New RF design of CLIC DB AS Alexej Grudiev, BE-RF

Acknoledgements Rolf for useful information about present design (R. Wegner and E. Jensen,CLIC-note- 945, 2012)

Present CDR design

Full beam loading in linear vg tapered structure Q 0 =const, R’=const but v g = v g0 (1+az) Full beam loading condition for a≠-2α: Efficiency in steady-state:

Full beam loading in Constant impedance TWS Efficiency in steady-state: Full beam loading condition: In order to maximum efficiency means maximum relative beam loading parameter at the full beam loading condition: => Maximum R’*vg*Q0

Transfer function Pin -> V i.e. PRST-AB 14, (2011) Const impedance (CI): - Transfer function from the input gradient G0~sqrt(Pin) to voltage V Linear tapered vg: In addition, there is time of flight effect. t_flight ~ 3-6 ns for 1-2 m long structure t_f’ => t_fill - t_flight in FWS and t_f’ => t_fill + t_flight in BWS BWS enhance filtering effect of accelerating structure

Optimization of the 4-spoke cell: 120 degree, a=30mm dzSpoke=10mm; even spokes Odd spokes even spokes dzSpoke=10mm; odd spokes eta2=R’*vg*Q0 dzSpoke=15mm; even spokes dzSpoke=h-gap~27mm; even spokes dzSpoke=15mm; odd spokes; P0=15MW -> eta = 98.6%; Ls = 2.8m; tfill=102ns; G0=2.5MV/m RRSpWall 20mm 25mm

Optimization of the 4-spoke cell: 150 degree dzSpoke=15mm; odd spokes dzSpoke=25mm; odd spokes

Optimization of the 4-spoke cell: 90 degree dzSpoke=10mm; odd spokes

Optimization of the 4-spoke cell, odd spokes: 120 degree, a = 25mm Odd spokes dzSpoke=15mm; dxSpoke=30mm ; dRdt=10mm; odd spokes; P0=15MW -> eta = 98.7%; Ls = 2.5m; tfill=102ns; G0=2.83MV/m dzSpoke=15mm; dxSpoke=40mm ; dRdt=10mm; odd spokes; dzSpoke=15mm; dxSpoke=30mm; dRdt=12mm; odd spokes;

Optimization of the 4-spoke cell, odd spokes: 120 degree, a = 20mm Odd spokes dzSpoke=15mm;; odd spokes; P0=15MW -> eta = 98.7%; Ls = 2.34m; tfill=99ns; G0=3MV/m dzSpoke=19mm;; odd spokes;

Cell and CI structure parameters summary table dphi [deg] a [mm]QR’/Q [Ω/m] vg/c Ls [m]t_fill [ns] ~ This can be improved by changing the cell shape.

Geometry of the BWS

Tapering vg Structure with a=30mm; R’/Q0 = 1846 Ohm/m; Q0 = P0=15MW; => G0=2.5MV/m Const Imp.; vg/c = 9.23%; solid lines eta = 98.6%; Ls = 2.8m; tfill=102ns; Linear vg/c from 9.23% to 2.9%. Dash lines eta = 98.4%; Ls = 2.2m; tfill=134ns; Const Imp.; vg/c = 5.6%; dash-dotted lines eta = 98.1%; Ls = 2.2m; tfill=131ns;

Making filling time 245 ns Structure with a=30mm; R’/Q0 = 1846 Ohm/m; Q0 = P0=15MW; => Const Imp.; vg/c = 1.54%; solid lines eta = 96.5%; G0=6.1MV/m Ls = 1.13m; tfill=246ns; Linear vg/c from 2.6% to 0.908%. Dash lines eta = 97.0%; Ls = 1.18m; tfill=244ns;

Material: why not Aluminium CLIC DB Acc. Structure with a=30mm; vg/c = 9.23%; R’/Q0 = 1846 Ohm/m; Q0Cu = P0=15MW; => G0=2.5MV/m Influence of conductivity on efficiency: conductivity = 100 %IACS (Cu) -> eta = 98.6% conductivity = 60 %IACS (Al) -> eta = 98.1% conductivity = 40 %IACS (6061-T6) -> eta = 97.7% Issues: 1.Multipactor due to high secondary emission yield of Al. More studies are needed to address this issue both simulations and high power testing. 2.RF and vacuum wise tight assembly. Prototyping is necessary. Material used: Al 6082-T6, conductivity: 35MS/m = 60%IACS

Advantages of high vg BWS High Rf-to-Beam efficiency 99% High group velocity -> less tolerance -> no tuning -> lower cost Variation of group velocity by magnetic coupling hole size is independent on the aperture radius -> max(R’) and max(vg) at the same time

Questions Aperture: the smaller the better for RF, lower limit comes from beam dynamics. Is a=30 mm acceptable? Avni is looking into it. Filling time t_fill ? How critical is to have factor 10 noise reduction at f=1/t_fill=4MHz ? Is factor 2 or 4 instead acceptable? Const impedance versus tapered? – Tapering can be done but, for the same filling time, it will reduce the lowest vg -> tighter tolerances Increase nose level at f_n=n/t_fill – Argument for the tapering are detuning of the HOMs but with the bunch spacing of 2 buckets it has small effect. We must rely on the strong damping anyway. IF higher average gradient od longer filling time is needed reduction of vg linearly along the structure provides slightly higher efficiency compared to overall reduction of vg in CI structure Gradient? The higher is the gradient the lower is the linac cost per MV, IF real estate gradient is limited by the structure and not by the RF power source layout. It seems that 2 times shorter DB linac still can be done by rearranging the RF power sources along the linac. To be discussed…

Next steps Minimum aperture limit to be defined by our beam dynamics experts For this minimum aperture a detailed RF design to be done to maximize vg, R’ and Q0 If higher gradient needed vg can be tapered down or/and reduced Design HOM damping (same type as for CDR) If Aluminium then – Multipactor studies which is probably main limitation for Al cavity – Prototypes of a few cells for fabrication/assembly studies – Full or half length prototype to be tested at a L-band test facility