# An approach to interfacing the brain with quantum computers: practical steps
and caveats

E. R. Miranda<EMAIL_ADDRESS>ICCMR, University of Plymouth,
Plymouth, UK  S. Venkatesh  ICCMR, University of Plymouth, Plymouth, UK  J. D.
Martin-Guerrero  C. Hernani-Morales  IDAL, Electronic Engineering Department,
ETSE-UV, University of Valencia, Valencia, Spain  L. Lamata  Department of
Atomic, Molecular and Nuclear Physics, University of Seville, Seville, Spain
E. Solano  QuArtist, Physics Department, Shanghai University, Shanghai, China
Ikerbasque, Bilbao, Spain  Kipu Quantum, Munich, Germany

###### Abstract

We report on the first proof-of-concept system demonstrating how one can
control a qubit with mental activity. We developed a method to encode neural
correlates of mental activity as instructions for a quantum computer. Brain
signals are detected utilising electrodes placed on the scalp of a person, who
learns how to produce the required mental activity to issue instructions to
rotate and measure a qubit. Currently, our proof-of-concept runs on a software
simulation of a quantum computer. At the time of writing, available quantum
computing hardware and brain activity sensing technology are not sufficiently
developed for real-time control of quantum states with the brain. But we are
one step closer to interfacing the brain with real quantum machines, as
improvements in hardware technology at both fronts become available in time to
come. The paper ends with a discussion on some of the challenging problems
that need to be addressed before we can interface the brain with quantum
hardware.

##  I Introduction

In a recent perspective paper [1], we proposed the concept of Quantum Brain
Networks (QBraiNs) as an emerging interdisciplinary endeavour, integrating
knowledge and methods from neurotechnology, artificial intelligence (AI), and
quantum computing (QC). The objective of QBraiNs is to establish direct
communications between the human brain and quantum computers. We foresee the
development of highly connected networks of wetware and hardware devices,
processing classical and quantum computing systems, mediated by Brain-Computer
Interfaces (BCI) and AI. Such networks will involve unconventional computing
systems and new modalities of human-machine interaction.

This paper introduces a first attempt at controlling a qubit with mental
activity. We developed a proof-of-concept system, which demonstrates how a
person can rotate and measure a qubit using brain signals.

However, due to limitations imposed by currently available quantum computing
hardware and brain sensing technology, our proof-of-concept runs on a software
simulation of a quantum computer. Nevertheless, we are one step closer to
interfacing the brain with real quantum machines, as improvements in hardware
technology at both fronts become available in time to come.

We invented a method to encode neural correlates of mental activity as
instructions for a quantum processor. Brain data are read utilising electrodes
placed on the scalp of a person, who learns how to produce the required mental
activity to issue instructions to rotate and measure a qubit.

By way of previous related work, Kanas et al. [2] hinted at the possibility of
interfacing the brain with quantum computers. Other speculative propositions
were put forward by Pesa and Zizzi [3] and Musha [4]. However forward-thinking
as these works may sound, none of them present a concrete experiment or
demonstration to support their cases. To the best of our knowledge, the first
ever practical demonstration of BCI using quantum computing was reported by
Miranda [5].

The goal of our research is to go a step beyond using quantum computing to
analyse brain signals for controlling devices, such as a robot, a vehicle, or
a musical instrument, as introduced in [5]. Rather, here we envisage the
possibility of forging deeper connections between brains and quantum
computers. The ultimate goal is to be able to affect the states of quantum
computers with the mind.

##  II Codes of Brain Activity

The Homo sapiens’ brain is one of the most complex systems known to science.
It has circa one hundred billion neurones forming a network of quadrillions of
connections [6]. The amount of information that circulates through this
network is, although probably bounded, immense. Essentially, neurones are
electrical entities. They communicate with one another through action
potentials and chemical neurotransmitters. These action potentials are often
referred to as spikes.

There exists technology nowadays to record neural communication at various
levels: from the microscopic level of neurone-to-neurone communication, to
higher levels of communication between networks of neurones. Unfortunately,
most of this technology is impractical for deployment outside highly
specialised research laboratories. At the same time, the engineering to
develop sensors made with bioelectronics and nanomaterials is progressing fast
to improve this scenario [7].

Even though sensing technology is becoming increasingly sophisticated, the
understanding of the meaning of sensed signals remains very problematic. We
may be able to detect neural signals fairly accurately nowadays, but we would
not necessarily know what they mean. For instance, it is not hard to render
sequences of spikes as sequences of binary numbers for a digital computer to
process. But we would have very little clues about what the neurones are
communicating to each other. Of course, AI can provide solutions here, as is
the case of the machine learning (ML) algorithms for neural decoding
introduced in [8].

A widely used method for reading electrical brain activity is to use
electrodes placed on the scalp of a person (Fig. 1). This recording is called
the electroencephalogram, or EEG [9]. There is a plethora of different EEG
recording systems commercially available. They are of varying reliability; the
low-cost ones usually relay more spurious signals than actual EEG. It is also
possible to record electrical brain activity with electrodes surgically
implanted under the skull, on the surface of the cortex, or deep inside the
brain; e.g., electrocorticography (ECoG) [10]. Surgically implanted electrodes
provide substantially better signals to work with than scalp electrodes. But
brain implants are not routinely used in research with humans at present for
obvious health and safety reasons111Other technologies for brain scanning
include functional Magnetic Resonance Imaging (fMRI), near-infrared
spectroscopy (NIRS), and magnetoencephalography (MEG). However, these are
prohibitively expensive, less portable, and (by the time of writing) offer
inadequate time-resolution for BCI purposes..

Figure 1: Brain activity can be read using electrodes strategically placed on
the human scalp.

###  II.1 The electroencephalogram

For this project, we adopted scalp EEG. We used an affordable off-the-shelf
mid-range device manufactured by g.tec, Graz, Austria222https://www.unicorn-
bi.com/. It consists of a cap furnished with electrodes and a transmitter that
relays the EEG wirelessly to a computer.

The standard scheme for positioning electrodes on the scalp is shown in Fig.
2. The terminology for referring to the positioning of the electrodes uses
letters to indicate a brain region and a number: Fp (pre-frontal), F
(frontal), C (central), T (temporal), P (parietal) and O (occipital). Odd
numbers are for electrodes on the left side of the head and even numbers for
those on the right side; the letter “z” stands for the central region. For
this project, we used eight electrodes (i.e., eight EEG channels) positioned
at F8, F7, Cz, Pz, C4, C3, T6 and T5, respectively.

Figure 2: Widely used scheme for positioning electrodes for EEG recording.

Power spectrum analysis is a popular method to extract information from EEG.
This method breaks the EEG signal into different frequency bands and reveals
the distribution of power between them. Power spectrum analysis is widely used
in BCI research because it reveals patterns of brain activity that can be
recognised automatically and translated into commands for a system. Research
exploring the mental correlates of EEG usually considers spectral components
up to 40 Hz [11]. There are four recognised spectral frequency bands, or EEG
rhythms, each of them associated with specific mental states (Table 1).

Frequency Bands | Rhythms | Mental States
---|---|---
$f<4$ | delta | Sleep
$4\leq f<8$ | theta | Drowsiness
$8\leq f<15$ | alpha | Low arousal; unfocused; relaxed
$15\leq f<40$ | beta | High arousal; focused; excited
Table 1: Typical EEG rhythms and associated mental states. Frequency bands are
expressed in Hertz (Hz).

###  II.2 Encoding method

We developed a simple method to encode EEG as instructions to rotate a qubit.
The method takes into account two mental states: low arousal (a.k.a. relaxed)
and high arousal (a.k.a. excited). However, to control the qubit, we need at
least four different instructions. As the number of instructions is greater
than the number of mental states, we sequentially relayed instructions to the
system through unique ‘brain codes’. These are Morse-like binary codes.

As shown in table 2, there is a unique brain code associated with each
instruction, where 0 and 1 correspond to relaxed and excited mental states,
respectively. The instructions are as follows:

  * •

{0, 1}: This is the instruction to start the program, which initializes the
connection with the quantum system. None of the other instructions would work
without this initialization.

  * •

{1, 1}: This instruction increases the angle of rotation, by a pre-defined
amount.

  * •

{0, 0}: This instruction decreases the angle of rotation, by a pre-defined
amount.

  * •

{1, 0}: This instruction has two functions. When it occurs for the first time,
it changes the axis of rotation on the Bloch sphere (Figure 3), from $z$
(vertical axis) to $y$ (horizontal axis), and vice-versa. Then, when it occurs
for the second time, the system measures the qubit.

Command | Brain Code | Description
---|---|---
Start program | {0, 1} |  | A relaxed state followed by
---
an excited state. This
initializes the connection
with the quantum computer.
Increase angle | {1, 1} |  | An excited state followed by
---
another excited state. This
increases the angle of rotation.
Decrease angle | {0, 0} |  | A relaxed state followed by
---
another relaxed state. This
decreases the angle of rotation.
| Change axis or
---
measure
{1, 0} |  | An excited state followed by
---
a relaxed state. On its first
occurrence, it shifts the axis
of rotation. On its second
occurrence, it measures the
qubit.
Table 2: Different instructions passed to the quantum computer through unique
brain codes.

##  III Machine Learning

Section II already hinted that the task of establishing what brain signals
mean is a fiendish problem. And the fact that the EEG signal is very noisy
makes this even more complicated.

The EEG signal captured by surface electrodes is severely distorted by
cortical fluids, the meninges333These are membranes that envelop the brain.,
the skull, skin and hair; sometimes even the type of shampoo one uses to wash
their hair with can cause problems. The signal is unreliable, even to identify
only two different classes of mental states. Hence, we use machine learning to
harness the capability of the system to identify them.

In order to teach the system to classify between two states of mind, we need
to compile a training set with labelled data produced by the user.

First of all, the system has to be calibrated for the specific user. And this
person needs to train themselves how to produce EEG corresponding to relaxed
and excited mental states, respectively [12]. For instance, closing the eyes
is one of the easiest and most pragmatic ways to induce the brain to produce
(‘relaxing’) alpha rhythms. Once the user has practised how to achieve a
relaxed state of mind, then this is effortlessly achievable with the eyes
open. People who are trained in meditation techniques (e.g., yoga) are able to
produce alpha rhythms with ease. Beta rhythms can be produced by imagining, or
remembering, a stressful situation. Mentally solving a puzzle or a
mathematical problem can induce the brain to produce (‘exciting’) beta
rhythms.

Once the user has rehearsed to switch between the two states of mind, then
samples of EEG signals corresponding to the respective states are recorded to
form a training data set for the classifier. Next, we perform short-time fast
Fourier transform (FFT) analysis on each sample to calculate their average
power in the alpha and beta frequency bands. These values are used as features
to teach the samples’ profiles to a machine learning algorithm.

For the machine learning, we adopted the $k$-Nearest Neighbors (kNN) method.
We implemented this using the scikit-learn Python library version
1.0.1444https://scikit-learn.org/stable/. kNN is a supervised machine learning
method widely used for classification and regression [13]. In the case of
classification, it is based on assigning a class (or label) to a given sample,
to which most of its $k$ neighbours (in a given metric space) belong to.

The sample data set was split into two subsets, a training and a test set,
respectively. The former is used for the calculation of distances (Eq. 1). And
the latter is used to simulate how the system would work in a real
environment.

$d_{ij}=||\mathbf{x_{i}}-\mathbf{x_{j}}||$ (1)

In particular, kNN calculates the distance from each sample in the test set to
the samples of the training set. Then, distances are ordered from smallest to
largest, and the $k$ closest samples are selected. The next step involves
querying the labels of the selected $k$ samples. As we are dealing with a
classification problem, a voting strategy is used to decide the class of the
test sample; i.e., the most voted label is used as the selected class.

The degrees of similarity between the samples are calculated using Euclidean
distance measurements. The algorithm calculates all possible pairwise
Euclidean distances between them. Samples that are close to each other are
assigned the same label. Our assumption is that similar brain activities have
EEG profiles that are close to each other. Thus, kNN enables the system to
determine the label (or, ‘class’) of new incoming EEG data using a distance
criterion.

##  IV Proof-of-Concept System

As explained in section II.2, a user alters their mental states to generate
brain codes, or instructions, to rotate a qubit. There is a metronome to
synchronize the brain with the system. It emits an audible ‘click’ every
second. The system builds the brain codes within a window of time lasting for
four clicks (i.e., four seconds). The flow diagram in Figure 4 illustrates how
the system works.

Figure 3: A snapshot of rotating the qubit using the brain code {1, 1}.

Initially, the system emits four clicks, which prompts the user to be ready to
start a session. Subsequently, the brain activity detected during the
following four clicks will correspond to the first digit in the code.
Similarly, the second digit is established through the next four clicks. Then,
a rest period of four clicks is provided to enable the user to monitor the
output; that is, to see if the desired qubit rotation has been achieved. Then,
the cycles recommences, and so on. Figure 3 shows a snapshot of rotating the
qubit with the code {1, 1}. In this case, the system detected two consecutive
excited mental states in the EEG. This instructed the system to rotate the
qubit to the right by a given angle. As a convention, in the context of Figure
3, to ‘increase the angle of rotation’ means to move the state vector to the
right side of the image. Conversely, to ‘decrease the angle of rotation’ means
to move the state vector to the left.

A video demonstration and programming code are available at the ICCMR GitHub
repository: https://github.com/iccmr-plymouth/Quantum-BCI.

Figure 4: System flow diagram.

##  V Concluding discussion

###  V.1 Towards BCI with quantum hardware

Our proof-of-concept demonstration currently runs on an IBM Quantum
simulator555https://www.ibm.com/quantum-computing/services. In general,
quantum simulators offer more controllability than real quantum computers and,
for a small number of qubits, there would be no much difference in
performance. Currently, to use a real quantum computer, a program needs to be
sent to a machine through a cloud service for batch processing. It is placed
in a queue to be computed at a later time. Then, the results are sent back to
the client computer. It is not uncommon to having to wait for dozens of
minutes until a queued job is processed. This is problematic because our
system needs real time access to a qubit.

It is important to note, however, that even if current providers of quantum
computing hardware facilities would grant us direct access to their machines,
our system would need a specific range of parameters that are not generally
available by the time of writing.

However, the fact that we used a simulator of a superconducting quantum
processor does not bind our work to superconducting technology. In fact, our
system would not work well on superconducting quantum devices as we know them
today. The caveat is that the operational timescales of EEG and
superconducting qubits are orders of magnitude apart, ranging from seconds (in
the EEG domain), to microseconds (in the qubits domain). In simpler words, the
machine would need to maintain qubits coherent for a prohibitively long time
until the brain produces a command. To rotate and measure a qubit directly
with human brain activity, we would need a huge leap in qubit coherence time
that cannot be afforded with current superconducting technology666Coherence
time is the length of time a qubit is able to hold quantum information. This
requires physical qubits to remain highly isolated from the surrounding
environment. When a qubit is disrupted by external interference (e.g.,
background noise from vibrations, temperature changes or stray electromagnetic
fields) information about the state of that qubit is destroyed, in a process
known as decoherence. This can ruin the ability to exploit quantum mechanics
for computation. Longer coherence times enable more quantum operations to be
utilised before this occurs.. It might be possible to alleviate this problem
with an operational system that would facilitate countless classical-quantum
iterations.

Fortunately, there are signs that quantum hardware platforms that would be
suitable for the types of systems that we are interested in developing are
already emerging in a number of academic research labs. For instance, qubits
built with spin pairs in diamond [14] seem to hold coherence for over one
minute, which would account for sequences of our brain-generated rotation
commands. At least theoretically, this specification matches the conditions
required for our proof-of-concept (Eq. 2), even before the optimisations
discussed in section V.2 below.

$\displaystyle t_{\rm rot}<t_{\rm step}<<t_{\rm coh}$ (2)

where $t_{\rm rot}$ is the time it takes to produce a finite rotation in the
qubit, $t_{\rm step}$ is the time of each step realized by our protocol, while
$t_{\rm coh}$ is the total coherent time of the qubit. Moreover, those qubits
operate at room temperature [15], which, on the long run, may enable the
manufacturing of more accessible workstations.

###  V.2 Looking Beyond EEG

Currently, the system takes four seconds to analyse and classify the EEG
signal to generate a digit for our brain code. Thus, it needs eight seconds to
compute a code. Obviously, this is a far cry from ideal. There definitely are
signal processing techniques [16] [17] and other robust classification methods
to optimise this [18] [19].

Moreover, EEG correlates of states of mind other than the EEG rhythms listed
in Table 1 have been harnessed for BCI; e.g., evoked potential [20] and motor
imagery [21]. Thus, there are additional alternatives to be explored.

For this project we used an affordable off-the-shelf mid-range EEG device,
using surface dry electrodes. There is EEG technology that offers much higher
fidelity than the fidelity offered by our equipment. And electrodes surgically
implanted under the skull capture considerably better EEG signals than surface
ones.

Furthermore, brain scanning technology that offers more precision than EEG,
but which until recently were deemed unsuitable for BCI, are important avenues
to be explored. These include Magnetic Resonance Imaging (MRI) [22] and
Magnetoencephalography MEG (MEG) [23]. For instance, emerging wearable
scanners based on non-cryogenic OPM-MEG777Optically Pumped Magnetometers MEG.
are promising new devices [24]. OPM-MEG technology uses quantum sensors to
measure magnetic fields generated by electrical activity within the brain.

Nevertheless, in addition to improving brain scanning fidelity and resolution,
and the timing scale discrepancy mentioned above (section V.1), we need to
further develop meaningful brain encoding schemes to communicate with quantum
states.

As a starting point, we proposed a Morse-like binary coding informed by the
way in which the brain functions at all levels. Excitatory and inhibitory
processes pervade the functioning of our brain, from the microscopic level of
neurones communicating with one another, to the macroscopic level of
interaction between larger networks of millions of neurones. The encoding
method introduced in II.2 works at the abstract level of EEG rhythms: think of
a high arousal (‘exciting’) mental state as an excitatory neural process and
low arousal (‘relaxing’) as an inhibitory one.

A better understanding of the meaning of the spiking behaviour of neurones,
and networks thereof, plus the ways in which we might be able to control them
- voluntarily or involuntarily - are sine qua non for progressing with our
approach to interfacing the brain with quantum computers.

##  VI Acknowledgements

The authors acknowledge support from the Spanish government (grant references
MCIU/AEI/FEDER PID2019-104002GB-C21 and PID2019-104002GB-C22), the Regional
Government of Andalusia, Spain (grant reference P20-00617) and Shanghai’s
Municipality, China (grant references 2019SHZDZX01-ZX04 and 20DZ2290900). We
are indebted to the University of Plymouth, UK, for access to its brain
imaging resources, and the QuTune Project, sponsored by UK’s QCS Hub.

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# Design of a HOM-Damped 166.6 MHz Compact Quarter-Wave Beta=1 Superconducting
Cavity for High Energy Photon Source

X.Y. Zhang1 Email<EMAIL_ADDRESS>J. Dai1 L. Guo1,2 T.M. Huang1,2
Z.Q. Li1,2 Q. Ma1,2
F.B. Meng1 Z.H. Mi1,2 P. Zhang1,2 H.J. Zheng1
1Institute of High Energy Physics  Chinese Academy of Sciences  Beijing 100049
China
2University of Chinese Academy of Sciences  Beijing 100049  China

###### Abstract

Superconducting cavities with low RF frequencies and heavy damping of higher
order modes (HOM) are desired for the main accelerator of High Energy Photon
Source (HEPS), a 6 GeV synchrotron light source promising ultralow emittance
currently under construction in Beijing. A compact 166.6 MHz superconducting
cavity was proposed adopting a quarter-wave beta=1 geometry. Based on the
successful development of a proof-of-principle cavity, a HOM-damped 166.6 MHz
compact superconducting cavity was subsequently designed. Ferrite damper was
installed on the beam pipe to reduce HOM impedance below stringent threshold
of coupled-bunch instabilities. Being compact, RF field heating on the cavity
vacuum seal was carefully examined against quenching the NbTi flange. The
cavity was later dressed with helium vessel and the tuning mechanism was also
realized. Excellent RF and mechanical properties were eventually achieved.
Finally, the two-cavity string was designed to ensure smooth transitions among
components and proper shielding of synchrotron light. This paper presents a
complete design of a fully dressed HOM-damped low-frequency beta=1
superconducting cavity for HEPS.

##  1 Introduction

High Energy Photon Source (HEPS) is 6 GeV diffraction limited synchrotron
light source under construction in Beijing[1]. Its main parameters of HEPS
storage ring are listed in Table. 1. A modified hybrid seven-bend achromat
(7BA) lattice has been designed to push the natural beam emittance down to 34
pm while preserving a high brightness of the X-ray synchrotron light. For the
storage ring with a circumference of 1360.4 m, five 166.6-MHz superconducting
cavities have been adopted as fundamental rf accompanied by two 499.8-MHz
superconducting cavities as third harmonic. This configuration is to
accommodate a novel injection scheme for the future while considering the
technology readiness of both the rf cavity and the fast kicker[2]. The choice
of frequency was extensively elucidated elsewhere from both physics[1] and
technology aspects[3]. The fundamental cavity makes use of a superconducting
quarter-wave beta=1 structure due to a low operating frequency.

Table 1: Main parameters of the HEPS storage ring. Parameter | Value | Unit
---|---|---
Circumference | 1360.4 | m
Beam energy | 6 | GeV
Beam current | 200 | mA
Energy loss per turn (w/IDs) | 4.4 | MV
Total beam power | 900 | kW
Fundamental RF frequency | 166.6 | MHz
Total RF voltage | 5.4 | MV
3${}^{\text{rd}}$ harmonic rf frequency | 499.8 | MHz

A proof-of-principle (PoP) cavity has been previously developed between 2016
and 2019 and its performances have been extensively studied in both vertical
tests and horizontal tests[3, 4, 5, 6]. The development of the PoP cavity
explored the design of the cavity’s main body, verified the feasibility of
manufacturing and related processes, transformed and developed a post-
processing system, and analyzed the test results. This provided a lot of
experience and lessons for us. Based on the successful development of a proof-
of-principle cavity, a HOM-damped 166.6 MHz compact superconducting cavity was
subsequently designed.

The electromagnetic (EM) design, multipacting (MP), mechanical design,
fabrication, and layouts of cavity string of the HOM-damped cavity are
described in the following sections.

##  2 The cavity design

The specifications of HEPS 166.6 MHz HOM-damped superconducting cavities are
listed in Table. 2. The design will focus on the HOM damped design, meanwhile,
the successful part of the PoP cavity should be kept as much as possible, and
the problems found in the test should be improved.

Table 2: Cavity specifications. Parameter | Value | Unit
---|---|---
Frequency | 166.6 | MHz
Design voltage $V_{d}$ | 1.5 | MV
$Q_{0}$ at $V_{d}$ | >1$\times$109 | -
$E_{peak}$ at $V_{d}$ | <40 | MV/m
$B_{peak}$ at $V_{d}$ | <65 | mT
Operating mode | CW | -
Loaded Q | 5$\times$104 | -
Loaded bandwidth | 3.33 | kHz
Operating temperature | 4.2 | K
Operating LHe pressure | 1230±3 | mbar
Sensitivity to LHe | <27.5 | Hz/mbar
pressure($df/dp$)
LFD coeff. | <5 | Hz/(MV/m)2
Longitudinal stiffness | <10 | kN/mm
Frequency of lowest | >100 | Hz
mechanical mode
Buckling critical factor | >2.0/16.1 | -
(cylinder/cone)
Remnant H field | <4 |  $\mu$T

###  2.1 The EM design

Since the cavity frequency is only 166.6 MHz, the most compact quarter-wave
cavity structure is uesed as the main body of the cavity to reduce the size to
the processable. The success of the PoP cavity test indicates that the cavity
structure has excellent rf performance. The optimized cavity geometry is shown
in Fig. 1, and the parameter differences with the PoP cavity are listed in
Table. 3.

Figure 1: The HOM-damped 166.6 MHz cavity. Table 3: Comparison of cavity geometry parameters. Fund. mode stands for fundamental mode. Parameter | Unit | PoP Cav. | HOM-damped Cav. | remarks
---|---|---|---|---
Length of flange to flange(L) | mm | 853 | 880 | Reduce power loss of rf leakage field
Length of LBP(L_LBP) | mm | 250 | 270
Length of FPC(L_FPC) | mm | 80 | 120
Length of cavity(L_cav) | mm | 523 | -
Cavity diameter($\Phi\text{\\_cav}$) | mm | 390 | 400 | Optimize EM parameters
Aperture diameter($\Phi\text{\\_LBP}$) | mm | 170 | 505 | Propagate HOMs/reject Fund. mode
Aperture diameter($\Phi\text{\\_iris}$) | mm | 170 | 240
Aperture diameter($\Phi\text{\\_SBP}$) | mm | 80 | -
Transition of the LBP(a, b) | mm | - | 60, 120 | Easy to tune

The main body of the cavity was basically the same as that of the PoP. Only
the diameter of the cavity ($\Phi\text{\\_cav}$) has been slightly increased
to 400mm to further improve EM performance.

Based on the PoP cavity, the cavity’s structure was further optimized to solve
the HOM problem. The aperture diameter of the cavity left beam pipe
($\Phi\text{\\_LBP}$) and the aperture diameter of the cavity iris
($\Phi\text{\\_iris}$) were increased from 170 mm to 505 mm and 240 mm,
respectively, to propagate the HOMs field and reject the fundamental mode.
Ferrite absorber will be installed on the enlarged beam pipe extension at room
temperature to extract the HOM power. The whole cavity impedance spectrum was
simulated by CST Studio Suite[7] and ABCI software[8]. All the impedance of
HOMs are under the impedance threshold, except for the second monopole (M2)
mode. The impedance for M2 mode is 1.28E4 $\Omega$ while the impedance
threshold is 1.14E4 $\Omega$. A detailed introduction of these impedance
results and power losses due to HOMs are given in [9].

After the beam pipe diameter of the cavity is increased, the length of the
pipe also needs to be reconfirmed. The stainless steel (SS) transition tube is
connected to the niobium tube of the cavity. In order to fully attenuate the
fundamental electromagnetic field of the cavity and reduce the power
dissipation of the leakage field on the SS transition tube, the large beam
pipe of the superconducting cavity should be long enough. Otherwise this will
reduce the $Q_{0}$ of the cavity operating mode, heat up the cavity
peripherals, and introduce a significant additional load of the system. The
simulation results are shown in Fig. 2. When the $Q_{0}$ on the stainless
steel transition tube reaches 1e10, which is an order of magnitude higher than
the cavity design 1e9, it is considered that the superconducting cavity rf
performance will not be affected. Due to the longitudinal compact design
requirements of the cavity string, the length of the large beam pipe is chosen
to be 270 mm.

Figure 2: Q and power loss on stainless steel transition tube.

An overheating at the cavity-coupler interface region was observed in high-
power tested, causing a “thermal runaway” and eventually quenched the cavity.
Solutions were proposed including an elongated niobium extension tube from 80
mm to 120 mm at the coupler port and an optimized helium gas cooling of the
power coupler’s outer conductor. More details can be found in [6].

The bend of the LBP transition has been changed from R20 mm to an elliptical
arc (60 mm, 120 mm) for the purpose of enhance the tuning ability.

Due to the enlarged cavity beam pipe and a accommodated large helium jacket,
the original electric-probe pickup of PoP becomes inevitably long with
unfavorable mechanical properties. Relocated to an existing high-pressure-
rinsing (HPR) port, a low-loss magnetic-loop pickup was designed. The
consequent removal of the original pickup port from the cavity largely
simplified the helium jacket fabrication and cavity contamination[10].

The electromagnetic field distribution of the fundamental mode is shown in
Fig. 3 and the RF parameters are listed in Table. 4. A 20% margin on peak
surface fields was reserved.

Figure 3: The distribution of electromagnetic field. Table 4: The RF parameters. Parameter | Value | Unit
---|---|---
$R/Q$ (=$|V|^{2}$/$\omega$U) | 139 | $\Omega$
$G$ (=$R_{s}\cdot Q_{0}$) | 56 | $\Omega$
$E_{peak}$ at $V_{d}$=1.5MV | 40 | MV/m
$B_{peak}$ at $V_{d}$=1.5MV | 62 | mT

###  2.2 Multipacting

CST Particle Studio and CST Microwave Studio[7] were used for multipacting
simulation of the 166 MHz HOM-damped SRF cavity. Argon discharge cleaned
niobium was selected, which has a low secondary emission coefficient. In order
to speed up the computation and to determine MP locations, the cavity inner
surface is divided into several initial particle source regions. Particles are
randomly emitted in all directions with the initial energy uniformly
distributed from 0 to 4 eV. Particle number, trajectories and energies are
tracked over 10 rf periods in fields with different acceleration voltages and
relative phases. The normalized secondary electron yield (<SEY>) is defined to
evaluate the probability of multipacting. Fig. 4 shows the <SEY> curves at
different regions and voltages. Two soft multipacting bands at low field (0.06
MV) on the LBP plate and at medium field (0.6 MV) on the HPR plate are similar
to those of the PoP cavity. A new soft band near the design voltage of 1.5 MV
appears at the LBP transition region. The <SEY> are all less than 1,
indicating that multipacting doesn’t occur when the cavity inner surface is
well treated.

Figure 4: <SEY> curves for different regions of the cavity.

###  2.3 The mechanical design

The mechanical design optimization of the 166.6 MHz dressed cavity was
conducted by using ANSYS software[11] and CST Studio Suite[7]. The model of
the dressed cavity is shown in Fig. 5. The wall thickness of cavity varies
from 3.5 mm to 6 mm for different components. The thickness of Liquid Helium
(LHe) vessel, bellow and end plates were chosen to be 4 mm, 0.5 mm, 26 mm and
35 mm. The dressed cavity will be made of high-purity niobium (Nb) with
RRR>300, the cavity flanges with Titanium Niobium alloy (NbTi), the stiffener
with reactor grade niobium, and finally the LHe vessel and bellow with Grade-2
Titanium (Ti). The properties of these materials are exerted from Fermilab
specification document: 5500.000-ES-371110. The maximum allowable stress value
was established. ASME Boiler and Pressure Vessel Code and Chinese code were
also followed. A detailed discussion can be found in a previous
publication[4]. Compared with the PoP cavity, a large helium jacket was
required to accommodate the HOM-damped cavity with the enlarged LBP. In order
to reduce the cavity stiffness to an acceptable range, the bellows was an
unavoidable choice, although it will cause an increase in the cavity’s peak
stress and sensitivity to LHe pressure ($df/dp$). The bend and thickness of
the niobium cavity HPR, the bend of junctions between the end plates and
cylinder of the LHe vessel, and the structure and position of the LHe bellows
were optimized.

Figure 5: The thickness and material of the dressed cavity.

The optimized results of mechanical properties are summarized in Table. 5. All
the results were simulated under supports fixed. The stress distribution of
the entire structure under 1.5 atm pressure inside the helium jacket volume is
shown in Fig. 6. The maximum stress reads 78 MPa on cavity marginally
exceeding the required value of 70.5 MPa at 293 K and 119 MPa on LHe bellow
fulfilling the allowable value. The frequency sensitivity and longitudinal
stiffness have eventually been reduced to -18 Hz/mbar and 9.7 kN/mm,
respectively. The Lorentz force detuning coefficient is -1.1 Hz/(MV/m)2,
similar to PoP cavity. Meanwhile, the frequency of lowest mechanical mode and
buckling critical factor also meet the design requirements.

Table 5: The mechanical parameters. Parameter | Value | Unit
---|---|---
Max. stress on cavity | 78 | MPa
Max. stress on bellow | 119 | MPa
$df/dp$ | -18 | Hz/mbar
$\Delta f$ under ±3mbar | ±55 | Hz
Longitudinal stiffness | 9.7 | kN/mm
Tuning range at 4.2 K | 67 | Hz
LFD coeff. | -1.1 | Hz/(MV/m)2
Frequency of lowest | 110 | Hz
mechanical mode
Buckling critical factor | 11.4/73 | -
(cylinder/cone)
Figure 6: The stress distribution of the entire structure under 1.5 atm
pressure.

The rf-thermal coupling simulation at the aluminum-magnesium(AlMg) alloy
sealing groove was performed to confirm the temperature safety of the
superconducting materials such as the NbTi flange and the niobium tube. The
model of the sealing groove was shown in Fig. 7. Peak temperatures of NbTi
flange, niobium tube, AlMg sealing ring and SS flange are simulated to be 4.52
K, 4.32 K, 5.44 K and 6.63 K, respectively. Since the temperature of NbTi and
Nb is less than the critical superconducting temperature, it will not cause
quenching, so the length of LBP (270 mm) is feasible.

Figure 7: Model of the sealing groove between cavity and transition tube.

The magnetic shielding has been designed for 166 MHz HOM-damped cavity to
reduce the residual surface resistance due to magnetic flux trapping during
cavity cool down. A thin layer (1.3 mm) of permalloy (1J79) was designed and
composed of three parts inside the jacket. Final equivalent contribution for
residual resistance caused by geomagnetic field and magnet fringe field was
calculated to be 2.36 n$\Omega$, and the equivalent residual magnet field on
cavity wall was 1.93 $\mu$T. More information was presented in detail in [12]

##  3 The fabrication

The dressed cavity is contracted to Beijing HE-Racing Technology Co., Ltd.
Some of the key fabrication processes and components are shown in Fig. 8. Deep
drawing, rolling, machining, and electron-beam welding are the main
manufacturing techniques used in the fabrication of this cavity. The prototype
HOM-damped 166 MHz cavity will be manufactured in July 2021, and vertical test
is planned for September.

Figure 8:  The fabrication of the HOM-damped cavity.

##  4 The cavity string

A HOM-damped 166.6 MHz quarter-wave superconducting cavity string will be used
for the HEPS storage ring and fit into a straight section of only 6 meters.
The large size of the low-frequency cavity, the increased large beam pipe for
the HOM, the transition tube, the smoother taper and synchrotron light
shielding pose severe challenges to the limited straight section. Four layouts
for the cavity string and the collimator design were presented in [13].
Considering the replaceability of the cryomodule, the broadband impedance of
the cavity string, synchronous light irradiation and future maintainability,
the solution of placing two cryomodules in sequence was finally selected, in
which the beam enters from the small beam pipe, as shown in Fig. 9. The loss
factor of the cavity string was 5.324 V/pC, and two collimators were design to
successfully blocked the synchronous light.

Figure 9:  The layout of the cavity string.

##  5 Final Remarks

A HOM-damped 166.6 MHz compact quarter-wave beta=1 superconducting cavity has
been proposed for High Energy Photon Source. Based on the PoP cavity, the
cavity’s structure was further optimized, and the HOM impedances can be
reduced below the threshold by a ferrite absorber mounted on the enlarged left
beam pipe. Excellent rf and mechanical properties were eventually achieved.
The layout of cavity string in rf section was also analyzed. The cavity is
being manufactured and will be tested in the fall of 2021.

##  6 ACKNOWLEDGEMENTS

This work was supported in part by High Energy Photon Source, a major national
science and technology infrastructure in China and in part by the National
Natural Science Foundation of China under Grant 12005241.

## References

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