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NASA NTRS2006

Topside sounders as mobile ionospheric heaters

There is evidence that satellite-borne RF sounders can act as mobile ionospheric heaters in addition to performing topside sounding. The main objective of topside sounding is to use sounder-generated electromagnetic (em) waves to obtain ionospheric topside vertical electron-density (N(sub e) profiles. These profiles are obtained from mathematical inversions of the frequency vs. delay-time ionospheric reflection traces. In addition to these em reflection traces, a number of narrowband intense signals are observed starting at zero delay times after the transmitted pulses. Some of these signals, termed plasma resonances, appear at characteristic frequencies of the ambient medium such as at the electron cyclotron frequency f(sub ce), the harmonics nf(sub ce), the electron plasma frequency f(sub pe) and the upper-hybrid frequency f(sub uh), where (f(sub uh))(exp 2) = (f(sub ce))(exp 2) + (f(sub pe))(exp 2) . These signals have been attributed to the oblique echoes of sounder-generated electrostatic (es) waves. These resonances provide accurate in situ f(sub pe) and f(sub ce) values which, in turn, lead to accurate N(sub e) and [B] values where B is the ambient magnetic field. Resonances are also observed between the nf(sub ce) harmonics both above and below f(sub uh). The former, known as the Qn plasma resonances, are mainly attributed to the matching of the wave group velocity of sounder-generated (Bernstein-mode) es waves to the satellite velocity. The frequency spectrum of these waves in the magnetosphere can be used to detect non-Maxwellian electron velocity-distributions. In addition, these resonances also exhibit components that appear to be the result of plasma emissions stimulated by the sounder pulses. The plasma resonances observed between the nf(sub ce) harmonics and below f(sub uh), known as the Dn plasma resonances, are entirely attributed to such sounder-stimulated plasma emissions. There are other sounder-stimulated plasma phenomena that also fall into this category, e.g., ion affects on electron-resonant phenomena, proton-cyclotron echoes and N(sub e) field-aligned irregularities (FAI). Some of these phenomena are more pronounced when f(sub pe)/f(sub ce) approx. = n where n is an integer significantly greater than one. The observations suggest that the sounder-stimulated plasma phenomena are stimulated, or enhanced, on a time scale much less than one second. The purpose of this presentation is to review the above topics with particular emphasis on the sounder-stimulated plasma phenomena.

Benson, R. F.↗

NASA NTRS2007

Coupled Groups of g-Modes in a Sun with Mixed Core

Groups of linear g-modes can sum to create long-lived nonlinear oscillations in small "hot volumes" very deep in the Sun that help drive the modes. In these volumes (dimensions -10 Mm), the time average rate of He-3 burning doubles as temperature fluctuations exceed 10% and rises by an order of magnitude for fluctuations of 25%. To be consistent with locally large motions, we impose a mixed shell on an otherwise standard solar model before computing g-mode solutions. Mixing in the assumed shell r = (0.10+/-0.03) R(sub sun) is rapid (<<10(exp 6) yr) with slower mixing somewhat beyond. If l is the principal spherical harmonic index, a set of g-modes for any single l less than or equal to 15 with five consecutive radial harmonics can be excited with nearly linear thermal amplitudes, A(sub T) less than or equal to 0.053, throughout the star and a fractional temperature fluctuation in its hot volume of (Delta)T/T less than or equal to 0.18. These thresholds for excitation will become smaller when sets for several values of l are computed simultaneously. There is some evidence for the rotation of g-mode sets in the long solar activity record and g-mode upward wave flux has been suggested to explain the 1.3 yr reversing flows tentatively detected below the Sun's convective envelope (CE). The large local amplitudes needed for excitation implies that g-modes may transport a non-negligible fraction of the solar luminosity, yet their near linear amplitudes outside the hot volume suggests amplitudes over most of the solar surface that would be barely detectable for l > 3. A formalism is presented for summing the g-modes and estimating growth rates under the approximation that modes are strictly linear except in a hot volume which holds only a few percent of mode kinetic energy. Finally over the range 2 less than or equal to l less than or equal to 30, we summed all zonal harmonics, m, for a given l and computed the relative angular orientations that would release the most nuclear energy. This should be close to the physically preferred angular state of such a family and a few examples were displayed.

Wolff, Charles L.↗

NASA NTRS2006

Application of the Convolution Formalism to the Ocean Tide Potential: Results from the Gravity and Recovery and Climate Experiment (GRACE)

A computationally efficient approach to reducing omission errors in ocean tide potential models is derived and evaluated using data from the Gravity Recovery and Climate Experiment (GRACE) mission. Ocean tide height models are usually explicitly available at a few frequencies, and a smooth unit response is assumed to infer the response across the tidal spectrum. The convolution formalism of Munk and Cartwright (1966) models this response function with a Fourier series. This allows the total ocean tide height, and therefore the total ocean tide potential, to be modeled as a weighted sum of past, present, and future values of the tide-generating potential. Previous applications of the convolution formalism have usually been limited to tide height models, but we extend it to ocean tide potential models. We use luni-solar ephemerides to derive the required tide-generating potential so that the complete spectrum of the ocean tide potential is efficiently represented. In contrast, the traditionally adopted harmonic model of the ocean tide potential requires the explicit sum of the contributions from individual tidal frequencies. It is therefore subject to omission errors from neglected frequencies and is computationally more intensive. Intersatellite range rate data from the GRACE mission are used to compare convolution and harmonic models of the ocean tide potential. The monthly range rate residual variance is smaller by 4-5%, and the daily residual variance is smaller by as much as 15% when using the convolution model than when using a harmonic model that is defined by twice the number of parameters.

models↗

NASA NTRS2007

On the Evolution of Localized Disturbances and their Spanwise Interactions Leading to Breakdown

Localized disturbances in a laminar boundary layer represent a more realistic model of transition than the extensively studies, two or quasi three-dimensional perturbations regardless of the fact if they evolve in a linear manner or not. Localized disturbances can originate by surface imperfections, insects or dust. The disturbances can be harmonic (i.e. containing a single frequency and a complete set of spanwise wave numbers) or Pulsed (i.e. containing a band of streamwise and spanwise wave numbers). At sufficiently low amplitudes localized disturbances behave according to a linear stability model. It is highly probably that in a natural transition process such localized disturbances will overslap and interact. These interactions could either delay transition because of a partial wave cancellation resulting in an attenuation of the disturbance, or adversely enhance it by promoting nonlinear interactions. The nonlinearity could be simply amplitude dependent or cause a triad resonance. Nonlinear processes in a wave packet lead to breakdown and to the formation of turbulent spots. When the amplitude of the harmonic disturbance saturates, nonlinear processes widen the band of the lower amplified frequencies adjacent to the frequency of excitation. Experimental results describing the spanwise interactions of harmonic and pulsed localized disturbances leading to breakdown will be presented and discussed. A comparison to the evolution and breakdown of a single localized disturbance will be provided.

Seifert, Avi↗

NASA NTRS2003

A High Power Frequency Doubled Fiber Laser

This viewgraph presentation reports on the development of a high power 780 nm laser suitable for space applications of laser cooling. A possible solution is to use frequency doubling of high power 1560 nm telecom lasers. The presentation shows a diagram of the frequency conversion, and a graph of the second harmonic generation in one crystal, and the use of the cascading crystals. Graphs show the second harmonic power as a function of distance between crystals, second harmonic power vs. pump power, tunability of laser systems.

laser cooling↗

NASA NTRS2009

Active Flap Control of the SMART Rotor for Vibration Reduction

Active control methodologies were applied to a full-scale active flap rotor obtained during a joint Boeing/ DARPA/NASA/Army test in the Air Force National Full-Scale Aerodynamic Complex 40- by 80-foot anechoic wind tunnel. The active flap rotor is a full-scale MD 900 helicopter main rotor with each of its five blades modified to include an on-blade piezoelectric actuator-driven flap with a span of 18% of radius, 25% of chord, and located at 83% radius. Vibration control demonstrated the potential of active flaps for effective control of vibratory loads, especially normal force loads. Active control of normal force vibratory loads using active flaps and a continuous-time higher harmonic control algorithm was very effective, reducing harmonic (1-5P) normal force vibratory loads by 95% in both cruise and approach conditions. Control of vibratory roll and pitch moments was also demonstrated, although moment control was less effective than normal force control. Finally, active control was used to precisely control blade flap position for correlation with pretest predictions of rotor aeroacoustics. Flap displacements were commanded to follow specific harmonic profiles of 2 deg or more in amplitude, and the flap deflection errors obtained were less than 0.2 deg r.m.s.

Hall, Steven R.↗

NASA NTRS2010

Measuring Parameters of Massive Black Hole Binaries with Partially-Aligned Spins

It is important to understand how well the gravitational-wave observatory LISA can measure parameters of massive black hole binaries. It has been shown that including spin precession in the waveform breaks degeneracies and produces smaller expected parameter errors than a simpler, precession-free analysis. However, recent work has shown that gas in binaries can partially align the spins with the orbital angular momentum, thus reducing the precession effect. We show how this degrades the earlier results, producing more pessimistic errors in gaseous mergers. However, we then add higher harmonics to the signal model; these also break degeneracies, but they are not affected by the presence of gas. The harmonics often restore the errors in partially-aligned binaries to the same as, or better than/ those that are obtained for fully precessing binaries with no harmonics. Finally, we investigate what LISA measurements of spin alignment can tell us about the nature of gas around a binary,

Lang, Ryan N.↗

NASA NTRS2011

Weekly Solutions of Time-Variable Gravity from 1993 to 2010

The GRACE mission has been highly successful in determining the time-variable gravity field of the Earth, producing monthly or even more frequent solutions (cf. 10-day) solutions using both spherical harmonics and mascons. However the GRACE time series only commences in 2002 - 2003 and a gap of several years may occur in the series before a GRACE follow-on satellite is launched. Satellites tracked by SLR and DORIS have also been used to study time variations in the Earth's gravitational field. These include (most recently) the solutions of Cox and Chao (2002), Cheng et al. (2004, 2007) and Lemoine et al. (2007). In this paper we discuss the development of a new time series of low degree spherical harmonic fields based on the available SLR, DORIS and GPS data. We develop simultaneous solutions for both the geocenter and the low degree harmonics up to 5x5. The solutions integrate data from SLR geodetic satellites (e.g., Lageos1, Lageos2, Starlette, Stella, Ajisai, Larets, Westpac), altimetry satellites (TOPEX/Poseidon, Envisat, Jason-1, Jason-2), and satellites tracked solely by DORIS (e.g. SPOT2-5). We discuss some pertinent aspects of the satellite-specific modeling. We include altimeter crossovers in the weekly solutions where feasible and time permits. The resulting geocenter time series is compared with geophysical model predictions and other independently-derived solutions. Over the GRACE time period the fidelity and consistency with the GRACE solutions are presented.

Lemoine, F.↗

NASA NTRS2010

High-Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

It has been known for some time that Taylor series (TS) integration is among the most efficient and accurate numerical methods in solving differential equations. However, the full benefit of the method has yet to be realized in calculating spacecraft trajectories, for two main reasons. First, most applications of Taylor series to trajectory propagation have focused on relatively simple problems of orbital motion or on specific problems and have not provided general applicability. Second, applications that have been more general have required use of a preprocessor, which inevitably imposes constraints on computational efficiency. The latter approach includes the work of Berryman et al., who solved the planetary n-body problem with relativistic effects. Their work specifically noted the computational inefficiencies arising from use of a preprocessor and pointed out the potential benefit of manually coding derivative routines. In this Engineering Note, we report on a systematic effort to directly implement Taylor series integration in an operational trajectory propagation code: the Spacecraft N-Body Analysis Program (SNAP). The present Taylor series implementation is unique in that it applies to spacecraft virtually anywhere in the solar system and can be used interchangeably with another integration method. SNAP is a high-fidelity trajectory propagator that includes force models for central body gravitation with N X N harmonics, other body gravitation with N X N harmonics, solar radiation pressure, atmospheric drag (for Earth orbits), and spacecraft thrusting (including shadowing). The governing equations are solved using an eighth-order Runge-Kutta Fehlberg (RKF) single-step method with variable step size control. In the present effort, TS is implemented by way of highly integrated subroutines that can be used interchangeably with RKF. This makes it possible to turn TS on or off during various phases of a mission. Current TS force models include central body gravitation with the J2 spherical harmonic, other body gravitation, thrust, constant atmospheric drag from Earth's atmosphere, and solar radiation pressure for a sphere under constant illumination. The purpose of this Engineering Note is to demonstrate the performance of TS integration in an operational trajectory analysis code and to compare it with a standard method, eighth-order RKF. Results show that TS is 16.6 times faster on average and is more accurate in 87.5% of the cases presented.

Scott, James R.↗

NASA NTRS2011

Wireless tamper detection sensor and sensing system

A wireless tamper detection sensor is defined by a perforated electrical conductor. The conductor is shaped to form a geometric pattern between first and second ends thereof such that the conductor defines an open-circuit that can store and transfer electrical and magnetic energy. The conductor resonates in the presence of a time-varying magnetic field to generate a harmonic response. The harmonic response changes when the conductor experiences a change in its geometric pattern due to severing of the conductor along at least a portion of the perforations. A magnetic field response recorder is used to wirelessly transmit the time-varying magnetic field and wirelessly detecting the conductor's harmonic response.

Woodard, Stanley E.↗

NASA NTRS2012

Method of detecting system function by measuring frequency response

Real-time battery impedance spectrum is acquired using a one-time record. Fast Summation Transformation (FST) is a parallel method of acquiring a real-time battery impedance spectrum using a one-time record that enables battery diagnostics. An excitation current to a battery is a sum of equal amplitude sine waves of frequencies that are octave harmonics spread over a range of interest. A sample frequency is also octave and harmonically related to all frequencies in the sum. The time profile of this signal has a duration that is a few periods of the lowest frequency. The voltage response of the battery, average deleted, is the impedance of the battery in the time domain. Since the excitation frequencies are known and octave and harmonically related, a simple algorithm, FST, processes the time record by rectifying relative to the sine and cosine of each frequency. Another algorithm yields real and imaginary components for each frequency.

Morrison, John L.↗

NASA NTRS2012

Phase Coupling Between Spectral Components of Collapsing Langmuir Solitons in Solar Type III Radio Bursts

We present the high time resolution observations of one of the Langmuir wave packets obtained in the source region of a solar type III radio burst. This wave packet satisfies the threshold condition of the supersonic modulational instability, as well as the criterion of a collapsing Langmuir soliton, i.e., the spatial scale derived from its peak intensity is less than that derived from its short time scale. The spectrum of t his wave packet contains an intense spectral peak at local electron plasma frequency, f(sub pe) and relatively weaker peaks at 2f(sub pe) and 3f(sub pe). We apply the wavelet based bispectral analysis technique on this wave packet and compute the bicoherence between its spectral components. It is found that the bicoherence exhibits two peaks at (approximately f(sub pe), approximately f(sub pe)) and (approximately f(sub pe) approximately 2f(sub pe)), which strongly suggest that the spectral peak at 2f(sub pe) probably corresponds to the second harmonic radio emission, generated as a result of the merging of antiparallel propagating Langmuir waves trapped in the collapsing Langmuir soliton, and, the spectral peak at 3f(sub pe) probably corresponds to the third harmonic radio emission, generated as a result of merging of a trapped Langmuir wave and a second harmonic electromagnetic wave.

Thejappa, G.↗

NASA NTRS2011

Fundamental Rotorcraft Acoustic Modeling From Experiments (FRAME)

A new methodology is developed for the construction of helicopter source noise models for use in mission planning tools from experimental measurements of helicopter external noise radiation. The models are constructed by employing a parameter identification method to an assumed analytical model of the rotor harmonic noise sources. This new method allows for the identification of individual rotor harmonic noise sources and allows them to be characterized in terms of their individual non-dimensional governing parameters. The method is applied to both wind tunnel measurements and ground noise measurements of two-bladed rotors. The method is shown to match the parametric trends of main rotor harmonic noise, allowing accurate estimates of the dominant rotorcraft noise sources to be made for operating conditions based on a small number of measurements taken at different operating conditions. The ability of this method to estimate changes in noise radiation due to changes in ambient conditions is also demonstrated.

Greenwood, Eric↗

NASA NTRS2012

Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion

Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.

Leffell, Joshua Isaac↗

NASA NTRS2012

Application of Out-of-Plane Warping to Control Rotor Blade Twist

The goal of this ongoing study is to develop and demonstrate the feasibility of a blade actuation system to dynamically change the twist, and/or the camber, of an airfoil section and, consequently, alter the in-flight aerodynamic loading on the blade for efficient flight control. The required analytical and finite element tools are under development to enable an accurate and comprehensive aeroelastic assessment of the current Full-Blade Warping and 3D Warping Actuated Trailing Edge Flap concepts. The feasibility of the current concepts for swashplateless rotors and higher harmonic blade control is also being investigated. In particular, the aim is to complete the following objectives, some of which have been completed (as noted below) and others that are currently ongoing: i) Develop a Vlasov finite element model and validate against the ABAQUS shell models (completed). ii) Implement the 3D warping actuation concept within the comprehensive analysis code DYMORE. iii) Perform preliminary aeroelastic simulations of blades using DYMORE with 3D warping actuation: a) Investigate the blade behavior under 1 per/rev actuation. Determine whether sufficient twist can be generated and sustained to achieve primary blade control. b) Investigate the behavior of a trailing edge flap configuration under higher harmonic excitations. Determine how much twist can be obtained at the harmonics 2-5 per/rev. iv) Determine actuator specifications such as the power required, load and displacements, and identify the stress and strain distributions in the actuated blades. In general, the completion of Item ii) above will give an additional research capability in rotorcraft dynamics analyses, i.e., the capability to calculate the rotor blade twist due to warping, something that is not currently available in any of the existing comprehensive rotorcraft analyses.

VanWeddingen, Yannick↗

NASA NTRS2015

AgMIP Training in Multiple Crop Models and Tools

The Agricultural Model Intercomparison and Improvement Project (AgMIP) has the goal of using multiple crop models to evaluate climate impacts on agricultural production and food security in developed and developing countries. There are several major limitations that must be overcome to achieve this goal, including the need to train AgMIP regional research team (RRT) crop modelers to use models other than the ones they are currently familiar with, plus the need to harmonize and interconvert the disparate input file formats used for the various models. Two activities were followed to address these shortcomings among AgMIP RRTs to enable them to use multiple models to evaluate climate impacts on crop production and food security. We designed and conducted courses in which participants trained on two different sets of crop models, with emphasis on the model of least experience. In a second activity, the AgMIP IT group created templates for inputting data on soils, management, weather, and crops into AgMIP harmonized databases, and developed translation tools for converting the harmonized data into files that are ready for multiple crop model simulations. The strategies for creating and conducting the multi-model course and developing entry and translation tools are reviewed in this chapter.

farm crops↗

NASA NTRS2016

Light Diffraction by Large Amplitude Ultrasonic Waves in Liquids

Light diffraction from ultrasound, which can be used to investigate nonlinear acoustic phenomena in liquids, is reported for wave amplitudes larger than that typically reported in the literature. Large amplitude waves result in waveform distortion due to the nonlinearity of the medium that generates harmonics and produces asymmetries in the light diffraction pattern. For standing waves with amplitudes above a threshold value, subharmonics are generated in addition to the harmonics and produce additional diffraction orders of the incident light. With increasing drive amplitude above the threshold a cascade of period-doubling subharmonics are generated, terminating in a region characterized by a random, incoherent (chaotic) diffraction pattern. To explain the experimental results a toy model is introduced, which is derived from traveling wave solutions of the nonlinear wave equation corresponding to the fundamental and second harmonic standing waves. The toy model reduces the nonlinear partial differential equation to a mathematically more tractable nonlinear ordinary differential equation. The model predicts the experimentally observed cascade of period-doubling subharmonics terminating in chaos that occurs with increasing drive amplitudes above the threshold value. The calculated threshold amplitude is consistent with the value estimated from the experimental data.

Adler, Laszlo↗

NASA NTRS2016

Banded Structures in Electron Pitch Angle Diffusion Coefficients from Resonant Wave Particle Interactions

Electron pitch angle (D (alpha)) and momentum (D(pp)) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies 10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = +/-1, +/-2,...+/-5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (alpha) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in D alpha and Dpp coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The Dpp diffusion coefficient for ECH waves is one to two orders smaller than D alpha coefficients. For chorus waves, Dpp coefficients are about an order of magnitude smaller than D alpha coefficients for the case n does not = 0. In case of Landau resonance, the values of Dpp coefficient are generally larger than the values of D alpha coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89 deg and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10 deg and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies (is) greater than1 keV, and for whistler mode chorus waves, structures appear for energies greater than 2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.

diffusion↗