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Sawtooth oscillations about helical current channels

An existing pseudospectral code for solving the three-dimensional equations of reduced magnetohydrodynamics is extended by adding a temperature equation. Resistivities and thermal conductivities are given their (isotropic) Braginskii temperature dependences, and are advanced self-consistently. Realistic-looking sawtooth oscillations are observed at modest Lundquist and Reynolds numbers. However, the oscillations are excited upon, and relax back to, a helical (rather than an axisymmetric) current channel.

Theobald, M. L.↗

Magnetospheric State of Sawtooth Events

Magnetospheric sawtooth events, first identified in the early 1990s, are named for their characteristic appearance of multiple quasiperiodic intervals of slow decrease followed by sharp increase of proton differential energy fluxes in the geosynchronous region. The successive proton flux oscillations have been interpreted as recurrences of stretching and dipolarization of the nightside geomagnetic field. Due to their often extended intervals with 210 cycles, sawteeth occurrences are sometimes referred to as a magnetospheric mode. While studies of sawtooth events over the past two decades have yielded a wealth of information about such events, the magnetospheric state conditions for the occurrence of sawtooth events and how sawtooth oscillations may depend on the magnetospheric state conditions remain unclear. In this study, we investigate the characteristic magnetospheric state conditions (specified by Psw interplanetary magnetic field (IMF) Btot, IMF Bz Vsw, AE, Kp and Dst, all time shifted with respect to one another) associated with the intervals before, during, and after sawteeth occurrences. Applying a previously developed statistical technique, we have determined the most probable magnetospheric states propitious for the development and occurrence of sawtooth events, respectively. The statistically determined sawtooth magnetospheric state has also been validated by using out-of-sample events, confirming the notion that sawtooth intervals might represent a particular global state of the magnetosphere. We propose that the sawtooth state of the magnetosphere may be a state of marginal stability in which a slight enhancement in the loading rate of an otherwise continuous loading process can send the magnetosphere into the marginally unstable regime, causing it to shed limited amount of energy quickly and return to the marginally stable regime with the loading process continuing. Sawtooth oscillations result as the magnetosphere switches between the marginally stable (loading) and unstable (unloading) phases.

Fung, Shing F.↗

A description of the software analysis from flight and simulation data of the course cut limiter in the TCV b-737 area navigation computer

During automatic horizontal path captures, the (Terminal Configured Vehicle) B-737 airplane maintained smaller than designed path intercept angles and experienced a sawtooth bank angle oscillation during its turn towards the path. From flight data, it was determined that these anomalies were caused by the improper output of the course cut limiter in the horizontal path control law. The output from the course cut limiter did not obtain its full value and it was calculated stepwise discontinuously. The automatic horizontal path captures were then conducted on the TCV B-737 airplane real-time simulation. The path intercept angles were maintained properly and no bank angle oscillation was encountered. Data showed that the course cut limiter was calculated at its full value in a continuous manner. The intermediate calculations of the course cut limiter in the airplane's navigation computer were rewritten and rescaled in such a manner that truncation errors could be minimized. The horizontal path capture tests were then reflown. The airplane maintained the proper path intercept angle and no bank angle oscillations occurred on any of the tests.

Knox, C. E.↗

Quasi-periodic oscillations of the magnetopause during northward sheath magnetic field

The Geotail satellite quasi-periodically crossed the dawn flank of magnetopause more than ten times during an interval of 1.5 hours on November 4, 1992. Magnetopause crossings were characterized by quasi-periodic pulses of a sawtooth wave form in the magnetic field and the plasma flow components tangential to the magnetopause. The magnetic field strength in the magnetosheath was larger than that in the magnetosphere. The direction of magnetic field outside the magnetopause current layer was northward with antisunward tilt, indicating the draping of magnetic field on the magnetopause. Boundary normals of wavy magnetopause systematically incline sunward on the upstream side, while they tend to incline antisunward with considerable deviation on the downstream side. Comparison with other multiple crossing events suggests that the November 4 event exhibits wavy structure of the dawn flank magnetopause associated with the northward interplanetary magnetic field (IMF).

Kokubun, S.↗

Coherent Detection of High-Rate Optical PPM Signals

A method of coherent detection of high-rate pulse-position modulation (PPM) on a received laser beam has been conceived as a means of reducing the deleterious effects of noise and atmospheric turbulence in free-space optical communication using focal-plane detector array technologies. In comparison with a receiver based on direct detection of the intensity modulation of a PPM signal, a receiver based on the present method of coherent detection performs well at much higher background levels. In principle, the coherent-detection receiver can exhibit quantum-limited performance despite atmospheric turbulence. The key components of such a receiver include standard receiver optics, a laser that serves as a local oscillator, a focal-plane array of photodetectors, and a signal-processing and data-acquisition assembly needed to sample the focal-plane fields and reconstruct the pulsed signal prior to detection. The received PPM-modulated laser beam and the local-oscillator beam are focused onto the photodetector array, where they are mixed in the detection process. The two lasers are of the same or nearly the same frequency. If the two lasers are of different frequencies, then the coherent detection process is characterized as heterodyne and, using traditional heterodyne-detection terminology, the difference between the two laser frequencies is denoted the intermediate frequency (IF). If the two laser beams are of the same frequency and remain aligned in phase, then the coherent detection process is characterized as homodyne (essentially, heterodyne detection at zero IF). As a result of the inherent squaring operation of each photodetector, the output current includes an IF component that contains the signal modulation. The amplitude of the IF component is proportional to the product of the local-oscillator signal amplitude and the PPM signal amplitude. Hence, by using a sufficiently strong local-oscillator signal, one can make the PPM-modulated IF signal strong enough to overcome thermal noise in the receiver circuits: this is what makes it possible to achieve near-quantum-limited detection in the presence of strong background. Following quantum-limited coherent detection, the outputs of the individual photodetectors are automatically aligned in phase by use of one or more adaptive array compensation algorithms [e.g., the least-mean-square (LMS) algorithm]. Then the outputs are combined and the resulting signal is processed to extract the high-rate information, as though the PPM signal were received by a single photodetector. In a continuing series of experiments to test this method (see Fig. 1), the local oscillator has a wavelength of 1,064 nm, and another laser is used as a signal transmitter at a slightly different wavelength to establish an IF of about 6 MHz. There are 16 photodetectors in a 4 4 focal-plane array; the detector outputs are digitized at a sampling rate of 25 MHz, and the signals in digital form are combined by use of the LMS algorithm. Convergence of the adaptive combining algorithm in the presence of simulated atmospheric turbulence for optical PPM signals has already been demonstrated in the laboratory; the combined output is shown in Fig. 2(a), and Fig. 2(b) shows the behavior of the phase of the combining weights as a function of time (or samples). We observe that the phase of the weights has a sawtooth shape due to the continuously changing phase in the down-converted output, which is not exactly at zero frequency. Detailed performance analysis of this coherent free-space optical communication system in the presence of simulated atmospheric turbulence is currently under way.

Vilnrotter, Victor↗

Time Resolved Irradiance of an Integrating Sphere Illuminated by a Mode-Locked Optical Parametric Oscillator

Tunable laser based illumination sources have been adopted by a number of recent hyperspectral instruments for pre-launch spectral radiometric calibration. Some of these sources use mode-locked cavity configurations, which produce a pulse train and create an undesirable fluctuation in the radiometric source at the mode locking frequency. Although typically this frequency is several orders of magnitude higher than the instrument response, care must be taken to ensure the resultant calibration is not biased due to detector or electronic saturation effects. The temporal averaging properties of an integrating sphere can be used to reduce high frequency fluctuations to an acceptable level. In this work, the time resolved output of an integrating sphere coupled with a mode-locked source was measured. A 76 cm diameter sphere with 30 cm output aperture was illuminated using a mode-locked pulse train at 76 MHz, with single pulse durations of 12 ps. The time constant of the sphere was found to be 36 ns, and the resultant temporal averaging of pulses produced a maximum time varying irradiance at the output of 20% of the mean. The form of this time variance is a sawtooth pattern, with a sharp rise during the introduction of each pulse into the sphere followed by a slower decay between pulses. A comparison of instrument calibration data generated with this integrating sphere using both a mode locked source and a continuous wave source is also given. .

McAndrew, Brendan↗