HAN TENIDO UN ABORTO PROVOCADO 2007-
TRASTORNO POR ESTRÉS POSTRAUMATICO
After detailing the use of coaxial couplers to both provide power to the fundamental mode and damp the HOMs, the dressed crab cavities for the SPS test1 (Sec. 2.2)
are shown in Fig. 2.20.
The Double Quarter Wave (DQW) cavity uses three on-cell, coaxial, super- conducting (internally cooled) HOM couplers to damp the HOMs. They have an L-C band-stop filter centred at 400 MHz to reject any power from the fundamental mode and use transmission line lengths to allow an increased damping at spe- cific frequencies (i.e. those of detrimental HOMs) at the expense of bandwidth (Sec. 2.3.4). The capacitive output gives a high-pass filter response, further re- jecting the fundamental mode but allowing transmission at the HOM frequencies. The fundamental mode pick-up of the DQW also acts as a HOM coupler for some high frequency modes.
1Before installation in the LHC, the crab cavities are scheduled for tests in the SPS (CERN’s
(a) DQW - vertical. (b) RFD - horizontal.
(c) DQW showing HOM couplers. (d) RFD showing HOM couplers.
Figure 2.20: Dressed crab cavities proposed for the HL-LHC. Designs are those proposed for the verification tests in the Super Proton Synchrotron (SPS).
The RFD cavity has two HOM couplers of differing geometries. The location of the couplers are chosen to damp the vertical and horizontal HOMs indepen- dently [101].
The ‘horizontal HOM coupler’ is located in a ‘wave-guide stub’ connected to one cavity end plate. The ‘hook-type’ coupling element, which couples to horizon-
tal and accelerating HOMs1, is connected to a high-pass filter which rejects the
operating mode, but has a high transmission at higher frequencies.
The second ‘vertical HOM coupler’ is placed in a wave-guide stub on the other end-plate. The wave-guide stub is in different plane to the one for the horizon- tal mode damping. Due to the fundamental mode’s polarity and symmetry, the location of the wave-guide stub gives a ‘natural’ rejection, meaning that there is no need for a rejection filter. The coupler uses a ‘probe-type’ coupling element to couple to the vertical and accelerating HOMs.
Chapter 3
SPS DQW HOM Coupler
As superconducting crab cavities had never before been used with protons, pro- totype tests in the Super Proton Sychrotron1 (SPS) were scheduled. The aim
of the tests was to identify any unforeseen risks and to demonstrate operational reliability, machine protection and cavity transparency [17].
The first test scheduled was for that of the Double Quarter Wave (DQW) crab cavity. A two-cavity cryomodule was scheduled for testing in the final quarter of 2018.
The HOM coupler designed for the SPS DQW crab cavity test is presented in this chapter. Firstly, the choice of HOM coupler design along with the RF perfor- mance is evaluated with the use of equivalent circuit analysis. The circuit response is then compared to that of 3D electromagnetic simulation software; Parametric analysis is applied.
Finally, ‘test-boxes’ are designed and used to measure the manufactured coupler response, comparing this to simulations to qualify that the transmission response of each coupler is as expected.
3.1
Design
The DQW HOM coupler evolved from the ‘4-Rod’ crab cavity HOM coupler design shown in [102]. The annotated vacuum cross-section for the DQW HOM coupler
is shown in Fig. 3.1 alongside photographs of the manufactured coupler.
(a) Two dimensional schematic of the SPS DQW HOM coupler’s vacuum geometry.
(b) Manufactured assembly. (c) Manufactured pieces.
Figure 3.1: HOM Coupler for the SPS DQW crab cavity.
The structure is an ‘on-cell’, niobium HOM coupler which is internally cooled by liquid helium to 2 K and operates in the superconducting regime. If the couplers were not superconducting they would not support the cavity’s high magnetic field and would significantly reduce the Q0 of the cavity.
The locations at which the HOM couplers are installed onto the cavity is shown in Chapter 2, Sec. 2.4. To evaluate why these locations were chosen, the modes for which damping is most important was evaluated. The bare cavity model, alongside ther/Qvalues for the HOMs under 1 GHz1, is detailed in Fig. 3.2. Ther/Qvalues
1Due to the profile of the proton bunch, the HOM excitation is inversely proportional to
the frequency with a ‘Gaussian-like’ dependence. Hence, low frequency HOMs generally have a stronger excitation.
are separated into ‘transverse vertical’, ‘transverse horizontal’ and ‘longitudinal’. For the crab cavities proposed for the HL-LHC upgrade, each of the HOMs is classified as ‘vertical (v)’, ‘horizontal (h)’, ‘longitudinal (l)’ or ‘hybrid (hy)’, as it is difficult to assign them to pillbox equivalences due to the complex field topologies of the ‘exotic’ structures.
(a) Bare cavity model.
f [MHz] r/Qv [Ω/m] r/Qh [Ω/m] r/Ql [Ω] 592.5 0.3 0.3 55.2 689.2 0.0 34.7 0.0 715.6 1.2 0.2 7.7 755.9 21.1 0.0 0.0 934.4 0.0 17.3 0.0 969.4 0.2 0.1 9.7
(b)r/Qvalues for the low frequency modes.
Figure 3.2: SPS DQW bare crab cavity detrimental mode evaluation. The field topology for the three modes with the highest r/Q values in each respective plane was evaluated to assess the best location to install the HOM couplers. As it was not possible to install ancillaries onto the side of the cavity structure, due to the transverse dimension restrictions arising from the second beam pipe in the LHC, the HOM couplers could only be installed on the top and bottom of the cavity. As such, the field topology was evaluated in this location specifically. The electric and magnetic fields for the three modes are shown as contour plots in Fig. 3.3 and as vector plots in Appendix Sec. 3, Fig. 8. The longitudinal mode at a frequency of 969 MHz is also shown. This is because, as a result of the filling schemes used in the LHC, modes close to multiples of the bunch spacing harmonic frequencies1 (multiples of 40.08 MHz) can be very detrimental
for HOM power generation.
1This concept will be expanded upon in the coming chapters but, for reference, it ‘flags’ this
(a) Plane used for field contour plots. (b) Field evaluation plane.
(c) 593 MHz - E-Field. (d) 593 MHz - H-Field.
(e) 689 MHz - E-Field. (f) 689 MHz - H-Field.
(g) 756 MHz - E-Field. (h) 756 MHz - H-Field.
(i) 969 MHz - E-Field. (j) 969 MHz - H-Field.
The electric field of each mode acts between the inner quarter wave resonator and the outer wall and the the magnetic field ‘flows’ around the central conductor; The field profiles in this plane are similar to that of a coaxial line. As there is a high magnetic field at the location shown for each of the modes, the DQW HOM coupler’s hook-type coupling mechanism was chosen to couple magnetically, but to also allow the couplers to be ‘de-mountable’. Electric coupling wasn’t chosen as, although there is an electric field component, for most HOMs the E-field is small at the coupler port area compared the central cavity region. Therefore ade- quate coupling would require a large coupling element to provide a significant area perpendicular to the electric field lines. Additionally, the axial electric field could be perturbed, contributing to larger multipole components of the fundamental mode [57].
Although it is difficult to exactly match any of the modes to those of a perfect cylindrical resonator (i.e. the ‘pillbox cavity’), the field ‘poles’ in this plane are clear. Referring to the contour plots (Fig. 3.3), for the 593 MHz mode, the angle at which the HOM coupler ports are placed does not matter since there are no defining poles and hence a uniform field distribution around the elliptical path. For the next two modes shown however, 689 and 756 MHz, there are two poles where both the electric and magnetic fields are enhanced. The planes of these two poles are perpendicular to one another, hence meaning that choosing HOM coupler port locations (Fig. 3.3b) at only 90◦ and 270◦ or at 0◦ and 180◦, would
only allow sufficient coupling to one of these modes. Hence, coupler ports in both planes should be used, or at angles in-between them (i.e. 45◦, 135◦, 225◦, 315◦.
The 969 MHz mode has four poles which align with the planes of the previous two modes.
Originally, for the Proof-of-Principle (POP) design [54], one Fundamental Power Coupler1 (FPC) port and one HOM coupler port were included on the top side of
the cavity at 270◦ and 90◦ respectively. On the bottom of the cavity, four HOM
coupler ports were included at 45◦, 135◦, 225◦ and 315◦. This allowed coupling to
all of the pole configurations shown in Fig. 3.3. Additionally, it allowed the LHC’s
1Device which couples power into the cavity. For the DQW this structure also uses a hook-
second beam pipe to pass if the cavity was used in the horizontal kicking scheme1.
Evolving from the PoP design to the SPS DQW crab cavity, two HOM couplers were removed from the bottom to reduce the number of cavity ancillaries. In terms of coupling to the HOM fields, one was left in the 45/225◦ plane and one in the
135/315◦ plane.
The HOM couplers are installed on each port with the hook orientated perpen- dicular to the magnetic field, in order to provide maximum coupling; this angle is equal to that of the port, i.e. 45◦ and 135◦ for the bottom couplers and 90◦ for the
top HOM coupler. For reference, the dressed DQW crab cavity is shown again in Fig. 3.4.
Figure 3.4: DQW crab cavity dressed with HOM couplers and pick-up probe.