Detecting high-frequency gravitational waves with microwave cavities
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Mechanically-stable integral storage-bulb/microwave cavity made out of single piece of fused quartz improves frequency stability. Single-piece construction eliminates joints, making cavity dimensionally and hence frequency-stable. Fused quartz is used because of its low thermal expansion coefficient.
The noncryogenic, single axis, gravity gradiometer which is characterized by a sensitivity of the order of 10 to the minus 2 power Eovos Units in a few sec integration time was investigated. The prototype of testing gradiometer on the earth surface by the free fall in vacuo method was expanded. An existing free fall tower facility and the possibility of adding inside the falling elevator cabin an air tight, sealed, cylindrical container with inside pressure or = -0.001 Torr were examined to test the gradiometer in free fall conditions inside this evacuated container. Earth's gravity anomalies are simulated with masses of suitable shape, weight, and location. The attitude of the falling gradiometer is monitored by a three axis gyro package mounted on the instrument package. It is concluded that the free fall testing of the gradiometer is both feasible and practical.
Technical approaches to increase the sensitivity of a non-cryogenic gradiometer toward the goal of 0.001 EU/square root of Hz, with solutions that have the potential of achieving an even more ambitious threshold, such as 0.0001 EU/square root of Hz are discussed. This goal can be achieved with a gradiometer design in which the proof masses are each suspended from two small arms, the torsion of which is directly related to the displacement of the sensing element. A negative-spring action, aimed at reducing the resonance frequency, is provided in this design by means of an external electrostatic field. This configuration of the instrument is also suitable for use in a tensorial arrangement.
A technique for measurement of individual hydrometeor absorption cross sections is presented. Cross sections are inferred by inserting the hydrometeor into a high Q resonant cavity and measuring the Q perturbation. Tests were conducted in a 10.64 GHz, TM(010) cavity. Absorption cross sections were measured at room temperature for 0.5 to 2.0 mm water drops, and were found to agree with the Rayleigh theory. Cross sections were also measured as a function of temperature, and from these the dielectric loss term lm(-K) was inferred for supercooled water down to -17 C.
A vibration technique his been developed to continuously maintain mode resonance and impedance much between a constant frequency magnetron source and resonant cavity. This method uses a vibrating metal rod to modulate the volume of the cavity in a manner equivalent to modulating an adjustable plunger. A similar vibrating metal rod attached to a stub tuner modulates the waveguide volume between the source and cavity. A phase sensitive detection scheme determines the optimum position of the adjustable plunger and stub turner during processing. The improved power transfer during the heating of a 99.8% pure alumina rod was demonstrated using this new technique. Temperature-time and reflected power-time heating curves are presented for the cases of no tracking, impedance tracker only, mode tracker only and simultaneous impedance and mode tracking. Controlled internal melting of an alumina rod near 2000 C using both tracking units was also demonstrated.
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A new experimental approach for high-precision density measurements of liquid helium near the lambda transition is proposed.
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We are investigating a microwave resonant cavity transducer for flow sensing in the vessel of a high temperature fluid advanced reactor (AR), such as a molten salt cooled reactor (MSCR) or a sodium fast reactor (SFR). This transducer is a hollow metallic cylindrical cavity, with one of the flat walls of the cylinder flexible enough to undergo microscopic deflection due to dynamic fluid pressure. Membrane deflection leads to a shift in the microwave resonant frequency, which can be detected with a spectrum analyzer. We have developed a continuum electromechanics model of the microwave resonant cavity transducer performance. The deflection of the membrane is calculated using equations from the theory of plates and shells for deflection of radially constrained thin circular disk under uniform load. The microwave frequency shift is calculated using the equations from the microwave cavity perturbation theory. The transducer model was validated with proof-of-concept experimental data of water flow sensing with a Brass 360 right circular cylinder with 22.2mm diameter and 203µm thick wall. The cavity was excited through a subwavelength hole in TE 011 mode with resonant frequency f ≈ 17.8GHz. Subsequently, we have performed a preliminary proof-of-principle test of flow sensing in high temperature liquid sodium in environment. For this test, we have developed a cylindrical resonator with the same dimensions as for the Brass 360 cavity. The resonator for high temperature liquid sodium test was machined from stainless steel 316 and electroplated with silver on the interior surfaces. We have also developed and insertion probe consisting of a 50cm WR-42 brass waveguide enclosed in a protective SS316 tube. The cavity was excited through a subwavelength hole on the side of the wall of the cylinder in the TE 011 mode with resonant frequency f ≈ 17.8GHz. The liquid sodium setup consists of a cylindrical vessel with a center feed line, where a transducer inserted through the top cap of the vessel measures velocity of the impinging liquid jet. The sodium flow sensing study was performed in a liquid sodium vessel at 340°C temperature and ambient pressure. The flow rate was changed by varying sodium pump power, and a frequency shift of several hundred kHz was observed. The transducer was removed after 70 days of testing. No visual damage was observed, and the electromagnetic response remained the same. As a calibration experiment, we have assembled a water vessel with a center feed, and with dimensions similar to those of the liquid sodium setup. Water flow sensing was performed before and after liquid sodium test. The responses in both cases are similar and agree with COMSOL computer simulations. Because long-term (multi-year) experimental tests of transducer resilience to harsh environment are not practical, we have developed a probabilistic model of creep to estimate transducer resilience to the harsh environment. The probabilistic model considers diffusion creep under the condition of high temperature and low stress, where the stress and temperature are allowed to be random variables with Gaussian distributions. Using the probabilistic model, we estimate inelastic membrane deflections due to creep for several temperature ranges. We conclude that for temperatures less than 650°C, creep has negligible long-term effect on the transducer performance.
High-temperature fluid reactors, such as molten salt cooled reactors (MSCR) and sodium fast reactors (SFR), are a promising advanced reactor option. Measurement of high-temperature fluid process variables, in particular the flow inside the pressure vessel, is a challenging task because of harsh environment, which includes high radiation, high temperature, and contact with highly corrosive coolant fluid. We are investigating a microwave cavity-based transducer for high-temperature fluid flow sensing. This sensor is a hollow metallic cylindrical cavity, which can be fabricated from stainless steel, and as such is expected to be resilient to radiation, high temperature and corrosive environment of MSCR and SFR. The principle of sensing consists of making one wall of the cylindrical cavity flexible enough so that dynamic pressure, which is proportional to fluid velocity, will cause membrane deflection. A cavity is characterized by its resonant frequencies. Membrane deflection causes cavity volume change, which leads to a shift in the resonant frequency. Feasibility of the flow sensor is evaluated with signal sensitivity using COMSOL computer simulations. A right cylinder geometry stainless steel cavity with dimeter of 0.8in was investigated. We choose membrane thickness of 10mil, so that corrosion anticipated to proceed at the rate of 1mil/year in liquid sodium would affect no more than 10% of the membrane. Using the properties of liquid sodium fluid, and stainless-steel material property values at 500oC, we calculate frequency shift for a range of values of fluid velocity from 0.5m/s to 2m/s. Results of computer simulations indicate measurable sensitivity to flow for this cavity design. Following these simulations, we have developed a preliminary design for fabrication of a transducer operating in microwave K-band for proof-of-principle tests.
We are investigating a microwave cavity-based transducer for in-core high-temperature fluid flow sensing in molten salt cooled reactors (MSCR) and sodium fast reactors (SFR). This sensor is a hollow metallic cylindrical cavity, which can be fabricated from stainless steel, and as such is expected to be resilient to radiation, high temperature and corrosive environment of MSCR and SFR. The principle of sensing consists of making one wall of the cylindrical cavity flexible enough so that dynamic pressure, which is proportional to fluid velocity, will cause membrane deflection. Membrane deflection causes cavity volume change, which leads to a shift in the resonant frequency. Feasibility of the sensor was initially investigated with analytical derivations and with COMSOL RF Module computer simulations of resonant frequency spectral shift due to uniform load. We also investigated the mechanical integrity of the flowmeter’s membrane through analytical modelling and COMSOL Structural Mechanics Module computer simulations. Both the analytic model and COMSOL model showed that maximum stresses on the plate, which are at the radial boundary of the plate, are three orders of magnitude smaller than the material’s yield strength and ultimate tensile strength. This indicates that the sensor is at a low risk of mechanical failure. Using results from models, we have developed an initial design for a microwave K-band sensor. A cylindrical resonator prototype was fabricated from brass for the initial tests. The external dimensions of the cavity are matched to the flange of a standard WR-42 waveguide. Microwave field is coupled into the resonant cavity through a subwavelength-size aperture. A test article was developed consisting of a piping Tee with a bulkhead WR-42 microwave waveguide installed in a leak-proof assembly. A microwave waveguide circulator was installed in the setup to suppress the effect of reflections at the cavity entrance by increasing the isolation between the input and the output port. Preliminary spectral characterization of cavity spectral response was performed with a portable PXIe chassis microwave VNA with a custom GUI. Preliminary dry tests of the transducer response were conducted with a set of calibrated weights. Transducer frequency shift was shown to be monotonically increasing with increasing pressure. The next steps will involve investigation of the transducer performance for water flow sensing.
We are investigating a microwave cavity-based transducer for in-core high-temperature fluid flow sensing in molten salt cooled reactors (MSCR) and sodium fast reactors (SFR). This sensor is a hollow metallic cylindrical cavity. The principle of sensing consists of making one wall of the cylindrical cavity flexible enough so that dynamic pressure, which is proportional to fluid velocity, will cause membrane deflection. Membrane deflection causes cavity volume change, which leads to a shift in the resonant frequency. To validate sensor physics, we have performed proof-of-principle test of flow sensing in water. For this test, we have developed a cylindrical resonator for K-band, which was machined from brass. The cavity was excited through WR-42 waveguide through a subwavelength hole on the side of the wall of the cylinder. To increase the spectral signal visibility, we developed a signal processing method for baseline subtraction. A flow loop for proof-of-principle test of transducer performance in water was assembled. A commercial flow meter was installed in the loop for reference measurements. Cylindrical cavity was excited in the TEM 011 mode with resonant frequency f ≈ 17.8GHz. Frequency shift of cavity spectral response was obtained by gradually increasing water flow rate from 0 to 60gpm. Corresponding monotonic increase of resonant frequency shift by several MHz was observed.
The microwave resonant cavity flow sensor has been proposed to address the difficulties of measuring high-temperature molten salt flow in reactor vessels. The flow sensor consists of a metallic cylindrical cavity coupled to a microwave waveguide. The cylindrical cavity has one of the flat surfaces thin enough to undergo microscopic deflection due to dynamic pressure of the exerted by the flowing fluid. Deflection of the membrane causes a shift in the microwave resonant frequency. Fluid velocity can be estimated from the calibration curve. The objective of this report is to investigate mechanical integrity of the flowmeter’s membrane. The membrane is a thin stainless-steel circular plate with a clamped edge, subjected to uniform load. By calculating the stress on the plate due to deflection and, comparing the stress to the material ultimate tensile strength and yield strength, it can be estimated if the plate will fail. If the maximum stress is greater than the yield strength, the plate will undergo plastic deformation, and the sensor will be disabled. A stress greater than the ultimate tensile strength will cause the plate to fracture. The stress on the plate was calculated with an analytic closed form solution model, and with COMSOL Structural Mechanics Module which does not involve any approximations. Stresses in both the analytic model and COMSOL numerical model were calculated for stainless steel 316 thin circular plates under room temperature conditions, where the fluid is water. The diameter of the circular plate is approximately one inch, and thickness is 10mil. Fluid flow velocity is in the range from 0.5m/s to 1m/s. The results from the two models are similar. Both the analytic model and COMSOL model showed that maximum stresses on the plate, which are at the radial boundary of the plate, are three orders of magnitude smaller than the yield strength and ultimate tensile strength. This indicates that the sensor is at a low risk of mechanical failure.