  Different terrestrial terahertz applications would benefit from large-format
arrays, operating in compact and inexpensive cryocoolers at liquid helium
temperature with sensitivity, limited by the 300-K background radiation only. A
voltage-biased Transition-Edge Sensor (TES) as a THz detector can have
sufficient sensitivity and has a number of advantages important for real
applications as linearity of response, high dynamic range and a simple
calibration, however it requires a low-noise current readout. Usually, a
current amplifier based on Superconducting Quantum-Interference Device (SQUID)
is used for readout, but the scalability of this approach is limited due to
complexity of the operation and fabrication. Recently, it has been shown that
instead of SQUID it is possible to use a current sensor, which is based on the
nonlinearity of the kinetic inductance of a current-carrying superconducting
stripe. Embedding the stripe into a microwave high-Q superconducting resonator
allows for reaching sufficient current sensitivity. More important, it is
possible with the resonator approach to scale up to large arrays using
Frequency-Division Multiplexing (FDM) in GHz range. Here, we demonstrate the
operation of a voltage-biased TES with a microwave kinetic-inductance current
amplifier at 4.2 K. We measured the expected intrinsic Noise-Equivalent Power
NEP ~$5\times 10^{-14} \; \rm W/Hz^{1/2}$ and confirmed that a sufficient
sensitivity of the readout can be reached in conjunction with a real TES
operation. The construction of an array with the improved sensitivity ~
$10^{-15}\; \rm W/Hz^{1/2}$ at 4.2 K could be realized using a combination of
the new current amplifier and already existing TES detectors with improved
thermal isolation.
