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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 NTRS1980

Some features of inverted-V events as seen from simulated double layers

Results from a numerical simulation of a double layer show some features similar to those of inverted-V events. The strong heating of thermal and precipitating electrons is observed along with extremely low frequency fluctuations found during inverted-V events. It is suggested that after the acceleration of auroral electrons by the double layer, the precipitating free electrons are heated by the nonlinear effects of the electron beam plasma instability. Fluctuations and pulsations of auroral electron fluxes during auroral events are caused by a relaxation type of oscillation. The finite extent of one dimensional plasma is simulated by solving the Vlasov and Poisson equations as an initial and boundary value problem.

Singh, N.↗

NASA NTRS1981

The plasma wake of mesosonic conducting bodies. I - An experimental parametric study of ion focusing by the plasma sheath

The experimental investigation considered is concerned with the deflection of ion streams resulting from the interaction of conducting test bodies with an unmagnetized, mesosonic (supersonic with respect to ions but subsonic with respect to electrons) plasma stream. The investigation is, therefore, limited to plasma-electrostatic interactions. The experimental conditions are similar to those of the spacecraft-ionospheric interaction in that the ionic mass and number density, the electron temperature, and the plasma drift velocity ranges include values appropriate for small satellites or diagnostic probes at 200 to 400 km altitude. The study provides direct observations of deflected ion streams for cylindrical test bodies and gives a detailed description of the effects of the governing, dimensionless parameter ratios obtained from the steady-state, nonmagnetic Maxwell-Vlasov system of equations.

Stone, N. H.↗

NASA NTRS1982

Dynamical features of moving double layers

Numerical simulations of the dynamics of double layers that form in response to an applied potential drop across a plasma are carried out for plasmas of lengths much greater than previously considered. The evolution of finite-size plasmas of lengths 100, 200 and 400 Debye lengths at the low-potential end of the simulation region was followed by the solution of the Vlasov and Poisson equations. Results show that the double layer moves towards the high-potential side of the layer, at a speed directly dependent on the length of the plasma. The moving double layer is accompanied by a moving density front which is similar to an ion acoustic shock created by the expansion of a high-density plasma into a low-density plasma, as well as plasma heating and evacuation, electron and ion current interruptions and recovery. Double layer formation, motion, and accompanying phenomena are found to repeat periodically. Results are in good agreement with laboratory experiments, and may be used to explain certain phenomena observed in auroral plasmas.

Singh, N.↗

NASA NTRS1983

Linear density drift instabilities in very low beta plasmas A different approach

This paper reports a study of the linear Vlasov electromagnetic dispersion equation for density drift instabilities in very low beta plasmas. A uniform magnetic field and a weak uniform density gradient are assumed. This paper differs from most other studies of this topic in three important ways: (1) no low frequency or long wavelength approximations are made, (2) no gauge condition is imposed and (3) a modification of the local approximation is used which is argued to be less arbitrary than the usual local approximation. Numerical solution of the resulting dispersion equation yields stabilization of the universal density drift instability at values of beta somewhat higher than those obtained from the local approximation, and near maximum growth shows no evidence of coupling between the universal and Alfven modes.

Gary, S. P.↗

NASA NTRS1990

High voltage plasma sheath analysis related to TSS-1

On the first mission of the Tethered Satellite System (TSS-1), a 1.8 m diameter spherical satellite will be deployed a distance of 20 km above the Space Shuttle Orbiter on an insulated conducting tether. The satellite will be held at electric potentials up to 5000 volts positive with respect to the ambient plasma. Due to the passage of the conducting tether through the Earth's magnetic field, an electromagnetic field (EMF) will be created, driving electrons down the tether to the Orbiter, out through an electron gun into the ionosphere and back into the positive-biased satellite. The main problem addressed here is the current-voltage characteristics of the ionospheric interaction with the satellite. The first problem is that while the satellite will be capable of measuring charged particle flow to the surface at several locations, the detectors have a limited range of acceptance angle. The second problem is that the angle of incidence of the incoming electrons will have to be relative to the local normal. This will be important in order to predict the magnitude of the detectable current at each detector location so the detector gain can be pre-set to the correct range. The plasma sheath was analyzed mathematically, and subroutines were written to solve relevant finite element, Taylor-Vlasov, and Poisson equations.

Sheldon, John W.↗

NASA NTRS1996

Formation of the Electric Double Layer and its Effects on Moving Bodies in a Space Plasma Environment

In this paper we solve the self-consistent Vlasov and Poisson equations by a numerical method to determine the local distribution function of the ion and the electron, within a thin layer near the moving body, respectively. Using these ion and electron distributions, the number density for the ions and electrons are determined, such that, the electric potential is obtained within this thin layer (i.e., measured by Debye length). Numerical results are presented for temporal evolution of the electron and ion density and its corresponding electric potential within the layer which shows the formation of electric double layer and its structures. From these numerical results, we are able to determine the maximum conditions of the electric potential, it may create satellite anomaly.

Yang, Qianli↗

NASA NTRS2009

Analysis of Electromagnetic Wave Propagation in a Magnetized Re-Entry Plasma Sheath Via the Kinetic Equation

Based on a theoretical model of the propagation of electromagnetic waves through a hypersonically induced plasma, it has been demonstrated that the classical radiofrequency communications blackout that is experienced during atmospheric reentry can be mitigated through the appropriate control of an external magnetic field of nominal magnitude. The model is based on the kinetic equation treatment of Vlasov and involves an analytical solution for the electric and magnetic fields within the plasma allowing for a description of the attendant transmission, reflection and absorption coefficients. The ability to transmit through the magnetized plasma is due to the magnetic windows that are created within the plasma via the well-known whistler modes of propagation. The case of 2 GHz transmission through a re-entry plasma is considered. The coefficients are found to be highly sensitive to the prevailing electron density and will thus require a dynamic control mechanism to vary the magnetic field as the plasma evolves through the re-entry phase.

Manning, Robert M.↗

DOE OSTI2025

Algebra of invariants for the Vlasov–Maxwell system

The algebra of invariants for both the relativistic and nonrelativistic multispecies Vlasov–Maxwell system is examined, including the case with a fixed ion background. Invariants and their associated fluxes are obtained directly from the Vlasov–Maxwell system. The invariants are shown to Poisson commute with the Hamiltonian and the rest of the Poisson bracket algebra of invariants is identified. Special attention is given to the role played by the monopole condition, ∇ · B.

Fundamental invariants↗

DOE OSTI2025

Cosmological perturbation theory for large scale structure in phase space

We develop a framework for Large Scale Structure (LSS) perturbation theory, that solves the Vlasov-Poisson system of equations for the distribution function in full phase space. This approach relaxes the usual apriori assumption of negligible velocity dispersion underlying the Standard Perturbation Theory (SPT). We apply the new method to rederive the usual SPT kernels up to third order in the perturbative expansion. We also show that a counterterm, identical to the one introduced by standard Effective Field Theory (EFT) methods, naturally arises within our framework. We finish by making a precise connection to EFT techniques, which reveals the necessity of the EFTofLSS to self-consistently model the long-wavelength fluid, and illustrates the importance of having theoretical control over short distance fluctuations.

Cosmological perturbation theory in GR and beyond↗

NASA NTRS1982

A mechanism for plasma waves at the harmonics of the plasma frequency foreshock boundary

A bump-on-tail unstable reduced velocity distribution, constructed from data obtained at the upstream boundary of the electron foreshock by the GSFC electron spectrometer experiment on the ISEE-1 satellite, is used as the initial plasma state for a numerical integration of the 1D-Vlasov-Maxwell system of equations. The integration is carried through the growth of the instability, beyond its saturation, and well into the stabilized plasma regime. A power spectrum computed for the electric field of the stabilized plasma is dominated by a narrow peak at the Bohm-Gross frequency of the unstable field mode but also contains significant power at the harmonics of the Bohm-Gross frequency. The harmonic power is in sharp peaks which are split into closely spaced doublets. The fundamental peak at the Bohm-Gross frequency is split into a closely spaced triplet. The mechanism for excitation of the second harmonic is shown to be second order wave-wave coupling.

Klimas, A. J.↗

NASA NTRS1983

A numerical method based on the Fourier-Fourier transform approach for modeling 1-D electron plasma evolution

A numerical method is presented for studying one-dimensional electron plasma evolution under typical interplanetary conditions. The method applies the Fourier-Fourier transform approach to a plasma model that is a generalization of the electrostatic Vlasov-Poisson system of equations. Conservation laws that are modified to include the plasma model generalization and also the boundary effects of nonperiodic solutions are given. A new conservation law for entropy in the transformed space is then introduced. These conservation laws are used to verify the numerical solutions. A discretization error analysis is presented. Two numerical instabilities and the methods used for their suppression are treated. It is shown that in interplanetary plasma conditions, the bump-on-tail instability produces significant excitation of plasma oscillations at the Bohm-Gross frequency and its second harmonic. An explanation of the second harmonic excitation is given in terms of wave-wave coupling during the growth phase of the instability.

Klimas, A. J.↗

NASA NTRS1983

A mechanism for plasma waves at the harmonics of the plasma frequency in the electron foreshock boundary

Klimas, A. J.↗

NASA NTRS1994

A splitting algorithm for Vlasov simulation with filamentation filtration

A Fourier-Fourier transformed version of the splitting algorithm for simulating solutions of the Vlasov-Poisson system of equations is introduced. It is shown that with the inclusion of filamentation filtration in this transformed algorithm it is both faster and more stable than the standard splitting algorithm. It is further shown that in a scalar computer environment this new algorithm is approximately equal in speed and far less noisy than its particle-in-cell counterpart. It is conjectured that in a multiprocessor environment the filtered splitting algorithm would be faster while producing more precise results.

Klimas, A. J.↗

NASA NTRS1971

Theory of the unmagnetized plasma.

The Vlasov mathematical model of a plasma, which has come to be thought more useful than any other in describing the dynamical behavior of the majority of plasmas of interest, is first examined. Macroscopic variables and moment equations; linear electrostatics solutions; plasma oscillations, ion acoustic waves, and linear instabilities are treated, as well as external fields, 'test' charges, and nonlinear Vlasov phenomena. Plasmas are statistically described, and attention is given to the kinetic theory of the stable, uniform plasma and the Balescu-Lenard equation; two-time ensemble averages and fluctuation spectra in stable plasmas; the kinetic theory of the unstable plasma; and ensembles of Vlasov plasmas. Some illustrative experiments are described. Four appendixes deal with the electrostatic approximation and transverse waves; solution of the linearized Vlasov equation in a magnetic field; estimates of correlation functions from thermal equilibrium; and equivalence of spatially uniform BBGKY and Klimontovich correlations.

Montgomery, D. C.↗

NASA NTRS1985

Spacecraft-environment interaction: The environmental plasma aspect

The effects involved in the interaction between an obstacle and a space plasma can be divided into: (1) effects on the obstacle itselt (i.e., its charging); and (2) effects on the environmental plasma due to the motion of the obstacle (i.e., the creation of shocks ahead of the obstacle and complicated wakes behind the obstacle). In the wake (or antisolar direction), plasma oscillations are excited and instabilities, wave-particle interactions, turbulence, etc., are believed to take place. The effects on the obstacle and on the environmental space plasma are coupled. Hence, simultaneous solutions to the Vlasov (or Boltzmann) and Poisson equations are sought. To obtain realistic solutions of practical use, three-dimensional and time-dependent models of the interaction are needed. Achieving the latter is indeed not simple.

Samir, U.↗

NASA NTRS1972

Conservation of quasiparticles in weakly turbulent plasmas.

An expansion making use of the eikonal is shown to yield a solution to the equations of a general weak turbulent plasma which is weakly dependent on space and time. The method is used to derive a quasi-particle conservation equation for quasi-static perturbations of Vlasov plasmas with general equilibrium field configurations.

Bloomberg, H. W.↗

NASA NTRS1977

Calculation of sheath and wake structure about a pillbox-shaped spacecraft in a flowing plasma

A computer program was used for studies of the disturbed zones around bodies in flowing plasmas, particularly spacecraft and their associated sheaths and wakes. The program solved a coupled Poisson-Vlasov system of nonlinear partial differential integral equations to obtain distributions of electric potential and ion and electron density about a finite length cylinder in a plasma flow at arbitrary ion Mach numbers. The approach was applicable to a larger range of parameters than other available approaches. In sample calculations, bodies up to 100 Debye lengths in radius were treated, that is, larger than any previously treated realistically. Applications were made to in-situ satellite experiments.

Parker, L. W.↗