Instrumentation & Measurement Magazine 24-9 - 18

Fig. 4. Flux-flow resistivity (red) and the characteristic frequency (blue)
measured at similar reduced temperature T/Tc
Fig. 5. Plot of the flux-flow resistivity ρff
on a bulk Nb3Sn sample at 6 K
(triangles) and on a YBCO thin film (full dots) at 27 K, for fields up to 12 T.
depth and λ the London penetration depth, and when the SC
film is deposited onto a dielectric substrate, Z =ρ/t. We refer
readers to [25] (and references therein) for a full discussion of
the uncertainties introduced in such approximation. Since the
variations ΔZ(H) = Z(H)−Z(H = 0) induced by the magnetic
field are measured, ΔZ(H)t Δρ(H) ≈ ρvm
. The first approximation
relies on the film being electromagnetically thin, a
geometrical property, and the second relies on a physical condition,
i.e., that the vortex motion resistivity is much larger
than other superconducting contributions, which is realized
not too close to the transition to the normal state. The ρvm
measurements
are shown in Fig. 3b and Fig. 3d. From these, the
vortex motion parameters are derived by means of (1) and
shown in Fig. 3e, Fig. 3f and Fig. 3g.
It can be noted how measurements of the surface reactance
and S12
require a rather accurate fitting of S21
. The '-3 dB method'
yields unacceptably large uncertainties in the vortex parameters
(see the scattering of the data in Fig. 3e, Fig. 3f and Fig. 3g).
The field dependence of the obtained parameters yields information
on pinning that is very useful for the optimization of
the SC material. In this specific case, for example, the field independence
of fc
and χ identifies, within the fluxon dynamics
theory, a regime in which the density of the PCs in the materials
is higher than the density of the fluxons, so that further
optimization is possible only by fine tuning the kind of defects
and not the density.
A comparison between S2 (YBCO) and S3 (Nb3
interesting. The surface impedance of a bulk sample of Nb3
=vm  i

Sn), is very
Sn
was measured with a single tone DR at ~14.9 GHz, down to
4 K and up to 12 T [26]. The low operating temperature allows
to safely neglect χ, so that single-frequency vm
yield fc
and ρff
Sn and Tc
vm still
. The results are shown in Fig. 4 up to 12 T, at
6 K for Nb3Sn and 27 K for YBCO. Due to the different critical
temperatures, Tc~18.0 K in Nb3
≈ 0.3.
~91.0 K in YBCO, the
selected temperatures correspond to similar reduced temperature
T/Tc
18
Te0.5
(pink).
measured at 10 K and 1 T on different SCs: Nb3Sn (orange), MgB2
YBCO (light blue) and FeSe0.5
and characteristic frequency fc
(green),
For practical use of SCs at high frequency in large dc magnetic
fields, operation at f << fc
is required. fc
in Nb3
Sn at e.g.,
10 T is ~5 times smaller than that of YBCO, which is rather discouraging
for RF applications. However, the field dependence
of fc
points to a different pinning regime, known as collective
pinning, in which a low density of PC is present in the SC with
respect to the density of the fluxons. This is not the most effective
pinning regime; thus further material improvements can
be made, e.g., by adding artificial PCs in the SC to optimize the
high frequency behavior of Nb3
Sn in the mixed state. This is a
completely new paradigm in high-frequency applications of
SCs: whereas for accelerator cavities (operating in zero field)
one looks for the purest SC material, a different approach may
be required for the requirements of new experiments. Additionally,
ρff
in the high frequency limit f >> fc
(H) has a similar slope in both SCs. This means that
, the losses in Nb3
Sn at 6 K are
of the same order than those in YBCO at 27 K in the same field
range up to 12 T, with only a factor of ~2 between the two. Since
ρff
is directly related to the microscopic properties of the material,
tuning of this property by material science is not expected.
The present measurements thus indicate that, by engineering
the PCs, it can be possible to improve the high-frequency,
in-field properties of a " SC workhorse " like Nb3
high fc
Sn, while the
of YBCO makes this material already mature, from
the point of view of the physical properties, for the perspective
high frequency applications of SCs in the mixed state.
Indeed, the properties of various commercial YBCO tapes
have been recently studied at 8 GHz and up to 9 T [13], showing
that even dc-optimized, industrial YBCO tapes could fulfil
the requirements of the aforementioned large scale applications.
However, it must be noticed that commercial tapes are
optimized for dc operations through the introduction of such
a large density of PCs that they have detrimental effects on
ρff
: despite the large fc
tapes, the slope of ρff
IEEE Instrumentation & Measurement Magazine
found in some nanoengineered YBCO
(H), on the same tapes, was measured to
be times larger than that obtained in pristine YBCO [13]. We
December 2021

Instrumentation & Measurement Magazine 24-9

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