[1] Theory of a beat-wave mechanism for very low frequency (VLF) wave generation in the ionosphere is presented. The VLF current is produced by beating two high power HF waves of slightly different frequencies through the nonlinearity and inhomogeneity of the ionospheric plasma. Theory also shows that the density irregularities can enhance the beat-wave generation. An experiment was conducted by transmitting two high power HF waves of 3.2 MHz and 3.2 MHz + f, where f = 5, 8, 13, and 2.02 kHz, from the HAARP transmitter. In the experiment, the ionosphere was underdense to the O-mode heater, i.e., the heater frequency f 0 > foF2, and overdense or slightly underdense to the X-mode heater, i.e., f 0 < fxF2 or f 0 ≥ fxF2. The radiation intensity increased with the VLF wave frequency, was much stronger with the X-mode heaters, and was not sensitive to the electrojet. The strongest VLF radiation of 13 kHz was generated when the reflection layer of the X-mode heater was just slightly below the foF2 layer and the spread of the O-mode sounding echoes had the largest enhancement, suggesting an optimal setting for beat-wave generation of VLF waves by the HF heaters.

This paper describes methods for reducing the statistical uncertainty in measurements made by noise thermometers using digital cross-correlators and, in particular, for thermometers using pseudo-random noise for the reference signal. First, a discrete-frequency expression for the correlation bandwidth for conventional noise thermometers is derived. It is shown how an alternative frequency-domain computation can be used to eliminate the spectral response of the correlator and increase the correlation bandwidth. The corresponding expressions for the uncertainty in the measurement of pseudo-random noise in the presence of uncorrelated thermal noise are then derived. The measurement uncertainty in this case is less than that for true thermal-noise measurements. For pseudo-random sources generating a frequency comb, an additional small reduction in uncertainty is possible, but at the cost of increasing the thermometer's sensitivity to non-linearity errors. A procedure is described for allocating integration times to further reduce the total uncertainty in temperature measurements. Finally, an important systematic error arising from the calculation of ratios of statistical variables is described.

[1] Beat-wave generation of very low frequency (VLF) waves by two HF heaters in the ionosphere is formulated theoretically and demonstrated experimentally. The heater-induced differential thermal pressure force and ponderomotive force, which dominate separately in the D and F regions of the ionosphere, drive an electron current for the VLF emission. A comparison, applying appropriate ionospheric parameters shows that the ponderomotive force dominates in beat-wave generation of VLF waves. Three experiments, one in the nighttime in the absence of D and E layers and two in the daytime in the presence of D and E layers, were performed. X mode HF heaters of slightly different frequencies were transmitted at CW full power. VLF waves at 10 frequencies ranging from 3.5 to 21.5 kHz were generated. The frequency dependencies of the daytime and nighttime radiation intensities are quite similar, but the nighttime radiation is much stronger than the daytime one at the same radiation frequency. The intensity ratio is as large as 9 dB at 11.5 kHz. An experiment directly comparing VLF waves generated by the beat-wave approach and by the amplitude modulation (AM) approach was also conducted. The results rule out the likely contribution of the AM mechanism acting on the electrojet and indicate that beat-wave in the VLF range prefers to be generated in the F region of the ionosphere through the ponderomotive nonlinearity, consistent with the theory. In the nighttime experiment, the ionosphere was underdense to the HF heaters, suggesting a likely setting for effective beat-wave generation of VLF waves by the HF heaters.

Technical advances and new results in noise thermometry at temperatures near the tin freezing point and the zinc freezing point using a quantized voltage noise source (QVNS) are reported. The temperatures are derived by comparing the power spectral density of QVNS synthesized noise with that of Johnson noise from a known resistance at both 505 K and 693 K. Reference noise is digitally synthesized so that the average power spectra of the QVNS match those of the thermal noise, resulting in ratios of power spectra close to unity in the low-frequency limit. Three-parameter models are used to account for differences in impedance-related time constants in the spectra. Direct comparison of noise temperatures to the International Temperature Scale of 1990 (ITS-90) is achieved in a comparison furnace with standard platinum resis-W. L. Tew (B) Process Measurements Division (836), National tance thermometers. The observed noise temperatures determined by operating the noise thermometer in both absolute and relative modes, and related statistics together with estimated uncertainties are reported. The relative noise thermometry results are combined with results from other thermodynamic determinations at temperatures near the tin freezing point to calculate a value of T − T 90 = +4(18) mK for temperatures near the zinc freezing point. These latest results achieve a lower uncertainty than that of our earlier efforts. The present value of T − T 90 is compared to other published determinations from noise thermometry and other methods.