Laboratory plasma wave experiments
Plasma wave theory and experiments, emphasizing stable Maxwellian plasmas and transverse and longitudinal wave modes in zero and nonzero magnetic fields
Crawford, F. W.↗
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Thermal fluctuations and the diffuse electrostatic emissions
The suggestion that the weak-banded electrostatic emissions observed in the magnetosphere at frequencies between the electron gyrofrequency and upper hybrid frequency are thermal fluctuations is quantitatively explored, by means of a hot-cold model for dayside electron distributions with density and temperature ratios much greater than unity. It is determined that, for typical dayside conditions, the observed waves are weakly damper Bernstein-Harris modes whose spectral density and polarization, perpendicular to the ambient magnetic field, can be accounted for by the theory. It is suggested that the formalism developed may be applicable to weak electron cyclotron emissions at Jupiter and Saturn, and can be extended to lower-frequency ion cyclotron fluctuations by modifying the theory to include ion contributions.
Sentman, D. D.↗
A numerical study of wave propagation in a confined mixing layer by eigenfunction expansions
It is well known that the growth rate of instability waves of a two-dimensional free shear layer is reduced greatly at supersonic convective Mach numbers. In previous works, it has been shown that new wave modes exist when the shear layers are bounded by a channel due to the coupling effect between the acoustic wave modes and the motion of the mixing layer. The present work studies the simultaneous propagation of multiple stability waves using numerical simulation. It is shown here that the coexistence of two wave modes in the flow field can lead to an oscillatory growth of disturbance energy with each individual wave mode propagating linearly. This is particularly important when the growth rates of the unstable waves are small. It is also shown here that the propagation of two neutrally stable wave modes can lead to a stationary periodic structure of rms fluctuations. In the numerical simulations presented here the forced wave modes are propagating at same frequency, but with different phase velocities. In order to track the growth of each wave mode as it propagates downstream, a numerical method that can effectively detect and separate the contribution of the individual wave is given. It is demonstrated that by a least square fitting of the disturbance field with eigenfunctions the amplitude of each wave mode can be found. Satisfactory results as compared to linear theory are obtained.
Hu, Fang Q.↗
Low-frequency fluctuations in the magnetosheath near the magnetopause
There are four low-frequency modes which may propagate in a high-beta nearly bi-Maxwellian plasma. These are the magnetosonic, Alfven, ion acoustic, and mirror modes. This manuscript defines a procedure based on linear Vlasov theory for the unique identification of these modes by use of transport ratios, dimensionless ratios of the fluctuating field and plasma quantities. A single parameter, the mode deviation is calculated using the plasma and magnetic field data gathered by the Active Magnetospheric Particle Tracer Explorers/Ion Release Module (AMPTE/IRM) spacecraft to identify the modes observed in the terrestial magnetosheath near the magnetopause. As well as determining the mode which best describes the observed fluctuations, it gives us a measure of whether or not the resulting identification is unique. Using 17 time periods temporally close to a magnetopause crossing, and confining our study to the frequency range from 0.01 to 0.04 Hz, we find that the only clearly identified mode in this frequency range is the mirror mode. Most commonly, the quasi-perpendicular mirror mode (with wave vector k roughly perpendicular to the background magnetic field B(sub zero) is observed. In two events the quasi-parallel mirror mode k parallel B(sub zero) was identified.
Denton, Richard E.↗
A General Computer Program for Ionospheric Ray-Tracing
The study of the ionosphere using the Faraday rotation effect has been undertaken recently by means of rocket, satellite, and moon echo experiments. Different approximations have been used by different authors, resulting in methods with different degrees of complexity, and it is possible to say that the more accurate a method is, the more difficult its application becomes. However, the use of modern high-speed digital computers offers the possibility of using more complex methods in the solution of this problem, The program described in this report was written for the ILLIAC, the digital computer of the University of Illinois. Only the general features common to most digital computers will be mentioned. This program was prepared having in mind the analysis of the Faraday rotation effect, as recorded from artificial satellites. It is intended to be as general as possible in the conditions imposed on the assumed propagating medium: specifically there are no restrictions on the models of the electron density distribution and the earth's magnetic fields. long as the ray theory Ls valid. The program will trace separately the ordinary and the extraordinary mode, and it will find the virtual phase path length of a ray of each mode between the transmitter (satellite) and a receiver (station). The difference between respective phase path-lengths is related to the Faraday rotation through a constant which depends on the frequency.
Gonzales, Victor H.↗
Comparison of inlet suppressor data with approximate theory based on cutoff ratio
Inlet suppressor far-field directivity suppression was quantitatively compared with that predicted using an approximate linear design and evaluation method based upon mode cutoff ratio. The experimental data was obtained using a series of cylindrical point-reacting inlet liners on a YF102 engine. The theoretical prediction program is based upon simplified sound propagation concepts derived from exact calculations. These indicate that all of the controlling phenomenon can be approximately correlated with mode cutoff ratio which itself is intimately related to the angles of propagation within the duct. The theory-data comparisons are intended to point out possible deficiencies in the approximate theory which may be corrected. After all theoretical refinements are made, then empirical corrections can be applied.
Rice, E. J.↗
The Reduction of Ducted Fan Engine Noise Via A Boundary Integral Equation Method
The development of a Boundary Integral Equation Method (BIEM) for the prediction of ducted fan engine noise is discussed. The method is motivated by the need for an efficient and versatile computational tool to assist in parametric noise reduction studies. In this research, the work in reference 1 was extended to include passive noise control treatment on the duct interior. The BEM considers the scattering of incident sound generated by spinning point thrust dipoles in a uniform flow field by a thin cylindrical duct. The acoustic field is written as a superposition of spinning modes. Modal coefficients of acoustic pressure are calculated term by term. The BEM theoretical framework is based on Helmholtz potential theory. A boundary value problem is converted to a boundary integral equation formulation with unknown single and double layer densities on the duct wall. After solving for the unknown densities, the acoustic field is easily calculated. The main feature of the BIEM is the ability to compute any portion of the sound field without the need to compute the entire field. Other noise prediction methods such as CFD and Finite Element methods lack this property. Additional BIEM attributes include versatility, ease of use, rapid noise predictions, coupling of propagation and radiation both forward and aft, implementable on midrange personal computers, and valid over a wide range of frequencies.
Tweed, J.↗
A model for generation of bow-shock-associated upstream waves
A model is proposed for the generation of upstream hydromagnetic waves by proton beams reflected at the earth's bow shock. It is assumed that the reflection process can produce some gyrophase bunching of the protons, thus creating a gyrophase disturbance that propagates with the beam as it streams back along interplanetary field lines. This leads to the production of driven hydromagnetic waves in the left-hand mode. The resulting theory predicts a wave amplitude, frequency, and polarization in the solar wind rest frame. The amplitude depends on the fraction of protons assumed to be phase coherent in their gyromotion and on the plasma beta, beam velocity, temperatures, and the Alfven Mach number. The theory also predicts the Doppler-shifted frequencies and the apparent sense of polarization that would be observed in satellite measurement frames.
Fredricks, R. W.↗
The Prediction of Ducted Fan Engine Noise Via a Boundary Integral Equation Method
A computationally efficient Boundary Integral Equation Method (BIEM) for the prediction of ducted fan engine noise is presented. The key features of the BIEM are its versatility and the ability to compute rapidly any portion of the sound field without the need to compute the entire field. Governing equations for the BIEM are based on the assumptions that all acoustic processes are linear, generate spinning modes, and occur in a uniform flow field. An exterior boundary value problem (BVP) is defined that describes the scattering of incident sound by an engine duct with arbitrary profile. Boundary conditions on the duct walls are derived that allow for passive noise control treatment. The BVP is recast as a system of hypersingular boundary integral equations for the unknown duct surface quantities. BIEM solution methodology is demonstrated for the scattering of incident sound by a thin cylindrical duct with hard walls. Numerical studies are conducted for various engine parameters and continuous portions of the total pressure field are computed. Radiation and duct propagation results obtained are in agreement with the classical results of spinning mode theory for infinite ducts.
Boundary integral equation↗
Theory of a ring laser
Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.
Menegozzi, L. N.↗
Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics
Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework [1, 2, 3]. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick [4, 5]. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, no slip boundary conditions, and the hybrid outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, thrust, ect.). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the Acoustic Velocity Potential Equation (AVPE). The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob [2, 3]. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.
Fischbach, Sean R.↗
Analytical investigation of the hygrothermal effects and parametric study of the Edge Crack Torsion (ECT) mode 3 test lay-ups
A shear deformation theory including residual thermal and moisture effects is developed for the analysis of either symmetric or unsymmetric laminates with mid-plane edge delamination under torsion loading. The theory is based on an assumed displacement field which includes shear deformation. The governing equations and boundary conditions are obtained from the principle of virtual work. The analysis of the (90/(+/- 45)(n)/(-/+ 45)(n)/90)(s) ECT mode 3 test lay-up indicates that there are no hygrothermal effects on the mode 3 strain energy release rate because the laminate, and both sublaminates above and below the delamination, are symmetric lay-ups. A further parametric study reveals that some other lay-ups can have negligible hygrothermal effects even when the sublaminates above and below the delamination are not symmetric about their own mid-planes. However, these lay-ups may suffer from distortion after the curing process. Another Interesting set of lay-ups investigated is a class of antisymmetric laminates with (+/-(theta/(theta -90)(2)/theta))(n) lay-ups. It is observed that when n takes on even numbers (2 and 4), both hygrothermal and mode 1 effects can be neglected. From this point of view, these lay-ups provide a way to determine the mode 3 toughness between two dissimilar layers. However, when n takes on odd numbers (1 and 3), both hygrothermal and mode 1 effects may be strong in these lay-ups. In particular, when theta equals 45 deg, the lay-ups are free from both hygrothermal and mode 1 effects irrespective of n.
Li, Jian↗
On the generation of magnetohydrodynamic waves in a stratified and magnetized fluid. II - Magnetohydrodynamic energy fluxes for late-type stars
Magnetohydrodynamic (MHD) wave energy fluxes for late-type stars are calculated, using previously obtained formulae for the source functions for the generation of MHD waves in a stratified, but otherwise uniform, turbulent atmosphere; the magnetic fields in the wave generation region are assumed to be homogeneous. In contradiction to previous results, it is shown that in this uniform magnetic field case there is no significant increase in the efficiency of MHD wave generation, at least within the theory's limits of applicability. The major results are that the MHD energy fluxes calculated for late-type stars are less than those obtained for compressible modes in the magnetic field-free case, and that these MHD energy fluxes do not vary enough for a given spectral type to explain the observed range of UV and X-ray fluxes from such stars. It is therefore concluded that MHD waves in stellar atmospheres with homogeneous magnetic fields in the wave generation region cannot explain the observed stellar coronal emissions; if such MHD waves are responsible for a significant component of stellar coronal heating, then nonuniform fields within the generation region must be appealed to.
Musielak, Z. E.↗
Fluid-Thermal-Structural Interactions Induced by an Asymmetric Shock-Wave/Boundary-Layer Interaction in a Mach-6 Compression Corner
An experimental study is conducted of the fluid-thermal-structural interaction of a clamped compliant panel exposed to a three dimensional shock-wave/boundary-layer interaction (SWBLI) induced by a Mach-6 compression ramp with a spanwise nonuniform incoming boundary layer. The nonuniform boundary layer was produced by placing trips on one side of the upstream flat plate, resulting in largely turbulent flow on the tripped side and transitional flow on the untripped side. Measurements of the flowfield confirmed that the tripped boundary layer contained elevated levels of unsteadiness, and the SWBLI was observed to vary from attached to fully separated as the ramp angle was increased from 10◦ to 38◦; the separation region on the tripped side of the panel was noticeably smaller, showing the elevated turbulence levels of the tripped-side flow to remain relatively localized rather than diffusing across the whole model. Full-field, time-resolved panel deformations were measured using high-speed photogrammetry and the vibrational response at each compression angle was characterized. Although the measured modes conformed largely to those from classical clamped-plate theory, some skewing of the mode shapes was observed. IR thermography highlighted regions of the compliant region where elevated temperatures were likely to promote thermal softening effects to the transient panel response. The quasi-static deformation and stress field was used to characterize the internal stress factor of each mode and showed a meaningful relationship between transient panel response and stress contained within each mode: modes with antinodes lying in high-stress areas of the plate tended to exhibit increases in vibrational frequency and decreases in vibrational power, whereas the opposite was true for modes with antinodes in low-stress areas.
Spectral Proper Orthogonal Decomposition↗
Substorm theories: United they stand, divided they fall
Consensus on the timing and mapping of substorm features has permitted a synthesis of substorm models. Within the synthesis model the mechanism for onset of substorm expansion is still unknown. Possible mechanisms are: growth of an ion tearing mode, current disruption by a cross-field current instability, and magnetosphere-ionosphere coupling. While the synthesis model is consistent with overall substorm morphology, including near-Earth onset, none of the onset theories, taken individually, appear to account for substorm expansion onset. A grand synthesis with unification of the underlying onset theories appears necessary.
Erickson, Gary M.↗
Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics
Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL Multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. This work builds upon previous efforts to verify the use of the acoustic velocity potential equation (AVPE) laid out by Campos. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, del squared psi - (lambda/c) squared psi - M x [M x del((del)(psi))] - 2((lambda)(M)/c + M x del(M) x (del)(psi) - 2(lambda)(psi)[M x del(1/c)] = 0. with M as the Mach vector, c as the speed of sound, and λ as the complex eigenvalue. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, axial velocity, exit velocity). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The one way coupled analysis is perform four times utilizing geometries determined through traditional SRM modeling procedures. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.
Fischbach, S. R.↗
Auroral, Ionospheric and Ground Magnetic Signatures of Magnetopause Surface Modes
Surface waves on Earth's magnetopause have a controlling effect upon global magnetospheric dynamics. Since spacecraft provide sparse in situ observation points, remote sensing these modes using ground-based instruments in the polar regions is desirable. However, many open conceptual questions on the expected signatures remain. Therefore, we provide predictions of key qualitative features expected in auroral, ionospheric, and ground magnetic observations through both magnetohydrodynamic theory and a global coupled magnetosphere-ionosphere simulation of a magnetopause surface eigenmode. These show monochromatic oscillatory field-aligned currents (FACs), due to both the surface mode and its non-resonant Alfvén coupling, are present throughout the magnetosphere. The currents peak in amplitude at the equatorward edge of the magnetopause boundary layer, not the open-closed boundary as previously thought. They also exhibit slow poleward phase motion rather than being purely evanescent. We suggest the upward FAC perturbations may result in periodic auroral brightenings. In the ionosphere, convection vortices circulate the poleward moving FAC structures. Finally, surface mode signals are predicted in the ground magnetic field, with ionospheric Hall currents rotating perturbations by approximately (but not exactly) 90° compared to the magnetosphere. Thus typical dayside magnetopause surface modes should be strongest in the East-West ground magnetic field component. Overall, all ground-based signatures of the magnetopause surface mode are predicted to have the same frequency across L-shells, amplitudes that maximize near the magnetopause's equatorward edge, and larger latitudinal scales than for field line resonance. Implications in terms of ionospheric Joule heating and geomagnetically induced currents are discussed.
M. O. Archer↗
An estimate of the momentum deposition in the lower thermosphere by the observed diurnal tide
This paper reports a calculation of the acceleration of the zonal mean flow induced by dissipating tides in the equatorial lower thermosphere. Estimates of the gravest symmetric gravitiational Hough mode (1,1) of the migrating diurnal tide are obtained from monthly composites of global winds observed by the Upper Atmosphere Research Satellite (UARS) High Resolution Doppler Imager (HRDI). Using the principles of classical tidal theory, the tidal momentum flux divergence is computed for a series of monthly mean (1,1) fields from January 1992 to May 1993. The contribution to the mean flow by the leading mode of the migrating tide ranges between -5 and -20 (easterly) m/s/day in the equatorial lower thermosphere. A semiannual variation is noted in the tidal amplitudes and the inferred tidal accelerations. These variations are consistent with observed trends in the zonal mean flow of the lower thermosphere.
Lieberman, Ruth S.↗