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Multi-harmonic electron cyclotron instabilities

The reported investigation constitutes an extension of studies conducted by Ashour-Abdalla and Kennel (1975, 1976, 1978) with respect to a basic plasma model of Young et al. (1973). The model involves a combination of a cold Maxwellian background plasma, a hot plasma, and a 'loss cone' type of free energy source. Previous results on the first cyclotron harmonic bands are extended to multiharmonics. The significance of the obtained relations is discussed and tentative conclusions are presented. Given that the spatial growth rates of the convective modes are comparable, and that simultaneous nonconvective instability (NCI) is possible, it is concluded that multiharmonic emissions ought to be a common feature of the magnetospheric electrostatic wave observations. Since the volume of parameter space for which the first harmonic is NCI, and the volume for which the convective first harmonic mode has significant spatial growth rates, exceed those for the higher harmonics, first harmonic waves should be the most commonly observed and the higher harmonics should usually be accompanied by the first harmonic.

Ashour-Abdalla, M.

Harmonic auroral kilometric radiation of natural origin

When the ISIS 1 satellite passes through the auroral kilometric radiation (AKR) source region the sounder receiver often detects harmonic bands of radiation associated with the fundamental AKR band. These harmonic components were earlier attributed to a nonlinear instrumental response to the strong wide-band bursty AKR fundamental signal. Evidence is here presented that indicates that these harmonics are of natural origin, namely: (1) all the harmonic signals are sometimes observed to have nearly the same bandwidth, (2) when the fundamental signal has two components the harmonic signal sometimes corresponds to the weaker rather than the stronger component, (3) a weak harmonic can be observed to be associated with a weak fundamental, and (4) a 'harmonic' signal can be observed when there is no fundamental.

Benson, R. F.

Harmonic multiplication using resonant tunneling

This paper demonstrates the use of resonant-tunneling diodes as varistors for harmonic multiplication. It is shown that efficient odd-harmonic conversion is possible and that even harmonics do not appear because of the antisymmetry of the current-voltage (I-V) curve. It is also shown that, with the proper choice of resonant-tunneling structure and pump amplitude, most of the harmonic output power can be confined to a single odd-harmonic frequency. Fifth-harmonic multiplication was demonstrated with an output at 21.75 GHz and a power conversion efficiency of 0.5 percent, and a fifth-harmonic efficiency of 2.7 percent was achieved in a circuit simulation using an improved I-V curve.

Sollner, T. C. L. G.

Failure of Harmonic Gears During Verification of a Two-Axis Gimbal for the Mars Reconnaissance Orbiter Spacecraft

The Mars Reconnaissance Orbiter (MRO) spacecraft has three two-axis gimbal assemblies that support and move the High Gain Antenna and two solar array wings. The gimbal assemblies are required to move almost continuously throughout the mission's seven-year lifetime, requiring a large number of output revolutions for each actuator in the gimbal assemblies. The actuator for each of the six axes consists of a two-phase brushless dc motor with a direct drive to the wave generator of a size-32 cup-type harmonic gear. During life testing of an actuator assembly, the harmonic gear teeth failed completely, leaving the size-32 harmonic gear with a maximum output torque capability less than 10% of its design capability. The investigation that followed the failure revealed limitations of the heritage material choices that were made for the harmonic gear components that had passed similar life requirements on several previous programs. Additionally, the methods used to increase the stiffness of a standard harmonic gear component set, while accepted practice for harmonic gears, is limited in its range. The stiffness of harmonic gear assemblies can be increased up to a maximum stiffness point that, if exceeded, compromises the reliability of the gear components for long life applications.

Johnson, Michael R.

STEREO and Wind Observations of Intense Cyclotron Harmonic Waves at the Earth's Bow Shock and Inside the Magnetosheath

We present the first observations of electron cyclotron harmonic waves at the Earth's bow shock from STEREO and Wind burst waveform captures. These waves are observed at magnetic field gradients at a variety of shock geometries ranging from quasi-parallel to nearly perpendicular along with whistler mode waves, ion acoustic waves, and electrostatic solitary waves. Large amplitude cyclotron harmonic waveforms are also observed in the magnetosheath in association with magnetic field gradients convected past the bow shock. Amplitudes of the cyclotron harmonic waves range from a few tens to more than 500 millivolts/meter peak-peak. A comparison between the short (15 meters) and long (100 meters) Wind spin plane antennas shows a similar response at low harmonics and a stronger response on the short antenna at higher harmonics. This indicates that wavelengths are not significantly larger than 100 meters, consistent with the electron cyclotron radius. Waveforms are broadband and polarizations are distinctively comma-shaped with significant power both perpendicular and parallel to the magnetic field. Harmonics tend to be more prominent in the perpendicular directions. These observations indicate that the waves consist of a combination of perpendicular Bernstein waves and field-aligned waves without harmonics. A likely source is the electron cyclotron drift instability which is a coupling between Bernstein and ion acoustic waves. These waves are the most common type of high-frequency wave seen by STEREO during bow shock crossings and magnetosheath traversals and our observations suggest that they are an important component of the high-frequency turbulent spectrum in these regions.

bow shock

Topsoil bulk geochemical compositions - An updated harmonized global dataset

Mineral weathering is a key biogeochemical process because of the capacity of minerals to stabilize organic matter. However, predicting soil weathering status across large spatial areas still isn’t possible due to a lack of global data and theoretical frameworks. To address this knowledge gap, multiple global datasets of bulk topsoil geochemical compositions have been harmonized using R. These datasets document topsoil bulk geochemical compositions across five continents (n = ~16,000 observations). Source data for these observations include the EuroGEOSurveys Geochemical Baseline Database (FOREGS), the US Geological Survey National Geochemical Database (NASGLP), the Geochemical Atlas of Australia (GAA), the US Geological Survey Alaska Geochemical Database (AGD84), the National Cooperative Soil Survey (NCSS), the European Geochemical Mapping of Agricultural Soil (GEMAS), Ecorespira-Amazon (ERA), the New Zealand Geochemical Baseline Survey (NZ_GBS), and the African Soil Information Service (AFSIS). Major elements observed include Aluminum (Al), Calcium (Ca), Iron (Fe), Potassium (K), Magnesium (Mg), Sodium (Na), Titanium (Ti), Manganese (Mn), Phosphorus (P), Carbon (C), and Sulfur (S). This data package includes the harmonized dataset itself, and the R scripts necessary to harmonize these datasets, in addition to metadata that describes all columns, files, and databases used in this project. Methods & Sampling Step 1 – Databases of geochemical data identified This study aimed to leverage existing measurements of topsoil geochemical data. Databases were first identified and deemed appropriate for inclusion if they were measuring soils and performed these measurements on the <2mm soil fraction. Databases such as NCSS and AGD84 needed more post processing to include in the database and this was done using the NCSS_datamerge_031626 R file and Alaska_USGSmerge_031626 R file, respectively. Step 2 – Database harmonization Once appropriate databases were identified, they were harmonized for ease of analysis using the R script Database_Harmonization_031826. This included removing columns from original datasets that would not be used in analysis (removed columns are noted in the code). Then, data cleaning procedures specific to each dataset were undertaken. This includes standardizing columns to include units and adding metadata columns regarding procedures for analyzing specific elements. Functions for standardizing measurements and units are outline in R files: calculate element_mg_kg_031626, calculate_oxide_wt_perc_031626, change_oxide_caps_031626, and conv_2_numeric_031626. This also included adding a unique identifier for each sample to identify it with its respective database (see CD_ID in data dictionary). Geographic information: Data reflect a compilation of datasets collected globally. Geographic areas covered by each of the datasets include: - EuroGEOSurveys Geochemical Baseline Database (FOREGS) - European continent - North American Soil Geochemical Landscapes (NASGLP) - continental United States and limited parts of Canada (see database key for more details) - National Geochemical Survey of Australia (GAA) - Australia - Alaska geochemical database (AGDB4) - Alaska - National Cooperative Soil Survey (NCSS) - Global measurements, but concentrated in the continental United States - Geochemical data for arable land and land under permanent grass cover in continental Europe (GEMAS) - continental Europe - Ecorespira-Amazon (ERA) - Geochemical data from the Amazon basin - Geochemical baseline data for New Zealand (NZGBS) - New Zealand - Geochemical data collected across continental Africa (AfSIS) - Measurements across Africa

EARTH SCIENCE > LAND SURFACE > SOILS

Harmonic structure of Pc 3-4 pulsations

Power spectra of magnetic pulsations observed at synchronous orbit by the ATS 6 satellite often show several spectral peaks simultaneously. Such pulsations, called harmonic events because of the nearly constant separation between successive peaks, are continuously observed in the dayside in the Pc 3-4 frequency range (6.6-100 mHz). The harmonic events are seen clearly only in the east-west magnetic field component. The spectral peaks are regularly spaced with a typical minimum separation of 14 mHz in the morning gradually decreasing to 10 mHz in the afternoon. In the dynamic spectra of harmonic events, the fundamental mode is usually absent. In addition, the relative amplitudes of the higher harmonics depend on the magnetic latitude. These observed features can be explained by a standing Alfven wave consisting of many discrete harmonic frequencies. A statistical analysis of power spectra demonstrates that at least 10-30% of Pc 3 pulsations can be classified as harmonic events. For a selected event on August 7, 1975, the plasma mass density at the synchronous orbit is estimated to be 3-8 hydrogen mass/cu cm.

Takahashi, K.

Multispacecraft observations of the harmonic structure of Pc 3-4 magnetic pulsations

Harmonically related Pc 3-4 pulsations (7-100 mHz) are observed simultaneously by the three geosynchronous satellites ATS 6, SMS 1, and SMS 2, which are separated 20 deg from one another. At a given instant the frequency of the same harmonic is different from one spacecraft to another and each spacecraft observes a decrease in the fundamental frequency as it moves from morning (15 mHz) to afternoon (10 mHz). This frequency behavior is explained in terms of standing Alfven waves, for which the frequency is determined by the local magnetic field and plasma density. Occurrence of harmonic Pc 3-4 waves only during daytime hours (0400-2000 LT) and their frequency characteristics suggest a broadband energy source located on the dayside. Possible azimuthal wave number m and azimuthal phase velocity V(phi) of the second through fourth harmonics are determined from an unusual interval during which identical harmonic frequencies were observed at SMS 1 and ATS 6. Under the assumption of tailward propagation of constant-phase fronts at the same velocity for all these harmonics, V(phi) of about 1700 km/s is obtained.

Takahashi, K.

DE 1 observations of harmonic auroral kilometric radiation

The plasma wave instrument on board the DE 1 spacecraft has observed several intervals of auroral kilometric radiation during which harmonic structure is clearly present. The paper presents evidence, some of which is based on unique capabilities of the DE instrument, which argues strongly that the harmonic structures are natural rather than instrumental in origin. The harmonic emissions occur infrequently, but when present may persist for intervals of up to an hour. The emissions are relatively narrow band and consist of a relatively weak fundamental accompanied by an even weaker second harmonic. The ratio of power in the fundamental band to the power in the harmonic ranges from 10 to 100. In all cases, polarization data indicate that the fundamental is a left-hand ordinary (L-O) mode emission while the harmonic is right-hand extraordinary (R-X) mode. These observations are consistent with predictions based on the cyclotron maser mechanism.

Mellott, M. M.

Electromagnetic ion beam instabilities - Growth at cyclotron harmonic wave numbers

The linear theory of electromagnetic ion beam instabilities for arbitrary angles of propagation is studied, with an emphasis on the conditions necessary to generate unstable modes at low harmonics of the ion cyclotron resonance condition. The present results extend the analysis of Smith et al. (1985). That paper considered only the plasma parameters at a time during which harmonic wave modes were observed in the earth's foreshock. The parameters of that paper are used as the basis of parametric variations here to establish the range of beam properties which may give rise to observable harmonic spectra. It is shown that the growth rates of both left-hand and right-hand cyclotron harmonic instabilities are enhanced by an increase in the beam temperature anisotropy and/or the beam speed. Decreases in the beam density and/or the core-ion beta reduce the overall growth of the cyclotron harmonic instabilities but favor the growth of these modes over the growth of the nonresonant instability and thereby enhance the observability of the harmonics.

Smith, Charles W.

Spherical Harmonic Analysis of Particle Velocity Distribution Function: Comparison of Moments and Anisotropies using Cluster Data

This paper presents a spherical harmonic analysis of the plasma velocity distribution function using high-angular, energy, and time resolution Cluster data obtained from the PEACE spectrometer instrument to demonstrate how this analysis models the particle distribution function and its moments and anisotropies. The results show that spherical harmonic analysis produced a robust physical representation model of the velocity distribution function, resolving the main features of the measured distributions. From the spherical harmonic analysis, a minimum set of nine spectral coefficients was obtained from which the moment (up to the heat flux), anisotropy, and asymmetry calculations of the velocity distribution function were obtained. The spherical harmonic method provides a potentially effective "compression" technique that can be easily carried out onboard a spacecraft to determine the moments and anisotropies of the particle velocity distribution function for any species. These calculations were implemented using three different approaches, namely, the standard traditional integration, the spherical harmonic (SPH) spectral coefficients integration, and the singular value decomposition (SVD) on the spherical harmonic methods. A comparison among the various methods shows that both SPH and SVD approaches provide remarkable agreement with the standard moment integration method.

Gurgiolo, Chris

Efficiency-optimized relativistic plasma harmonics for extreme fields

Bright harmonic radiation from relativistically oscillating laser plasmas offers a direct route for generating extreme electromagnetic fields. Theory predicts that under optimized conditions, the plasma medium can support strong spatiotemporal compression of laser energy in a coherent harmonic focus (CHF), delivering intensity boosts many orders of magnitude greater than the incident driving laser pulse. Although diffraction-limited performance (spatial compression) and attosecond phase locking (temporal compression) have been demonstrated experimentally, efficient coupling of relativistically intense laser pulse energy into the emitted harmonic cone has not been realized so far. Here we demonstrate that this highly nonlinear interaction can be tailored to deliver the maximum conversion efficiencies predicted from simulations. By fine-tuning the temporal profile of the driving laser on sub-picosecond (<10 −12 s) timescales, energies >9 mJ between the 12th and 47th harmonics are observed. These results are in agreement with the theoretically expected efficiency dependence on harmonic order, verifying that optimal conditions have been achieved in the generation process. This is the important final element required to achieve the expected intensity boosts from a CHF in experiments. Although obtaining spatiotemporal compression and optimal efficiency simultaneously remains challenging, the path to realizing extreme optical field strengths approaching the critical field of quantum electrodynamics (the Schwinger limit at >10 16 V cm −1 or >10 29 W cm −2 ) is now open, permitting all-optical studies of the quantum vacuum and new frontiers for intense attosecond science.

High-harmonic generation

Theoretical Study of High Harmonic Generation in Monolayer NbSe 2

High harmonic generation (HHG) is a powerful probe of electron dynamics on attosecond to femtosecond time scales and has been successfully used to detect electronic and structural changes in solid-state quantum materials, including transition-metal dichalcogenides (TMDs). Among TMDs, bulk NbSe 2 exhibits charge density wave (CDW) order below 33 K and becomes superconducting below 7.3 K. Monolayer NbSe 2 also has superconducting and CDW behavior and is therefore interesting as a material whose different structural and electronic properties could be probed via HHG. Here, we predict the HHG response of the pristine 2H and CDW phases of monolayer NbSe 2 using real-time time-dependent density functional theory under the application of a simulated laser pulse excitation. We find that due to the lack of inversion symmetry in both monolayer phases, it is possible to excite even harmonics and that the even harmonics appear as the transverse components of the current response under excitations polarized along the zigzag direction of the monolayer, while odd harmonics arise from the longitudinal current response in all excitation directions. This suggests that the even and odd harmonic responses can be controlled via the polarization of the probing field, opening an avenue for potentially useful applications in optoelectronic devices.

36 MATERIALS SCIENCE

A problem in representing the core magnetic field of the earth using spherical harmonics

Although there are computational advantages to the representation of the earth's magnetic field by spherical harmonic coefficients of the magnetic potential, up to the thirteenth degree and order, the following disadvantages emerge: (1) the use of spherical harmonics of up to a certain degree does not remove wavelengths greater than a certain value from the surface fields, and (2) the total field magnitudes represented by spherical harmonics up to a certain degree have minimum wavelengths equal to the circumference of the earth divided by twice the maximum degree of the harmonic used. The implications of the ways in which surface fields are separated into core and crustal components are discussed, and it is concluded that since field signals are generated in the core, the representation of the core field by spherical harmonics of potential does not adequately represent all core field components.

Carle, H. M.

Fundamental and harmonic emission in interplanetary type 2 radio bursts

Three interplanetary type II radio bursts which show two prominent and long duration bands in their dynamic spectra were analyzed in detail and compared to similar bands in meter wavelength type II events. These bands, which differ by a factor of about two in frequency, were interpreted in terms of fundamental and harmonic emission. The fundamental component has a greater average intensity than the harmonic, due largely to short intense brightenings. The fundamental spectral profile is more narrow than that of the harmonic, with harmonic band typically exhibiting a larger bandwidth to frequency ratio than the fundamental by a factor of two. The fundamental has a larger source size than the harmonic, 160 degrees versus 110 degrees, on average, as viewed from the Sun. Two of the events have source positions which correlate well with the associated flare positions.

Lengyel-Frey, D.

Fundamental and harmonic emission in interplanetary type II radio bursts

Three interplanetary type II radio bursts which show two prominent and long duration bands in their dynamic spectra were analyzed in detail and compared to similar bands in meter wavelength type II events. These bands, which differ by a factor of about two in frequency, were interpreted in terms of fundamental and harmonic emission. The fundamental component has a greater average intensity than the harmonic, due largely to short intense brightenings. The fundamental spectral profile is more narrow than that of the harmonic, with harmonic band typically exhibiting a larger bandwidth to frequency ratio than the fundamental by a factor of two. The fundamental has a larger source size than the harmonic, 160 degrees versus 110 degrees, on average, as viewed from the sun. Two of the events have source positions which correlate well with the associated flare positions.

Lengyel-Frey, D.

The Local Stellar Velocity Field via Vector Spherical Harmonics

We analyze the local field of stellar tangential velocities for a sample of 42,339 nonbinary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism.We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships, we determine the solar velocity with respect to the local stars of (V(sub X), V(sub Y), V(sub Z)) = (10.5, 18.5, 7.3) +/- 0.1 km s(exp -1) not for the asymmetric drift with respect to the local standard of rest. If only stars more distant than 100 pc are considered, the peculiar solar motion is (V(sub X), V(sub Y), V(sub Z)) = (9.9, 15.6, 6.9) +/- 0.2 km s(exp -1). The adverse effects of harmonic leakage, which occurs between the reflex solar motion represented by the three electric vector harmonics in the velocity space and higher degree harmonics in the proper-motion space, are eliminated in our analysis by direct subtraction of the reflex solar velocity in its tangential components for each star...

kinematics

Driving an Active Vibration Balancer to Minimize Vibrations at the Fundamental and Harmonic Frequencies

Vibrations of a principal machine are reduced at the fundamental and harmonic frequencies by driving the drive motor of an active balancer with balancing signals at the fundamental and selected harmonics. Vibrations are sensed to provide a signal representing the mechanical vibrations. A balancing signal generator for the fundamental and for each selected harmonic processes the sensed vibration signal with adaptive filter algorithms of adaptive filters for each frequency to generate a balancing signal for each frequency. Reference inputs for each frequency are applied to the adaptive filter algorithms of each balancing signal generator at the frequency assigned to the generator. The harmonic balancing signals for all of the frequencies are summed and applied to drive the drive motor. The harmonic balancing signals drive the drive motor with a drive voltage component in opposition to the vibration at each frequency.

Holliday, Ezekiel S.