Hybrid designs - directions and potential 1 Alessandro D’Elia, R. M. Jones and V. Khan

Outline 1.Conventional DDS limitations 2.A Hybrid Design as a possible CLIC_DDS_B 3.Single cell studies 4.Full structure designs and related wakefield damping 5.CLIC_G + Rect. Manifold studies 6.Conclusions 2

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 CLIC_DDS_A- 8 Fold Interleaving Cell shape optimization for fields DDS1_CDDS2_E 3 CLIC_DDS_A-Single

A new approach: a Hybrid Structure for CLIC_DDS_B 4 WGD_Structure + DDS_Structure = Hybrid Structure

First steps on the Hybrid Structure 5 Erf distribution of the dipolar frequencies as in DDS Very high coupling of first dipolar band from cell to manifold via slot as in WGDS + The Erf distribution of the dipolar modes prevent to these modes to add in phase and this will result in a rapid decay of the wakefield in the short time scale; a high coupling will help when the mode will start to recohere in a longer time scale First three dipole bands are shown in the picture above; encircled is the avoided crossing region which is related to the coupling: here is ~1GHz in DDS_A was <200MHz

Some preliminary calculation 6 The following calculations refer to Str#3 (see Slide#39) V/[pc mm m] s (m) Damped (Q=270) Undamped (Q=6500) No interleaving V/[pc mm m] s (m) Damped (Q=600) Undamped (Q=6500) 2-Fold interleaving V/[pc mm m] s (m) Damped (Q=270) Undamped (Q=6500) 2-Fold interleaving

Summary table for new CLIC structure prototypes StructureCLIC-G-CDRCLIC-GCLIC-MCLIC-NCLIC-OCLIC-P Average loaded accelerating gradient [MV/m]100 RF phase advance per cell [rad]2π/3 Average iris radius to wavelength ratio Input, Output iris radii [mm]3.15, , , , , 1.94 Input, Output iris thickness [mm]1.67, 1.00 Input, Output group velocity [% of c]1.65, , , , , 0.53 First and last cell Q-factor (Cu)5536, 5738 First and last cell shunt impedance [ MΩ/m] 81, 103 Number of regular cells26 Structure active length [mm] Bunch spacing [ns]0.5 ns Filling time, rise time [ns]67, , , , , , 38.9 Number of bunches in the train Total pulse length [ns] Bunch population [10 9 ] Peak input power [MW] RF-to-beam efficiency [%] Maximum surface electric field [MV/m] Max. pulsed surface heating temperature rise [K] Maximum Sc [MW/mm 2 ] , , 6.9 P/C [MW/mm] , , 2.27 Luminosity per bunch X-ing [10 34 /m 2 ] Figure of Merit [10 25 %/m 2 ]

Basic Cell Parameters First CellLast Cell a (mm) L (mm) t (mm)40.7 eps22 b (mm) vg (%) fsyn (GHz) ksyn (V/[pc mm m]) g=L-t L b t/2 eps*t/2=elip First CellLast Cell

Cell 1 with manifold 9 Geometric Parameters b (mm) WGW (mm) 6 WGH (mm) 5 SlotH (mm) 2.5 Geometric Parameters b (mm) WGW (mm) 6 WGH (mm) 5 SlotW (mm) 3.5

Proposed 1 st Cell WGW SlotW WGH SlotH Parameters a (mm) 4.04 L (mm) t (mm) 4 eps 2 b (mm) WGW (mm) 6 WGH (mm) 5 SlotW (mm) 3.5 SlotH (mm) 3 Htot (mm) fsyn (GHz)  (GHz) Htot 10

Last Cell with Manifold 11 Geometric Parameters WGW (mm)6 WGH (mm)5 SlotH (mm) Fsyn (GHz) Vg (%)

Proposed 1 st and Last cells WGW SlotW WGH SlotH ParametersFirst Cell Last Cell Big Av. Cross Last Cell Big Band a (mm) L (mm) t (mm)40.7 eps222 b (mm) WGW (mm)666 WGH (mm)555 SlotW (mm) SlotH (mm) Htot (mm) fsyn (GHz)  (GHz) Vg (%) R/Q (k  /m) ksyn (V/[pC m mm]) Htot 12

Procedure adopted to build the full structure Build 1 st, Mid and Last Cells Distribute the frequencies in Erf fashion Optimize Erf sigma minimizing the wake on the first trailing bunch Use this sigma to distribute iris radii and thicknesses Tune the correct monopole frequency using cavity radius 13

First, Last and Mid cell parameters (Big Band) WGW SlotW WGH SlotH ParametersFirst Cell Mid Cell (Cell#14) Last Cell (Cell#27)* a (mm) L (mm) t (mm) eps222 b (mm) WGW (mm)666 WGH (mm)555 SlotW (mm) SlotH (mm) Htot (mm) fsyn (GHz)  (GHz) Vg (%) R/Q (k  /m) ksyn (V/[pC m mm]) Htot * This is used only to optimize the Erf 14

From 3 cells to the full structure From First, Mid and Last cell fsyn’s and kicks, we enforce a Gaussian distribution of Kdn/df as a function of f (for the details, please refer to Vasim’s PhD thesis or Roger Jones papers). The wake is  Kdn/df. Kick Distribution Fsyn Distribution 2 Kdn/df Wake envelope 15

Best n Best n=3.64   =

Geometrical parameters of the cells from Erf a 26 = SlotW 26 = t 26 = b will be used to tune the cell and SlotH will change accordingly to have Htot constant 17

Wakefield Str#1 (Large Band) 18 V/[pc mm m] s (m) Damped (Q=1350) Undamped (Q=6500) “Uncoupled” Wake NB: Reconstructed wake  Only 1 st Dipole band

Impedance Full Transverse Impedance (all dipoles) Transverse Impedance (First two dipole bands) 19 Peak Number

First, Last and Mid cell parameters (Big Av. Cross.) WGW SlotW WGH SlotH ParametersFirst Cell Mid Cell (Cell#14) Last Cell (Cell#27)* a (mm) L (mm) t (mm) eps222 b (mm) WGW (mm)666 WGH (mm)555 SlotW (mm) SlotH (mm) Htot (mm) fsyn (GHz)  (GHz) Vg (%) R/Q (k  /m) ksyn (V/[pC m mm]) Htot * This is used only to optimize the Erf 20

Wakefield Str#2 (Large Av. Crossing) GdfidL Reconstructed wake (only 1 st Dipole Band) 21 V/[pc mm m] s (m) Damped (Q=156) Undamped (Q=6500) “Uncoupled” Wake

Impedance Full Impedance First Dipole Impedance 22 Peak Number

What’s wrong? Design strategy is not correct to ensure Erf distribution on dipoles!!! 23 Non Erf distribution ~ Erf distribution Samples Str#1 Str#2 Peak Number

New strategy Fix First, Mid and last cell Optimize  Vary “a” and “t” accordingly to Erf with previous  Find out 7 fiducial values (4 + the 3 already found for 1 st, Mid and Last cell) in order to get fsyn vs “a/t/b” Get the distribution of fsyn corrected by ksyn Then optimize again  of the distribution of fsyn Known fsyn evaluated from Mathematica in the previous point, go back to fsyn vs “a/t/b” to find the geometrical parameters of the full structure 24

Detailed Procedure 25  in Re-optimize Sigma

First, Last and Mid cell parameters (Str#3) WGW SlotW WGH SlotH ParametersFirst Cell Mid Cell (Cell#14) Last Cell (Cell#27)* a (mm) L (mm) t (mm) eps222 b (mm) WGW (mm)666 WGH (mm)555 SlotW (mm)333 SlotH (mm) Htot (mm) fsyn (GHz)  (GHz) Vg (%) R/Q (k  /m) ksyn (V/[pC m mm]) Htot * This is used only to optimize the Erf 26

Optimized theoretical Fsyn vs Fsyn HFSS simulations for regular cells 27 Max  F=5MHz =1MHz

Wakefield: Comparison Str#2 and Str#3 28 Str3 Str2

Wakefield GdfidL Reconstructed wake (only 1 st Dipole band) 29

Impedance Full Impedance First Dipole Impedance 30 Peak Number

Comparison: Str3 coupled and uncoupled Coupled (reconstructed wake from GdfidL) Uncoupled It seems that the coupling changes the nature of the wake in the early meters 31

Is Q distribution playing a role? Uncoupled Q distribution plays a marginal role 32 Coupled

Let’s go back to Kdn/df (1) From Fsyn distribution we get dn/df, then we multiply by the kicks and we would expect to get a Gaussian-like distribution Uncoupled-DDS_A Coupled-DDS_A 33

Let’s go back to Kdn/df (2) Uncoupled-Str3 Coupled-Str3 34 First Dipole Impedance

What is the problem? 35 First Dipole Impedance Uncoupled Uncoupled with all 27 Fsyn’s Uncoupled with only 16 Fsyn’s

CLIC_G + Rect. manifold Linear tapering Cell parameters: CLIC_G Tapering: CLIC_G i.e. linear 36

WW=7.5 WH =6.5 Wpos=14.5 Wpos WW WH 37

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H-H Boundary condition HFSS single cell simulations E-H Boundary condition 40 H-H Boundary condition E-H Boundary condition Hybrid DDS Hybrid “CLIC_G”

Conclusions We have shown that an average Q<200 can be achieved with this structure with a bandwidth ranging from 2.4-3GHz However strong coupling results in a change of the nature of dipole distribution The next step is to analyze the structure for a moderate damping (as in NLC, Q~ ) in order to preserve the nature of Erf distribution We have shown that with a Q<600, with 2-fold interleaving a good damping can be anyway achieved Further studies are needed but the structure looks promising 41

Additional slides 42

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