Abstract: We report results of the numerical solution by the Euler method of the system of heat balance equations written in recurrent form for the superconducting hot-electron bolometer (HEB) embedded in an electrical circuit. By taking into account the dependence of the HEB resistance on the transport current we have been able to calculate rigorously the RF heating efficiency, absorbed local oscillator (LO) power and conversion gain of the HEB mixer. We show that the calculated conversion gai nis in excellent agreement with the experimental results, and that the substitution of the calculated RF heating efficiency and absorbed LO power into the expressions for the conversion gain and noise temperature given by the analytical small-signal model of the HEB yields excellent agreement with the corresponding measured values

Abstract: Context. Supplementing the publications based on the first-light observations with the German REceiver for Astronomy at Terahertz frequencies (GREAT) on SOFIA, we present background information on the underlying heterodyne detector technology. This Letter complements the GREAT instrument Letter and focuses on the mixers itself.
Aims. We describe the superconducting hot electron bolometer (HEB) detectors that are used as frequency mixers in the L1 (1400 GHz), L2 (1900 GHz), and M (2500 GHz) channels of GREAT. Measured performance of the detectors is presented and background information on their operation in GREAT is given.
Methods. Our mixer units are waveguide-based and couple to free-space radiation via a feedhorn antenna. The HEB mixers are designed, fabricated, characterized, and flight-qualified in-house. We are able to use the full intermediate frequency bandwidth of the mixers using silicon-germanium multi-octave cryogenic low-noise amplifiers with very low input return loss.
Results. Superconducting HEB mixers have proven to be practical and sensitive detectors for high-resolution THz frequency spectroscopy on SOFIA. We show that our niobium-titanium-nitride (NbTiN) material HEBs on silicon nitride (SiN) membrane substrates have an intermediate frequency (IF) noise roll-off frequency above 2.8 GHz, which does not limit the current receiver IF bandwidth. Our mixer technology development efforts culminate in the first successful operation of a waveguide-based HEB mixer at 2.5 THz and deployment for radioastronomy. A significant contribution to the success of GREAT is made by technological development, thorough characterization and performance optimization of the mixer and its IF interface for receiver operation on SOFIA. In particular, the development of an optimized mixer IF interface contributes to the low passband ripple and excellent stability, which GREAT demonstrated during its initial successful astronomical observation runs.

Abstract: Aims. We aim to study the physical conditions, particularly the excitation state, of the intermediate-temperature gas components in the protoplanetary nebula CRL 618. These components are particularly important for understanding the evolution of the nebula.
Methods. We performed Herschel/HIFI observations of several CO lines in the far-infrared/sub-mm in the protoplanetary nebula CRL 618. The high spectral resolution provided by HIFI allows measurement of the line profiles. Since the dynamics and structure of the nebula is well known from mm-wave interferometric maps, it is possible to identify the contributions of the different nebular components (fast bipolar outflows, double shells, compact slow shell) to the line profiles. The observation of these relatively high-energy transitions allows an accurate study of the excitation conditions in these components, particularly in the warm ones, which cannot be properly studied from the low-energy lines.
Results. The 12CO J = 16–15, 10–9, and 6–5 lines are easily detected in this source. Both 13CO J = 10–9 and 6–5 are also detected. Wide profiles showing spectacular line wings have been found, particularly in 12CO J = 16–15. Other lines observed simultaneously with CO are also shown. Our analysis of the CO high-J transitions, when compared with the existing models, confirms the very low expansion velocity of the central, dense component, which probably indicates that the shells ejected during the last AGB phases were driven by radiation pressure under a regime of maximum transfer of momentum. No contribution of the diffuse halo found from mm-wave data is identified in our spectra, because of its low temperature. We find that the fast bipolar outflow is quite hot, much hotter than previously estimated; for instance, gas flowing at 100 km s-1 must have a temperature higher than ~200 K. Probably, this very fast outflow, with a kinematic age <100 yr, has been accelerated by a shock and has not yet cooled down. The double empty shell found from mm-wave mapping must also be relatively hot, in agreement with the previous estimate.