LHC 5 TeV run

Consequences of running at reduced energy

In 2008 5 TeV was considered in some detail (below) - have to revisit the issues raised in light the 3.5 TeV running energy of the 2009 - 2010 run.

Factor of 2 in momentum - convenient number, compared with 7 TeV gamma is halved, emittance is doubled, beam size up by root 2, luminosity halved.
Minimum beta* with crossing angle off - 1 m - at the limit.
For smaller β* and lower energy a larger crossing angle is required. See W. Herr at Chamonix 2009. For 50 ns spacing, 300 μrad should be OK down to β* = 2 to 3 m in IR1 & 5.
Longitudunal parameters to be re-visited
Separation and crossing angles at all points to be re-visited.
Maximum intensity around 6 e13 protons per beam (See Ralph Assmann at the LMC)

Momentum [TeV]	3.5 TeV/c	7 TeV/c
Normalized emittance [metre rad]	3.75 x 10^-6	3.75 x 10^-6
gamma	3730.26	7460.52
emittance [m]	1.00*10^-9	5.02*10^-10
beam size beta = 11 m [microns]	105.2	74.4
beam size beta = 2 m [microns]	44.8	31.7
Bunch length - 16 MV	~6 cm (1 sigma) with 1 eVs (no blow-up*)	Emittance: 2.5 eVs (after blow-up) Bunch length: 7.55 cm Rms energy spread: 1.13 ×10-4 (1 sigma)

*The base line machine operation assumes that the longitudinal emittance is deliberately blown up at the middle of the ramp in order to reduce the intra beam scattering growth rates. Blow-up not likely to be available at end 2009 - shouldn't be a problem.
* Longitudinal emittance ~1 eVs - including emittance blowup due to injection oscillations and mismatch. Note that SPS is capable of delivering 0.6 - 0.7 eVs and even 0.5 eVs at low intensity.

Injection and ramp optics will be exactly the same as 7 TeV
- 11 m beta* in IR 1 & 5,
- 10 m beta* in IR 2 & 8
First collisions at 11 m unsqueezed - beam sizes as below
Crossing angles will be off. Transverse postion will not change in any systematic way because of running at 5 TeV.
Squeeze optics exactly the same in terms of quadrupole strengths - because of increased beam size might be limited in beta* (increased beam size in inner triplets).
Some crossing angle limitations because of bigger beam sizes at parasitic crossings - if we get that far.
For any given optics, beam sizes at the IP will be larger as described below, but a such variation must be anticpated anyway as we push through the squeeze from 11 to 2 m during commissioning of the squeeze.
Luminosity reduction factor - 71% for any given beta*
Will bring Alice and LHCb dipoles on a full field at 5 TeV.

Momentum [TeV]	5 TeV/c	7 TeV/c
Normalized emittance [metre rad]	3.75 x 10^-6	3.75 x 10^-6
gamma	5328.95	7460.52
emittance [m]	7.03*10^-10	5.02*10^-10	emittance goes with gamma (and beta) simple factor of 0.714286
beam size beta = 11 m [microns]	88.0	74.4	beam size at IP goes with sqrt[emittance] simple factor of 0.845154
beam size beta = 2 m [microns]	37.5	31.7
Luminonisity reduction factor - any beta	0.714286
RMS Bunch length [cm]	5.41 (16 MV)	7.55	Longitudinal blow-up might not be available immediately - would imply shorter bunch length at 5 TeV.