DDS limits and perspectives Alessandro D’Elia on behalf of UMAN Collaboration 1

Damped and detuned design Detuning: A smooth variation in the iris radii spreads the dipole frequencies. This spread does not allow wake to add in phase Error function distribution to the iris radii variation results in a rapid decay of wakefield. Due to limited number of cells in a structure wakefield recoheres. Damping: The recoherence of the wakefield is suppressed by means of a damping waveguide like structure (manifold). Interleaving neighbouring structure frequencies help enhance the wake suppression 2

3 VDL

Why a Detuned Damped Structure (DDS) for CLIC 4 Huge reduction of the absorbing loads: just 4x2 loads per structure Inbuilt Wakefield Monitors, Beam Position Monitors that can be used as remote measurements of cell alignments Huge reduction of the outer diameter of the machined disks

CLIC_DDS_A: regular cell optimization The choice of the cell geometry is crucial to meet at the same time: 1.Wakefield suppression 2.Surface fields in the specs Consequences on wake function Cell shape optimization for fields DDS1_CDDS2_E 5

RF Properties of CLIC_DDS_A in comparison with CLIC_G 6 ParametersUnitsCLIC_DDS_A8 x DDS_A 8 x DDS (Circular cells) CLIC_G Fc (Amplitude)-1.29 x *3.4 x 10 5 *6573 *1.06 ** Frms (Amplitude)-1.25 x *2.8 x 10 7 *5 x 10 6 *5.9 ** Fworst (Amplitude)-1.32 x *7.5 x 10 8 *1.55 x 10 8 *25.3 ** Pulse lengthns Peak input power (Pin)MW No. of bunches Bunch population Max EsurfMV/m TT K51--53, 47 SCSC W/  m  bX m x x RF-to-beam efficiency% RF cycles-8--6 Cost-- * 312 bunches, only first dipole band ** 120 bunches, quarter structure GdfidL wake

A new approach: a Hybrid Structure for CLIC_DDS_B 7 WGD_Structure + DDS_Structure = Hybrid Structure

Study of the wake function The problem FF   571MHz;  F=2GHZ Question: How big must be  F in order to have acceptable wake damping starting from 0.5ns? 8

Study of the wake function W t1  6-7V/[pC mm m], considering that W(0)  V/[pC mm m], the maximum acceptable bump must be  4%  F  2.9GHz and  0.830GHz  F=2GHZ  F=2.5GHZ  F=2.9GHZ 9

What about a “Sinc” wake? Wake uncoupled Wake coupled This is the wakefield considering only the first dipole band 2Kdn/df Real(Zx) 10

GdfidL “Full Wake” 1 st Dipole wake from GdfidL The presence of the higher order bands makes the scenario even less comfortable Conclusion: It is not possible to control the position of the zeros along the wake, a smooth function of the impedance is needed What about a “Sinc” wake? 11

Can other types of distributions improve the wake decay?  906MHz  F=2.9GHZ  830MHz 12

Can other types of distributions improve the wake decay?  967MHz  F=2.9GHZ  1.036GHz 13

Can other types of distributions improve the wake decay?  =1GHz  926MHz  F=2.5GHZ 14

What about 0.67ns?  F=2GHZ 15

How big is the bandwidth we may achieve? Assuming SlotW constant throughout the full structure We must consider that <Av. Cross.< in order to get Qs in the order of which will preserve the fsyn distribution NB: The BW has been evaluated considering the difference between 1 st Reg. Cell and Last Reg. Cell, i.e. Cell#27, but the total number of the cells is 26 (26 cells  27 irises); then the real BW will slightly decrease in the real structure Geometric Parameters a (mm) L (mm) t (mm)4-0.7 eps2 WGH (mm)5 WGW (mm)6 16

Bandwidth coupled and uncoupled - Uncoupled 27 cells:  F= 2.685GHz - Uncoupled 26 cells (not shown):  F= 2.47GHz - Coupled (GdfidL):  F= 2.363GHz From theoretical distribution to real structure one must take into account a reduction of ~200MHz in the BW Av. Cross~600MHz 17

What is the bandwidth of the real coupled structure? GdfidL Reconstructed wake (only 1 st Dipole band) Uncoupled wake with 25 peaks (  F=2.314GHz) The uncoupled wake with 25 frequencies (black dashed curve,  F=2.314GHz) falls faster than the 1 st dipole band reconstructed wake from GdfidL (red dashed curve): is there any strange effect from uncoupled to coupled that further reduce the bandwidth? 18

Non Linear Fit to improve wake reconstruction The procedure: I take GdfidL wake as “objective” function of my non linear regression I use reconstruction formula as my fitting function Fsyn are considered as given from Lorentzian fit of the impedance peaks while Qdip and Kicks are the parameters to be optimized Initial guess for Qdip and kicks are from Lorentzian fit 19

Results (1) The agreement with GdfidL is quite good and, as expected, the new procedure produces a major correction at the beginning of the curve while for the rest there are no appreciable variation with the wake reconstructed using the data from Lorentzian fit. =312 =512  =94  =67 It is clear that the wake is reconstructed from unphysical values of kicks and Qdip. Constraints on the parameters are needed. 20

Results (2) =312 =337  =94  =67 With same constraints and an appropriate length of the wake, kicks and Qdip starts to converge. 21

First results for sech 1.5 2Kdn/df Very sharp deep, before 0.15m Need to finalize the simulation to finalize the analysis 22 Very preliminary

Conclusions With conventional DDS (DDS_A) it seems very difficult to meet beam dynamics criteria With hybrid DDS, using Gaussian distribution, it seems non realistic to get damping within 6 RF cycles With different distribution (in particular sech 1.5 ) it is possible to relax the constraint on the BW and this could allow to stay in the 0.5ns bunch spacing Play with Kdn/df would be interesting to see what happen and especially whether it is possible to increase the bandwidth by distributing differently the frequencies However the requirement of 0.5ns is quite tricky and we have not yet considered surface fields… I would not close totally the door to 8 RF cycles 23

24 THANKS Igor 

Additional slides 25

Physical interpretation of the result Constraints: First and last three peaks in the impedance are well separated then their Qdip and kicks are considered fixed The rest of the kicks must be positive and spanning in a range from zero to roughly 10 The rest of the Qdip can span from zero to a maximum of 1500 =312 =576  =94  =67 Wake is still well approximated but kicks and especially Qdip do not seem correct. The constraints I gave are still not enough. 26

Extrapolation for longer wake If I extrapolate for a longer wake it is clear that Qdip and kicks evaluated from Non Linear Fit are not correct. I need more wake to improve Qdip calculation 27

Increasing the length of the wake: 10m =315 =312  =67 This makes me much more confident on the wake reconstruction 28

Going back to the beginning Question was: can I evaluate the bandwidth reduction from uncoupled? From GdfidL Uncoupled 25 Cells Uncoupled 27 Cells Uncoupled 25 Cells Uncoupled 26 Cells 2Kdn/df Answer: It seems Yes, with some minor approximation. In particular in this case it is clear that the major reduction comes from one peak which is missed. Then I estimate a reduction of ~230MHz and not of 322MHz  if I choose ~2.75GHz, I should stay around 2.5GHz which is the minimum required for sech 1.5 distribution. 29