a first look at the performance for pb-pb and p- pb collisions in fcc- hh

A First Look at the Performance for Pb-Pb and p-Pb collisions in FCC-hh

Michaela Schaumann (CERN, RWTH Aachen)

In collaboration with J.M. Jowett and R. Versteegen (CERN)14th February 2014

FCC Study Kickoff Meeting, Geneva

M. Schaumann, Pb-Pb and p-Pb performance of FCC 2

Outline

2014/02/14

• General assumptions (Pre-accelerator chain, ring and beam parameters)

• Estimates for: • IBS and radiation damping• Luminosity and beam evolution• Beam-beam tune shift• Power in secondary beams emerging from collision

point

• Parameter table• Conclusions


General FCC-hh Parameters

2014/02/14

Units Injection Collision

Circumference [km] 80 80

Main dipole strength [T] 1.2 20

Bending radius [m] 8339.1 8339.1

Proton equivalent energy [TeV] 3 50

Lead ion energy [TeV] 246 4100

Lead ion energy/nucleon [TeV] 1.2 19.7

C.M. energy [TeV] 2.4 39.4

Based on a working p-p collider exists.

M. Schaumann, Pb-Pb and p-Pb performance of FCC

Heavy Ion Pre-Accelerator Chain

42014/02/14

Straw-man assumption to estimate (conservative) beam parameters and luminosity: LHC, as it is today, but cycling to 3 Z TeV, is assumed to be the injector for FCC-hh.

The requirements and performance of the pre-accelerator chain for FCC are not studied yet.

Present heavy-ion pre-injectors

LEIRHI source + Linac 3

Inject one LHC beam into 1/3 FCC, no waiting. Will see later that injector cycle time is similar to time taken to burn-off all beam in FCC.

PS

SPS

LHCFCC

R&D


Pb Beam Parameters in LHC and FCC-hh

LHCDesign

LHC 2011

LHC 2013

FCC-hh

Beam Energy [Z TeV] 7 3.5 4 50

β-function at the IP [m] 0.5 1.0 0.8 1.1

No. Ions per bunch [] 0.7 1.4

Transv. normalised emittance [] 1.5 1.5

RMS Beam Size at IP [] 15.9 33.9 26.6 8.8

RMS bunch length [] 7.94 10

Number of bunches 592 358 358 432

Peak Luminosity [] 1 (Pb-Pb) 110 (p-Pb) ?

2014/02/14

Best injector performance achieved in 2013 p-Pb run.

Average beam parameters from 2013 are assumed as VERY conservative baseline for FCC-hh!

→ Improvements are already under study for HL-LHC!


Effects on the Emittance – a new regime

2014/02/14

Intra-Beam Scattering (IBS) Radiation DampingEmittance Growth Emittance Shrinkage

twice as fast as for protons!!Growth rate dynamically changing with beam properties: Damping rate is constant for a given energy:

Damping Times

Unit FCCcollision

[h] 0.16

[h] 0.31

[h] 0.31

Growth Times

Unit FCC collision

[h] 144.7

[h] 39.1

[h]

IBS is weak for initial beam parameters, but increases with decreasing emittance .

Fast emittance decrease at the beginning of the fill, until IBS becomes strong enough to counteract the radiation damping.


Beam Evolution in Pb-Pb Collisions (1 Experiment)

2014/02/14

• “Analytical calculation” considers only burn-off and radiation damping , becomes unrealistic as !

• In simulation horizontal IBS counteracts radiation damping for small emittances:o Without betatron coupling .o With coupling, horizontal IBS growth is

transferred to vertical plane.o Equilibrium emittance in both planes.

Horizontal Emittance Vertical Emittance

Intensity


Pb-Pb Luminosity Evolution (1 Experiment)

2014/02/14

• “Analytical calculation” neglects IBS, so over-estimates luminosity peak and burn-off speed

• Simulation with coupling is most realistic case.

• Emittances and bunch length become very small instabilities and artificial blow-up may have to be studied.

Unit per Bunch whole Beam

[Hz/mb] 0.0075 3.2

[Hz/mb] 0.029 12.7

[] 0.2 83

• Very high • Is detector able to take hadronic rates >

100 kHz ?• Levelling required? → Evolution with varying see back-up slides

1 experiment in collisions

R&D

R&D


Beam-Beam Tune Shift

2014/02/14

Beam-Beam Parameter per Experiment

Unit LHC Designp-p

LHC DesignPb-Pb

FCCPb-Pb

Initial [ 3.7 0.18 0.37

Peak [ 3.7 0.18 2.0

Beam-beam tune shift per experiment.For round beams :

The tune shift due to beam-beam interactions remains well below assumed limit.


p-Pb Luminosity Evolution (1 Experiment)

2014/02/14

“Analytical calculation” only! – Neglecting IBS

Initial conditions:• Pb-beam as for Pb-Pb operation.• Equal geometric beam sizes for p and Pb.• 2 = const.• = const.

→ Fast Pb burn-off: Fill Length

Maximum integrated luminosity is achieved, when all Pb ions are converted into luminosity

Unit per Bunch whole Beam[Hz/mb] 0.6 267

[Hz/mb] 13 5477

[] 70 30240


BFPP Beam Power

2014/02/14

Main: 208-Pb-82+

BFPP1: 208-Pb-81+BFPP2: 208-Pb-80+

EMD1: 207-Pb-82+EMD2: 206-Pb-82+

LHC

Example: LHC Pb beam right of IP2

Countermeasures (e.g., DS collimators) have to be considered in initial lattice & hardware design.

Main contribution to fast Pb-Pb burn-off:

R&D

FCC-PbPb

peak


Summary Table (1)

2014/02/14

Unit LHC Design FCCInjection

FCCCollision

FCCCollision

Operation mode - Pb-Pb Pb Pb-Pb p-Pb

Particle type - Pb Pb Pb p

Beam Energy [TeV] 574 246 4100 50

Lead ion energy/nucleon [TeV] 2.76 1.2 19.7 50

Relativistic γ-factor - 2963 1270 21168 53290

Number of bunches - 592 432 432 432

No. Ions per bunch [] 0.7 1.4 1.4 115

Transv. normalised emittance [] 1.5 1.5 1.5 3.75

RMS bunch length [] 7.94 10 10 10

Synchrotron frequency [Hz] 23.0 5.5 1.9 1.9

Longitudinal emittance (4σ) [eVs/charge] 2.5 4 23 23

RMS energy spread [ 1.1 3.3 1.1 1.1

Circulating beam current [mA] 6.12 3.0 3.0 3.0

Stored beam energy [MJ] 3.81 2.4 40 40

Longitudinal IBS emit. growth time [h] 7.7 16.9 144.7 1

Horizontal IBS emit. growth time [h] 13 8.5 39.1 3

Longitudinal emit. rad. damping time [h] 6.3 725 0.16 0.32

Horizontal emit. rad. damping time [h] 12.6 1451 0.31 0.63


Summary Table (2)

2014/02/14

Unit LHC Design FCCInjection

FCCCollision

FCCCollision

Operation mode - Pb-Pb Pb Pb-Pb p-PbPeak RF voltage [MV] 16 11 22 22

RF frequency [MHz] 400 400 400 400Harmonic number - 35640 106740 106740 106740Power loss per ion [W]Energy loss per ion per turn [MeV] 1.12 0.01 969.1 5.8Synchrotron radiation power per ring [W] 83.9 0.7 53732 26587Critical photon energy [eV] 2.77 0.07 336.7 5376β-function at the IP [m] 0.5 - 1.1 1.1RMS beam size at IP [] 15.9 - 8.8 8.8 Initial luminosity [] 1 - 3.2 267Peak luminosity [] 1 - 12.7 5477Integrated luminosity per fill [] <15 - 83 30240Beam-beam tune shift [] 1.8 - 3.7 3.7Total cross-section [b] 515 - 597 2Peak BFPP beam power [W] 26 - 2947 0Initial beam current lifetime (1 exp.) [h] <11.2 (2 exp.) - 8.7 24Initial luminosity lifetime [h] <5.6 (2 exp.) - 3.7 3.2


Peak and Integrated Luminosity per Month

2014/02/14

https://indico.cern.ch/event/288576/material/1/0

Luminosity values discussed with the Ion Physics Working Group for FCC-hh.


Conclusions and Outlook

2014/02/14

Conservative assumptions based on existing injector-chain:• High peak luminosity

( nominal LHC) – consider levelling?

• Max. int. luminosity: ~100% of particles converted into luminosity as fast as injectors can produce them.

• N.B. Two experiments would share approx. same integrated luminosity.

Strong rad. damping, small emittances and effective intensity burn-off.

• High potential for luminosity improvement from injectors:• Luminosity is rather insensitive to the

initial emittance coming from the injectors, due to rad. damping.

• New ion source and injector chain to deliver higher beam current (higher smaller bunch spacing).

• Faster cycling of injectors; more injections to increase the number of bunches.

• Small emittances and bunch lengths might require artificial blow-up to prevent instabilities; could be used as levelling method.

R&D

Watch compatibility of evolving hadron collider design with nuclear beams.


THANK YOU FOR YOUR ATTENTION

2014/02/14


Bunch-by-Bunch Differences after Injection in the LHC

• Structure within a train (1st to last bunch):

• increase: - intensity - bunch length

• decrease: emittance.

• IBS, space charge, RF noise … at the injection plateau of the SPS:• while waiting for the 12 injections from the PS to construct a LHC train.

• First injections sit longer at low energy strong IBS, emittance growth and particle losses.

Intensity

Design

Horizontal / VerticalEmittance

Design

2014/02/14

1 train

E = 450 Z GeV


Smooth Lattice Approximation

2014/02/14

A lattice design does not yet exist!Approximations for smooth lattice functions are used where necessary.

Cell Length from aperture constraints

Unit LHC Design FCC

Arc Filling Factor - 0.78 0.78

Average β-function [m] [66, 71] [100, 125]

Average Dispersion (hor.) [m] 1.4 [1.3, 2.0]

Gamma Transition - 55.7 [78, 100]

Assume FODO cell with

M. Schaumann, Pb-Pb and p-Pb performance of FCC

Intra-Beam Scattering

2014/02/14 19

Handbook of Accelerator Physics and Engineering, 1st Edition, 3rd Print, pp. 141

A. Piwinski Formalism for IBS growth rates: Particle Type

Energy Beam properties

Lattice and beam sizes

IBS strength changes dynamically with beam properties.


Intra-Beam Scattering

2014/02/14

Growth Times

Unit LHC Design

FCC injection

FCC collision

[h] 7.7 16.9 144.7

[h] 13 8.5 39.1

[h] -75000 -6604

Variation of IBS growth times for initial beam conditions with FODO cell length.

Effect of long. (hor.) IBS decreases (increases) with increasing cell length.At collision energy, IBS is weak for initial beam parameters.

Injection Energy Collision Energy

Expected Range

Expected Range


Radiation Damping

2014/02/14

Radiation Integrals

Energy Particle Type Ring

Constant depending on particle’s mass and charge

Isomagnetic ring with separated

function magnets &

Damping Rates

Handbook of Accelerator Physics and Engineering, 1st Edition, 3rd Print, pp. 210


Luminosity Evolution

2014/02/14

Consider burn off and radiation damping:IBS is weak at top energy and dominated by radiation damping: → approximate constant emittance damping time.

System of two differential equations to be solved:


Beam Evolution Simulations

2014/02/14

Evolution of 3 typical Pb-bunches in collisions.

HeadCoreTail

Dashed lines: without couplingSolid lines: with coupling


Pb-Pb Luminosity for varying β*

2014/02/14

CTE simulation assuming full IBS coupling.

Red curve corresponds to solid red curve on slide 8.


p-Pb Beam Evolution

2014/02/14

is assumed to be constant at approximately 100

Pb emittance damps twice as fast as p emittance; assuming exponential emittance damping with constant rad. damping rate and no IBS.


Longitudinal Beam Parameters

2014/02/14

Unit LHC Design FCC

Synchrotron frequency [Hz] 23.0 1.9

Momentum spread [ 1.1 1.1

Longitudinal emittance [eVs/charge] 2.5 23

S.Y.Lee, Accelerator Physics, 3rd edition

at top energy


Circulating Beam Current and Stored Beam Energy

2014/02/14

Circulating beam current:

Stored beam energy:

Unit LHC Design

FCC injection

FCC collision

[mA] 6.12 2.98 2.98

[MJ] 3.81 2.38 39.73


Energy Loss per Turn

2014/02/14

Radiated power per ion:

Radiated power per beam:

Energy loss per ion per turn:

Damping Times

Unit LHC Design FCC injection

FCC collision

[W]

[MeV] 1.12 0.01 969.1

[W] 83.9 0.7 53732

[eV] 2.77 0.07 336.7

Critical photon energy:

Handbook of Accelerator Physics and Engineering, 2nd Edition, pp. 215


Initial Beam Current Lifetime

2014/02/14

Lifetime due to burn-off only!

Unit LHC Design(2 experiments)

FCC (1 experiment)

FCC(2 experiments)

[h] 11.2 8.7 4.3

Total cross-section at 50Z TeV:H. Meier et al, Phys. Rev. A, vol. 63, 032713. 02/2011


Cycle with LHC as Last Injector

2014/02/14

3h LHC turn around time = time between 2 injections to FCC. Luminosity lifetime FCC

→ Refill LHC during physics in FCC.→ No waiting time for FCC due to cycling

in LHC.

If 2 experiments are considered, they have to be placed at opposite positions in the ring to be provided with luminosity!

Intensity Evolution in FCC with 1 exp. in collisions


Smaller Z Ions – Impact on Luminosity

2014/02/14

• New ions source & injectors possibly higher are available. No studies on improved heavy ion injectors done yet!

• Contribution of ultra-peripheral electromagnetic processes to the total cross-section would be reduced:

Increased luminosity lifetime, more particles available for hadronic interactions.

Reduced secondary beam power emerging from collision point.

• Radiation damping rate does not change much for Z>60:o

a first look at the performance for pb-pb and p- pb collisions in fcc- hh

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