DB long transfer line - a first pass -

1. DB long transfer line- a first pass - B. Jeanneret CLIC Dynamics ABP, 4th July 07 Acknowledments: Hans for many discussions Alessandra Lombardi for permanent magnet issues Stephane Fartoukh for optics issues

2. Outline • Optics • Magnets • Ions • Other • Further work

3. CR2 … 26 x Optics • Requirements • Connect last combiner ring to every turnaround in the Main Linac • Keep emmitance • Entrance : 1.e-4 m rad • Decelerator : 1.5e-4 • most of the margin : for the turnaround/compression (see with Frank Stulle next in 10 days) • Be cheap • One option is to use permanent magnets • This implies that not many correctors are needed (or none, only quadrupoles?)

4. Regular FODO cell, no dipoles • Thin lens limit can be treated analytically • Use phase advance/cell of pi/2 to see • Skip a few steps :

5. Transport over 20 km • Match to a turnaround every 800 m • b ~10/20 m, while large b / long cells more economical • Do we need a chromatic correction ? sp = 0.01 • Yes, otherwise full filamentation after any kick (even static) • need your feed-back • Need a dispersion wave (close/open at every turnaround ?) • Need more work, and a error/tolerance analysis

6. Quadrupoles • L_cell = 100 m  G lq = 0.25 T/m x m • Usual iron shaped field – not studied here • Cos 2f coil, ~allowed by low gradient • Permanent magnets

7. Cos 2f coil - I • For L_cell=100m • 11 wires • I = 30 A • S_wire =2mm^2 • P=400W • 400 Q / Linac • V_tot = 5000V A bit limit, if shorter cell. Need more work (on-going with help fromAT/MCS)

8. Cos 2f coil - II • No lamination • No glue • Maybe only two external weldings • Hopefully no cooling • Sextupole doable as well Iron cylinder to increase field and minimize stray field, shrink everything Aluminium shell with surface insulation External diameter < 100mm Insulator with printed or incrusted copper

9. Permanent magnets • Small series under way for Linac IV (A.Lombardi) • Two cylinders of CoSm rods in Al matrix • Inner radius 10mm, length 40mm • G = 60 T/m, dG/G = 0.5%, dB/B_nonlin<1% • Tc = 1500 C (weaker field species ~3000 C) • Price 2300Eu per piece for 100 ordered We need less gradient : • G = 5 T/m , lq = 0.05m  Glq = 0.25 T/m m • Use simpler prismatic geometry •  cheaper (2000 Q x 1000Eu = 2MEu – add sextupoles …) • Large enough w.r.t. to pipe to keep away from beam losses and keep good field quality • Combine permanent with Cos 2ffor adjustment • Low power  one power supply per station ?

10. Logistics in the tunnel • Survey team and Carlo worry about space at the tunnel roaf • Quad with small transverse size : better • Proposal to adopt the same cell length for Main-beam and DB  Single support  Single survey system • Imply similar technology for MB and DB  thinkable ?

11. Ion production and counter-effect on the beam • The electron beam ionises the residual gas • Electrons are repelled rapidly (light objects) • Ions are attracted (or focused) by the beam and can be trapped inside (so called ‘neutralisation’ of the beam’)  induces tune-shift & tune spread

12. Ion data Mean free path for electrons to produce a ion : One DB train , Ne = 1.78e14, p=10-8 T : rlit = 1.11e7 ion/m Coherent tune-shift : (copied from HAPE, FZ p.128) b = 100 m : Dn = 0.15 But coherent tune is not the whole story, and there is another issue,see below

13. Ion trapping • Atomic numbers > Atrap are trapped • Inside train, Ne = 5e10, DL = 2.5e-2 m Atrap = 1.3e-4  CO is trapped • Train-train, Ne = 1.8e14, DL = 1500 m Atrap = 4e5  CO fully untrapped

14. Ion motion - I Initial ion distribution: -Beam profile + thermal speed Tracking : - Motion : in exact field for round+ gaussian beam -enough slices for smooth motion X [m] • Nice continuous focusing inside the train • Note the central accumulation at the end of the train Time [s] Train length

15. Ion motion - II X [m] • Soon after the train passed, ions are projected to the wall • Good : no accumlation between trains • Less good : desorption at impact on the wall (see below) Time [s] Train Gap

16. Transverse ion distribution • Beam & initial ion distribution • Ion at the end of the train Coherent tune-shift applies only for very small amplitudes • Does tune-shift formula consider the sharpening of the ion profile? • Most likely not (only sbappears) • 3Dn = 0.45 ? • Between small and large (> sb ) • Between head and trail of train  NEED DEEPER STUDY

17. Desorption and pressure rise • Static density at 10nT : rgas,lin = 5e19 mol/m • Ion production per meter : • dn/dt = rion,train Ntrain fr x ISD = 10e11 atom/s (with ISD = 5 at 1KeV on unbaked ss • Marginal if pumping time ~< 1month …

18. Open issues • Optics : • chromatic correction • Dispersion bumps, stregth and longitudinal granularity • Sensitivity to misalignment, ground motion, correction schemes • Similar issues for 9 GeV MB line ? • Matching to turnaround • ‘matching sections’ in turnaround or in transfer line • More work needed with ionsto say if p=10nT OK • Otherwise : better inner surfaces (gold) or getter/bake-out (Eu ..) • Yet untouched : • resitive wake-fields • Beam loss issues • Integration and cost