JLAB-TN-09-50

Critical Higher Order Modes

in

CEBAF Upgrade Cavities

Frank Marhauser

Kai Tian

Haipeng Wang

September, 2009

Jefferson Laboratory

12000 Jefferson Avenue

VA, 23606

Abstract

An experimental Higher Order Mode (HOM) survey has been carried out recently for a string

of eight seven-cell SRF cavities at 2 Kelvin to investigate the damping efficiency of cavities fully

equipped and installed in a realistic cryomodule configuration. Results and their consequences for

the 12 GeV upgrade cryomodules are detailed in this technical note focusing on parasitic HOMs

above the beam tube cutoff. A review and analyses of experimental and numerical data for

individual and cavity-pair configurations are presented to understand the different phenomena that

can sensitively alter the loaded Q of these HOMs.

Contents

1. Introduction ................................................................................................................................................. 1

2. Review of HOM Surveys of C100 Cavities in the HTB and VTA ................................................................. 2

3. On the Parasitic Modes of the 3rd Dipole Passband ..................................................................................... 5

4. HOM Survey for a String of Eight Cavities ................................................................................................ 18

5. Summary and Outlook ............................................................................................................................... 23

6. Acknowledgement ...................................................................................................................................... 24

References ...................................................................................................................................................... 25

1

1. Introduction In reference [1] we have reported on the necessity to thoroughly characterize the Higher Order

Mode (HOM) damping performance of cavities including a review of cavity design, prototyping

and operational experience, problems encountered and measures taken towards a reliable CW

cavity cryomodule concept for the CEBAF 12 GeV upgrade. This included a detailed HOM survey

of the first two prototype upgrade cavities installed in a quarter cryomodule. Updated results

have been published recently revealing a sufficiently broadband HOM damping efficiency with

respect to potential beam break-up (BBU) instability thresholds in CEBAF at the envisaged

operating currents [2]. Whereas for trapped cavity modes - resonating below the cavity beam tube

cutoff - experimental conditions could be established resembling the final 12 GeV cryomodule

environment, BBU-critical high frequency modes have been identified above the cutoff frequency

with propagating fields interacting differently and sensitively on variable boundary conditions

not representative for the final design. Since the variations are significant, it is essential to

understand the underlying phenomena. We have performed extensive experimental and

numerical analyses for upgrade style cavities with the aim to explain the involved data. These are

focused on the HOM-damping performance of the most critical dipole mode pairs above cutoff

frequency. The analyses include the influence of results by individual and combined effects

comprising

I. beam tube boundary variations

II. coupled cavity configurations

III. fabrication tolerances

IV. mode polarization

V. multimodal waveguide coupling

VI. rf characteristics of coaxial-to-waveguide adapters

VII. combined external losses

VIII. fundamental mode coupler absorbing performance

Subsequently we describe the experimental results for a string of eight cavities in an upgrade

style cryomodule environment. Consequences of our analyses are detailed with proposed

improvements to guarantee a stable beam operation of CEBAF for the 12 GeV era.

2

2. Review of HOM Surveys of C100 Cavities in the HTB and VTA

The CEBAF 12 GeV upgrade cryomodules (“C100”) will consist of eight seven-cell HOM-

damped Low Loss (LL) type 1497 MHz cavities (Figure 1). With the new cavities the cryomodule

length usable for acceleration has been increased from 4 to 5.6 meters compared to the original

CEBAF design. Furthermore, with the advance in chemical processing and improved

understanding of limiting factors much higher cavity operating fields are targeted to yield an

energy gain of 108 MeV per cryomodule (19.2 MV/m average per cavity in CW at Q0 = 8e9).

Figure 1: C100 cavity layout with the HOM endgroup illustrated in more detail on the left. Other than in the

original CEBAF cavities, where two cold HOM absorbers are utilized in a waveguide endgroup fully

immersed in the Helium bath, the upgrade cavities utilize two DESY-type coaxial HOM couplers. These are

spaced apart in azimuth such to facilitate coupling to different mode polarizations. The coaxial couplers are

located outside the Helium vessel on the opposing side of the fundamental power coupler (FPC). The

outcoupled HOM energy is transferred via type-N cables to standard room temperature 50 Ohm loads.

Figure 2: High power performance for the first produced 1.5 GHz1 upgrade style cavities C100-1 (left) and C100-2

(right) tested at 2K(CW) both vertically (VTA) and in the horizontal test bed (HTB) [3].

The first two C100 cavity prototypes (C100-1 and C100-2) were manufactured during 2006 and

high power tested within 2006 and 2007 [3]. These tests have been carried out for both cavities

separately in the vertical test area (VTA) and after assembly as a cavity-pair in the horizontal test

bed (HTB), a dedicated upgrade style quarter cryomodule. At this time the cavities met all

fundamental mode specifications for the 12 GeV project with a thermally stable CW operation up

1 A frequency tuning of the cavities has not been conducted at the time. The untuned cavities were resonating at 1499.171 MHz (C100-1) and

1499.339 MHz (C100-2) at 2K measured in the HTB. The higher frequencies are uncritical for the test results. The fundamental mode field amplitude

variation within individual cavity cells was < 10%.

3

to Eacc = 25 MV/m (Figure 2). As crucial as the fundamental mode performance is the broadband

suppression of unwanted beam generated cavity HOMs [1], particularly for recirculating

accelerators like CEBAF to avoid BBU instabilities at the desired operating currents. The

importance to experimentally survey critical HOMs before the assembly in a cryomodule has

become apparent in November 2007 when the first multipass BBU at CEBAF has been observed

[4]. The consequence was beam loss at surprisingly low currents which for some optics

configurations limited the maximum injection current to 40 µA compared to the nominal 85 µA.

The source of the BBU was quickly confined as originating from a cryomodule (dubbed

“Renascence”) in the north linac (1L04) - installed shortly before the incident and removed only

recently - that has served as a test bed for demonstrating key technological components towards

C100 [5]. It houses intermediate designs of upgrade High Gradient (HG) and LL seven-cell

cavities. Dedicated beam experiments could pinpoint the cause to one out of five HG cavities.

Inspection records revealed that this cavity has been deformed inadvertently during fabrication

exceeding tolerable measures at a single cell. Extensive numerical analysis taking into account

experimental data have predicted the expected cell deformations, large enough to generate tilted

dipole fields not sufficiently captured by the HOM-endgroup [6]. Although successful measures

were applied to mitigate the BBU by adjusting the CEBAF optics in the recirculating arcs, large

efforts have been invested to characterize the BBU phenomena to prevent a recurrence in future

C100 cavities.

Figure 3: Loaded HOM Qs measured in the HTB at 2K for C100-1 and C100-2 respectively.

It has triggered a series of HOM measurements for C100-1 and C100-2 both in the HTB and

VTA in 2008. The outcome of the HTB measurements is summarized in Figure 3 by means of the

loaded quality factor Ql. The Ql is a figure of merit best characterizing the ability to suppress a

specific HOM. It takes into account both the rf losses in the cavity walls (described by the

unloaded Q0) and the energy dissipated externally (Qext) due to HOM couplers, waveguides and

beam tubes. We have focused our attention on modes up to 3 GHz. This includes the most

parasitic dipole modes responsible for the strongest deflection to be considered for transverse BBU

4

.m

104.2Qrk

1

Q

RkQ

Q

RR 10

l2lthreshold,Ω⋅≤

⋅=⋅= ⊥

⊥

scenarios. More specifically, the spectral range covers the trapped dipole mode passbands (TE111,

TM110) below the first cutoff frequency of the beam tubes (fc,TE11 = 2.51 GHz) as well as a dipole

passband (TM111) with HOMs resonating around 2.9 GHz that generally tend to propagate

through the beam tubes via the TE11 mode. The latter effect usually helps to increase the external

losses, i.e. reducing the quality factor Ql. When the Ql of a specific HOM is multiplied with the

R/Q-value (“characteristic shunt impedance”, calculated numerically) the so-called shunt

impedance can be derived. It is a measure of the parasitic interaction of the beam and the specific

HOM, which has to be kept within acceptable limits by design. A general aim is to assess the

shunt impedance of each HOM as accurate as possible to obtain a proper characterization of the

cavity damping efficiency, which in turn is needed to provide an accurate understanding of beam

current limitations in an accelerator facility. The objective required by the 12 GeV baseline physics

is to provide full machine stability for all operating conditions up to 100µA injected beam. With

these constraints, the impedances for all deflecting dipole modes have to be restricted to [7]:

(1)

Herein R/Q^ = R/Q/(kr)2 denotes the transversely normalized characteristic shunt impedance

derived from the longitudinal R/Q at a radial beam offset r. This value is transit-time corrected for

a speed of light particle. By multiplication with the HOM wave number k = 2πf/c this formulation

takes into account the dependence of the threshold impedance with frequency f. Considerations

also regard physics outside the original baseline design to support lower energy, lower pass beam

operation with up to 400µA injected beam, restricting the threshold to:

(2)

In Figure 4 the shunt impedances of dipole HOMs are plotted together with the more stringent

goal as recently published in ref. [1]. It reveals that among all dipole modes a safety margin of at

least an order of magnitude can be achieved.

Figure 4: Dipole shunt impedances for C100-1 and C100-2 respectively as derived from measured Ql values.

.m

100.1Qrk

1

Q

RkQ

Q

RR 10

l2lthreshold,Ω⋅≤

⋅=⋅= ⊥

⊥

5

3. On the Parasitic Modes of the 3rd Dipole Passband As shown in Figure 4 the problematic modes found in the deformed HG cavity to generate

BBU instabilities (TM110-like 4π/7 and 5π/7 modes) principally do not pose a threat for the 12 GeV

operation. Although trapped below the beam tube cutoff frequency, these modes couple to the

HOM couplers positioned close to the end cells thanks to sufficiently strong evanescent fields.

However, prominent HOMs around 2.9 GHz are drawn with reservation (transparent bars). The

damping of these modes is depending on the real boundary conditions in the final cavity string

assembly, since fields tend to propagate through the beam tubes. In fact, HOM surveys for

individual cavities in the VTA revealed significant alterations of loaded Qs described in detail in

the following. We have taken data in the VTA with the original configuration as used for the high

power tests and subsequently by assembling 249.2 mm long stainless steel beam tube extensions

on each side. Figure 5 illustrates the HTB and VTA configurations investigated.

Figure 5: HTB (left) and VTA setup (right). Stainless steel beam tubes have been used in a second VTA test.

We will refer to the configurations as:

case A: single cavity in VTA plus 83mm long Nb cylinder attached to FPC side flange. The

other flange provides a pumping port. This is the original configuration.

case B: single cavity in VTA plus 9+13/16” long stainless steel tubes attached to both sides

of the cavity. One extension provides a pumping port.

case C: two cavities joined in HTB, the outer cavity beam tube diameter steps down to half

the size down immediately behind the cavity flanges (see Figure 5 left).

Figure 6 depicts the transmission spectra recorded for case A and C covering the TM111

passband modes. The first two mode pairs in this regime are most distinctive. These are explicitly

shown on the right side of Figure 6 as recorded for C100-1. The modes resonate after a comparably

broad stopband. This provides a chance for mode identification with numerical help. We have

used CST Microwave Studio (MWS) [8] to model a single cavity in 3D. By analyzing the vector

6

fields at that frequency level we have found the horizontally (henceforth: “H”) and vertically

(henceforth “V”) polarized TM111 modes with a phase advance of π/7 and 2π/7 per cell

respectively as the first dipole mode pairs of the passband. The H/V TM111 π/7-modes in fact are of

highest interest as they possess the strongest R/Q-values among all dipole modes.

Figure 6: HOM transmission spectra measured in the HTB and VTA (with beam tube extensions) at 2K containing

both TM111 and TM210 modes. The most parasitic dipole mode pairs resonating around 2.9 GHz are shown on the

right side in more detail (for C100-1 in VTA).

Table 1 summarizes the measurement results for all cases comprising the first frequencies in

the spectral range of interest. The outcome is not conclusive on first sight and we try to explain the

involved phenomena step by step. We need to refer to Table 1 several times throughout this

course and even enhance the table with additional data.

Table 1: Parasitic TM111-like modes recorded in C100-1 and C100-2 around 2.9 GHz in different

configurations, i.e. for individual cavity assemblies in the VTA w/o (case A) and with beam tube

extensions on both cavity sides (case B) and for a cavity pair in the HTB (case C)

case C100-1 C100-1 C100-2 C100-2

frequency Ql frequency Ql

MHz MHz

A 2895.180 8.9e4 2898.458 8.1e5

temp. = 4K 2895.473 4.0e5 2900.047 5.1e6

date: July 2008 2899.319 1.7e4 2904.938 9.0e4

2900.118 1.0e5 2906.840 2.9e5

B 2895.076 2.0e6 2898.369 4.1e6

temp. = 4K 2895.419 1.2e6 2900.013 6.5e5

date: March/April 2009 2898.886 2.9e5 2904.474 4.8e5

2899.810 2.3e5 2906.600 1.2e5

C 2894.992 6.7e4 2894.981 7.2e4

temp. = 2K 2895.396 1.4e5 2897.116 5.9e3

date: May/June 2008 2896.887 5.9e3 2898.251 1.9e5

2898.250 1.6e5 2899.852 2.6e5

2899.256 2.0e4

2899.980 5.6e4 2899.955 1.7e4

2904.338 4.3e4 2904.354 5.7e4

2906.024 2.7e4 2906.030 2.6e4

7

Impedimental, about twice as many resonances have been detected in the HTB compared to

the VTA for each cavity in the same spectral range. Such additional modes can be created in the

coupled cavity system by crosstalk effects due to the propagating fields (see also Figure 13 further

below). For instance, a mode concentrated in one cavity can be excited (weaker) from the

neighboring cavity2. E.g. we were able to analyze a comparably weak resonant transmission level

(≤ -80 dB) at 2894.981 MHz (C100-2). In that case we concluded that we excited the mode at

2894.992 MHz in the adjacent cavity (within error bar of C100-2 measurement, similar Ql).

Similarly, the modes recorded at 2904.338 MHz and 2906.024 MHz for C100-1 can be attributed to

C100-2. Modes with such frequencies have been observed in C100-2 when individually measured

in the VTA but were missing in C100-1. Analyzing the measurement data, we have denoted

HOMs with smaller fonts in Table 1 when assumed to belong to the adjacent cavity.

As previously documented ([1],[2]), the TM111-modes overlap with quadrupole modes (TM210).

This makes mode identification more doubtful. Additional resonances in the beam tubes or FPC

waveguides can complicate the situation even further. To assess the shunt impedance of the most

parasitic modes we need to provide full clarity about the field nature. To gather unambiguous

data we have carried out field profile (“bead-pull”) measurements for both C100-1 and C100-2

separately on the bench. The room temperature setup is shown in Figure 7 with one of the cavities

still in the helium vessel. Our main aim was to identify the proclaimed TM111 π/7- and 2π/7-modes

by recording the electrical field profile that can be compared with corresponding numerical data.

Figure 7: Bead-pull measurement setup with C100-2 on the bench. To resolve for longitudinal electric fields in a

resonating cavity in the presence of both radial and longitudinal fields - as prevalent for transverse modes in an

elliptical cavity - usually two (calibrated) dielectric objects of different geometrical shapes (needle, disc) need to be

moved subsequently through the cavity. Such a two-bead-pull measurement method also delivers the R/Q-value

of the mode of interest. This time only a dielectric sphere made of Teflon (∅= 6.3mm) - probing the radial and

longitudinal field with equal strength - has been utilized to simplify the measurement since we were only

interested in mode identification. The sphere has been moved through the structure, while the phase shift of the

resonant mode signal under investigation - measured in transmission - is recorded with a Vector Network

Analyzer. This phase shift is proportional to the absolute electric field squared. A more detailed description of

both the measurement setup and method can be found in [9].

Measurement results are shown in Figure 8. The normalized electric field amplitude is plotted

along the cavity probed at a 10 mm offset parallel to the beam axis either horizontally or vertically.

The cavity outline on the abscissa depicts the longitudinal field location with respect to the cavity

cells and beam tubes. For comparison the MWS result is shown (black lines) for the H mode (the V

2 We have used an Agilent ENA 5071C Vector Network Analyzer of high dynamic range. For each cavity the power

was launched in at the FPC port via a coaxial-to-waveguide adapter and picked up at one of the HOM coupler ports

on the opposing beam tube side.

8

mode not shown yields similar results). Obviously the HOMs are influenced with the beam tubes

shorted too close at the end cell on the HOM coupler side. This causes a strong resonant coupling

to the artificially shorted beam tube volume. The cavity mode couples to the TE11 mode in the

tube, propagates to the end plate and is reflected back to form a standing mode pattern. The TM111

π/7-mode and 2π/7-mode amplitude distributions along the cavity are distorted such to produce

an asymmetry with respect to the centre cell. Even an additional mode concentrated mainly in the

beam tube is produced. A theoretical approach describing the dependency of cavity field

amplitudes on different boundary conditions has been detailed in [1].

Figure 8: Absolute electric field versus longitudinal position in the cavity. Numerical field profile data are

compared with “bead-pull” measurement results for the beam tube mode (left) and the (distorted) TM111 π/7-

(middle) and 2π/7-mode (right) respectively probed 10 mm of axis either horizontally or vertically depending on

the mode polarization. The simulations are for electrically shorted beam tubes on both sides in agreement with

the setup, where we shorted the tubes and left only small holes for the sphere carried on a nylon wire. Measured

frequencies given in the legend are taken at room temperature3.

Although the fields are relatively high in the beam tube on the HOM coupler side, the

miminum of the standing mode pattern is located at the position of the HOM cans, which is

unfavourable for HOM damping. Figure 8 reveals that much lower fields are present on the HOM

coupler side in C100-2 compared to C100-1. Since the energy scales with the field squared it yields

a strong impact on damping, i.e. we observe consistently higher Ql values (about a factor of ten

larger in C100-2) for the π/7-modes. The increase is less severe for the 2π/7-modes, in agreement

with the recorded field levels (comp Figure 8 middle and right). Responsible for the differing

fields and frequencies4 are cavity cell shape deviations caused during fabrication. Due to

fabrication tolerances HOM frequencies can vary - by experience - as high as several MHz in same

type of cavities. Here similar modes resonate higher in C100-2 throughout. We assume that C100-2

exhibit slightly smaller cell geometries. The experimental findings can hardly be resembled

numerically without the cell dimensions available. Nevertheless we could identify the prominent

modes unambiguously. Generally, due to the smaller iris diameter in LL cavities compared to HG

3 The simulated frequencies deviate by several MHz, which is a typical result for this problem size. The actual deviation depends on the total

number of mesh cells limited by numerical and hardware (memory and CPU time) constraints. For example, the fundamental mode frequency for a

reasonable discretization in 3D (~3 Million hexahedral mesh cells in MWS for the seven-cell geometry (half symmetry)) amounts to ~1492 MHz

compared to ~1493 MHz for twice as much cells (prohibitively large CPU times). A simulation with the 2D code Superfish [10] for the bare cavity

(no HOM coupler, no waveguides) yields a more accurate frequency converging to ~1496 MHz by discretizing the cavity with a comparably fine

triangular mesh. Measured frequencies were 1496.539 MHz (C100-1) and 1496.385 MHz (C100-2) at room temperature. 4 In fact, the fundamental mode frequency was ~170/150 kHz higher in C100-2 compared to C100-1 at 2K/room temperature. Consider also, that the

cavities have not been tuned mechanically at the time to yield 1497 MHz at 2K.

9

cavities, a weaker cell-to-cell coupling of fields has to be taken into account. It increases the risk of

tilted field profiles due to non-uniform cell deformations. In turn, this sensitively impacts the

HOM damping efficiency as experienced in the VTA.

However - as far as propagating modes are concerned - the VTA setup is not representative for

a cryomodule cavity string. In case B we tried to resemble more closely the condition in a

cryomodule, where cavities are joined through larger beam tube connections. A corresponding

numerical model took into account the extensions for this case. For the “bead-pull” setup we

could not reuse the VTA extensions. Instead a single copper cylinder of 42 mm length was

attached on the HOM coupler side. This extension proved to be sufficiently long to strongly

decouple the mode from the beam tube section. Consequently more symmetrically distributed

field profiles have been obtained. This is more typical for undistorted modes in well agreement

with the simulation. The findings are presented in Figure 9 by means of the most parasitic π/7-

mode pair (we could also identify the 2π/7-mode not shown here). Similar to case A, the HOM

couplers are positioned close to the minima of the standing TE11 wave and lower amplitudes have

been recorded at this position for C100-2 compared to C100-1. Overall however, the field levels are

much smaller in case B increasing the Ql values even further. We need to mention, that the wall

losses in the stainless steel extensions in case B are obviously not significant to reduce the Qs

below those recorded in case A. Two exceptions are marked with bold fonts in Table 1. Noticeable

as well is a disproportional increase of the Ql for V and H HOMs. The responsible effect will be

detailed further below.

Figure 9: Most parasitic TM111 π/7- mode above cutoff as measured with beam tube extensions. This produces a

more symmetrical field typical for the π/7-mode.

We have seen, that the Ql values sensitively depend on outer boundary conditions, thereby

spanning about two orders of magnitude in the different cases. Although the mode tends to

propagate through the field tubes on both sides, it exhibits a rather confined nature. This limits the

damping efficiency. To understand the limitations, the external losses need to be itemized

separately. This not only involves the HOM couplers, but also has to include the FPC waveguide

port presenting yet another option for external losses. The rectangular cross-section of the FPC

yields a cutoff frequency of 1.11 GHz for the TE10- and 2.22 GHz for the TE20-mode respectively.

Both cutoff frequencies are far below the TM111 passband mode frequencies and consequently

allow coupled energy to escape the cavity through the FPC port. We have determined the external

Qs experimentally both at the HOM couplers and the FPC waveguide adapter. The findings are

10

summarized in Table 2 for the TM111 π/7 and 2π/7-mode respectively. This extends Table 1 for case

A and B.

Table 2: Loaded and external Qs for the first two TM111 passband mode pairs in C100-1 and

C100-2 for case A (upper rows) and B (lower rows). Bold fonts refer to overcoupled ports

dominating the loaded Q (C1 = upper HOM coupler, C2 = lower HOM coupler).

C100-1 C100-2

frequency Ql Qext FPC Qext C1 Qext C2 frequency Ql Qext FPC Qext C1 Qext C2

MHz MHz

2895.180 8.89e4 1.5e10 2.1e5 1.7e5 2898.458 8.06e5 1.4e11 2.0e6 1.5e6

2895.473 4.02e5 2.9e9 4.2e5 2.3e7 2900.047 5.14e6 1.4e9 5.9e6 9.1e7

2899.319 1.71e4 3.0e9 5.4e4 2.5e4 2904.938 8.96e4 1.6e10 1.6e5 1.9e5

2900.118 1.04e5 1.8e10 1.1e5 9.2e6 2906.840 2.86e5 3.4e7 2.9e5 8.2e6

2895.076 2.0e6 V 1.3e7 1.3e7 4.8e6 2898.369 4.1e6 V 1.3e7 9.8e7 3.3e7

2895.419 1.2e6 H 1.8e6 8.3e6 1.3e7 2900.013 6.5e5 H 6.8e5 4.7e7 1.2e8

2898.886 2.9e5 V 8.5e6 1.2e6 5.0e5 2904.474 4.8e5 V 2.8e6 3.3e6 1.6e6

2899.810 2.3e5 H 4.2e5 1.0e6 1.6e6 2906.600 1.2e5 H 1.6e5 8.2e5 3.3e6

In agreement with the “bead-pull” data, the Qext values at both HOM couplers (C1, C2) are

consistently higher in C100-2 than in C100-1 (except for the mode around 2906 MHz at C1). The

overcoupled port in each case (lowest Qext) dominates the Ql and is highlighted in bold fonts. In

various cases no port is overcoupled, implying that the internal surface losses are higher than each

of the individual external losses. This scenario - logically valid - is only found in case B due to

more significant rf losses in the stainless steel extensions. The superconducting losses in the

Niobium walls are negligible (either at 2K or 4K). In case A the Qext at the FPC is several orders of

magnitude higher for all modes and polarizations (>>1e7) due to the weaker coupling to the FPC.

To substantiate this argument, Figure 10 presents computed contour plots of the electric field

amplitude for the first two passband mode pairs respectively. Obviously, in case A comparably

strong fields are visible at the HOM couplers, whereas in case B the FPC can capture a higher

amount of energy. The FPC therefore compensates for some of the lost damping efficiency in the

HOM couplers. To assess the external losses at the FPC port, we have calculated the

corresponding Qext, denoted explicitly in Figure 10. These are significantly smaller in case B, which

is in principal agreement with the experimental findings. This plays an important role in the

overall damping efficiency, especially for the H modes. The measured Q values however are much

higher than simulated. The reason for this is the bandlimited performance of the FPC adapter used

in the VTA. It is a Niobium coaxial-to-waveguide adapter (Figure 11 left), which is directly

attached to the cavity FPC flange (no rf window)5. It features a central copper antenna and a type-

N ceramic vacuum feedthrough. This adapter is not optimized for the transmission around

2.9 GHz with only about 18% of the incident energy transmitted to the coaxial output port (TEM

mode) as simulated with MWS (Figure 11 middle). Moreover, it is not a multimodal device, but

only supports the TE10 mode. The TE20 mode is not able to couple efficiently to the TEM mode due

to its vanishing fields at the antenna position (Figure 11 bottom right). Only some minor leakage

of energy is possible. We need to emphasize that the H modes preferably couple to the TE10

5 The adapter is immersed in Helium (vacuum sealed with an AlMg serpentine gasket) and has been used both for the

low and high power rf tests of the cavities.

11

waveguide mode, the V modes to the TE20 mode as clearly visible in Figure 10. It is due the

orientation of the TE11 fields in the tube which determines the coupling mechanism.

Figure 10: 3D contour plots of the electrical field amplitude computed with MWS for the first and second TM111

passband mode pair in case A (top) and B (bottom). The intensity level increases from blue to red. For better

visibility of weak field levels, the amplitudes have been logarithmically scaled and normalized to a tenth of the

maximum field amplitude at a stored energy of 1 Joule. The Qext calculated is given explicitly at each FPC port.

Figure 11: Broadband transmission characteristic of the Niobium coaxial-to-waveguide transformer (left) used in

the VTA as simulated with MWS (middle) for the TE10- (green curve) and TE20-mode (red curve) in the waveguide

(right, field plots at 2.9 GHz). The latter can not efficiently be transmitted with the copper antenna centered in the

waveguide.

12

It actually gave us a chance to identify the mode polarization in Table 2 for case B, since only

here the H modes can possibly exhibit an overcoupled FPC adapter and are more efficiently

damped. The simulated Qext values are typically too optimistic (low) even with the HOM output

ports shorted. The numerical model in fact assumes the propagating energy to be fully absorbed

either in TE10 and/or TE20 mode6. We tried to compensate for this effect by allowing for the

bandlimited rf performance of the real Niobium adapter. Therefore the original Qext values have

been scaled by the fraction of energy transmitted in the TE10 mode, i.e. 1/0.18=5.5. For the H modes

we eventually obtain a more reasonable agreement with the measured values as summarized in

Table 3. The scaling factor can be significantly higher for the V modes (indefinite).

Table 3: External Qs as measured and estimated numerically for case B.

C100-1 C100-2

mode ID phase advance R/Q (Ω) polarization Qext FPC Qext FPC Qext FPC

per cell r = 10 mm measured measured simulated

TM111 π/7 38.6 V V 1.3e7 V 1.3e7 >> 1.8e5

TM111 π/7 39.4 H H 1.8e6 H 6.8e5 4.8e5 (scaled from 8.6e4)

TM111 2π/7 6.1 V V 8.5e6 V 2.8e6 >> 3.8e4

TM111 2π/7 6.1 H H 4.2e5 H 1.6e5 1.0e5 (scaled from 1.8e4)

Table 3 also includes the R/Q value simulated 10mm off axis either horizontally or vertically

depending on mode polarization. We have omitted case A, since the fields are distorted such to

unrealistically alter the R/Q-values. The TM111 π/7-mode possesses the highest R/Q value among

all dipole modes. Given the R/Q, the maximum acceptable Ql value of a mode can be estimated

according to the impedance thresholds for CEBAF specified in eq.(1) and eq.(2). This has been

done for both the TM111 π/7- and 2π/7-mode in Table 4.

Table 4: Maximum acceptable loaded Q for the TM111 π/7-mode and 2π/7-mode respectively.

Mode CEBAF energy beam current Rthreshold f R/Q at r = 10mm R/Q/(k∙r2) max. Ql

µA Ω/m MHz Ω Ω/m

TM111 π/7 12 GeV 100 2.4e10 2900 40 6.58e3 3.6e6

TM111 π/7 6 GeV two-pass 400 1.0e10 2900 40 6.58e3 1.5e6

TM111 2π/7 12 GeV 100 2.4e10 2900 6.1 9.87e2 1e7

TM111 2π/7 6 GeV two-pass 400 1.0e10 2900 6.1 9.87e2 2.4e7

For the 12 GeV baseline physics a Ql of 3.6e6 should not be exceeded for the TM111 π/7-mode.

The other modes in the passband exhibit much lower R/Q-values with relaxed constraints

(allowable Ql ≥ 1e7).

6 In MWS we have calculated the cavity modes with the real Eigenmode solver (AKS solver), which does not deliver

travelling but standing modes in a closed volume. Nevertheless, the external Q at a predefined waveguide port can be

evaluated by computing the travelling waveguide mode from the standing mode pattern. Thus, each of the

waveguide modes (TE10 or TE20) can be considered separately in the Qext calculation with a symmetry planed used.

The method assumes the full absorption of the mode at the waveguide port. We could not simulate the Qext at the

HOM coupler ports in MWS due to the complex antenna details that would lead to unreasonably large number of

mesh cells. For the same reason we did not simulate the coaxial-to-waveguide adapter used in the VTA. Instead the

waveguide port has been defined at a cross-sectional area of the FPC some distance away from the cavity.

13

In the HTB the maximum Ql measured among both dipole pairs was only 2.6e5 (Table 1), much

lower than both in case A and B. Consequently it is important to examine the HTB boundary

conditions more specifically. Here both cavities are joined symmetrically around the centre with

the HOM coupler endgroups facing to the outside (see Figure 13, also Figure 5). The outer cavity

beam tubes step down to a pipe incorporating vacuum gate valves and a pumping port at some

distance from the cavity. The tube has a diameter of 1.37”, small enough to reflect the TM111 mode

within a short distance (TE11 cutoff ~5 GHz). The length of the cavity beam tube on the HOM

coupler side is the same as in case A. Thus, it can lead to field distortions similar to case A. The

central FPC ports share the same cavity interconnecting beam tube. As a benefit both FPCs can

capture the fields from each of the cavity. We could measure significantly reduced Qext values at

the FPC for both the H and V modes, with lower values for the H modes as explained above.

Differently to the VTA, the FPC waveguide configuration includes the complete transition from

2K to room temperature including a warm rf vacuum window. On the air side a waveguide bend

tapered to a standard WR650 waveguide has been used. In reality, the efficiency of the external

losses in the FPC depends on the achievable return loss of the waveguide up to the klystron. For

our low power HOM survey we attached commercial WR650 coaxial-to-waveguide adapters close

to the cavity (Figure 12 left). These adapters are specified for a broadband transmission within

1.12-1.7 GHz (TE10 cutoff is 0.908 GHz) verified by a simulation as shown in Figure 12 (middle).

The rf performance is rather poor above this range. Nevertheless a transmission of 47% in energy

has been calculated at 2.9 GHz.

Figure 12: Broadband transmission characteristic of the coaxial-to-WR650 waveguide transformer (left) used in the

HTB as simulated with MWS (middle) for the TE10- (green curve) and TE20-mode (red curve) in the waveguide

(right, field plots at 2.9 GHz).

As in case A and B we numerically simulated the cavity fields to understand the coupling

effects to the FPC waveguide(s). The physical mirror plane in the centre of the HTB theoretically

yields mirrored field configurations with modes resonating at exactly the same frequency for

identical cavities. This scenario is very unlikely due to prevalent fabrication tolerances. As

mentioned initially, typical tolerances can lead to HOM frequency alterations in the MHz-level.

Trying to resemble the real world more closely, we have scaled one cavity in lateral size

(uniformly by -0.2%), which increased the frequencies by roughly the same amount as observed in

14

C100-2 compared to C100-1. Figure 13 shows the outcome for the first eight modes in the TM111

dipole passband for H (left) and V modes (right) in spectral order of appearance from top to

bottom.

Figure 13: 3D contour plots of the electrical field amplitude computed with MWS for the eight TM111 passband

mode frequencies in case B for H (left) and V modes (right). The intensity level increases from blue to red. For

better visibility of weak field levels, the amplitudes have been logarithmically scaled and normalized to a tenth of

the maximum field amplitude at a stored energy of 1 Joule. The Qext calculated is given explicitly, which is for both

FPC ports combined.

The field amplitudes obtained in cavities and beam tubes - hence the amount of transmitted,

stored and reflected energy from on to the other cavity - depend strongly on the mutual

interaction of resonances in the coupled cavity system. This produces involved field

configurations of passband modes not obeying the theoretically possible phase advance per cell

period for a single cavity. Hence it is hardly possible to proclaim a typical cavity mode/phase

advance merely by the HOM’s spectral order of appearance. The spectrum recorded in case C

(Figure 6 above) is evidence of the more involved scenario in the coupled cavity-pair system

compared to the rather “clean” spectra measured for individual cavities. Additional resonances

strongly concentrated within the interconnecting beam tube are also possible. The overlap with

quadrupole modes complicates the situation at higher frequencies. A proper determination of the

shunt impedance is difficult. Additionally, the R/Q can be altered significantly due to field

distortions. Since the sum of the R/Q (total loss factor) is fixed by the cavity geometry, an

alteration of the R/Q in one mode will be compensated by a change of the R/Q for adjacent modes.

This explains the different R/Q values listed in Figure 13. Note, that the R/Q has been evaluated by

integrating the field over the total length of both cavities. The H/V TM111 π/7-modes are the most

15

parasitic since these exhibit both the highest R/Q values and rather confined field configurations.

The mode identification remains still ambiguous due to the existence of close-by 2π/7-modes or

distorted derivatives (0.5π/7 and 1.5π/7, cf. [1]). The impedances for the V/H TM111 π/7-modes

evaluated in Figure 4 above are therefore a worst case estimate using the maximum Ql among the

first two pairs of passband modes observed.

Figure 13 illustrates that all HOMs principally couple to both FPCs and - depending on the

level of confinement - to one or both HOM coupler endgroup(s). This effect can explain the lower

Q values experienced in case C compared to case A and B. The external Qs in case C are itemized

in Table 5 to provide additional insight in the dominant loss mechanisms. The Qext have been

recorded at the ports of the primary cavity under investigation, i.e. with the HOM couplers and

FPC adapter of the neighbouring cavity terminated with 50 Ω loads. It is obvious that in most

cases no port is overcoupled. This verifies that the losses are dominant somewhere else in the

coupled system. The Ql is thus determined by the combined losses in all HOM couplers and the

FPC taking the adjacent cavity into account (rf surface losses in the Niobium can be neglected).

Table 5: Loaded and external Qs for the first two TM111 passband mode pairs in C100-1 and

C100-2 as measured in the HTB (case C). The bold fonts refers to the overcoupled ports

dominating the loaded Q (C1 = upper HOM coupler, C2 = lower HOM coupler).

C100-1 C100-2

frequency Ql Qext FPC Qext C1 Qext C2 frequency Ql Qext FPC Qext C1 Qext C2

MHz MHz

2894.992 6.7e4 4.4e7 (V) 2.6e5 2.0e5 2898.251 1.9e5 2.1e8 (V) 1.2e7 2.14e8

2895.396 1.4e5 5.9e5 (H) 2.8e7 3.6e5 2899.852 2.6e5 1.0e7 (H) 1.1e7 4.50e10

2899.256 2.0e4 6.4e6 (V) 3.5e4 4.8e4 2904.354 5.7e4 7.6e7 (V) 3.0e5 2.05e7

2899.980 5.6e4 6.4e5 (H) 9.2e6 7.4e4 2906.030 2.6e4 8.2e5 (H) 7.1e5 4.59e9

The simulated external Qs at the FPC are given in the descriptions of Figure 13. These Qs

combine the damping of both FPCs. It reveals, that the FPC waveguides bear the chance to damp

both H and V modes below 1e6 even with the HOM couplers shorted (one exception is the second

H mode (0.5π/7) tilted to the HOM endgroup with Qext=5.6e67).

How well the FPC can absorb the outgoing energy in reality depends on the reflection

response of the transmission line up to the klystron circulator load. We have measured this

quantity over a wide spectral range (30 kHz - 6GHz) for a typical CEBAF transmission line

configuration “as is”. This has been done at an empty slot in the CEBAF tunnel prior to the

installation of a refurbished C50 cryomodule, i.e. at north linac slot 4 (1L04) after removal of the

cryomodule Renascence. A schematic of the setup is shown in Figure 14. The transmission line

consists of a long (~15m) WR650 waveguide (including bellows and bends not illustrated) which is

tapered to the quasi half height WR650 cavity FPC waveguide close to the cryomodule. Using a

Vector Network Analyzer (HP 8753ES) the power was launched at the lower end of the

waveguide close to the nominal cryomodule position via a coaxial-to-waveguide adapter (Figure

14 bottom left). To substract the bandlimited performance of the adapter from the return loss of

the transmission line, the time-domain gating option of the Vector Network Analyzer (option 010)

7 Such a mode can exist in the C100 cryomodule end cavity with the beam tube stepping down close to the cavity. The

corresponding R/Q is still significantly high. Yet we can improve the damping of such modes by using an insert in the

beam tube as proposed further below.

16

has been applied. A waveguide filter is implemented in the transmission line as an integral part of

the original FPC configuration. This component has been designed to filter out harmonics of the

klystron output as well as to provide damping of HOMs [11]. The broadband measurement result

shown in Figure 14 (right) reveals its beneficial effect in a wide spectral range covering the TE111,

TM110, and TM111 passband mode frequencies. Without the filter most of the losses are mainly due

to the circulator and load, optimized specifically around 1.5 GHz to protect the klystron from the

reflected fundamental mode. The attenuation in the WR650 waveguide does not contribute

significantly to the total reflection response and can be neglected (~10 mdB/m estimated at 2.9

GHz).

Figure 14: Schematic to measure the reflection response of the CEBAF FPC transmission line in the accelerator

tunnel (left). Each cavity is powered by an individual klystron and the transmission line configuration is similar

for each cavity. The typical reflection loss of a CEBAF FPC transmission line with and without the waveguide

filter as measured at slot 1L04 (cavity 1) is shown right. The signal has been launched close to the nominal

cryomodule position upwards to the circulator load.

Table 6: Reflection loss (TE10 mode only) in CEBAF transmission line at 2.9 GHz.

reflection loss HOM energy absorbable

dB %

without waveguide filter 10.5 91.0

with waveguide filter 19.3 98.8

The reflection loss obtained at 2.9 GHz is listed in Table 6. A ~20 dB loss can be regarded as a

well optimized HOM absorber and is therefore a very satisfying result.

As explained previously (cf. Figure 11, Figure 12), the coaxial-to-waveguide adapter can not

transmit the TE20 mode effectively. The measured return loss is therefore associated with the TE10

waveguide mode only. The return loss needs to be measured separately for the TE20 waveguide

mode, to which the vertically polarized TM111 modes preferably couple to. A TE10-to-TE20 mode

converter has been designed recently to enable such a measurement. The aim was to maximize the

TE20-mode transmission within 2.8-3.0 GHz by simultaneously suppressing the TE10-mode as far as

possible. The findings are depicted in Figure 15 revealing an acceptable conversion/suppression of

17

the TE20/TE10-mode with a simple waveguide construction. It uses a constant half height WR650

cross-section, so that available adapters can be flanged to the input side. The use of such a

converter is foreseen to characterize the pure TE20-mode return loss of the transmission line and

waveguide filter.

Figure 15: TE10- to TE20 mode converter waveguide (right) optimized for maximum conversion within 2.8-

3.0 GHz (left, red curve) by suppressing the TE10 mode content as far as possible (green curve).

18

4. HOM Survey for a String of Eight Cavities

In the previous section we have shown, that the damping efficiency of the parasitic TM111

dipole modes is affected sensitively on outer beam tube boundary conditions and fabrication

tolerances, which determines the field levels at the location of the HOM couplers and FPCs. Since

the HOM field can be distributed along several cavities, the loaded Q is determined by the

combined losses in all involved HOM couplers and FPCs. It is important to study, how

propagating fields can be reflected to form standing waves within a string of cavities and how this

influences the loaded Q in a cavity depending even on its location in the cryomodule. Neither of

the investigated configurations (HTB or VTA) are fully representative for the final C100

cryomodule cavity arrangement. Consequently, we took the opportunity to perform an HOM

survey for the full cavity string in the upgrade cryomodule “Renascence” recently removed from

CEBAFs north linac. Renascence in its original arrangement comprises three LL (LL001-003) and

five HG cavities (HG001-005) as illustrated in Figure 16 [12]. As in the C100 cryomodule the cavity

orientation is mirrored at the centre of the cryomodule, so that the HOM endgroups of both end

cavities are pointing outwards.

Figure 16: Cryomodule “Renascence” housing intermediate designs of 7-cell upgrade cavities, i.e. three LL seven-

cell and five HG seven-cell cavities.

We have surveyed HOMs up to 3 GHz for all eight cavities in the CMTF at 2K, but will focus

our attention to LL001-003 since the LL cavities have been favored for the 12 GeV upgrade

cryomodules. This includes a cavity (LL001) positioned at the end of the cryomodule. The loaded

Qs measured are depicted in Figure 17. The different passband modes observable are denoted.

High Q modes (1e9 level) either belong to trapped quadrupole or TE011 monopole modes, which

are not relevant for CEBAF. In the following we solely concentrate on the TM111 modes of interest

resonating around 2.9 GHz. The measurements have been carried out initially coupling in from

the FPC with either using WR650 (see Figure 18 left) or half-height WR650 (see Figure 14 bottom

left) coaxial-to-waveguide adapters depending on availability and space constraints. The signal

has been picked up at one of the HOM couplers at the same cavity, whichever yielded the best

signal-to-noise ratio. In Renascence a single warm rf vacuum windows is used in the FPC

waveguide located at the access ports of the cryomodule, where the outer cryomodule

waveguides and adapters have been mounted to. The overall waveguide length has been kept as

short as possible to minimize the amount of interfering waveguide modes.

19

Figure 17: Loaded HOM Qs measured in the HTB at 2K for C100-1 and C100-2 respectively.

As described in section 3, the FPC transmission line can provide an adequate damping of

HOMs coupling to the FPC particular around 2.9 GHz, whereas the type of adapters used are

strongly performance limited.

Figure 18: Measurement setup using absorbing foam (right) instead of an FPC adapter (left) to investigate the

impact on the loaded Q by the FPC transmission line.

To resemble the good HOM absorbing capabilities of the transmission line we have removed

the FPC adapters and inserted Eccosorb [13] absorbing foam elements in the waveguide section

outside the cryomodule (Figure 18). These have been cut in shape to fully cover the cross-section

of the waveguides. The first five cryomodule cavities have been equipped with the foam. In this

configuration the power was launched in from the HOM coupler endgroup of the cavity under

investigation and extracted at the HOM coupler endgroup of an adjacent cavity. The transmission

signal between HOM couplers at the same endgroup typically suffers from crosstalk effects. The

loaded Qs of the first five modes observable around 2.9 GHz - appearing after a broad stopband

20

beyond the trapped TE011 modes with comparably high Qs - are tabulated below both before and

after insertion of the absorbing foam.

Table 7: First five TM111 passband modes measured around 2.9 GHz in LL001, LL002 and LL003

respectively either with the FPC adapters or with absorbing foam inserted in the FPC waveguides

of all involved cavities.

with FPC adapters LL001 LL001 LL002 LL002 LL003 LL003

temp. = 2K frequency Ql frequency Ql frequency Ql

date: May 2009 MHz MHz MHz

2913.895 6.3e6 2917.727 2.1e5 2916.113 1.0e6

2915.105 1.8e7 2919.320 4.6e5 2917.576 4.4e4

2920.919 3.9e4 2920.961 4.8e4 2918.179 2.6e4

2921.390 9.2e5 2921.250 6.2e4 2921.243 2.8e4

2921.741 9.9e5 2921.393 6.2e5 2921.794 1.7e5

with absorbing foam LL001* LL001 LL002** LL002 LL003*** LL003

temp. = 2K frequency Ql frequency Ql frequency Ql

date: May 2009 MHz MHz MHz

2913.387 1.7e6 2917.718 8.2e4 2916.081** 7.6e3**

2915.083 1.1e6 2919.319 1.7e5 2916.104 3.3e4

2920.939 6.0e4 2920.936 5.9e4 2917.104 7.0e4

2921.357 1.0e5 2921.221 3.5e4 2917.609 7.1e4

2921.739 8.2e5 2921.776 1.3e5 2917.996 6.2e4

* measured from HOM endgroup of LL002 to HOM endgroup of LL001

** measured from HOM endgroup of LL003 to HOM endgroup of LL002

*** measured from HOM endgroup of HG001 to HOM endgroup of LL003

Following the arguments on mode identification in section 3 - eventually verified by bead-pull

measurements - we proclaim that the V/H TM111 π/7- and 2π/7-modes are among these

resonances. The measured Qs then can be drawn against the maximum allowable Qs according to

Table 4 as done in Figure 19 (black and red lines).

Figure 19: Loaded Q values of the first five observable TM111 modes around 2.9 GHz before (left) and after

inserting absorbing foam in the FPC waveguide outside the cryomodule.

It shall be noted, that similar to the HTB measurements we have observed crosstalk effects

between cavities in several cases such that resonances could not purely attributed to one cavity. In

none of the cases we have observed overcoupled external ports. This clearly indicates the

21

propagating field character of the modes, so that the combined losses in the cavity string dominate

over the individual external losses at the HOM couplers or the FPC port of the cavity under

investigation. The damping via the FPC port(s) thus can be crucial if the HOM couplers can not

provide a sufficient suppression. This is revealed clearly in Figure 15 particularly for the end cell

cavity. After inserting the absorbing foam, critical modes with Qs in the 1e7 level could be

lowered below the threshold specified for the baseline physics at 12 GeV. Whereas the HOMs in

LL002 and LL003 satisfy both specifications with a reasonable safety margin, the HOMs in LL001

are close to the threshold evaluated for a beam current of 400 µA at 6 GeV (two recirculating

passes).

The results above indicate - although lacking from good statistics among different

cryomodules - that the end cavities in a cryomodule can exhibit elevated Qs due to their peculiar

location sharing less external ports with neighbouring cavities than all other cavities in the string.

The C100 end cavity configurations are depicted in Figure 20. The boundary conditions are similar

on both sides with identical gate valves attached to the cavity end flanges and a subsequent step

down of the beam tube to a smaller diameter (∅ = 1.37”).

Figure 20: C100 cryomodule end cavity configurations.

The lateral beam tube lengths in this configuration are different from the measurements

performed in the HTB or VTA. The field level of a propagating TM111 mode at the HOM endgroup

is fixed by the standing mode pattern obtained depending on the beam tube length including the

section of the gate valve up to the ∅ = 1.37” tube, which acts as a rather sharp reflection plane. In

such a configuration we have observed comparably high Qs for LL001. The external Qs measured

for both HOM couplers of LL001 ranged from 4.3e6 to as high as 6.7e9 among the modes in Table

7. However it has to be pointed out, that other than in the final C100 design, the Renascence LL

cavities exhibit an intermediate HOM endgroup layout with different angular orientations of

coupler hooks and probe tips as well as a shorter distance of the cans to the cavity end cell (see e.g.

ref. [1] Figure 3).

We have performed numerical studies to look into the feasibility to enhance the coupling of the

TM111 π/7-mode to the HOM endgroup with a minor design change of the C100 end cavity

configuration. The aim was to alter the reflection plane at the outer boundary (Figure 21 left) in

order to enhance the field amplitudes at the HOM coupler position such to minimize the external

Q at the HOM couplers. In this principal study a cylindrical beam tube insert has been used to

show the effect on the external Qs merely varying the length of the insert L with respect to the

22

cavity flange. The insert used here reduces the inner cavity tube diameter from 70 mm to 60 mm

increasing the TE11 cutoff from 2.51 GHz to 2.92 GHz, i.e. slightly above the TM111 π/7 mode

frequency. To evaluate the external Q of the HOM couplers we needed to employ the Finite

Element Analyses (FEA) Code Omega3P [14] rather than MWS in order to discretize the complex

HOM coupler details with sufficient resolution (Figure 21 right). Omega3P also yields the chance

to evaluate the external Q at the coaxial output ports ending arbitrary in space as a major

advantage to MWS.

Figure 21: Proposed insert (left) to lower the Q for the parasitic H/V TM111 π/7 modes for the cryomodule end

cavity. The insert elevating the TE11-mode beam tube cutoff frequency from nominally 2.51 GHz to 2.92 GHz.

Omega3P has been used to calculate the external Q of the C100 HOM coupler(s). The finite element meshing of

the HOM endgroup is shown on the right side revealing the coupler hook and probe tip within an HOM can.

The Qext variation for the H TM111 π/7 mode is shown in Figure 22 in dependence on L. The

length L is positive when the insert is passing over the cavity flange as shown in Figure 21 left.

The Qext spans about four orders of magnitude. The repetitive pattern of the local maxima and

minima follows approximately half the guide length in the cavity beam tube at 2.9 GHz

(~103 mm). The outcome is promising as the external Q could be lowered down to the 1e4 level.

Further studies are under way, which will include the convergence of results with mesh cells and

will eventually focus on the realization of a feasible mechanical design just changing the diameter

of the end tube behind the gate valve (see Figure 20).

Figure 22: Loaded Q variation by changing the position of a cylindrical insert in the beam tube of the cryomodule

end cavity. The length L is given with respect to the cavity end flange and positive when the insert is passing over

the cavity flange as shown in Figure 21 left, otherwise negative. The beam tubes on both sides are electrically

shorted. The tube lengths are fixed but have been chosen wisely on both sides to coincide with the minima of the

electrical field pattern evaluated for a center cavity within a string of three detuned cavities. The electrical shorts

therefore have minimum influence on the cavity mode well resembling the fields expected within a string of

cavities.

23

5. Summary and Outlook We have analyzed extensive experimental data of HOM surveys carried out for currently

available upgrade seven-cell Low Loss cavities in different cryogenic configurations comprising

measurements for individual cavities in vertical Dewars and for a cavity-pair in a dedicated

upgrade style quarter cryomodule. We have unambiguously identified transverse beam break-up

(BBU) critical TM111 passbands modes resonating around 2.9 GHz far above the beam tube cutoff

(2.51 GHz). Whereas for TE111 and TM110 passband modes -trapped within the cavity -

experimental conditions can be guaranteed representing the final 12 GeV cryomodule

environment, the propagating TM111 modes can vary their fields at the HOM coupler position

depending sensitively on boundary conditions. To forecast the damping efficiency in a final

configuration more realistically, we have recently performed HOM Q measurements for a string

of eight cavities in the upgrade cryomodule “Renascence” housing three Low Loss and five High

Gradient type cavities. Hereby we have focused our attention on the most critical TM111 π/7-like

mode pair in the Low Loss cavities. We have shown that the loaded Q of the HOMs in a string of

cavities depends on the combined rf losses in multiple cavities governed by all participating

external ports. This includes - apart from losses in the HOM couplers - the losses in the

fundamental mode power coupler (FPC) transmission line, hence serving doubly duty. Verified by

numerical calculations, the horizontally polarized TM111 modes prefer to couple to the first TE10

waveguide mode in the FPC (cutoff is 1.1 GHz), the vertically polarized modes to the TE20

waveguide mode (cutoff is 2.2 GHz). The cryomodule end cavities take a peculiar position since

less external ports are available compared to the inner cryomodule cavities. In fact, the loaded Qs

of the TM111 π/7-like mode pair measured for such a cavity were significantly elevated. We have

verified - particular for this cavity - that the losses in the FPC play a crucial role. By using low

power absorber material in the open waveguide ends of the FPC we could reduce the Qs of the

critical modes below the BBU baseline threshold for the 12 GeV upgrade project. A measurement

in the CEBAF tunnel revealed that the transmission line in fact serves well to absorb modes

around 2.9 GHz when using waveguide filters outside the cryomodule (~19dB reflection loss).

This is true for the TE10 waveguide mode and still needs to be verified for the TE20 mode, for which

a special mode converter has been designed to conduct the measurement.

Furthermore, to improve the HOM damping specifically for the cryomodule end cavities, we

have proposed to slightly change the end tube configuration with the potential to improve the

coupling to the HOM endgroup considerably. A mechanical design is under development that

will have a minimal impact on the existing cryomodule tube layout.

24

6. Acknowledgement Our thanks go especially to Kirk Davis and Christiana Grenoble for their experimental support

throughout the rather tedious HOM survey of the Renascence cavities.

25

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[10] K. Halbach, R.F. Holsinger, SUPERFISH, Published in Particle Accelerators 7: 213-222, 1976.

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