Design and testing of a four rod crab cavity for High Luminosity LHC

A 4-rod deflecting structure is proposed as a possible crab cavity design for the LHC high luminosity upgrade. Crab cavities are required for the LHC luminosity upgrade to provide a greater bunch overlap in the presence of a crossing angle, but must fit in the existing limited space. The structure has two parallel sections consisting of two longitudinally opposing quarter-wave rods, where each rod has the opposite charge from each of its nearest neighbors. The structure is transversely compact because the frequency is dependent on the rod lengths rather than the cavity radius. Simulations were undertaken to investigate the effect of rod shape on surface fields, higher order multipole terms and induced wakefields in order to obtain the optimal rod shape. The simulation results presented show that the addition of focus electrodes or by shaping the rods the sextupole contribution of the cavity voltage can be negated; the sextupole contribution is $321.57\mathrm{mTm}/{\mathrm{m}}^2$, ${\mathrm{E}}_{\text{peak}}=27.7\mathrm{MV}/\mathrm{m}$, and ${\mathrm{B}}_{\text{peak}}=63.9\mathrm{mT}$ at the design voltage of 3 MV. The damping requirements for the LHC are critical and suitable couplers to damp all modes but the operating mode are presented. The results of various testing cycles of the first SRF 4 rod prototype cavity are presented and show that the cavity has reached the required transverse voltage of 3 MV.

Figure 1

Electric (a) and magnetic (b) fields (arbitrary units) in a 4RCC.

Figure 2

A cross sectional diagram of a 4RCC.

Figure 3

Diagrams of the conical elliptical 4RCC, viewed along the beam axis (a) and a transverse cross-section (b) to show the parameterization of the rod design parameters.

Figure 4

Fringe transverse electric fields vs longitudinal position for different rod gaps.

Figure 5

$B_{\mathrm{peak}}/V_T$ vs base width for different values of base breadth. The tip width and breadth were fixed at 45 mm and 40 mm, respectively.

Figure 6

$\frac{G}{2}\frac{R}{Q}$ vs base width for different values of base breadth. The tip width and breadth were fixed at 45 mm and 40 mm, respectively.

Figure 7

$B_{\mathrm{peak}}/V_T$ vs tip width for different values of tip breadth. The base width and breadth were fixed at 110 mm and 65 mm, respectively.

Figure 8

$E_{\mathrm{peak}}/V_T$ vs tip width for different values of tip breadth. The base width and breadth were fixed at 110 mm and 65 mm, respectively.

Figure 9

Sketches of the rod polarity configurations for the monopole and dipole modes in a 4RCC.

Figure 10

R/Q of the LOM vs width for different values of breadth for the base ellipse with the tip width and breadth fixed at 45 mm and 40 mm, respectively.

Figure 11

Plot of the ${\mathrm{R}}_T/\mathrm{Q}$ (blue) and LOM R/Q (red) vs. radius for the outer can.

Figure 12

Frequency of the LOM vs width for different values of breadth for the base (a) and tip (b) ellipses.

Figure 13

Sextupole component vs rod width for the base ellipse (a) and tip ellipse (b).

Figure 14

(a) Sextupole component of wing shaped rods vs angle for a base width of 60 mm and (b) and the parametrization of the wing shapes.

Figure 15

Parametrization of the kidney shaped 4RCC.

Figure 16

Sextupole component vs cutting ellipse width for different rod widths and offsets.

Figure 17

$E_{\mathrm{peak}}/V_T$ vs cutting ellipse width for different rod widths and offsets.

Figure 18

$B_{\mathrm{peak}}/V_T$ vs cutting ellipse width for different rod widths and offsets.

Figure 19

The Niobium 4RCC prototype (Design A) dressed for cold rf testing.

Figure 20

CAD drawings of the final cavity designs viewed along the beam axis.

Figure 21

Cross-sectional diagram of final cavity design C (a) and an isometric view (b).

Figure 22

The Aluminum cavity without the outer can, showing the inner rods.

Figure 23

Transverse E field (blue) and H field (green) vs horizontal position in arbitrary units (A. U.).

Figure 24

Comparison of bead pull measurements and CST simulations of relative voltage with predicted longitudinal voltage against bead or beam offset. “EC” represents the elliptical conical cavity.

Figure 25

LOM coupler geometry (top) and transmission spectrum (bottom).

Figure 26

Filter design for the vertical and horizontal HOM couplers.

Figure 27

A CAD drawing of the 4RCC with the HOM and LOM couplers as well as the fundamental power coupler (FPC).

Figure 28

Modal impedance for the final 4RCC design.

Figure 29

Q verses transverse voltage measurements, and radiation monitor readings of the Niowave 4RCC tests.