1. Large emittance scenario for the Phase II Upgrade of the LHC
S. Fartoukh with precious help from E. Laface
Phase II Brainstorming meetings 24/03/2009
Basic principle
Parameter list
Preliminary results, optics, X-scheme, aperture, b-b footprint.
Conclusions

2. S. Fartoukh, 24/03/2009
Basic idea
It is a dream to gain something substantial with the optics, i.e. reducing b*, w/o reducing L*!
At cst L*=23 m, the limit is given by a full chromatic correction of the inner triplet by the arc (possibly 600A) and is given by (e.g. see LIUW#15, May 2008)
For a gradient of ~ 120 T/m, this limit corresponds to a minimum b* of 30 cm (~25cm assuming 600A can be reached in the MS)
1. Leaving no aperture margin for NbTi (120 mm 120 T/m)  Phase I triplet
2. Leaving a huge aperture margin for Nb3Sn (~160 mm ID 120 T/m).
Of course this margin could be used for pushing the gradient above 120 T/m in order to reduce further b*, at cst J, up to reaching the Nb3Sn technology limit in terms of aperture for a given gradient.
In this case the min. possible is b*~23-24 cm for Nb3Sn (~100mm 230 T/m)
Far too expensive compared the lumi gain: only ~1025% at cst beam parameters w/o or with crab-cavity or D0!!
A much better scenario is to fully count on the expected performance of the new CERN injector complex, ~ nominal LHC emittance (????), and to blow up the beam emittance during the ramp (by a factor of ~3 to stick to the beam-beam limit of DQ~0.01), as partially demonstrated last year in the SPS!
In this case (see later), a Nb3Sn IT (120 T/m-160 mm) with exactly the same layout as the one foreseen for PhaseI, still warrant b*= 30 cm!!
Then, if too pessimistic in our evaluation of the b.b. limit (e.g. see Tevatron working with a b.-b. tune shift of ), nothing will prevent us from reducing the emittance blow-up during the ramp and then even further reduce b* after some upgrade of the arc sextupoles.

3. Short parameter wish list
S. Fartoukh, 24/03/2009
Short parameter wish list
Parameter
LHC nom.
Phase I
Phase II
Beam Parameters
Bunch spacing [ns] 25
Proton / bunch [1011]
1.15
1.7
5.55
(perhaps 30% too high for 25 ns??
 SPS/LHC-450GeV impedance??)
Norm. emittance [mm]
@450 GeV / 7 TeV
3.75 / 3.75
3.75 / 12
Bunch 7 TeV [cm]
7.5
IT specifications and Optics
IT nominal gradient [T/m]
205
~120
IT Coil ID [mm] 70
120
160
IT Technology
NbTi
Nb3Sn
b* [cm] 55 30
Full X-angle [s]
9.5 (285 mrad)
10 (410 mrad)
10 (730 mrad)
Performance
Beam sizes at the IP [mrad]
16.6
12.3
22.0
Geometric Loss factor [%]
83.9
62.5
Tot. Head-on b.-b. tune shift
(3 h.o & halo coll. in Alice)
0.0104
0.0106
Peak Lumi [1034cm-2s-1] 1 3 10

4. Layout & Optics (same as Phase I)
S. Fartoukh., 24/03/2009
Layout & Optics (same as Phase I)
Nb3Sn Inner Triplet
120 T/m-160mm
b*=30 cm
 See presentation at next LIUWG (26/03/2009)

5. X-scheme  10 s b.-b. separation 730 mrad full xing-angle
S. Fartoukh, 24/03/2009
X-scheme
 10 s b.-b. separation
730 mrad full xing-angle
~20 mm peak orbit excursion in the IT
Will need to ~double the Q4/5/6

6. Aperture (with nom. matching section, inc. TAN)
S. Fartoukh, 24/03/2009
Aperture (with nom. matching section, inc. TAN)
(after correction of the spurious dispersion by H/V orbit bumps in the arcs).
Q1 (ID-160mm)
with 9 mm shielding
D2/Q4 Q7 Q6
Phase I-D1
(ID-CB=140 mm ) Q5
New TAS
(ID-65mm)
TAN to be changed !!
Q2-Q3
(ID-160mm)
 TAN to be changed, possibly D2/Q4/Q5, or only b.s. rotation (see LIUWG#2)
n1 just 7 in the IT (assuming 21 mm between coil ID and b.s. ID, perhaps a bit optimistic?)
In any case, why sticking to n1=7 in collision when the beam sizes will be ~180% bigger??
i.e. some compromise to be found for impedance keeping in mind that the MO landau
damping efficiency scales directly with the beam emittance, i.e. 320% improvement.

7. Tune footprint (1/2) Courtesy of E. Laface
S. Fartoukh, 24/03/2009
Tune footprint (1/2)
Courtesy of E. Laface
 MO’s assumed to be used both for Phase I and Phase II to compensate for residual Q’’ in collision.
 Perhaps no longer needed for Phase II, if the LHC IR tunability can improve by adding new quad’s (the logic behind this beyond purpose, see next LIUWG presentation for more details)
This explain the more or less big H/V dissymmetry observed for the PhaseI/II tune footprints.
(OD’s stronger in the optics because 4 times less efficient than OF’s w.r.t. Q’’, but of course as efficient as OF’s w.r.t. amplitude detuning)
 Said differently, for large emittance beam, we might well have an knob to “shape” the tune footprint

8. Tune footprint (2/2) Courtesy of E. Laface
S. Fartoukh, 24/03/2009
Tune footprint (2/2)
Courtesy of E. Laface
As expected, when MO’s switched off in the case of Phase II

9. Conclusions Nb3Sn new triplet 160 mm-120 T/m .. Y a qu’a!
S. Fartoukh, 24/03/2009
Conclusions
Nb3Sn new triplet 160 mm-120 T/m .. Y a qu’a!
p/bunch with 25 ns bunch spacing w/o impedance problems in SPS and LHC at injection … Y a qu’a!
Controlled beam emittance blow up during the ramp: Why not
(we have 20 min. to do it)?
Pile-up events not discussed, but given, as usual, as soon as the peak lumi and the bunch spacing is defined…. Perhaps bigger s* combined
with smaller exp. pipe could help to push a bit further the limit??
… As usual, the final parameter list will be a compromise of several little gains, but the beam emittance is certainly the most efficient knob (at large intensity), at least by far much more efficient than b*!