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SC TW ACCELERATING STRUCTURE FOR ILC. SC Traveling Wave Accelerating Structure for ILC. P. Avrakhov 1 , A. Kanareykin 1 , S. Kazakov 2 , N. Solyak 3 , V. Yakovlev 3 , W.Gai. 1 Euclid Techlabs LLC, Rockville, MD 2 KEK, Tsukuba, Japan 3 FNAL, Batavia, USA. Motivation.

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SC Traveling Wave Accelerating Structure for ILC

P. Avrakhov 1, A. Kanareykin1, S. Kazakov2, N. Solyak3, V. Yakovlev3, W.Gai.

1Euclid Techlabs LLC, Rockville, MD

2KEK, Tsukuba, Japan

3FNAL, Batavia, USA


  • ILC Main Linac contains 27920 9-cell 1.3 GHz SC cavities.

  • Loaded acceleration gradient is ~31.5 MeV/m.

  • Main Linac length is 211 km.

  • Total length of RF structure is 28224 m, or 75% of the main linac length.

  • ILC cost reduction is one of the most important problems.

  • One of the ways to reduce the length of the ILC is to increase the acceleration gradient.

Gradient Limitations

  • The accelerating gradient in a SC structure is limited mainly by quench, i.e, by the maximum surface RF magnetic field.

  • Techniques developed to increase the gradient:

  • Development of surface processing in order to avoid the field enhancement caused by surface microstructure. A recently developed electropolishing technique allows microtips less than 0.1 micrometers.

  • Improvement of niobium material. For example, large grain and mono-crystal materials are currently being considered.

  • Improvement of the structure shape in order to decrease surface magnetic field for a given accelerating gradient.

Surface RF Magnetic Field

  • There are two ways to decrease the surface RF magnetic field:

  • Homogeneous RF magnetic field distribution over the cavity surface:

    - Reentrant structure, Cornell;

    - Low-Loss structure, DESY;and

    - Ichiro structure, KEK.

  • Improvement of the beam interaction with the structure – increased transit time factor.

  • The maximal gradient achieved in the one-cell cavity is 54 MeV/m for an aperture of 70 mm and 59 MeV/m for 60 mm (Reentrant, H. Padamsee et al).

Cavity Geometries

(a) (b) ( c)

The cavity geometry and RF magnetic field pattern in the TESLA cavity (a), Low-Loss cavity (b) and Re-Entrant cavity (c).

Standing Wave SC 9-cell RF cavities. Problems:

  • Small transit time factor T (T=Eacc/Eaverage, Eacc – acceleration gradient, Eaverage – average field over the cell gap). Note, that if acceleration gradient is limited by maximum surface RF magnetic field, Eacc ~T. The higher T is, the higher the acceleration gradient! For SW -structure T~0.7 .

  • Poor stability of the field distribution with respect to small geometrical perturbations:

  • δE ~ δf/kN2,

  • where δE is the maximal field perturbation, δf is the cell resonance frequency perturbation, k is the coupling coefficient, and N is the number of cells. Note strong (quadratic) increase of the field perturbation with the number of cells.

  • -The field perturbation gives the field enhancement in the structure and limits the acceleration gradient;

  • - The field perturbation limits the number of the cells in the structure that leads in turn to

    • small length of the structure (9 cells for ILC);

    • large number of input couplers and HOM dampers;

    • great number of gaps between the structures and thus,

    • effective decrease in the acceleration gradient.

Trapped Modes

c. Trapped modes. If the cells of the structure have the same length, the field in the end cells is the same as in the regular cells only for the operating mode. For all other modes the maximal field may occur not in the end cells, but in the regular cells. It may happen that the field in the end cells is small, preventing high-order mode (HOM) extraction – the so-called trapped modes.

SC Traveling Wave Structure

Alternative structures should be discussed and developed!

Our proposed alternative approach – a superconducting traveling wave acceleration structure (STWA)


Higher transit time factor (T~1) – higher acceleration gradient for the same surface RF magnetic field. For an ideal structure with a small aperture


( is phase advance per cell) and the acceleration gradient gain compared to SW  -structure is

Gain = E /E = 2/sin(/2)

SCTW Structure Advantages (1)

1. Higher Gradient. The gain in the accelerating gradient of the traveling wave accelerating structure relative to a standing wave -structure versus the phase advance per cell for the ideal case. For  = /2 (90) the gain is √2, or 42% (!) - for the ideal structure, of course.

SCTW Structure Advantages (2)

  • 2. Stability of the field distribution along the structure with respect to geometrical perturbations. This permits

    • a much longer structure length (if technology allows), up to the length of a cryostat (~10 m);

    • a much smaller number of input couplers, at most two couplers per cryostat;

    • no gaps between short cavities (for the ILC there is a 280 mm gap between each 1 m long 9-cell cavity). This results in an additional effective gradient increase of 27%!

  • 3. No trapped modes for the lower dipole mode passband ! Two HOM dampers for a long structure.

  • Note, that the STWA structure has the same behavior in the case of breakdown as the SW structure (J. Haimson, HG meeting, SLAC-2007), i.e., in the case of breakdown the power from the source is reflected from the structure but not dissipated in the structure destroying the walls.

SCTW Structure Advantages. (3)

  • Pay-off:

  • The STWA has a negligibly small RF field attenuation, and thus high power feedback is necessary. Technology needs to be developed to fabricate and process long SC structures with a feedback waveguide;

  • High-power coupler could be required to feed a long SC accelerating structure (the number is defined by the length).

  • Two tuners are necessary instead of one for the SW structure in order to

    - compensate for microphonics and Lorentz force and

    - provide good VSWR ratio in the structure and feedback waveguide.

SC Feedback Structure (1)

  • Traveling wave structures with feedback waveguides have a long history.

  • First acceleration structures were TW structures with feedback! (R.B. Shersby-Harvi and L.B. Mullett,1949).

  • First SC acceleration structures were TW structures with feedback (R.B. Neal, 1968)

TW structure with feedback (R.B. Neal, 1968)

SC Feedback Structure (2)

3. First suggestion to use STWA for SC linear collider in order to increase

acceleration gradient by decrease of the electric field on the aperture to avoid

breakdown (N. Solyak, 1998)

SC TW structure for linear collider with the feedback waveguide excited through directional coupler. The structure is optimized in order to decrease the aperture electric field (N. Solyak, 1998).

SC Feedback Structure (3)

4. Suggestion to use a STWA structure with small phase advance per cell in order to minimize surface RF magnetic field to eliminate quenches that limit the acceleration gradient in SC structures. Two-coupler concept without high power bridge (V. Yakovlev, 2001).

The Resonant Loop of the Superconducting Traveling Wave Accelerating Structure powered with two TESLA TTF-III 250 kW couplers spaced at (n+1/4)wg (V. Yakovlev, 2001) .

We propose the development of a STWA structure for ILC

  • The following problems are under investigation:

  • Optimization of the STWA structure cells in order to minimize surface

  • magnetic field without sacrificing surface RF field on the aperture.

  • Optimization of the end coupler that couples the structure to the feedback

  • waveguide.

  • Optimization of the feedback waveguide.

  • Investigation of structure stability versus geometrical perturbation

  • and determination of the maximal possible structure length.

  • Investigation of the structure excitation and tuning.

  • Investigation of the possibility of dipole mode trapping in the structure.

  • Preliminary engineering design of the structure has been performed.

  • Development of the strategy for structure development.

  • A one-cell cavity with feedback waveguide for preliminary HG tests was

  • developed and ideas for mechanical preliminary design have been explored.



Schematic of an example of a traveling wave structure with a feedback waveguide and feedback couplers. The input coupler is not shown. Above: The gain in accelerating gradient versus phase advance per cell. The aperture is 60 mm, the diaphragm thickness is 11.5 mm wide, and the surface magnetic and electric fields are the same as for the Reentrant structure .Left: gain in the gradient of the TW structure compared to a SW, ideal case.

The cavity geometry and RF magnetic field pattern in the superconducting TW accelerating (STWA) cavity. The TESLA, Low-Loss and Re-Entrant cavities are presented above for comparison.








Cavity Shape ~ 24 % gain

The cell shape has been optimized to reach the maximum accelerating gradient while keeping the magnitude of surface magnetic and electric fields less than the experimentally verified limits.

1050 phase advance 24 % gradient gain

Field Flatness ~ 26 % gain

The stability of the /2-mode gives the possibility of using long accelerating structures. It allows further accelerating gradient increase of 26 % - see the gap of 283 mm at TESLA.

Ideal gain ~ 50 %

Field unflatness for π and ~π/2 structures

Flatness vs. phase advance

The End Couplers

Electric (a) and magnetic (b) fields in the

coupling section

Optimized Coupling Section

Magnetic field of the 18-cell SCTW cavity with the optimized coupling section.

Passband of the 18-cell SCTW structure with couplers.

Optimization of the Feedback Waveguide.

Magnetic field enhancement in the waveguide caused by the bend. Rin is the internal bend radius.

Wave reflection from the bend.

Waveguide Height

10 mm

Taking into account a possible field enhancement in the waveguide bend and coaxial coupler elements, the 20 mm height was chosen.

20 mm

30 mm

Structure Excitation and Tuning

  • TW structure tuning:

    - two independent tuners are necessary in order to tune both partial standing wave modes to the resonance:

    - main tuner that compensates for the structure frequency deviation caused by microphonics, Lorentz force, etc;

    - special “matcher” in the feedback waveguide that compensates reflections from the structure-waveguide coupler, bends, etc.

  • The field distribution inside the ring is critically sensitive to the reflection coefficient of the matcher.

  • Coupling reflection should be adjusted to -40 dB or VSWR ≤ 1.021

  • Tolerances are tough but comparable with those achieved in the TESLA cavity

Model of the resonant TW ring excited by two couplers

Two couplers for the excitation of the resonant ring containing the SC TW

Backward wave – 5%

10% power of nominal

–- S-matrix developed with HFSS with the couplers and beam loading taken in account
















- S-matrix

of the six-pole (Altman)

P input

The resonant ring model: single coupler and a tuner

Model of the resonant TW ring excited by one coupler

Multipactor, simple analysis

Multipactor near the cavity “equator” (V. Shemelin).

Rc, Req- geometrical parameters, B0 –RF magnetic field near the cavity “equator”.

For the considered TW structure, p=0.9:

no multipactoring at any M!


High Order Modes

Dispersion curves for the first six dipole modes

High Order Modes in TW structure. Mode Damping

Transmission |S12| for the lowest dipole dispersion curve for 9 cells

Transmission |S12| for the second dipole and second monopole modes

Transmission for higher frequencies is good enough to extract the modes from the structure (HOM couplers)

Development Strategy

In first part of the project, we propose to demonstrate high gradient operation and conduct RF field measurements for a single-cell cavity experiment that is customary for experimental high power testing of all new types of SC cavities like the Reentrant, Low-Loss or Ichiro designs proposed especially for the ILC application.

The single test cavity will have the same geometry as full-sized STWA and feedback waveguide.

This experiment will establish a baseline for characterization of the proposed methods and technology and will validate the suitability of the STWA structureconcept for potential ILC applications.

Problems to be solved in the first stage

●refinement of the single-cell cavity and feedback waveguide electrical parameters in order to achieve the same ratio of the RF field in the feedback waveguide to the field in the cavity as those in the full-sized STWA structure.

● conceptual design to be done of the single-cell cavity with feedback waveguide.

● engineering design development of the single test cavity to be done by AES Inc.

●fabrication of two or three single-cell test cavities by AES Inc. More than one cavity will be necessary to reduce uncontrollable negative factors that may influence the high-gradient test results, again a common practice in SC cavity development.

Problems to be solved on the first stage (2)

● full surface processing of a single test cavity with feedback to be carried out at the FNAL SC surface processing facility

● high gradient testing of the single test cavity at the FNAL vertical cryomodule

● theoretical analysis and computer modeling for a) tuning parameters, b) HOM damping, c) high-power input, and d) beam loading issues

One-cell cavity with feedback waveguide

The magnetic field distribution in the test cavity. The field in the feedback waveguide is about 60% of the field in the cavity.

(a) a layout of the single-cell STWA test cavity with feedback waveguide.

Symmetrized Cavity



General dimensions of the cavity and the waveguide in mm. The waveguide width is 160 mm.

Single-cell cavity parameter refinements

The Sequence of Cavity Manufacturing

AES, Inc.

SC Traveling Wave Structure Studies

  • Shape Optimization of Cells of a Superconducting TW Accelerating Structure.

  • Parameter Optimizations of the Rectangular Feedback Waveguide.

  • Design and Development of the Coupling Section.

  • Superconducting TW Accelerating Structure Parameters.

  • Flatness Studies for the SC TW Structure.

  • Modeling of the TW Regime and Tuning.

  • Multipactoring Performance Analysis.

  • HOM Modes Simulations and Damping of Long Range Wakefields.

  • Engineering Aspects of Superconducting TW Structure Fabrication.

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