The Zipper Structure: A Novel Accelerator Structure Configuration

1. The Zipper Structure:A Novel Accelerator Structure Configuration Christopher Nantista SLAC AAC Workshop ’08 Santa Cruz, CA July 31, 2008

2. Opening Statements • I present a novel normal-conducting accelerator structure. • The design is not necessarily fully optimized and features still need to be added. • The concept seems to offer some advantages over traditional structures. • When limiting mechanisms are not completely understood, sometimes it’s worth trying something different just to be different. (i.e. It may have virtues not immediately apparent.) • Feedback, suggestions and comments are welcome.

3. Some Considerations Large iris apertures, for large group velocity (TW) or mode spacing (SW), seem to exacerbate breakdown problems in TW structures and reduce shunt impedance in SW structures. What if we decouple power flow/cell coupling from beam irises, and keep the latter as small as short-range wakefield considerations allow? Coupler cells (and those near them) seem to be particularly prone to gradient limiting RF breakdown. Even if pulsed heating is minimized, squeezing the full structure power through such cells seems a bad idea. What if we eliminate coupler cells by coupling to all cells identically? Coupling out HOM power is a problem (slots, chokes, manifolds,…). What if all the cells were heavily coupled, with a wide-open geometry, into an easily damped volume? A p/2 phase advance may offer improved R/Q compared to larger phase advances, since the cell transit time factor can be significantly larger (0.90 vs. 0.64 for a p mode in a simple pillbox). But, if SW, what about empty cells? Biperiodic – off-axis, short,…? What if we use the empty cells by interleaving two /2 modes?

4. The Zipper Structure* • A p/2-mode structure that • fills like a SW structure but • uses all cells like a TW structure. Periodic stubbed waveguides interfaced with square accelerator. The stubs serve to reduce the guide wavelength. p-mode SW Because the fields in the central region are equivalent to the p/2 mode, with zero field in every other cell, the interleaved combs don’t couple, despite the irises. “p/2-mode TW” p-mode SW * with apologies to Kroll, et al. (“PLANAR ACCELERATOR STRUCTURES FOR MILLIMETER WAVELENGTHS” PAC ’99)

5. The Basic Circuit coupling irises excited in quadrature

6. Iris Optimization Consider just the square structure region. What is the R/Q dependance on the iris thickness with simple radiusing and a/l=0.11 (a=0.113648”=2.887 mm)? round 1.27 mm tamago elliptical asp. rat.=3

7. The Field Patterns Re E Re H

8. The Axial Field blue – real red – -imaginary green – complex mag. cyan – -RF phase/p yellow – beam phase/p magenta – effective field Normalized Amplitude mean(green) = 0.8661 mean(magenta) = 0.8562 mean(magenta)/mean(green) = 0.9885 z (mm)

9. Design Parameters H = 1.4766” = 37.5056 mm 0.1875” = 4.7625 mm (half WR75 height) p = 0.25829” = 6.5606 mm s = 0.7591” = 19.2811 mm = W r/Q = 10.896 kW/m Q = 6,369.9 r = 69.408 MW/m Ep/Ea = ~1.770 a/ = 0.11 = 2.887 mm normal conducting (warm) standing-wave (TW to beam) X-band (11.424 GHz)

10. Intra-Structure Coupling PERIODIC SUB-STRUCTURES: f(0)f(p/2)f(pk=(f-f0)/2f/2 Square structure: 11.2811 GHz 11.424 GHz 11.5564 GHz 0.0120 Stub waveguide: 7.7749 GHz 9.26171 GHz 11.424 GHz 0.1970 coupling through waveguide >> coupling through beam iris COMB ISOLATION: 3 1 HFSS S matrix < -30 dB coupling and dropping (w/ iterations) 2 No coupling between input waveguides at resonance.

11. External Coupling and Length For critical coupling when the beam is present, we want to match: Iris coupling of each “comb” to input waveguide The required power is: The length of the structure may be limited by the power handling capacity of the waveguide. Sample Operating Parameters: Ib = 1 A G = 100 MV/m Q0 = 6,370 r/Q = 10.9 kW/m 100 MW  L= 0.307m = ~46 cells ti = 88.0 ns QL = 2,124 Large mode spacing due to strong coupling may allow ~23 cells per comb.

12. Feeding RF power is fed in through a Magic-T, slightly offset from axis (because guide wavelength differs fom free-space wavelength), plus bends. Reflected power goes to a load on the fourth port of the Magic-T. This is like a built-in circulator. Structure pairing is not needed. Waveguide height is stepped/tapered down, perhaps as part of coupling irises. 1.4766” 0.7591” WR75 Magic-T 1.1016” transition in vertical mitered H-plane bends 0.7500” 0.04761” mitered E-plane bends

13. Damping and Tuning cutoff end waveguide HOM loads HOM/SOM loads tuning buttons

14. The Octupole Content of Accelerating Gradient f = p/4 x Normalized Gradient G(r,f) = G0(1 - r4cos4)  = ~1.4610-5 mm-4 f = 0 Normalized Gradient r (mm) Over a transverse beam size of 100 , the gradient should be flat to the scale of 1.510-9 ! y (mm) x (mm)

15. Efficiency What would be the RF-to-beam power efficiency of such a “zipper structure” if implemented in a linear collider? energy into beam per unit length per pulse = RF energy into structure per unit length per pulse For an NLC beam (Ib=0.864 A, Tb=267 ns) and a gradient of 90 MV/m, a maximum efficiency of h=0.2978 is achieved with b=1.846, Tf=90.55 ns, and PRF/L = 195 MW/m. For a CLIC_G beam (Ib=1.192 A, Tb=155.5 ns) and a gradient of 100 MV/m, a maximum efficiency of h=0.3032 is achieved with b=2.0198, Tf= 76.098 ns, and PRF/L = 263.9 MW/m. For optimized CLIC_C and CLIC_G structures:  = 0.24 and .277, respectively*. *Alexej Grudiev

16. Concluding Remarks • I’ve not yet completely developed this idea and answered all questions (It’s slightly more than half-baked). • However, the zipper structure seems to be a promising structure candidate inasmuch as it appears to offer: • good efficiency • simple geometry / easy fabrication (low cost) • easy heavy damping • tunability • low breakdown rate? • Input/feedback from the community of experts gathered at this workshop is welcome. Any show-stoppers I’ve missed?