On bilinear invariant differential operators acting on tensor fields on the symplectic manifold

Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\rho: GL(n)\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\subset M$, in other words, $T(V)$ is the space of tensor fields of type $V$ on $M$ on which the group \Diff (M) of diffeomorphisms of $M$ naturally acts. Elsewhere, the author classified the \Diff (M)-invariant differential operators $D: T(V_{1})\otimes T(V_{2})\longrightarrow T(V_{3})$ for irreducible fibers with lowest weight. Here the result is generalized to bilinear operators invariant with respect to the group \Diff_{\omega}(M) of symplectomorphisms of the symplectic manifold $(M, \omega)$. We classify all first order invariant operators; the list of other operators is conjectural. Among the new operators we mention a 2nd order one which determins an ``algebra'' structure on the space of metrics (symmetric forms) on $M$

Terahertz Spectroscopy System of Gas Mixtures Based on a Solid State Superconducting Source and a Terahertz Receiver

Abstract: The application of a Josephson generator of the terahertz range based on a long superconductor–insulator–superconductor tunnel junction matched with a transmitting antenna and emitting a signal into open space is demonstrated for gas spectroscopy. The generator is used as an active source, the signal of which is absorbed by a sample of a gas mixture in a cell with a length of 60 cm and then recorded by a spectrometer based on a superconductor–insulator–superconductor receiver with a spectral resolution better than 100 kHz. In the experiment, the absorption lines of ammonia and water in the terahertz range were recorded, and the dependence of the spectral characteristics of the absorption lines on the pressure of the gas mixture in a wide range (from 0.005 to 10 mbar) was demonstrated

Terahertz Spectroscopy of Gas Absorption Using the Superconducting Flux-Flow Oscillator as an Active Source and the Superconducting Integrated Receiver

We report on the first implementation of a terahertz (THz) source based on a Josephson flux-flow oscillator (FFO) that radiates to open space. The excellent performance of this source and its maturity for practical applications has been demonstrated by the spectroscopy of gas absorption. To study the radiated power, we used a bolometric detection method and additionally calibrated the power by means of pumping the superconductor–insulator–superconductor (SIS) junction, integrated on a single chip with the FFO. For calibration, we developed a program using the SIS-detected power calculations in accordance with the Tien and Gordon model. The power emitted to open space is estimated to be from fractions of µW to several µW in the wide region from 0.25 THz up to 0.75 THz for different designs, with a maximum power of 3.3 µW at 0.34 THz. Next, we used a gas cell and a heterodyne superconducting integrated receiver to trace the absorption lines of water and ammonia with a spectral resolution better than 100 kHz. Our experiment for gas absorption is the first demonstration of the applicability of the FFO as an external active source for different tasks, such as THz spectroscopy, near-field THz imaging and microscopy

Low-Noise Sis Receivers for New Radio-Astronomy Projects

We have developed, manufactured, and tested a waveguide mixer in the range 211-275 GHz on the basis of the superconductor-insulator-superconductor (SIS) tunnel structures. The methods of manufacturing high-quality tunnel structures on quartz substrates have been worked out. To extend the receiver band, the Nb/AlOx/Nb and Nb/AlN/NbN tunnel junctions with a high current density of up to 20 kA/cm2 are employed. The dependence of the characteristics of the receiving elements on the signal frequency is simulated for the intermediate-frequency band 4-12 GHz. The measurements demonstrate a good agreement of the input band of the receiving structures with the calculated results. The uncorrected noise temperature of the receiver amounts to 24 K at a frequency of 265 GHz, which is only two times higher than the quantum limit. The receivers under development are intended for a number of newly-built ground-based radio telescopes ("Suffa" and LLAMA), as well as for the "Millimetron" space program

An Antenna with a Feeder for a Superconducting Terahertz Josephson Oscillator with Phase Locking

A principal layout of a Josephson terahertz radiation oscillator integrated with a transmitting antenna-lens system and a harmonic mixer (HM) for phase locking of radiation has been proposed and was successfully implemented. Two antenna-feeder systems designed for the central frequencies of 0.3 and 0.6 THz and located on the same chip with the oscillator are numerically simulated and fabricated. A microstrip transmission line between the oscillator and the antenna is used as the feeder. A study was carried out on matching the oscillator power and HM for two designs; the frequency range of pumping HM was 0.25-0.45 and 0.5-0.68 THz for the designs at 0.3 and 0.6 THz, respectively. Good agreement was obtained between experimental results and numerical simulations. A study of the spectral characteristics of the radiation of the oscillator into the external space for the 0.6 THz design using a superconducting integrated spectrometer was carried out. The linewidth of an emission line in free-running regime was of the order of several megahertz; in the phase locking regime down to tens of kilohertz with a signal-to-noise ratio of more than 20 dB was obtained

Comparing the performance of 850 GHz integrated bias-tee superconductor-insulator-superconductor (SIS) mixers with single- and parallel-junction tuner

We present and compare the design and performance of two 850 GHz radial probe fed superconductor-insulator-superconductor mixers, where the antenna is aligned perpendicular to the E-Plane of the input full-height rectangular waveguide connected to a multiple flare-angles smooth-walled horn. Both designs are comprised of 0.5 µm2 hybrid niobium/aluminium-nitride/niobium-nitride tunnel junction, fabricated on top of a niobium titanium nitride ground plane with an Al wiring layer. The entire superconducting circuit is supported with a 40 µm thick quartz substrate. The major difference between the two designs is the method used to cancel out the parasitic junction capacitance for broadband performance. The first design utilises two identical junctions connected in parallel with a short transmission line to convert the capacitance of one junction into the equivalent inductance of the other junction, commonly known as the twin-junction tuning scheme; whilst the second design employs an end-loaded scheme with only one tunnel junction. We found that both methods offer similar radio frequency performances, with close to 2× the double sideband quantum noise temperature, but the twin-junction design is more resilient to fabrication tolerances. However, the end-loaded design offers a much better intermediate frequency (IF) bandwidth performance, made possible by the sub-micron and high current density tunnel junction technology. The improved IF performance is important for many millimetre (mm) and sub-mm observatories, such as future upgrades of Atacama Large Millimetre/sub-mm Array receivers, as well as forthcoming space-borne far-infrared missions. Therefore, we conclude that the single-junction mixer design is the preferred option for THz applications, as long as the fabrication error can be minimised within a certain limit

Characterization of superconducting NbTiN films using a dispersive Fourier transform spectrometer

We have built a Terahertz Dispersive Fourier Transform Spectrometer \cite{Birch1987} to study frequency properties of superconducting films used for fabrication of THz detectors. The signal reflected from the tested film is measured in time domain, which allows to separate it from the other reflections. The complex conductivity of the film depends on frequency and determines the reflection coefficient. By comparing the film reflection in the superconducting state (temperature is below $T_c$) with the reflection of the normal state, we characterise the film quality at terahertz frequencies. The method was applied to 70 and 200nm thick Nb films on a silicon wafer and to 360nm thick NbTiN films on silicon and quartz wafers. The strong-coupling coefficient, $\alpha$, was found to be 3.52 for Nb, and 3.71-4.02 for the NbTiN films. The experimental results were fitted using extended Mattis-Bardeen theory \cite{Noguchi2012} and show a good agreement.Comment: The following article has been accepted by Applied Physics Letters. After it is published, it will be found at https://aip.scitation.org/journal/ap

Statistical features of edge turbulence in RFX-mod from Gas Puffing Imaging

Plasma density fluctuations in the edge plasma of the RFX-mod device are measured through the Gas Puffing Imaging Diagnostics. Statistical features of the signal are quantified in terms of the Probability Distribution Function (PDF), and computed for several kinds of discharges. The PDFs from discharges without particular control methods are found to be adequately described by a Gamma function, consistently with the recent results by Graves et al [J.P. Graves, et al, Plasma Phys. Control. Fusion 47, L1 (2005)]. On the other hand, pulses with external methods for plasma control feature modified PDFs. A first empirical analysis suggests that they may be interpolated through a linear combination of simple functions. An inspection of the literature shows that this kind of PDFs is common to other devices as well, and has been suggested to be due to the simultaneous presence of different mechanisms driving respectively coherent bursts and gaussian background turbulence. An attempt is made to relate differences in the PDFs to plasma conditions such as the local shift of the plasma column. A simple phenomenological model to interpret the nature of the PDF and assign a meaning to its parameters is also developed.Comment: 27 pages. Published in PPC

A superconducting flux-flow oscillator of terahertz range

We have elaborated, fabricated and tested a THz source radiating to open space based on the superconducting flux-flow oscillator (FFO). In this concept, the oscillator is integrated with the transmitting lens antenna based on a slot structure in Nb film with a thickness of ∼200 nm located on the same chip. The slot planar antenna is matched to the oscillator (by input) and to the semielliptical Si lens with a diameter of 10 mm (by output) providing a narrow output beam of THz emission. A harmonic mixer based on the superconductor-insulator-superconductor junction embedded in the "FFO and antenna" integrated structure has been used for the phase locking of the oscillator. Several designs of antenna coupled with the oscillator by microstrip lines have been numerically simulated, and the batches of experimental samples based on Nb-AlN-NbN superconducting trilayers with Rn •A ∼ 20 Ω•μm2 (jc ∼ 10 kA/cm2) have been fabricated and tested. Two different setups were used for experimental study: A THz spectrometer based on the SIS receiver with a high spectral resolution (better than 0.1 MHz) and a Si bolometer. The overall operating range of 250 to 700 GHz is covered by all the developed designs

Index

The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell–Jüttner model distributions. The main properties of the competing modes (developing parallel, transverse, and oblique to the beam) are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.Original Publication: Antoine Bret, Laurent Gremillet and Mark Eric Dieckmann, Multidimensional electron beam-plasma instabilities in the relativistic regime, 2010, Physics of Plasmas, (17), 12, 120501-1-120501-36. http://dx.doi.org/10.1063/1.3514586 Copyright: American Institute of Physics http://www.aip.org/</p