TDI longitudinal impedance simulation with CST PS A.Grudiev 20/03/2012

Geometry All metal and dielectric parts are from PEC. No losses. No ferrites are included. Magnetic wall BC is applied at the horizontal plane PML BCs are applied at the up/downstream ends

Mesh, sigma_z=500mm

Longitudinal Wake, sigma_z=500mm

Longitudinal impedance, sigma_z=500mm

Mesh, sigma_z=200mm

Longitudinal Wake, sigma_z=200mm

Longitudinal impedance, sigma_z=200mm

Mesh, sigma_z=100mm

Longitudinal Wake, sigma_z=100mm

Longitudinal impedance, sigma_z=100mm

Mesh, sigma_z=50mm

Longitudinal Wake, sigma_z=50mm

Longitudinal impedance, sigma_z=50mm

Mesh, sigma_z=20mm

Longitudinal Wake, sigma_z=20mm

Longitudinal impedance, sigma_z=20mm

Longitudinal Wake, Summary plots

Longitudinal Impedance, Summary plots

Different beam locations: b0, b1, b2 b0; X=0 b1; X=-8mm b2; X=-68mm

Longitudinal Wake, σ z =100mm: b0, b1, b2

Longitudinal Impedance, σ z =100mm: b0, b1, b2

Longitudinal Impedance, real part, σ z =100mm: b0, b1, b2

Longitudinal Impedance, imaginary part, σ z =100mm: b0, b1, b2 Half gap = 8mm b0: Z/n = 155 Ohm/250MHz * 400.8MHz/35640 = 7.0 mOhm b1: Z/n = 150 Ohm/250MHz * 400.8MHz/35640 = 6.7 mOhm b2: Z/n = 70 Ohm/200MHz * 400.8MHz/35640 = 3.9 mOhm

Longitudinal Wake, σ z =100mm: b0 PML8 -> PML16

Longitudinal Impedance, real part, σ z =100mm: b0, PML8 -> PML16 Almost no difference

Longitudinal Wake, σ z =100mm: b0 beam pipe length: 200mm -> 100mm and 300mm

Longitudinal Impedance, σ z =100mm: b0, beam pipe length 200mm -> 100mm and 300mm

Beam pipe length of 300 mm is better, but the difference is only at f ~ 0 And the negative offset of the ReZl is always there at the same level.

Ti coating of hBN blocks Dear all, Here is a coating report from Wil (please follow the link), for a batch of BN coated in The specifications we had been asked to meet were Rsquare<0.5 Ohm. For a thickness of about 5 µm that means a resistivity of about 250 e-8 Ohm.m, larger than the nominal Ti value. This is likely due to the large amount of outgassing from the porous BN material. Cheers, Sergio & Wil See EDMS link For this coating skin depth in the range from 10 MHz to 1 GHz is 250 um to 25 um which is bigger than the coating thickness of 5 um.

Longitudinal Wake, σ z =100mm: b0 PEC -> hBN

Longitudinal Impedance real part, σ z =100mm: b0, PEC -> hBN

Longitudinal Impedance, imaginary part, σ z =100mm: b0, PEC  hBN Half gap = 8mm b0, PEC: Z/n = 155 Ohm/250MHz * 400.8MHz/35640 = 7.0 mOhm b0, hBN: Z/n = 2620 Ohm/400MHz * 400.8MHz/35640 = 73.7 mOhm

Longitudinal Impedance, real part, : b0, hBN, σ z =100 - > 50 mm

Influence of the ferrite 4S60

Longitudinal impedance gap 16mm hBN, with and w/o 4S60 NO DIFFERENCE

Influence of Mask for RF fingers region

Longitudinal impedance gap 16mm hBN, σ z = 100 mm, with and w/o Mask No big difference in CST wakefield solver BUT Saves a lot of mesh in HFSS eigenmode solver

Longitudinal impedance gap 16mm hBN, σ z = 50 mm, with and w/o Mask No big difference in CST wakefield solver BUT saves a lot of mesh in HFSS eigenmode solver

R/Q estimate from PEC impedance Reminder from classical P. Wilson, SLAC-PUB-4547 For impedance of N modes with Q >> f/df, where df=c/s_max, for PEC Q~∞

R/Q estimated from longitudinal impedance, hBN, b0, σ z = 50 mm 4(Zl-Zl0)*df/πf is plotted where Zl0 = 71 Ohm to make the real part positive

Go to HFSS results

Power estimated from ReZl, hBN, hgap=8mm, σ z = 85 mm, same HWHH: b0,b1,b2

Power estimated from ReZl, hBN, hgap=20mm, σ z = 85 mm, same HWHH : b0,b1,b2

Power estimated from ReZl, hBN, hgap=55mm, σ z = 85 mm, same HWHH : b0,b1,b2

Power estimated from ReZl, hBN, hgap=8->20->55mm, cos^2 bunch, HL-LHC 25 ns beam : b0,b1,b2 hgap=8mm hgap=20mm hgap=55mm The impedance of the low frequency modes (<200MHz) weakly (far from linear) depends on the gap! At fully open jaws position a few 100s of Watts can be dissipated mainly on the block keepers and beam screen. The impedance of the higher frequency modes (> 1 GHz) depends on the gap, roughly linear with the gap. Power dissipation is reduced from a few kilowatts down to the level of 100 Watts.

Transverse impedance

Transverse impedance dy=2mm, hgap=8mm, b0 different materials for the hBN blocks: PEC and hBN PEC+PEC(pure geometrical): Im{Zy}(f->0) = 600Ω/2mm = 300 kΩ/m PEC+hBN(geometrical+dielactric): Im{Zy}(f->0) = 5400Ω/2mm = 2.7 MΩ/m Non coataed hBN blocks result in 9 times higher transverse BB impedance

Transverse impedance dy=2mm, hgap=8mm, b0 hBN blocks with and without ferrite 4S60 No significant difference. Ferrite does not damp transverse modes significantly. Its location is not optimal.

Some conclusions The ferrite 4S60 are not very effective in its present location Imaginary part of the Broad band impedance both longitudinal and transverse is increased by ~ factor 9 if no coating is assumed on the hBN blocks Parameters (f0, Q, R/Q) of all significant trapped modes has been calculated in FD using HFSS. R/Q and f0 agree rather well with CST estimate. RF heating estimate based on the CST results for half gap of 8, 20 and 55 mm are made for HL-LHC beam parameters. For cos^2 bunch shape it can reach few kW level if no coating is assumed on the hBN blocks

Recommendations Maximum LHC beam parameters are assumed to be 2808 b x 1.15e+11 p/b for the operation between LS1 and LS2 1.Cu coating of hBN blocks of at least 10 um or more if possible 2.Improve cooling of the jaws to be adequate to the RF heating of the absorber block keepers which can reach 1 kW level at injection (half gap 8 mm) or 100 W level at collisions (half gap 55 mm) 3.The stainless steel beam screen must be coated with at um of Cu. Adequate cooling if necessary has to be implemented in order to evacuate the RF heating power load of 100 W all along the screen.