Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP30

MULTI-CAVITY FIELD EMISSION AT STF-2 ACCELERATOR IN KEK
P. Joshi∗1 , T. Matsumoto1,2 , S. Michizono1,2 , Y. Yamamoto1,2 , T. Oyama1,2
1 SOKENDAI (The Graduate University for Advanced Studies), 240-0193, Hayama, Japan
2 KEK (High Energy Accelerator Research Organization), 305-0801, Tsukuba, Japan

Abstract
In December 2022, an experiment was conducted in an
STF-2 accelerator to measure neutron and gamma radiationlevels both upstream and downstream by tuning eight cavities with an average gradient of 31 MV/m. The model was
evaluated to understand the measured data. In this model,
the electrons generated by field emission (FE) are accelerated through multiple cavities applied and discussed. The
key finding emphasized the dominance of multi-cavity FE
over a single cavity based on the FE number, FE point, selfcavity loss, adjacent cavity loss, tune loss, and detune loss
according to the tuning and detuning of the cavity.

INTRODUCTION
The superconducting RF test facility (STF) of the HighEnergy Accelerator Research Organization (KEK) is a facility for the R&D of the technologies of the International
Linear Collider (ILC) main linacs [1]. These include R&D inradio frequency (RF) production, RF distribution, superconducting (SC) cavities, and cryomodules. The STF-2 L-band
photocathode RF gun serves as an injector for the two SC
cavities in a capture cryomodule, eight SC cavities in CM-1,
and four SC cavities in CM-2a [2]. The RF power for the 12
SC cavities is generated using a 10 MW pulsed multibeam
klystron (CETD Co. Ltd, E3736H) [3]. Different modelsof the local power distribution systems developed at STF
are installed in STF-2. Table 1 summarizes the operationalparameters of the STF-2 accelerator.
Table 1: STF-2 Accelerator Operational Parameters in 2022
Parameters

Value and Unit

Operational frequency
Accelerating mode
Average gradientRF pulse width
Pulse repetition rate
Beam energy
Bunch spacing
Bunch charge
Bunch current
Operational temperature

1.3 GHz𝑇 𝑀010 , 𝜋-mode
31 MV/m
1.65 ms
5 Hz≈400 MeV
6.15 ns
35.7 pC
5.8 mA
2K

EXPERIMENT
Four cavities of CM-1 and four cavities of CM-2a wereused in the experiment of FE. To measure the radiation, a neutron counter and gamma detector were placed downstream
and upstream, respectively, as shown in Fig. 1. The gate
valves on both sides remained closed, and the SC quadrupole
magnet between CAV#4 and #5 was shut down during theexperiments. The radiation level on the downstream side
was measured as the average accelerating gradient of theeight cavities increased from 18 MV/m to 31.5 MV/m. Furthermore, the radiation level was measured on both sides bytuning and detuning the individual cavities, maintaining an
average gradient of 31 MV/m.

Figure 1: Position of the neutron counter and gamma detector in the schematic of the STF-2 accelerator.

MEASUREMENTIn Figs. 2 and 3, the dark blue colored bar shows theradiation detected when all the cavities were tuned, andthe green colored bar shows the radiation level when thecavity was detuned. The fluctuations in the blue bar indicate
probable statistical and instrumental errors.

Downstream

Field emission (FE) plays a major role in the degradationof SC cavity performance [4]. The effect of the FE on theperformance of the cavity can be understood from the relationship between the quality factor, X-ray, and accelerating
gradient [5]. When several cavities are operated, identifying∗ prakashj@post.kek.jp

the contribution of FE by each cavity becomes more complex. Therefore, a model is considered to understand the FEof an individual cavity (CAV#) and its contribution to thetotal FE during the multi-cavity operation.

When CAV#12 was detuned, FE decreased significantly,
whereas on detuning CAV#11, FE also decreased significantly. The magnitude increased gradually on detuning
cavities from #12 to #8, as shown in Fig. 2. The magnitudeof radiation is the sloped line from the detuning of CAV#12,#11, #10, #9, and #8 to all tuned cavities, as shown in Fig. 2.
The magnitude of gamma radiation is approximately fourtimes that of neutrons, as shown in Fig. 2. The radiation- 572 -

Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP30

level remained the same for the detuning CAV#1, #2, and#5, as shown in Fig. 2.

The magnitude of radiation on the upstream side wasminimal compared to that on the downstream side. Upon
detuning CAV#10, the radiation level is significantly higher
than those of the others, as shown in Fig. 3. In addition,
there was a high FE for detuning CAV#5. The difference inthe gamma and neutron radiation levels is small, as shownin Fig. 3.

Single Cavity
Table 2 shows the FE for single cavity operation when adetector is placed just below each cavity. The cavity gradientduring the multi-cavity operation is listed in Table 2.
Table 2: X-ray Dose below each Cavity during Single Cavity
Operation [6]Cavity
1
2
5
8
9
10
11
12

Figure 2: (a) Measured data of gamma radiation downstream
when cavities were tuned and detuned individually. (b) Measured data of neutron radiation downstream when cavities
were tuned and detuned individually.

Gradient (MV/m)

X-ray (𝜇Sv/hr)

29.0
31.0
35.0
30.9
33.4
30.9
29.8
28.2

20
180
820
5,540
3,480
340
90
7,000

ANALYSIS OF MEASUREMENT
The data is analyzed based on the following assumptions:First, the FE number, FE point, self-cavity loss, and adjacentcavity loss are distinct for each cavity, upstream and downstream. The tune loss is the same for all tuned cavities, andthe detune loss is the same for all detuned cavities. Here the
FE number is the assumed number of emitted electrons froma cavity, and the FE point is the assumed most probable pointof FE, whose value ranges from 0 to 1, as shown in Fig. 4.
The self-cavity loss is the fraction of electrons lost inside
the field-emitting cavity, whereas the adjacent cavity loss isthe fraction of electrons lost in the neighboring cavity. The
tune loss is the fraction of electrons lost in a tuned cavity,
whereas the detuned loss is the fraction of electrons lost in
the detuned cavity. Second, the irises are considered as FE
points, as shown in Fig. 4 [7].

Upstream

Figure 4: Assumed field emission point for each cavity. Because the dose below CAV#10 and #11 is small, two fieldemission point is considered.
Figure 3: (a) Measured data of gamma radiation upstream
when cavities were tuned and detuned individually. (b) Measured data of neutron radiation upstream when cavities weretuned and detuned individually.

Third, when electrons are emitted from any cavity,
self-cavity loss is applied in the first, adjacent-cavity loss inthe second, and tune or detune loss in the third according to- 573 -

Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP30

the tuning and detuning of the cavity. The survived electrons are stopped at the gate valve. Finally, the X-ray dose
below each cavity is due to FE particles lost inside the cavity.
In general, the phase of the following cavity is delayed
relative to that of the previous cavity by +90◦ (5.75𝜆0 =1326mm) on the downstream side. Therefore, the emitted electrons are either lost by collision with the cavity surface or
accelerated downstream, as shown in Fig. 5. The operating
cavities are in the decelerating phase on the upstream side,
as shown in Fig. 5. However, electrons are accelerated inboth directions for CAV#5 and #2 because of the 180-degree
phase difference between CAV#4 and #5, as shown in Fig. 6.
In upstream, CAV#1 to #8 behaves as detuned cavities for
CAV#9 to #12 because of the 45◦ phase relationship between
CAV#8 and #9, as shown in Fig. 6. The spacing between thecavities is shown in Fig. 6.

Figure 6: Spacing between the STF-2 cavities. Operated
cavities are numbered on the cryomodule and the spacing
between cavities is in mm.
There was a loss of electrons in the non-operated cavities,
which is referred to as the detune loss. The space between
CAV#4 and #5 behaved as a detuned cavity. Furthermore,
the radiation level decreased with the square of the distance
between the source and the detector.
There were three measured data, including the radiationlevel on the downstream and upstream sides and the
X-ray dose below each cavity. The parameters used tounderstand multi-cavity FE were considered based on thethree measured datasets. The self-cavity loss varies withthe emission point, as shown in Fig. 7. The dose produced
due to self-cavity loss was optimized using the measured
data. The percentages of electrons directed downstream andupstream also differ according to the location of the FE
point, as shown in Fig. 7.
In Fig. 7, for emission point A, the self-cavity loss issmall with a high adjacent cavity loss, and the electrons are
directed upward. At emission point B, the electrons weredirected downward, with maximum loss inside the cavity.
At emission point C, all FE were trapped inside the cavity.

Figure 7: An example illustrating the variation in self-cavity
loss and adjacent cavity loss with changes in the emitter
point for the same iris located between cells 3 and 4 [8].

Figure 5: The figures show the variation in the direction of
the electric field with time. (a) Acceleration of electrons
when moving from Line 1 to Line 3 downstream. (b) Deceleration of electrons when moving from Line 1 to Line 3
upstream.

The X-ray dose produced by a cavity depends on the number of lost electrons and the energy of the electrons, which
can be calculated using the following relations:Downstream dose ∝ [(1-FE point)*Gradient]*Lost FE number, and Upstream dose ∝ [FE point*Gradient]*Lost FE
number, then Dose below a cavity = Downstream dose + Upstream dose. The lost FE number measures different typesof losses such as self-cavity loss, adjacent cavity loss, tune
loss, and detune loss.

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Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP30

Calculation for Model in case of Cavity 8
Suppose the FE point located on the iris between cells 5
and 6, i.e., 0.55, contributes to the total dose below theCAV#8. The assumed FE number for CAV#8 in downstream is 375, of which 95% are lost in the cavity itself
after gaining energy from 4 cells that produce a dose of
4,950 [(1-0.55)*30.9*(375*0.95)], as shown in Fig. 8. Furthermore, 70% of the surviving particles (70% of 19) arelost in the adjacent CAV#9 after gaining energy from 4
cells of CAV#8 and all cells of CAV#9 that produces a doseof 629 [[(1-0.55)*30.9+33.4]*(19*0.70)] when CAV#9 istuned, as shown in Fig. 8. Furthermore, when CAV#9 is
the detuned dose by adjacent cavity loss becomes 185 [[(10.55)*30.9]*(19*0.70)]. In the following cavities, either atune loss of 5% or a detune loss of 10% is applied according
to the tuning and detuning of the cavity. The lost particles
produce FE, and finally, the surviving particles are stopped
at the gate valve, emitting radiation.

producing a dose of 3,580, as shown in Fig. 9. If CAV#5
is detuned, the electrons travel with the same energy,
experiencing detune losses in each cavity and the space
between CAV#4 and #5 and decelerate at CAV#2 with theemission of radiation, as shown in Fig. 9.
The cumulative dose, the sum of the upstream and downstream doses, is 5,502 (Figs. 8 and 9), which almost matches
the measured data (Table 2) in magnitude. The large number of electrons lost on the downstream side and the small
number on the upstream side are determined based on the
X-ray dose measured on the upper and lower sides of theoperating CAV#8. In the downstream, electrons either movewith the same energy and detune loss or accelerate with atune loss. In the upstream, the electron either moves with adetune loss or decelerates the FE from CAV#8.

COMPARISON
Measured and Modeled Data
The modeled data is optimized based on the measured
data of the X-ray dose below each cavity, multi-cavity FE on
downstream and upstream, and the assumptions. The violet
bars in Fig. 10 show the measured gamma radiation dataon the downstream and upstream sides, respectively. The
rust color bars in Fig. 10 represent the modeled data on thedownstream and upstream sides, respectively.

Figure 8: Schematic of losses in the downstream of cavity-8.
(a) Considered types of losses with cavity number. (b) The
magnitude of loss and its contribution to field emission.

Figure 9: Schematic of losses in the upstream of cavity-8.
(a) Considered types of losses with cavity number. (b) The
magnitude of loss and its contribution to field emission.
The assumed FE number for CAV#8 upstream is325, of which 10% is lost in the cavity itself after gaining energy from five cells that produce a dose of 552[0.55*30.9*(325*0.10)], as shown in Fig. 9. Furthermore,
20% of the surviving particles (20% of 293) are lost in
CAV#7 as an adjacent cavity loss, producing a dose of 995[0.55*30.9*(293*0.20)], and the survived particles movewith the same energy, as shown in Fig. 9. The detune loss
is applied in CAV#6, which is a non-operated cavity. If
CAV#5 is tuned, all surviving electrons are decelerated by

Figure 10: Comparison between measured data and modeled
data. (a) Downstream (b) Upstream
The ratio of the measured downstream and upstream datais the same as that of the modeled downstream and upstream
data, as shown in Fig. 10. The nature of the graph for modeled and measured data is the same for upstream and downstream, as shown in Fig. 10. The first bars in Fig. 10 show
eight cavities tuned cases, and the number on the bar indicates that the cavity is detuned.

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Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 WEP30

Multi-cavity and Single Cavity FE
The FE increases exponentially with an increase in theaccelerating gradient in 9 cell SC cavities [9]. CAV#12 is
the most contaminated cavity with the lowest accelerating
gradient, as shown in Fig. 11. However, CAV#9 exhibits thebest performance with a maximum operational accelerating
gradient of 36 MV/m and a small FE, as shown in Fig. 11.
The measured value of gamma radiation due to multi-cavity
FE is approximately twice that of the most contaminated
CAV#12. This relationship remains consistent in modeled
data. Hence, multi-cavity FE enhances gamma radiation.

tions. According to the model, the maximum number ofelectrons was lost in the field-emitting cavity and then in theadjacent cavity, and the loss was small in the following cavity. The surviving electrons were stopped at the gate valve.
In the downstream, the survived electrons were accelerated
by the succeeding cavities. Therefore, the contribution of
the following cavity to the field emission was higher. This
was the reason for high field emissions on the downstreamside. The radiation level on the upstream side was small owing to the deceleration of electrons in the preceding cavity
and small field emission from CAV#1. Furthermore, when
CAV#10 was detuned, the field emission from CAV#11 wasaccelerated in #9 and survived up to the gate valve with adetuning loss in CAV#8 to #1. Thus, the field emission was
high. Additionally, the measured data indicated the dominance of multi-cavity field emissions over a single cavity,
which matched the modeled data. Finally, a model prepared
to understand multi-cavity field emission based on theseassumptions almost satisfied the measured data. Thus, themodel could explain the phenomenon that occurred inside
the superconducting cavity.

ACKNOWLEDGEMENTS
I am thankful to Kazuya Ishimoto, Naoto Numata, andTaiga Hanawa of the NAT group for their help with theexperimental setup and measurements.

REFERENCES[1] ILC, https://linearcollider.org[2] STF-KEK, https://www2.kek.jp/stf/[3] https://etd.canon/en/product/category/microwave/klystron.html

Figure 11: (a) Comparison between the measured data of
gamma radiation for single and multi-cavity field emission
with increasing accelerating gradient. (b) Comparison between the measured data of neutron radiation for single andmulti-cavity field emission with increasing accelerating gradient.

[4] B. Bonin, “Field emission in RF cavities”, Atomic Energy
Commission, DSM/DAPNIA, France. https://cds.cern.
ch/record/399571/files/p221.pdf

The measured value of the neutron radiation due to themulti-cavity FE is approximately four times the FE due to
CAV#12 at an accelerating gradient of 28 MV/m, as shown in
Fig. 11. The multi-cavity FE enhances the neutron radiation,
which is higher than gamma radiation because energetic electrons striking the metal surface produce neutrons, and theenergy of electrons is higher in the multi-cavity FE than ina single cavity. Among the single cavities, the neutron number increases significantly for CAV#12, as shown in Fig. 11.
This implies that most of the electrons are accelerated in
multiple cells in this cavity.

[6] Yasuchika Yamamoto et al., “Report on the operation of STF-2
cryomodule for ILC”, 20th Annual Meeting of the Accelerator
Society of Japan, Funabashi, Aug. 29 - Sep. 01, 2023, THP58.

SUMMARY[9] Yasuchika Yamamoto et al., “Stable beam operation at 33
MV/m in STF-2 cryomodule at KEK”, 20th International Conference on RF Superconductivity, East Lansing, USA, May
2021, pp. 382-386.

The multi-cavity field emission was analyzed using amodel based on single-cavity field emission and assump-[5] Yasuchika Yamamoto et al., “Achievement of stable beam
operation at 36 MV/m in STF-2 Cryomodules at KEK”, 18th
International Conference on RF Superconductivity, Lanzhou,
China, July 2017, pp. 722-728.

[7] Enrico Cenni, “Field emission study on CW superconducting cavity”, Ph.D. Thesis, Acc. Science Dept., The Graduate
University for Advanced Studies, SOKENDAI, Japan, 2013.
https://ir.soken.ac.jp/records/4901[8] Hiroshi Sakai et al., “Field emission studies in vertical test and during cryomodule operation using precise
X-ray mapping system”, Physical Review Accelerators
and Beams 22, 022002, 2019. doi:https://doi.org/10.
1103/PhysRevAccelBeams.22.022002- 576 -