Optics of e-ring, towards v2.0

• v1.0 is released on 08/01

• Since then, a lot of discussions, comments, ideas, etc.

• Progress in August and September towards v2.0:

operation modes: from 2 to more than 8

interaction region: more rigorous design

IR optics: quads closer to IP, flat beam

polarization: phase, dipole in rotators

dynamic aperture: more sextu. families, SAD, LEGO

working points: focus on above integer

arc and utility sec.: changes in matching sections

Lattice configurations (arc)

Mode Lepton Hadron Beams at IP Emittance Weak bb optics

1 10 GeV 100GeV/c,Au round 18/18 nm done

2 10 GeV 250GeV/c, p round 23/23 nm done

3 10 GeV 100 GeV/c, Au flat ~50/9 nm done

4 10 GeV 250 GeV/c, p flat ~60/12 nm done

5 5 GeV 100GeV/c, Au round 36/36 nm 72/72 nm done

6 5 GeV 50 GeV/c, p round 46/46 nm 92/92 nm* done

7 5 GeV 100 GeV/c, Au flat ~100/20nm ? tbd

8 5 GeV 50 GeV/c, p flat ~120/24nm ? tbd

Beta*: ranges from 0.1m-0.25m for round beam. flat beam:TBDLow energy: weak damping, small bb parameter, input from Vadim, Chris, etc.

Interaction region

• Input from Brett (new design), Christoph (SR check),

Vadim(3-ring), Paul (detector), etc.• Current situation:

1st Q closer to IP (Brett): 0.8m~1.0m now (good)

still triplet: for both round and flat beams

weak bending: 14 mr is not enough (bad)

bend too late(1,5,8 mr), limited by magnet?

crossing angle is not good solution.

increase bending: ~ 20 mr is needed, or more.

early bending? Small perm. B for 10/5GeV?

e.g., 3/6mr for 10/5GeV, adjust other Qs then.

anti-solenoid: address now? or CDR?

Beam separation issue

* ~ 50 mm separation at septum magnet for hadron, ~4.2m from IP.* need to achieve it without crossing angle* minimizing hori emittance and beta-functions.

Brett’s slide

An example to minimize beta at septum

flat beam, 0.25/0.15m beta*10m beta_x at 4.2m from IP

hori. emittance is not a free parameter!

IR optics

More powerful quads help reducing maximum beta-functions.

with Brett’s new powerful quad,s (5 time more in gradients than v1.0)

for 0.1/0.1m beta*

L* = 0.8 m L* = 1.0 m L* = 1.25 m

Beta_x_max 85 m 100 m 120 m

Beta_y_max 40 m 50 m 60 m

Beta_x at 4.2m 27 m 35 m 45 m

Beta_y at 4.2m 35 m 45 m 55 m

IR optics including spin rotator dipoles

* new IR quads, 0.8m from IP, round beam* weaker dipoles(Desmond)

* short dipole + drift: for polarimeter (Townsend)

Other polarization related

• Phase advance issues (Desmond)

different phase advances are matched and sent to Des for comparison.

90/90 to 90/60

75/75 to 75/60

etc.• More spin-matching are tried out.

• Correction considerations

• Format for polarization codes

Dynamic aperture

Fuhua will talk in detail.

optics related:• Another reason for 60 phase advance in vertical plane. • Multi families of sextupoles for improving momentum acceptance.• So far old IR optics. New IR should be easier!

Very glad to see Alex and Vadim using SAD for dynamic aperture. ZDR needs at least 2 DA codes for cross check.

Flat beam

• round beam is ultimate goal. (still trying hard to make it)• flat beam is realistic for now.

Principle and optics are explored.Good news• Refined parameter list for flat beam, Chris’s input.• e- beam-beam is fine now• IR optics with Brett parker’s new configurations

Bad news• Inevitable asymmetric beam-beam tune-shifts, have to reduce e-

bunch current for hadron beam-beam limit• Limit on hadron bunch length(15cm, Vadim) results in even lower

luminosity(30-40% of round)

Dedicated discussions later today to reach some agreement.

Working points

• Luminosity performance, above half integer

experimentally proved in medium e+e- colliders: CESR, B-factories(KEK initally above integer, changed later), BEPC, etc.

• Polarization, above integer (Desmond, Vadim, etc.)

spin tune is around half integer.

• Optics

easy to choose

• Dynamic aperture

so far, both seems OK.

Now fractional tunes above integers(0.1~0.25) are chosen as polarization is more sensitive to this issue.

Arc and utility sections

• Arc:

dispersion suppressor: very large emittance at 5 GeV needs additional cell for DS matching (720nm at 10 GeV!)

• Compress injection sections.

• Longer tuning sections.

Summary of e-ring optics

From v1.0 to v2.0

Things are likely to be kept:• Circumference and other basic parameters• Arc and utility, with some minor changes• Rotator solenoid section

Things are going to be modified:• IR (first three quads) optics• Rotator dipole arrangement • Phase advances in vertical plane, working points.

New:• Complete set of arc configurations • Flat beam

Typical parameters of elliptical(flat)

beam scheme for eRHICA lot of choices for elliptical beam parameters.

Here we propose some typical parameters for discussions.

Assuming both beams are matched, i.e.,

Luminosity and beam-beam formulae can be written as

py

px

px

ep

e

INL

4

)(2 ,

,

, py

px

eyxe

pyxpee

yx

Nr

(HERA convention)

pyx

eyx ,,

Beam-beam parameters

Formula for beam-beam in eRHIC

)(2

)(2

,

,,

,

,,

ey

ex

eyx

iyx

i

eiiyx

iy

ix

iyx

eyx

e

ieeyx

Z

Nr

ZNr

)(2

)(2

,,

,,

,

,,

ey

ex

eyx

eyx

iyx

i

iiyx

iy

ix

iyxi

eyx

e

ieeyx

Ner

ZNr

Determine the flat beam parameters

• What are fixed: hardron emittance• Hadron vertical(smaller) beta-function:

~0.15m due to heat load problem. (big!)• h/v size ratio, 2:1, 3:1, 4:1, (less flat beam is good, but ..)

hori. beta* of hadron is fixed.• Match e beam to hadron. Vert. emittance is limited by beam-beam,

~a few nm.rad. • Then vert. beta* of e-. (no bunch length limit)• Choose hori. emittance and beta*.

Here IR optics and aperture are the key.

we should focus on this issue!

Luminosity and beam-beam effects

Flat beam:

due to asymmetric beta-functions, beam-beam tune-shifts are unequal for both beams.

for e- we can play with emittance and beta in some way. for hadron, it is fixed.

Considering beam-beam limits(0.005 for p and 0.05 for e):

(assuming same beam area: )

3:1 x/y size ratio: L=66.7% of round beam

4:1 x/y size ratio: L=62:5% of round beam

Bunch length problem

Hadron bunch length: length control, cooling ~12cm for cryogenic load( Vadim) , changeable?

Flat beam : 3:1 beam size ratioassuming common beam-beam limits (p:0.005/e:0.05)

(10 GeV e- vs. 250GeV p beams)

eRHIC (flat) HERA (flat) eRHIC (round)Proton: Beta_x at IP 0.75 m 2.45 m 0.25 m Beta_y at IP 0.083 m 0.18 m 0.25 m

Emittance(geo.) 9 nm 5.1 nm 9 nmTune shift 0.005/0.0017 0.003/0.001 0.005/0.005

Electron: Beta_x at IP 0.36 m 0.63 m 0.1 m Beta_y at IP 0.125 m 0.26 m 0.1 m

Hori./ver. Emittance 50/9 nm 20/3.4 nm 23/23 nm Tune shift 0.036/0.050 0.034/0.052 0.05/0.05

(electron bunch current must be lowered by factor of 1.5 to not let proton bb tuneshift exceeds 0.005 limit)

Luminosity: 1.00E33 (cm-2s-1), for smaller beam area (Beta-x/y:0.57/0.064m)0.67E33 (cm-2s-1), for same beam area (Beta-x/y:0.75/0.083m)0.50E33 (cm-2s-1), for larger beam area (Beta-x/y:1.125/0.125m)

Next question is bunch length and IR optics.

Parameters for a flat beam schemeTo reach same luminosity as round beam

(10 GeV e- vs. 250GeV p beams as an example for discussions)

eRHIC (flat) HERA (flat) eRHIC (round)

Proton:

Beta_x at IP 2.0 m 2.45 m 0.5 m

Beta_y at IP 0.125 m 0.18 m 0.5 m

Emittance(geo.) 9 nm 5.1 nm 9 nm

Tune shift 0.008/0.002 0.0033/0.0009 0.005/0.005

Electron:

Beta_x at IP 0.24m 0.63 m 0.1 m

Beta_y at IP 0.09 m 0.26 m 0.1 m

Hori./ver. Emittance 62/10 nm 20/3.4 nm 43/43 nm

Tune shift 0.038/0.050 0.034/0.052 0.05/0.05

Proton bunch population is assumed to be 1E11. I_e-=450mA For same luminosity: proton tune shifts exceed limits 0.005(p) a little bit.

Optics at IR with flat beam, 1.25m to IP

• Easier than round beam (same beam size).

• Doublet can replace triplet (if flat scheme only),

1, save space for hadron quads

2, help SR fan problem.

• Need to see hadron optics still.

Example of a flat beam IR optics

New IR optics for flat beam, 0.8m from IP

Beta*: 0.25/0.09mDoublet: start at 0.8m, finish at 2.4m, Field strength: 75T/m, 50T/m, (Brett Parker’s) More space for hadron magnets, flexible betaBending in doublet: ~10 mrad is needed

Smaller beta*, 0.14/0.05mflexible from optics point of view

In case 1st quad is 0.8 m or 1.0 m from IP

• e- optics is in much better shape

lower beta

lower chromaticities

no bunch length problem yet

• separation

still tight. Doublet can save space.

depending on hadron beam.

Major limitations to flat beam

• Asymmetric beam-beam tune-shifts

‘not too flat’ is better, now we focus on 3:1 size ratio

• Bunch length

proton and ion bunch length may limit luminosity

• Optics, (less challenging)

e- optics seems OK.

• Interaction Region,

not easy if we need both round and flat beam options.

0.25/0.25m beta*, problem is the bunch length of hadron ?

Observations • relaxed electron beta functions, especially low beta

function at 5m• closer hadron magnets possible, ~3.0m, also help SR fan

problem. • beam-beam is ok for e beam.• bending angle(magnet)• Need to see hadron optics

Compare to 0.5/0.5m beta* hadron schemeLuminosity is same for flat beamElelctron tune shift is below limit

Lepton IR optics: round beamBeta* : 0.1/0.1 m• 1st quad, ~1.3m from IP, max gradient, ~13 T/m,• combined funciton, (BNL made such one for HERA). • 2nd quad, finish at ~4.5m( 1st quad for hadron at ~5m) • 3rd quad, ~8m from IP.

Beta_max: ~380/380, too large, but DA is still acceptable Brett Parker’s new design: 1st Q is 0.8m to IP and stronger , beta_max is ~80 m, much better!! ( if detector allows )

Beam separation (hori. scheme, BINP)PEP-II type, 0.6m long dipole next to IP + following Qs,

Abandoned, permanent magnet is not flexible

HERA-type, move first Q to 0.9 m or so from IP, SR fan problems seen by Montag.

Aperture..

e-RING IR optics (including rotator)

Flat beam: why consider it?

• about this scheme, everything is proved in HERA operation (luminosity and polarization) • less concerns for e- beam polarization• natural for e beam• less constraints on optics: tunes, special insertions, etc. Known disadvantage:• unequal beam-beam parameters. may reduce luminosity performance a little bit. The question is how much?• need shorter bunch (proton, e beam has no problem)

Beam sizes in IP, elliptical beam in eRHIC

A typical case: eRHIC e-p collision(10GeV vs. 250GeV) Example: a h/v beam size ratio at IP of 4:1(HERA: ~3.7:1)Not so ‘flat’. In e+e- colliders, it is 10:1 to 100:1.

0.07 mm (rms) 0.14 mm (rms)

0.035 mm

round beam eRHIC elliptical beam(4:1)Beta*=0.5m proton beta*=2.0/0.125mBeta*=0.1m elecrton beta*=0.14~0.25/0.05~0.09m

Electron-ring design activities at BatesDong Wang, Fuhua Wang

Sept. 25, 2003, eRHIC tele-conference

• Arc arc configurations: different emittances.

• IR optics: flat beam

• DA: phase issue, enlarge momentum acceptance

• Working points: beam-beam, DA, polarization

• Beam instabilities, details in next meeting for collective effects.