Instrumentation & Measurement Magazine 24-9 - 12

Surface Impedance Measurements
in Superconductors in DC Magnetic
Fields: Challenges and Relevance
to Particle Physics Experiments
Andrea Alimenti, Nicola Pompeo, Kostiantyn Torokhtii and Enrico Silva
P
article physics and radio-frequency (RF) superconductivity
have driven each other on since the 1970s.
The unique properties of superconductors (SC) have
been the enabling keys for the realization of accelerators with
always increased performances thanks to the realization of
all-superconducting cavities. The use of increasingly pure superconducting
coatings for accelerating cavities, with lower
and lower RF losses, determined such high-quality factors [1]
that the need to operate at low temperatures (below the superconducting
transition temperature Tc
) was well paid for.
Recently, with respect to the path followed by the high frequency
superconductivity [2], a new field opened since SCs
are being considered for GHz operation in high dc magnetic
fields, and measurements (and optimization) of totally different
quantities are needed. The possibility of successfully using
SCs in high magnetic fields for these purposes is far from obvious
and it depends on the outcome of accurate measurements
of usually overlooked quantities.
In fact, new accelerators such as the Future Circular Collider
(FCC) at CERN [3] or the Super Proton-Proton Collider
(SPPC) in China [4] will need 100-km long beam screens able
to screen the synchrotron radiation with power spectra up to
~ 2 GHz, in dc fields up to 16 T, and at temperatures T~50 K.
Low surface impedance Z materials are needed to this aim,
with   
Z RX
H
E
field components parallel to the surface of the materials, R is
the surface resistance and X is the surface reactance. It is still

unclear whether copper is a suitable solution; hence, high-Tc
SCs are under scrutiny to assess if they can be once more the
enabling solution.
In parallel, in the context of the hunt for dark matter, a
new generation of hybrid super/normal-conductive resonating
cavities operating at several GHz, known as haloscopes,
is being developed to detect the radio-frequency/microwave
photon in which a virtual photon is converted by a supposed
dark-matter constituent, an axion, in the presence of magnetic
fields. The sensitivity of these detectors is ∝ Qu
B2
[5], with Qu
the cavity quality factor and B the externally applied magnetic
flux density. SCs are then an obvious possible solution.
12
i , where E
and H
are the electric and magnetic
Finally, and looking further ahead in time, a future generation
of muons circular colliders would be based on muon
cooling radio frequency (0.5-1 GHz) cavities, which will operate
in stray fields up to 5 T. Again, materials with low Z in high
magnetic fields are a key enabler and SCs are taken into consideration
[6].
The new player to be challenged in the RF superconductivity
is the dc magnetic field: all technologically relevant
superconductors are so-called type-II superconductors. There,
in even moderate dc fields H > Hc1
−102
μ0Hc1 of the order of (101
, with the lower critical field
) mT depending on the material,
magnetic flux tubes known as 'fluxons' proliferate, driving the
superconductor in the so-called 'mixed state.' Quantum mechanics
dictates that each fluxon carries exactly a magnetic
flux quantum Φ0
= h/(2e) ≈ 2.067 × 10−15
Wb (h is the Planck
constant, e is the electric charge quantum), sustained by lossless
circular superconducting currents (whence also the name
of 'vortices'). The challenge resides in the fact that external
currents exert an effective Lorentz force on fluxons, which can
set them in motion. Due to the normal core of the fluxons and
the related scattering phenomena, the motion of the fluxons is
highly dissipative. Thus, pinning the fluxons on 'pinning centers'
(PCs), which are defects of the material lattice, is a central
issue in material science [7]. RF and microwave currents are
even trickier, since they produce an alternating fluxon motion
that is more difficult to hinder.
The frequency dependence of the radio-frequency/microwave
power losses in superconductors in dc magnetic
fields was first shown in a seminal experimental study in
1966 [8], as reported in Fig. 1a. Two important features of
the real part of the material resistivity Re (ρ) (proportional to
the material power absorption P in electromagnetically thin
samples) emerge. First is the presence of a characteristic frequency
fc
, which is proportional to the strength of the pinning
force acting on fluxons and that marks the crossover between
the low-frequency, low dissipation regime and the high-frequency,
high dissipation regime. Thus, information on fc
is
essential to engineer suitable SC materials for RF applications:
as a rule, for applications at a given frequency f one looks for
IEEE Instrumentation & Measurement Magazine
1094-6969/21/$25.00©2021IEEE
December 2021

Instrumentation & Measurement Magazine 24-9

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