Instrumentation & Measurement Magazine 24-9 - 13

jumping between equilibrium sites, resulting in so-called flux
creep dissipation. In high-frequency superconductivity, flux
creep is measured by the adimensional normalized parameter
0 ≤ χ ≤ 1 which weighs the effect of thermally excited fluxon
jumps out of the pinning well, from zero jumps (χ = 0) to jumps
so frequent (χ = 1) that the pinning wells effect is practically
irrelevant.
The three parameters fc
, ρff and χ are the main quantities of
interest and require a nontrivial combination of methods and
models to be determined. A metrological approach involves:
the introduction of an appropriate physical model relating the
parameters to directly measurable quantities; a suitable experimental
setup, with a study of the uncertainties and of the
methods to reduce them; and experimental results for the desired
quantities. These aspects are presented in the following
sections, thus providing a focus on the measurement methods,
and on their main critical issues, useful for the characterization
of SCs in the operating conditions of the aforementioned
applications. Short conclusions with a view on unresolved
aspects and future developments are reported at the end. It
should be stressed that, although the path depicted here has
been explored in moderate fields in the past [8], [10], the need
for reliable measurements in high magnetic fields is somewhat
a game changer due to the increased complexities.
Physical Background
A more complete physical picture beyond Fig. 1a is essential to
define the measurement strategy and to understand and support
the technological requirements.
First, it is important to note that the zero-field contribution
to the surface impedance, so relevant for accelerating cavities,
is negligible with respect to the fluxon motion contribution for
even small magnetic fields ~ 0.1 T. Thus, in the linear response
(i.e., E ∝ Jrf
with E the electric field and Jrf
Fig. 1. Vortex motion resistivity in superconductors as a function of the
normalized frequency f / fc
absorption in low-Tc superconductor [8] (here f0
. (a) Original experimental data for the power
= fc
real resistivity; (c) Calculated normalized imaginary resistivity with the
inclusion of the thermal effects.
f << fc
. Secondly, the high frequency saturation value that Re (ρ)
approaches, called flux-flow resistivity ρff
is of the order of the fraction H/Hc2
resistivity in the normal state ρn, ρff ~ρnH / Hc2
[9] with Hc2
can attain rather large values.
, corresponds to the
effective resistivity of completely free moving fluxons. The
flux flow resistivity ρff
of the
the
upper critical field above which the superconductivity is suppressed.
Thus, ρff
Since 1966 many other, more technologically suitable
SCs were discovered, with higher Tc and Hc2. Even if Nb3
(Tc
Sn
≈ 18 K) has been employed for a long time in the production
of high-field magnets, its potential for RF superconductivity
is still unexpressed. Obvious interest is also in High Tc
perconductors (HTS), with transition temperatures Tc
for, e.g., YBa2
peratures imply a relevant role of thermally activated fluxon
December 2021
Su≈
90 K
Cu3O7-x, (YBCO). However, high operating tem);
(b) Calculated normalized
the radio frequency
current densities inside the conductor), the 'material property'
ac resistivity ρ essentially coincides with the vortex motion resistivity
ρvm
which, in turn, on very general grounds, can be
described through the following [11]:
i
  



vm ff
1i

f
f
f
f
c
Eq. (1) ceases to apply when the fluxons oscillation width
around their equilibrium positions (PCs, typically) is a sizeable
fraction of their separation, as it is expected at low frequencies
(below ~ 1 GHz) or at high RF drive (yielding also non-linear
effects). These different regimes require a specific theoretical
and experimental treatment.
The vortex parameters fc
, χ and ρff
are each connected to a
specific physical mechanism, as depicted above. We refer to
specialized reviews [10], [12] for an in-depth discussion on
their nature and roles.
With χ = 0, (1) reproduces the data taken on low-Tc
c   i
vm

.
vm
(1)
superconductors
of Fig. 1a, and it has been for a long time the
reference model for RF vortex motion [8], [10], [13]. The full
IEEE Instrumentation & Measurement Magazine
13
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