Comparison of coaxial higher order mode couplers for the CERN Superconducting Proton Linac study

Higher order modes (HOMs) may affect beam stability and refrigeration requirements of superconducting proton linacs such as the Superconducting Proton Linac, which is studied at CERN. Under certain conditions beam-induced HOMs can accumulate sufficient energy to destabilize the beam or quench the superconducting cavities. In order to limit these effects, CERN considers the use of coaxial HOM couplers on the cutoff tubes of the 5-cell superconducting cavities. These couplers consist of resonant antennas shaped as loops or probes, which are designed to couple to potentially dangerous modes while sufficiently rejecting the fundamental mode. In this paper, the design process is presented and a comparison is made between various designs for the high-beta SPL cavities, which operate at 704.4 MHz. The rf and thermal behavior as well as mechanical aspects are discussed. In order to verify the designs, a rapid prototype for the favored coupler was fabricated and characterized on a low-power test-stand.

Figure 1

Examples of HOM coupler design approaches: (a) probe coupler, (b) hook coupler, (c) modified TESLA design [3].

Figure 2

HOMs with high ($R/Q$) for the high beta SPL cavity [4, 6] and a typical $S_{21}$ transmission curve (black) of an optimized HOM coupler.

Figure 3

Measured intrinsic quality factors $Q_0$ at room temperature for the four niobium SPL cavities in comparison with eigenmode simulations. The fundamental pass band is shown in detail. Modes with the $(R/Q)>10$ are highlighted.

Figure 4

Maximum frequency spread for the measured modes between 690 and 2100 MHz. Modes with highest ($R/Q$) values are highlighted and labeled.

Figure 5

Bead-pull measurement for the ${\mathrm{TM}}_{011}$ $\pi$ mode (1.333 GHz) compared with the electric field magnitude resulting from an eigenmode simulation (contour plots with dark blue representing areas of low field strength).

Figure 6

HOM coupler design approaches for the high-beta SPL cavity, the dashed line indicates the flange. In the following “stages” refers to parts of the couplers separated by gaps. (a) Probe Coupler Version 1 with single notch filter, two stages, and centered output port. (b) Probe Coupler Version 2 with double notch filter, two stages, and centered output port. (c) Probe Coupler Version 3 with double notch filter, three stages, and centered output port. (d) Hook Coupler Version 1 with single notch filter, two stages, and centered output port. (e) Hook Coupler Version 2 with single notch filter, two stages, and shifted output port. (f) Hook Coupler Version 3 with double notch filter, three stages, and centered output port. (g) Modified TESLA design.

Figure 7

Parametrized model of the PROBE V3 coupler.

Figure 8

Equivalent lumped circuit and transmission line model of the PROBE V3 design in comparison to the cross section of the three dimensional model. Only the filter is considered, not the antenna penetrating the beam pipe.

Figure 9

Input impedance of the transmission line equivalent circuit model (a) and of the corresponding 3D model simulated by hfss (b) assuming a $50\mathrm{\Omega }$ load at the output (Fig. 8). Three parameters of the model were varied in a range between $-20\%$ (light blue) and $+20\%$ (dark blue) from the nominal value. The parameter (1/C3) is proportional to the gap size of the capacitor (gap2 in Fig. 7).

Figure 10

(a) and (b) ${\mathrm{TM}}_{01}$-TEM transmission (monopole coupling) of the different design approaches optimized for the high-beta SPL cavity. (c) and (d) ${\mathrm{TE}}_{11}$-TEM transmission (dipole coupling for the most favorable polarization) of the different design approaches optimized for the high-beta SPL cavity.

Figure 11

Notch bandwidth as a function of the gap distance of the primary notch (compare Fig. 8). For the coupler with a single notch filter (PROBE V1), the bandwidth is measured at $-100\mathrm{dB}$. For the couplers with double notches (PROBE V2, V3), it is measured via the distance between both notch frequencies. The more they deviate the less damping will be achieved in between and they become separate single notch filters.

Figure 12

Simulated $Q_{\mathrm{ext}}$ considering a HOM coupler on both sides of the cavity. (a) Modes of the 1st and 2nd dipole bands. (b) Modes of the ${\mathrm{TM}}_{011}$ and ${\mathrm{TM}}_{021}$ monopole bands.

Figure 13

Schematic sectional view of a five-cell SPL cavity inside its helium tank [1]. HOM couplers are on both sides of the cavity (left one is hidden).

Figure 14

Magnetic field strength $\mathbf{H}$ of the fundamental mode of different couplers. The field is scaled to a gradient of $25\mathrm{MV}/\mathrm{m}$ in the 5-cell cavity.

Figure 15

Magnetic field $\mathbf{H}$ of different higher order modes in case of the PROBE V3 coupler. The fields are scaled to an extracted power of 1 W.

Figure 16

Surface currents $I_{\mathrm{surf}}$ of the HOM coupler on the tuner side for different modes calculated via (2). Each of the HOMs are normalized to an extracted power of 1 W.

Figure 17

Boundary conditions for the steady state thermal simulations using ansys. Left: Power dissipation caused by the electromagnetic fields in the coupler (mode heating). Right: Heat load coming from the rf cable.

Figure 18

Maximum temperature on the PROBE V3 surface versus the surface resistance with the thermal boundary conditions described in the text. The critical temperature of 9.2 K is highlighted in red. For comparison, the BCS resistance computed by [26] is shown in dashed black for different frequencies. A thermal equilibrium may only exist within the gray highlighted zones. (a) $\mathrm{RRR}=60$. (b) $\mathrm{RRR}=380$.

Figure 19

Left: Maximum temperature on the coupler surface for different radii of the inner conductor of the rf cable as a function of the cable length (distance to the 50 K shield). The heat source is the 50 K shield itself and the heat sink is the cavity wall at 2 K. The values are consistently above the critical temperature of 9.2 K. Right: the corresponding heat.

Figure 20

Maximum temperature on the coupler surface for different contact temperatures of the cooling heat sink around the coupler tube. The heat source is the 50 K shield, the heat sink is the cavity wall at 2 K and the cooler in contact with the coupler tube. The critical temperature of 9.2 K is highlighted.

Figure 21

Secondary electron yield for copper and niobium (after $300°\mathrm{C}$ bake) [12].

Figure 22

Resonant trajectories between the tube and the lower part of the notch filter plate of (a) original PROBE V3, (b) modified PROBE V3, and (c) modified HOOK V3 coupler.

Figure 23

Impact energy and averaged secondary electron yield of resonant trajectories at the notch filter for the models shown in Figure 22. Below the darker colors are related to copper while the lighter colors are related to niobium.

Figure 24

Particle evaluation at $0.25\mathrm{MV}/\mathrm{m}$ for the first two models in Fig. 23 simulated with cst ps. Initial electrons are directly emitted from the notch plates.

Figure 25

Resonant trajectories at the HOM passband filter of the PROBE V3 coupler for (a) the original concave gap, (b) the flat gap, and (c) convex gap.

Figure 26

Impact energy and averaged secondary electron yield of resonant trajectories at the HOM passband filter for the models shown in Fig. 25. Below the darker colors are related to copper while the lighter colors are related to niobium.

Figure 27

Resonant trajectories at the probe and hook antenna. (a) PROBE V3. (b) HOOK V3.

Figure 28

Impact energy and averaged secondary electron yield of resonant trajectories at the probe or hook antenna (refer Fig. 27). Below the darker colors are related to copper while the lighter colors are related to niobium.

Figure 29

The 3D printed HOM coupler. The prototype is made of plastic and covered by a copper layer of approximately 0.1 mm thickness (PROBE V3).

Figure 30

HOM coupler prototype mounted on a copper SPL cavity with a rotatable flange. Here, the rf transmission of the coupler is measured using a reference antenna at the beam pipe port close to the HOM antenna. The input coupler used for measurements involving the cavity characteristics (e.g. $Q_{\mathrm{ext}}$) is on the other side of the cavity (not shown).

Figure 31

$S_{21}$ Transmission from the beam pipe (using a probe antenna) to the HOM coupler port (Fig. 30).

Figure 32

Measured and simulated external $Q$ for the HOMs of several bands considering one coupler on the tuner side with a penetration depth of 11.5 mm. Modes with an ($R/Q$) larger than 10 Ohm are highlighted in red.

Figure 33

Simulated and measured $Q_{\mathrm{ext}}$ as a function of the azimuthal angle of the HOM coupler for two dipole modes and their polarizations in the ${\mathrm{TE}}_{111}$ band. Below, it was not possible to measure $Q_{\mathrm{ext}}$ for both polarizations.