Injection Energy Review

D. Schulte

Introduction

Will review the injection energy

So could answer the following questions:

Which injection energy can be accommodated in the baseline?• To identify the minimum energy that is acceptable with

reasonable risk• Requires to identify margins and budgets for effects that have

not been considered in detail

Which changes are required to adapt to a given injection energy? • Allows to understand the design and cost impact of different

energies if we stay at the same risk level• We can at some level answer with a relative comparison

Assumptions Made for Baseline

The main drivers for the injection energy are

• Impedance• the main impedance is coming from the beamscreen• other collective effects are not dominating

• Dynamic aperture• we need at least the same beam stay clear as in LHC• in beam sizes

• the same ratio of top to injection energy as in LHC may ensure the magnet field quality• a tentative choice to deal with the uncertainty of the

magnet errors

• (Amount of beam that can be transferred in one pulse)

Lattice Baseline

The goal has been to minimise the magnet apertureThis requires to minimise the beamscreen aperture

Tentative assumptions• Cell design similar to LHC• The shortest cell that reaches the same dipole filling factor as LHC• This minimises the average beta-function, which minimises the

impedance effects

Cell length about 2 times LHC cell length

Tentative Conclusions for Baseline

The injection energy should be at least 3.3 TeV• Tentative assumption is based on magnetic field error

consideration

At this energy the impedance is the dominating factor for the beam screen aperture, the beam stay clear is larger than in LHC

This is opposite to the LHC, where mainly the beam stay clear has been an issue and the impedance less critical

The impedance requires a≈13mm

This translates into 1.8 times more space in the arcs

For the same emittance it would be 1.4 times

D. Schulte: Beam pipe kickoff meeting

Impedance Effect Scalings

Coupled-bunchimpedance effectper turn scales as

totIE

CZ

QbZ

rev

13

FHC

revFHC

LHCrevLHC

totLHC

totFHC

FHC

LHC

LHC

FHC

LHC

FHC

LHC

FHC

FHC

LHCLHCFHC Q

Q

I

I

E

E

C

C

b

bR

1

13

/

Local resistive wall impedance

Ratio of FHC to LHC coupled-bunch effect scale

Example at 50K and 25ns spacing at injection

Or: Why was a potential problem to be expected?

Assuming the same fractional tune in FCC and LHC

Impedances, Instability and Feedback

First, preliminary conclusions from impedance studies:• Beamscreen resistive wall at injection• Multi-bunch instability rise time is O(25 turns) • Copper layer on beamscreen must be 300mm thick• TMCI threshold is 5x1011 protons

• Pumping holes• TMCI threshold is reduced to 2x1011 protons Worth to reduce amount of holes (as considered by vacuum team)

• Synchrotron radiation slit• Little impact on the impedance

• Beamscreen and collimation at collision energy• TMCI threshold is 1.5x1011

Close to the limit Feedback is of great importance Much better performance than in LHC required Novel solutions? HTS?

O. Boine-FrankenheimU. Niedermayer,B. Salvant, N. MounetX. Buffat, E. Metral

There seems to be little margin

Can gain margin by increasing the injection energy• initially used as fallback safety margin (assuming LHC as injector)• now have to spell it out

Have to be very careful in choosing the stability criteria• e.g. assumptions about chromaticity• determining how much margin is required and in which form

Remember two decisions were made in the process:

Fractional tune below 0.5

Give up parameter set for 50ns bunch spacing

=> Check if we still agree with them

Impact on Injection

Currently assuming that total energy per injected train has to remain below 5MJ

Higher energy means less charge per train

Requires shorter gaps between trains

Requires faster kickers or more charge per bunch, which we would like to avoid

Check if this is a serious concern or if we can accept shorter rise times for the moment

Also check impact of injection energy on turn-around time

Next Steps

Have to determine the minimum injection energy• field errors• dynamic aperture

Have to more precisely determine the impedance limit• include all relevant terms• sometimes with guesses

• agree on model of beam stability• chromaticity etc.

• include proper feedback models• as transfer functions

• include sufficient margin• Since this seems to give the limit we have to really explore the limits

Verify that the other assumptions are OK• i.e. that only dynamic aperture and impedance are important limits

Then have to understand the impact of the other potential injection energies• identify a small set of potential values matching to the injector options

Example for Illustration

Multi-bunch instability example

Assuming:

• a=13mm beamscreen radius is just right for 3.3TeV

• ΔBS=12mm are need between beamscreen and magnet

• the cost scales as

Cost goes up 5% at 2TeV and down by 4% at 5TeV

Beamscreen Design

• Centre of the beamscreen is not he centre of the magnet– Need to explore the options to

deal with this• The pumping holes are an important

part of the impedance– Need to agree on the amount of

holes needed

Conclusion

Much more work to be done to give as precise answers as possible:

Does our rational hold true?• Did we miss something?

Which injection energy can be accommodated in the baseline?• Get full evaluation process in control

Which energy ranges could be provided by each injector?• Pick a limited number of values to limit the study

Which changes are required to adapt to a given injection energy?• To evaluate the cost impact