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Stability of an inhomogeneous two-component plasma with magnetic viscosity

The stability of a semiinfinite quasi-neutral inhomogeneous plasma with magnetic viscosity has been discussed by using JWKB approximation in which the parameters are regarded slowing varying. Dispersion relation is obtained and discussed. It is found that the inhomogeneous system is unstable for all perturbations with k(y) = 0. A dispersion relation for homogeneous plasma is also obtained and discussed. It is shown that fast and slow-MHD waves propagate in the homogeneous plasma in the limit of almost perpendicular propagation under certain conditions.

Kumar, Nagendra

Theory of high-harmonic rectangular gyrotron for TE(mn) modes

In this paper, the linearized relativistic Vlasov equation is solved and a dispersion relation is calculated for the interaction between a relativistic electron beam and the electromagnetic fields of a rectangular waveguide supporting TE(mn) modes. The dispersion relation is simplified to the special case of a frame of reference moving with the electrons and the resulting coupling coefficient epsilon(mn)super l is calculated for various TE(mn) modes. The dependence of epsilon(mn)super l on the parity of the harmonic number l and various mn modes of the waveguide are discussed.

Ferendeci, A. M.

Inverting a dispersive scene's side-scanned image

Consideration is given to the problem of using a remotely sensed, side-scanned image of a time-variant scene, which changes according to a dispersion relation, to estimate the structure at a given moment. Additive thermal noise is neglected in the models considered in the formal treatment. It is shown that the dispersion relation is normalized by the scanning velocity, as is the group scanning velocity component. An inversion operation is defined for noise-free images generated by SAR. The method is extended to the inversion of noisy imagery, and a formulation is defined for spectral density estimation. Finally, the methods for a radar system are used for the case of sonar.

Harger, R. O.

Nonlinear wave scattering and electron beam relaxation

The role played by nonlinear scattering during the relaxation of a warm electron beam is investigated through a numerical code based on kinetic equations. The code encompasses the quasi-linear wave-electron interaction and wave-wave scattering off ion clouds. Ions with velocities 2 nu sub i (nu sub i being the ion thermal velocity) are found to be the most efficient for scattering the Langmuir waves off their polarization clouds. The transfer rate of the spectrum out of resonance with the beam is larger by a factor 3 compared to usual estimates. The changes produced in the dispersion relation by the presence of the beam electrons dramatically alter the characteristics of the secondary spectrum. In a late phase the classic condensate K of about 0 is depleted, with the formation of a new condensate in resonance with the flat-topped beam distribution, which follows from the fact that the mere presence of the beam electrons creates a minimum in the frequency-wave-number relation. For strong and slow beams, the predictions of the code are found to be in excellent agreement with the results of the particle simulation if a dispersion relation that includes the beam is used.

Muschietti, L.

A kinetic cross-field streaming instability

In a high-beta plasma the so-called modified-two-stream instability, which results from strongly magnetized electrons drifting relative to unmagnetized ions across a homogeneous magnetic field, is misnamed because the mode is highly kinetic, particularly when the relative streaming velocity exceeds the Alfven speed of the plasma. This kinetic cross-field streaming instability is investigated in detail, examining the effect of the electromagnetic terms and the stability boundaries in both low- and high-beta plasmas. An approximate dispersion relation showing the relation of this mode to the whistler is derived and solutions of it are compared with those obtained from the exact dispersion relation. The kinetic mode, unlike the usual modified-two-stream instability, is not stabilized by electromagnetic effects when the relative electron-ion drift speed exceeds the Alfven speed.

Wu, C. S.

Electrostatic wave generation above and below the plasma frequency by electron beams

The unmagnetized electrostatic dispersion equation is solved numerically to study the growth of electrostatic waves near the plasma frequency resulting from a unstable electron beam. An attempt is made to find the dispersion relations, frequencies of maximum growth, and the resonant or nonresonant character of the waves for particular beam parameters. It is found that the unstable waves do not have the Langmuir dispersion relation except in the limit of a very dilute beam with growth on the connected mode of O'Neil and Malmberg. The properties of the unstable mode depend strongly on beam parameters such as beam density, speed, and temperature.

Cairns, Iver H.

Pulse asymptotics of the Charney baroclinic instability problem

The asymptotic response of the Charney baroclinic instability problem to a localized perturbation is determined using the formalism of Briggs (1964) and exploiting a recently obtained highly accurate WKB approximate dispersion relation (Lindzen and Rosenthal, 1981). Comparison is made with previous results for two-level and Eady models. Small scales and rapid growth characteristic of the initial stages of cyclogenesis are found and the linear dispersion relation, which can be obtained from observation of zonal wind and stability, emerges as a forecast tool for prediction of geographically local cyclogenesis.

Farrell, B. F.

Role of Compressive Viscosity and Thermal Conductivity on the Damping of Slow Waves in Coronal Loops with and Without Heating–Cooling Imbalance

In the present article, we derive a new dispersion relation for slow magnetoacoustic waves invoking the effect of thermal conductivity, compressive viscosity, radiation, and an unknown heating term along with the consideration of heating–cooling imbalance from linearized MHD equations. We solve the general dispersion relation to understand the role of compressive viscosity and thermal conductivity in the damping of slow waves in coronal loops with and without heating–cooling imbalance. We have analyzed the wave damping for the range of loop length L=50--500 Mm, temperature T=5--30 MK, and density ρ=10^(−11)--10^(−9) kg/cu.m. It was found that the inclusion of compressive viscosity along with thermal conductivity significantly enhances the damping of the fundamental mode oscillations in shorter (e.g. L=50 Mm) and super-hot (T>10 MK) loops. However, the role of viscosity in the damping is insignificant in longer (e.g. L=500 Mm) and hot loops (T≤10 MK) where, instead, thermal conductivity along with the presence of heating–cooling imbalance plays a dominant role. For shorter loops at a super-hot regime of temperature, the increment in the loop density substantially enhances the damping of the fundamental modes due to thermal conductivity when viscosity is absent, however, when the compressive viscosity is added the increase in density substantially weakens the damping. Thermal conductivity alone is found to play a dominant role in longer loops at lower temperatures (T≤10 MK), while compressive viscosity dominates the damping at super-hot temperatures (T>10 MK) in shorter loops. The predicted scaling law between damping time (τ) and wave period (P) is found to better match the observed SUMER (Solar Ultraviolet Measurements of Emitted Radiation) oscillations when the heating–cooling imbalance is taken into account in addition to thermal conductivity and compressive viscosity for the damping of the fundamental slow mode oscillations.

Abhinav Prasad

Relativistic dispersion, the cyclotron maser instability, and auroral kilometric radiation

It is demonstrated that relativistic effects can significantly modify the wave dispersion in auroral kilometric radiation (AKR), even for only mildly relativistic electrons, when the ratio of the square of the electron plasma frequeny omega(pe) to the square of the electron cyclotron frequency Omega(e) is much less than one, which is frequently the case in the AKR source region. The k-parallel dispersion relation for waves in a relativistic Maxwellian plasma is considered for the case of omega(pe) much less than Omega(e). The results of Shkarovsky (1966) are used to evaluate the relativistic corrections to the R-X mode cutoff. The general relativistic dispersion tensor is applied to evaluate the dispersion relation for a delta function ring distribution in p-perpendicular, again assuming omega(pe) much less than Omega(e). The effect of finite velocity spread is studied by analyzing the Dory-Guest-Harris distribution in the semirelativistic approximation. The results of computer simulations for ring and shell distributions are presented.

Pritchett, P. L.

The possible role of MHD waves in heating the solar corona

The possible role of waves in the heating of the solar corona has been investigated. A general dispersion relation has been derived for waves propagating in a homogeneous plasma subject to dissipation by viscosity and thermal conduction. The dissipation mechanisms have been incorporated self-consistently into the equations, and no assumptions about the strength of the damping have been made. Solutions of the sixth-order dispersion relation provide information on how the damping of both slow and fast mode waves depends upon the plasma density, temperature, field strength, and angle of propagation relative to the background magnetic field. We provide a detailed comparison to the standard approach, which is to solve for the wave quantities in the absence of dissipation and then to use these quantities in expressions for the heating due to viscosity and thermal conduction.

Porter, Lisa J.

The possible role of high-frequency waves in heating solar coronal loops

We investigate the role of high-frequency waves in the heating of solar active region coronal loops. We assume a uniform background magnetic field, and we introduce a density stratification in a direction perpendicular to this field. We focus on ion compressive viscosity as the damping mechanism of the waves. We incorporate viscosity self-consistently into the equations, and we derive a dispersion relation by adopting a slab model, where the density inside the slab is greater than that outside. Such a configuration supports two types of modes: surface waves and trapped body waves. In order to determine under what conditions these waves may contribute to the heating of active regions, we solve our dispersion relation for a range of densities, temperatures, magnetic field strengths, density ratios, wavevector magnitudes, wavevector ratios, and slab widths. We find that surface waves exhibit very small damping, but body waves can potentially damp at rates needed to balance radiative losses. However, the required frequencies of these body waves are very high. For example, the wave frequency must be at least 5.0/s for a slab density of 10(exp 9,5)/cc, a slab temperature of 10(exp 6,5) K, a field strength of 100 G, and a density ratio of 5. For a slab density of 10(exp 10)/cc, this frequency increases to 8.8/s. Although these frequencies are very high, there in no observational evidence to rule out their existence, and they may be generated both below the corona and at magnetic reconnection sites in the corona. However, we do find that, for slab densities of 10(exp 10)/cc or less, the dissipation of high-frequency waves will be insufficient to balance the radiative losses if the magnetic field strength exceeds roughly 200 G. Because the magnetic field is known to exceed 200 G in many active region loops, particularly low-lying loops and loops emanating from sunspots, it is unlikely that high-frequency waves can provide sufficient heating in these regions.

Porter, Lisa J.

Rigid-Mode Limit of the Yokoya Matrix Formalism and the Burov-Lebedev Dispersion Equation

Transverse single-bunch instabilities of space-charge-dominated coasting beams with round and flat transverse geometries are studied using a unified dispersion-relation framework. The analysis combines the Burov-Lebedev formalism, which captures space-charge tune spread, Landau damping, and instability threshold behavior, with Yokoya’s projection method for representing coherent transverse mode structure and its dependence on beam aspect ratio. In the rigid-beam limit, the formulation reduces to a scalar dispersion relation of Burov-Lebedev paper. For non-rigid transverse oscillations, truncation of Yokoya’s Hermite-based expansion yields a finite-dimensional matrix eigenvalue problem in which space-charge and coupling impedance effects enter through Burov-Lebedev–type denominators. This approach provides a consistent basis for comparing rigid and non-rigid instability behavior in round and flat beams and for assessing the role of beam ellipticity in modifying coherent mode structure and stability thresholds.

43 PARTICLE ACCELERATORS

Wave evolution in the marginal ice zone - Model predictions and comparisons with on-site and remote data

The ocean-wave dispersion relation and viscous attenuation by a sea ice cover were studied for waves in the marginal ice zone (MIZ). The Labrador ice margin experiment (Limex), conducted off the east coast of Newfoundland, Canada in March 1987, provided aircraft SAR, wave buoy, and ice property data. Based on the wave number spectrum from SAR data, the concurrent wave frequency spectrum from ocean buoy data, and accelerometer data on the ice during Limex '87, the dispersion relation has been derived and compared with the model. Accelerometers were deployed at the ice edge and into the ice pack. Data from the accelerometers were used to estimate wave energy attenuation rates and compared with the model. The model-data comparisons are reasonably good for the ice conditions observed during Limex' 87.

Liu, A. K.

Current driven instabilities of an electromagnetically accelerated plasma

A plasma instability that strongly influences the efficiency and lifetime of electromagnetic plasma accelerators was quantitatively measured. Experimental measurements of dispersion relations (wave phase velocities), spatial growth rates, and stability boundaries are reported. The measured critical wave parameters are in excellent agreement with theoretical instability boundary predictions. The instability is current driven and affects a wide spectrum of longitudinal (electrostatic) oscillations. Current driven instabilities, which are intrinsic to the high-current-carrying magnetized plasma of the magnetoplasmadynmic (MPD) accelerator, were investigated with a kinetic theoretical model based on first principles. Analytical limits of the appropriate dispersion relation yield unstable ion acoustic waves for T(i)/T(e) much less than 1 and electron acoustic waves for T(i)/T(e) much greater than 1. The resulting set of nonlinear equations for the case of T(i)/T(e) = 1, of most interest to the MPD thruster Plasma Wave Experiment, was numerically solved to yield a multiparameter set of stability boundaries. Under certain conditions, marginally stable waves traveling almost perpendicular to the magnetic field would travel at a velocity equal to that of the electron current. Such waves were termed current waves. Unstable current waves near the upper stability boundary were observed experimentally and are in accordance with theoretical predictions. This provides unambiguous proof of the existence of such instabilites in electromagnetic plasma accelerators.

Chouetri, E. Y.

Comparison of Non-Parabolic Hydrodynamic Simulations for Semiconductor Devices

Parabolic drift-diffusion simulators are common engineering level design tools for semiconductor devices. Hydrodynamic simulators, based on the parabolic band approximation, are becoming more prevalent as device dimensions shrink and energy transport effects begin to dominate device characteristic. However, band structure effects present in state-of-the-art devices necessitate relaxing the parabolic band approximation. This paper presents simulations of ballistic diodes, a benchmark device, of Si and GaAs using two different non-parabolic hydrodynamic formulations. The first formulation uses the Kane dispersion relationship in the derivation of the conservation equations. The second model uses a power law dispersion relation {(hk)(exp 2)/2m = xW(exp Y)}. Current-voltage relations show that for the ballistic diodes considered. the non-parabolic formulations predict less current than the parabolic case. Explanations of this will be provided by examination of velocity and energy profiles. At low bias, the simulations based on the Kane formulation predict greater current flow than the power law formulation. As the bias is increased this trend changes and the power law predicts greater current than the Kane formulation. It will be shown that the non-parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation are limited due to the binomial approximation which was utilized in the derivation.

Smith, A. W.

Azimuthal spoke propagation in Hall Effect Thrusters

Spokes are azimuthally propagating perturbations in the plasma discharge of Hall Effect Thrusters (HETs) that travel in the E × B direction and have been observed in many different systems. The propagation of azimuthal spokes are investigated in a 6 kW HET known as the H6 using ultra-fast imaging and azimuthally spaced probes. A spoke surface is a 2-D plot of azimuthal light intensity evolution over time calculated from 87,500 frames/s videos. The spoke velocity has been determined using three methods with similar results: manual fitting of diagonal lines on the spoke surface, linear cross-correlation between azimuthal locations and an approximated dispersion relation. The spoke velocity for three discharge voltages (300, 400 and 450 V) and three anode mass flow rates (14.7, 19.5 and 25.2 mg/s) yielded spoke velocities between 1500 and 2200 m/s across a range of normalized magnetic field settings. The spoke velocity was inversely dependent on magnetic field strength for low B-field settings and asymptoted at B-field higher values. The velocities and frequencies are compared to standard drifts and plasma waves such as E × B drift, electrostatic ion cyclotron, magnetosonic and various drift waves. The empirically approximated dispersion relation yielded a characteristic velocity that matched the ion acoustic speed for 5 eV electrons that exist in the near-anode and near-field plume regions of the discharge channel based on internal measurements. Thruster performance has been linked to operating mode where thrust-to-power is maximized when azimuthal spokes are present so investigating the underlying mechanism of spokes will benefit thruster operation.

Polk, James E.

Azimuthal Spoke Propagation in Hall Effect Thrusters

Spokes are azimuthally propagating perturbations in the plasma discharge of Hall Effect Thrusters (HETs) that travel in the E x B direction and have been observed in many different systems. The propagation of azimuthal spokes are investigated in a 6 kW HET known as the H6 using ultra-fast imaging and azimuthally spaced probes. A spoke surface is a 2-D plot of azimuthal light intensity evolution over time calculated from 87,500 frames/s videos. The spoke velocity has been determined using three methods with similar results: manual fitting of diagonal lines on the spoke surface, linear cross-correlation between azimuthal locations and an approximated dispersion relation. The spoke velocity for three discharge voltages (300, 400 and 450 V) and three anode mass flow rates (14.7, 19.5 and 25.2 mg/s) yielded spoke velocities between 1500 and 2200 m/s across a range of normalized magnetic field settings. The spoke velocity was inversely dependent on magnetic field strength for low B-field settings and asymptoted at B-field higher values. The velocities and frequencies are compared to standard drifts and plasma waves such as E x B drift, electrostatic ion cyclotron, magnetosonic and various drift waves. The empirically approximated dispersion relation yielded a characteristic velocity that matched the ion acoustic speed for 5 eV electrons that exist in the near-anode and near-field plume regions of the discharge channel based on internal measurements. Thruster performance has been linked to operating mode where thrust-to-power is maximized when azimuthal spokes are present so investigating the underlying mechanism of spokes will benefit thruster operation.

Cylindrical Hall Thruster (CHT)

Modification of ion-temperature-gradient turbulence by impurities in stellarator plasmas

Recent nonlinear gyrokinetic simulations have shown that impurities can strongly modify the turbulent heat flux in stellarator plasmas. Here, the ion-temperature-gradient (ITG) dispersion relation in a plasma containing impurities is analytically solved in certain limits and an expression for the modification of the ITG growth rate by impurities is derived. The analytical expression is the sum of three terms corresponding to three different physical causes (impurity density gradient, impurity temperature gradient and dilution) of the change in the growth rate. The scalings predicted analytically for the modification of the growth rate are shown to be reproduced by linear gyrokinetic simulations. The conditions for reduction or increase of the ITG growth by impurities are also correctly predicted by the analytical solution to the dispersion relation. Finally, a remarkable correlation is found between the analytical expression for the modification of the growth rate and the modification of the turbulent heat flux obtained from nonlinear gyrokinetic simulations.

Calvo, Iván [Research Centre for Energy, Environme