Two nominally identical ultra-stable cryogenic microwave oscillators are compared. Each incorporates a dielectric-sapphire resonator cooled to near 6 K in an ultra-low vibration cryostat using a low-vibration pulse-tube cryocooler. The phase noise for a single oscillator is measured at -105 dBc/Hz at 1 Hz offset on the 11.2 GHz carrier. The oscillator fractional frequency stability is characterized in terms of Allan deviation by 5.3 × 10 −16 τ −1/2 + 9 × 10 −17 for integration times 0.1 s < τ < 1000 s and is limited by a flicker frequency noise floor below 1 × 10 −16 . This result is better than any other microwave source even those generated from an optical comb phase-locked to a room temperature ultra-stable optical cavity. PACS numbers: 77.90.+k, 06.30.Ft, 07.20.Mc The time and frequency standards community is ever advancing the state-of-the-art in both stability and accuracy of atomic clocks [1]. With the development of atomic fountain clocks it was found that a more stable microwave interrogation oscillator was required than was available from an ultra-stable quartz oscillator to avoid the Dick effect [2][3][4][5]. The latter results from the fact that most atomic fountain clocks have significant dead time in their interrogation cycle, simply due to the fact that they are pulsed devices where one has to wait until the detection process is finished before the next cloud of cold atoms is launched [6]. This results in the introduction of the phase noise of the local reference oscillator, from which the microwave cavity frequency is derived, to the short-term stability of the fountain clock. The problem was overcome through the use of cryogenic sapphire oscillators with significantly much better short-term frequency stability [7] and consequently it has resulted in atomic fountain clocks reaching a performance limited only by quantum projection noise [8].These microwave oscillators based on a dielectricsapphire resonator cryogenically cooled to nearly 6 K are in use in several standards labs and have been found to be useful for various applications [9][10][11][12]. The oscillators [13][14][15], until recently, have relied on large dewars of liquid helium to cool the resonator with a few exceptions [16][17][18][19] where a cryocooler was used. However the latter had their short-term performance compromised by vibrations from the cryocooler itself. More recently low vibration pulse-tube cryocoolers and specially designed cryostats [20] have enabled cryogenic oscillators as equally stable [21-25] yet without being limited by the noise from the cryocooler.The present design is currently state-of-the-art. A silver-plated copper cavity encloses a 51 mm diameter * Electronic address: john.hartnett@uwa.edu.au and 30 mm high HEMEX grade sapphire cylindrical resonator and is the same as previously reported [13] (see Fig. 1 therein) but the thermal design for housing it in the cryostat is significantly different [24]. See Fig. 1. Also long coaxial cables connecting the cryogenic resonator to the room temperature loop o...

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Streambed horizontal hydraulic conductivity (Kh) has a substantial role in controlling exchanges between stream water and groundwater. We propose a new approach for determining Kh of the shallow streambed sediments. Undisturbed sediment samples were collected using tubes that were horizontally driven into streambeds. The sediment columns were analysed using a permeameter test (PT) on site. This new test approach minimizes uncertainties due to vertical flow in the vicinity of test tube and stream stage fluctuations in the computation of the Kh values. Ninety‐eight PTs using the new approach were conducted at eight sites in four tributaries of the Platte River, east‐central Nebraska, USA. The Kh values were compared with the nondirectional hydraulic conductivity values (Kg) determined from 12 empirical grain‐size analysis methods. The grain‐size analysis methods used the same sediment samples as Kh tests. Only two methods, the Terzaghi and Shepherd methods, yielded Kg values close to the Kh values. Although the Sauerbrei method produced a value relatively closer to Kh than other nine grain‐size analysis methods, the values from this method were not as reliable as the methods of Terzaghi and Shepherd due to the inconsistent fluctuation of the average estimates at each of the test sites. The Zunker, Zamarin, Hazen, Beyer, and Kozeny methods overestimated Kh, while the Slichter, US Bureau of Reclamation (USBR), Harleman, and Alyamani and Sen methods underestimated Kh. Any of these specific grain‐size methods might yield good estimates of streambed Kh at some sites, but give poor estimates at other sites, indicating that the relationship between Kg and Kh is significantly site dependent in our study. Copyright © 2011 John Wiley & Sons, Ltd.

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