each multipole from each bend:

B1/B0 = 0.21%, B2/B0 = 0.27%, B3/B0 = 0.30%, B4/B0 = 0.33%.

* Sector-20 new bends: tolerances Bn/B0 are specified at X = 1 cm based on 2% growth of core rms IP size from each multipole from each bend:

B1/B0 = 0.023%, B2/B0 = 0.028%, B3/B0 = 0.022%, B4/B0 = 0.015%.

* An alternative requirement is to achieve <10% growth from all multipoles in both bends based on designed magnetic field.

Quadrupole tolerances in Sector-20

• The shown field and alignment tolerances are based on 2% luminosity growth from one beam (using the code by P. Emma). • Tolerances were calculated for the flat emittance option (this proposal) and the coupled emittance option (upgrade) and the tighter values are used.

Bend and sextupole tolerances in Sector-20

• The shown field and alignment tolerances are based on 2% luminosity growth from one beam (using the code by P. Emma).• Multipole field tolerances for B1L, B1R bends are evaluated separately using DIMAD tracking to include the effect of large trajectory offset.

Additional slides

* Chromatic and SR emittance growth.* Tracking simulations for upgrade option with e+ chicane

in Sector 20.

Chromatic and SR growth in Sector-20

No SRand p/p = 0 (sext geometric)

No SR (chrom + sext geom)

+ISR +ISR + CSR

Gaussian fit rms

xm

4.4 8.2 11.6 15.0

y 4.1 7.0 7.1 7.1

Full rms

xm

4.7 16.0 17.1 19.9

y 4.1 19.4 19.3 19.2

x m-rad

54.2 176.6 194.8 246.0

y 5.1 30.2 30.0 30.1

• ELEGANT tracking with and without SR and energy spread to evaluate chromatic and SR growth. E = 23 GeV, * = 1.5 / 15 cm, 0 = 50 / 5 m-rad.• Chromatic and SR growth is large. This is caused by large incoming energy spread and strong bends in Sector-20. Compensation options are limited due to lack of space and other optical and geometric constraints in Sector-20 (R56, transfer matrix, compatibility with future e+ chicane). Small nominal * is used to compensate for this growth.• Enlargement of full rms relative to Gaussian fit is due to chromatic tails at large p/p.

Tracking results for Sector-20 upgrade optics with both e- and e+ chicanes

E = 23 GeV,*x,y = 6 cm, x,y = 25 m·rad for e- and e+ beams.

These results will need to be updated.

e-

e+upgrade

X Y Z

ZYX

FACET Optics Design

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