Two beam coupling impedance simulations

1. Two beam coupling impedance simulations Grudiev 28/09/2012 AP forum on Two beam impedance

2. outline • What was done in the past • TCTVB impedance simulations: two beam RF heating • What was not done • Beam-beam broad band coupling impedance • RF Multipoles of the trapped modes: longitudinal and transverse • ….

3. TCTVB impedance simulation and mitigation (LHC Project Note 413) Summary of the findings concerning the initial design • An increase of the longitudinal broad-band impedance by 0.66 mΩ at injection and 1.06 mΩ at top energy is acceptable. • An increase of the transverse broad-band impedance by 0.04 MΩ/m at injection and 0.47 MΩ/m at top energy is not acceptable. A reduction to a level of about 1 % of the total LHC budget (0.014 MΩ/m and 0.028 MΩ/m, respectively) is strongly recommended. • Both overall power loss of 391 W in the whole device and the local heating of rf-fingers of 2.5 W due to monopole trapped modes are too high and must be reduced by at least factor 10. • The coupled-bunch instability tune shift only due to dipole trapped modes is very close to the stability limit. Taking into account all other sources of impedance in the LHC can lead to the loss of stability. It is strongly recommended to reduce the impedance of the dipole modes by at least factor 10.

4. TCTVB impedance (cont.)

5. TCTVB impedance (cont.) That is all what has been studied concerning the two beam coupling in TCTVB. The same treatment has been applied to TDI.

6. Beam-beam broad band coupling impedance • BB impedance: • Longitudinal • Transverse • B1-to-B1 and B2-to-B2 BB coupling impedance has been calculated. • B1-to-B2 and B2-to-B1 terms of the BB impedance could be calculated as well by using different integration paths • Does it make sense? • Is it included already in some other way?

7. TDI beam locations: b1, b2, half gap=8mm b2; X=-68mm b1; X=-8mm b0; X=0 N.B. in fact, there is also a small vertical shift from the horizontal symmetry plane which is neglected in the simulations

8. RF multipoles in TDI RF multipolar expansion: Half gap = 55 mm Panofsky-Wenzel theorem: • Mode f=60.6 MHz, Q=189, R/Q[b1,b2] =[0.43,0.1] Ohm; • Ib1=1A => Vb1 = 81V • n=2 multipole: RF quadrupolar strength integrated along TDI is 58 µTm/m • b2 will experience horizontal kick of 58 µTm/m*0.068m = 4 µTm • ??? What could be the effect of this RF quadrupole excited by the beam(s), not by external source ??? Seems to be very week in this case

9. Measuring frequency of the resonant impedance • If the phenomenon is resonant and the beam-beam interaction takes place over many turns then the longitudinal position of the location where the beam 1 encounter beam 2 does not correspond to the location of the beam-beam “impedance” source • On the other hand, in this case, a careful scan of dp (the difference in the longitudinal position of the beam1 versus beam2) should exhibit some kind of periodic behaviour of the instability. This related to the fact that at certain values of dp two beams are interacting with the “impedance” (resonant) in phase and at some others values of dp they are out of phase. Measuring and analysing the periodic behaviour if any can give us frequency of the resonant. • Scan of dp with the step of 1 ns over 1 us will probe the spectrum up to 1 GHz with the resolution of 1 MHz