Search NASA⌕ Search

SEARCH · Search NASA

Results for “PLASMA DISPERSION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

The incomplete plasma dispersion function: Properties and application to waves in bounded plasmas

The incomplete plasma dispersion function is a generalization of the plasma dispersion function in which the defining integral spans a semi-infinite, rather than infinite, domain. It is useful for describing the linear dielectric response and wave dispersion in non-Maxwellian plasmas when the distribution functions can be approximated as Maxwellian over finite, or semi-infinite, intervals in velocity phase-space. A ubiquitous example is the depleted Maxwellian electron distribution found near boundary sheaths or double layers, where the passing interval can be modeled as Maxwellian with a lower temperature than the trapped interval. The depleted Maxwellian is used as an example to demonstrate the utility of using the incomplete plasma dispersion function for calculating modifications to wave dispersion relations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

The modified plasma dispersion function

The modified plasma dispersion function (MPDF), based on the generalized Lorentzian (kappa) particle distribution function, is introduced, and a comprehensive set of graphs of the real and imaginary parts of the MPDF is presented. For any positive integral value of kappa, MPDF is calculated in closed form as a finite series. It is demonstrated how the MPDF approaches the plasma dispersion function in the limit as kappa yields infinity, a result to be expected since the kappa distribution function formally approaches the Maxwellian as kappa yields infinity. It is concluded that the MPDF can provide a tool in studying microinstabilities in plasmas when the particle distribution function is not only the standard generalized Lorentzian, but also of the Lorentzian type, including the loss-cone, bi-Lorentzian, and product bi-Lorentzian distributions.

Summers, Danny↗
NASA NTRS2004

Plasma Dispersion Function for the Kappa Distribution

The plasma dispersion function is computed for a homogeneous isotropic plasma in which the particle velocities are distributed according to a Kappa distribution. An ordinary differential equation is derived for the plasma dispersion function and it is shown that the solution can be written in terms of Gauss' hypergeometric function. Using the extensive theory of the hypergeometric function, various mathematical properties of the plasma dispersion function are derived including symmetry relations, series expansions, integral representations, and closed form expressions for integer and half-integer values of K.

Podesta, John J.↗
DOE OSTI2015

Applying the cold plasma dispersion relation to whistler mode chorus waves: EMFISIS wave measurements from the Van Allen Probes

Most theoretical wave models require the power in the wave magnetic field in order to determine the effect of chorus waves on radiation belt electrons. However, researchers typically use the cold plasma dispersion relation to approximate the magnetic wave power when only electric field data are available. In this study, the validity of using the cold plasma dispersion relation in this context is tested using Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) observations of both the electric and magnetic spectral intensities in the chorus wave band (0.1–0.9 f ce ). Results from this study indicate that the calculated wave intensity is least accurate during periods of enhanced wave activity. For observed wave intensities >10⁻³ nT², using the cold plasma dispersion relation results in an underestimate of the wave intensity by a factor of 2 or greater 56% of the time over the full chorus wave band, 60% of the time for lower band chorus, and 59% of the time for upper band chorus. Hence, during active periods, empirical chorus wave models that are reliant on the cold plasma dispersion relation will underestimate chorus wave intensities to a significant degree, thus causing questionable calculation of wave-particle resonance effects on MeV electrons.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1973

Approximations to the plasma dispersion function

Two simple approximations to the plasma dispersion function are analyzed and compared. One, is the resonance distribution approximation which is based on the utilization of resonance velocity distributions; the other, is the two-pole approximation proposed by Fried, Hedrick, and McCune (1968). The approximations are applied to Landau and whistler waves. Possible means of improving the two-pole approximation are discussed.

Brinca, A. L.↗
DOE OSTI2013

Generalized plasma dispersion function: One-solve-all treatment, visualizations, and application to Landau damping

A unified, fast, and effective approach is developed for numerical calculation of the well-known plasma dispersion function with extensions from Maxwellian distribution to almost arbitrary distribution functions, such as the δ, flat top, triangular, κ or Lorentzian, slowing down, and incomplete Maxwellian distributions. The singularity and analytic continuation problems are also solved generally. Given that the usual conclusion γ∝∂f{sub 0}/∂v is only a rough approximation when discussing the distribution function effects on Landau damping, this approach provides a useful tool for rigorous calculations of the linear wave and instability properties of plasma for general distribution functions. The results are also verified via a linear initial value simulation approach. Intuitive visualizations of the generalized plasma dispersion function are also provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

The evolution of strongly modulated, low-frequency, moderate-amplitude wave packets in a dispersive plasma

The evolution of strongly modulated wave packets in a dispersive plasma that propagate parallel to the magnetic field is studied. Modulation effects are shown to reduce significantly (about 30 percent) the rate of spreading from that due to dispersion alone. For fluidlike behavior, nonlinearity has its greatest impact on evolution when the linear sound speed and initial wave packet speeds are well matched, resulting in a strong coupling between the wave magnetic and sonic components. Ion kinetic processes reduce the impact of nonlinearity and cause the rate of spreading to approach that expected from dispersion alone as the ratio of ion and electron temperatures, Ti/Te approaches 4. For Beta equal to or greater than 1 and Ti/Te of about 1, the coupled waveforms correspond qualitatively to kinetic treatments of the derivative nonlinear Schroedinger equation.

Vasquez, Bernard J.↗
DOE OSTI2016

A generalized plasma dispersion function for electron damping in tokamak plasmas

Radio frequency wave propagation in finite temperature, magnetized plasmas exhibits a wide range of physics phenomena. The plasma response is nonlocal in space and time, and numerous modes are possible with the potential for mode conversions and transformations. Additionally, diffraction effects are important due to finite wavelength and finite-size wave launchers. Multidimensional simulations are required to describe these phenomena, but even with this complexity, the fundamental plasma response is assumed to be the uniform plasma response with the assumption that the local plasma current for a Fourier mode can be described by the Stix conductivity. But, for plasmas with non-uniform magnetic fields, the wave vector itself is nonlocal. When resolved into components perpendicular (k ) and parallel (k ||) to the magnetic field, locality of the parallel component can easily be violated when the wavelength is large. The impact of this inconsistency is that estimates of the wave damping can be incorrect (typically low) due to unresolved resonances. For the case of ion cyclotron damping, this issue has already been addressed by including the effect of parallel magnetic field gradients. In this case, a modified plasma response (Z function) allows resonance broadening even when k || = 0, and this improves the convergence and accuracy of wave simulations. In our paper, we extend this formalism to include electron damping and find improved convergence and accuracy for parameters where electron damping is dominant, such as high harmonic fast wave heating in the NSTX-U tokamak, and helicon wave launch for off-axis current drive in the DIII-D tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1993

Strongly nonlinear evolution of low-frequency wave packets in a dispersive plasma

The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for p < 1, while fast (fight heIicity) wave packets hardly steepen for any beta. Substantial regions of opposite helicity form on the leading side of steepened Alfven wave packets. This behavior differs qualitatively from that exhibited by the solutions to the derivative nonlinear Schrodinger (DNLS) equation.

Vasquez, Bernard J.↗
DOE OSTI2014

Exchange effects in Coulomb quantum plasmas: Dispersion of waves in 2D and 3D quantum plasmas

We describe quantum hydrodynamic equations with the Coulomb exchange interaction for three and two dimensional plasmas. Explicit form of the force densities are derived. We present non-linear Schrödinger equations (NLSEs) for the Coulomb quantum plasmas with the exchange interaction. We show contribution of the exchange interaction in the dispersion of the Langmuir, and ion-acoustic waves. We consider influence of the spin polarization ratio on strength of the Coulomb exchange interaction. This is important since exchange interaction between particles with same spin direction and particles with opposite spin directions are different. At small particle concentrations n{sub 0}≪10{sup 25}cm{sup −3} and small polarization the exchange interaction gives small decrease of the Fermi pressure. With increase of polarization role the exchange interaction becomes more important, so that it can overcome the Fermi pressure. The exchange interaction also decreases contribution of the Langmuir frequency. Ion-acoustic waves do not exist in limit of large polarization since the exchange interaction changes the sign of pressure. At large particle concentrations n{sub 0}≫10{sup 25}cm{sup −3} the Fermi pressure prevails over the exchange interaction for all polarizations. We obtain a similar picture for two dimensional quantum plasmas.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

Approximations to the plasma dispersion function

Linear wave propagation in hot collisionless plasmas is described by the linearized Vlasov and Maxwell equations. In uniform media, the utilization of spatial and temporal transforms of those equations leads to the consideration of integrals of the Hilbert transform type. Analysis and comparison of two simple approximations are provided based on the utilization of resonance velocity distributions. Application is then made to the Landau and whistler waves, along with a discussion of the results, and commentary on possible improvements.

Brinca, A. L.↗
NASA NTRS1988

Approximation of the dielectric properties of Maxwellian plasmas - Dispersion functions and physical constraints

The dielectric properties of Maxwellian plasmas are approximated using high Pade approximants to the dispersion function and direct approximation of the distribution. Physical constraints on permissible approximations are discussed, and it is found that some previously published results can lead to predictions of qualitatively incorrect wave properties, including unphysical negative damping. Approximate dispersion functions for Maxwellian distributions are given explicitly, and some of the effects of these approximations on the resulting dispersion are discussed. The approximations discussed here are of use both in analytical work and in accelerating large-scale numerical computations.

Robinson, P. A.↗
NASA NTRS1992

Comparison of weakly and strongly nonlinear wave evolution in a dispersive plasma

An investigation of the evolution of strongly nonlinear, low frequency (ion gyrofrequency), parallel propagating wave packets in a dispersive, collisionless, and low beta(= 8piP/B-squared = 0.3) plasma is undertaken using a hybrid numerical code. These strongly nonlinear wave packets have a transverse magnetic field strength, or wave amplitude, which is of order or greater the field strength along the direction of propagation, and their evolution can differ qualitatively from that of weakly nonlinear packets. The development of spreading fast wave (right helicity) and rarefraction regions competes strongly with steepening, and leads to a long time waveform which differs greatly from that for weak nonlinearity. Results are used to suggest that strongly nonlinear wave evolution occurs frequently in the earth's foreshock.

Vasquez, Bernard J.↗
DOE OSTI2015

Longitudinal oscillations in a non-uniform spatially dispersive plasma

Longitudinal oscillations of the electron fluid in the hydrodynamic model of a metal are examined with pressure effects taken into account. It is well-known that this entails spatial dispersion. The equilibrium electron number density is taken to be non-uniform and a non-self-adjoint fourth order differential equation obeyed by the electric potential is derived. A velocity potential necessary for the description of sound waves is introduced in the standard fashion and the generalized version of Bloch orthogonality appropriate to a non-uniform background is deduced. We observe a duality between electric and velocity potentials in the sense that the respective differential operators are adjoint to each other. The spectrum is calculated in the special case of an exponential profile for the equilibrium electron number density. The surface plasmons are connected with the analytic properties of the scattering amplitude in the complex plane. The phase shift at threshold is expressed in terms of the number of surface plasmon modes via an expression reminiscent of Levinson’s statement in quantum mechanics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1982

Multi-ion resonances in finite temperature plasma

Dispersion properties of electrostatic waves in a multi-ion plasma are examined, with an analysis that incorporates the effects of finite temperature, finite parallel wavenumber, and wave growth/damping in a systematic development of equations. Numerical solutions and analytic formulas are given for an ion plasma consisting of H(+), O(+), and S(+) for application to Jupiter's magnetosphere. It is demonstrated how observations of plasma resonance lines may be used as a diagnostic of ion composition in magnetospheric plasma. This potential use of high-sensitivity/high-resolution plasma wave instrumentation may provide information necessary to resolve issues concerning the origin of plasmas in the earth's neighborhood.

Barbosa, D. D.↗
DOE OSTI2022

Generation of Intense Low-Divergence Isolated Soft-X-Ray Attosecond Pulses in a Gas-Filled Waveguide Using Three-Color Synthesized Laser Pulses

Isolated attosecond pulses (IAPs) in the soft-x-ray (SXR) region have been successfully produced via high-order harmonic generation in a gas medium at several laboratories, but pulse energies are much lower compared to the IAPs in the extreme ultraviolet. Here, we show that in a gas-filled hollow waveguide, an efficient gating method using a few-cycle three-color synthesizer is able to generate stronger SXR IAPs. We show that an 104-as IAP in the SXR region (central energy of 210 eV) with a higher pulse energy (0.9 nJ) and a lower divergence (within 1.5 mrad) can be generated with a three-color laser beam for input pulse energy at 0.62 mJ, under the condition of optimal gas pressure and waveguide length. The enhancement of the IAP is attributed to favorable phase matching of SXR high harmonics caused by the evolution of the three-color waveform during its propagation in the waveguide, which can be understood by analyzing the time shift of the waveform due to the interplay of the waveguide mode, atomic dispersion, and plasma dispersion. We check that the gating method is quite robust with respect to the phase jitter in the waveform. The advantage of this method is further demonstrated by comparing the generation of SXR high harmonics and attosecond pulses with two other schemes: the three-color waveform in a gas cell and a previously optimized two-color waveform in a gas-filled waveguide.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2013

THE DISPERSION RELATIONS AND INSTABILITY THRESHOLDS OF OBLIQUE PLASMA MODES IN THE PRESENCE OF AN ION BEAM

An ion beam can destabilize Alfven/ion-cyclotron waves and magnetosonic/whistler waves if the beam speed is sufficiently large. Numerical solutions of the hot-plasma dispersion relation have previously shown that the minimum beam speed required to excite such instabilities is significantly smaller for oblique modes with k Multiplication-Sign B {sub 0} {ne} 0 than for parallel-propagating modes with k Multiplication-Sign B {sub 0} = 0, where k is the wavevector and B {sub 0} is the background magnetic field. In this paper, we explain this difference within the framework of quasilinear theory, focusing on low-{beta} plasmas. We begin by deriving, in the cold-plasma approximation, the dispersion relation and polarization properties of both oblique and parallel-propagating waves in the presence of an ion beam. We then show how the instability thresholds of the different wave branches can be deduced from the wave-particle resonance condition, the conservation of particle energy in the wave frame, the sign (positive or negative) of the wave energy, and the wave polarization. We also provide a graphical description of the different conditions under which Landau resonance and cyclotron resonance destabilize Alfven/ion-cyclotron waves in the presence of an ion beam. We draw upon our results to discuss the types of instabilities that may limit the differential flow of alpha particles in the solar wind.

79 ASTRONOMY AND ASTROPHYSICS↗