Plasmasphere Research Articles

3D FDTD Implementation for Scattering of Electric Anisotropic Dispersive Medium Using Recursive Convolution Method

The finite-difference time-domain method based on recursive convoltion method (RC-FDTD) for the electric anisotropic dispersive medium is discussed in detail. To exemplify the availability of the three-dimensional RC-FDTD algorithm, the backscattering Radar-Cross-Section(RCS) of a non-magnetized plasma sphere is computed, and the numerical results are the same as the one of the Shift Operater-FDTD method, and show that the RC-FDTD method is correct and efficient. In addition, the co-polarized and cross-polarized backscattering time-domain of a magnetized plasma sphere are obtained by the RC-FDTD algorithm. The results show that when the external magnetic field is implemented, the cross-polarized component appear, evidently.

FDTD Study on Back Scattering of Conducting Sphere Coated with Double-Negatibe Metamaterials

The shift operator method in finite-difference time-domain method for anisotropic double-negative (DNG) metamaterials is derived. The problem which incorporates both anisotropy and frequency dispersion at the same time is solved for the electromagnetic wave propagation in DNG media. By comparing with the mie series solution, the numerical verification of the method and program are confirmed by computing the back scattering of isotropic unmagnetized plasma sphere. The back scattering of conducting sphere coated with DNG media with different parameters is computed by using the shift operator method. One finds that the degree of DNG media’s match and isotropy plays important parts in the decrease of the back scattering of the conducting sphere.

Computation of the effect of neutral collisions on ion current to a floating sphere in a stationary plasma

The Specialized-Coordinate Electrostatic Particle and Thermals in Cell (SCEPTIC) code [I. H. Hutchinson, Plasma Physics and Controlled Fusion 45, 1447 (2003)] is used to compute the ion flux to a floating sphere in a stationary plasma, including the effects of charge-exchange collisions with neutrals. The results agree well with the available prior calculations at very low and very high collisionality thus validating the code and those prior calculations. In addition, SCEPTIC provides quantitative results at intermediate collisionalities where no analytic theory is available. Reasonable agreement in the floating potential is found there with some prior numerical results. For λDe much greater than the sphere radius, enhancements of the ion collection above the orbital motion limited value by factors as high as 5 occur, enough to exceed slightly the radial motion value, but only over a restricted range of collisionality. An explicit analytic fit to SCEPTIC’s results is provided for easy evaluation over the entire range of collisionality.

Three-dimensional finite-difference time-domain implementation for anisotropic dispersive medium using recursive convolution method

The permittivity in the frequency domain is transformed to the time domain, and the complex electric susceptibility dyadic matrix and the complex electric displacement vector in time domain are introduced. The three_dimensional finite_difference time_domain method based on the recursive convolution principle(RC_FDTD) for the electric anisotropic dispersive medium is discussed in detail. To exemplify the availability of the RC-FDTD algorithm, the backscattering RCS of a non-magnetized plasma sphere is computed, and the numerical results are the same as that of shift operator_FDTD method, which shows that the RC-FDTD method is correct and efficient. In addition, the co-polarized and cross-polarized backscattering waves in time domain for a magnetized plasma sphere are obtained by the RC-FDTD algorithm. The results show that when the external magnetic field is implemented, the cross-polarized component appear evidently.

Efficient modeling of isotropic cold plasma media using JE-TLM method

New simulation technique, by the transmission line matrix method(TLM), of electromagnetic waves in dispersive cold plasma media is proposed. This technique exploits the dependence of the current density J and the electric field E, and the derivation of the ordinary differential equations (ODE) by the exponential fitting method. The TLM Model uses the standard symmetrical condensed node(SCN) with 12 principal ports and 3 additional ports in which we incorporate voltage sources to model the dispersive behavior of cold plasma media. To investigate the accuracy of this approach, reflection and transmission coefficients of non-magnetized plasma wall are computed. Also the far-zone scattering results of a cold plasma sphere are presented. All the obtained results, using the new modeling technique named JE-TLM are in good agreement with those of the theoretical ones.

Theoretical and Experimental Study of Scattering of a PlaneWave by an Inhomogeneous Plasma Sphere

Scattering of electromagnetic waves by an inhomogeneous plasma spherehas been studied theoretically and experimentally. The offset angles ofelectromagnetic waves caused by the plasma sphere have been observedexperimentally. The effects of the electromagnetic wave frequency andplasma density on the offset angle are discussed. The plasma density isestimated with the offset angle.

The electrostatic potential of E ring particles

Saturn's E ring is remarkable not only for its huge size. Based on optical measurements the ring was surprisingly found to mainly consist of ice particles of uniform size (radii between 0.3 and 2 microns) [Nicholson et al., 1996. Observations of Saturn's ring-plane crossing in August and November. Science 272, 509–516], though the source of the ring, the icy moon Enceladus, feeds the ring with grains having a much broader mass distribution [Spahn et al., 1999. Dynamics of dust ejected from enceladus: application to the cassini dust detector. J. Geophys. Res. 104, 24111–24120]. Because of this contradiction, the mass distribution of the ring must be closely connected to the dynamics of the ring particles which is governed by the competition of various disturbing forces acting on the grains. It was realised early that the dynamics of the charged ring particles is strongly affected by electromagnetic forces as well as by plasma drag. Understanding the implications on the ring dynamics thus requires knowledge of the electrostatic equilibrium potential of the dust grains. The charge-sensitive grid system of the cosmic dust analyser (CDA) on the Cassini spacecraft allows an in situ determination of the charge of grains bigger than 2–3 microns. Since the CDA detector determines the grain mass simultaneously with the dust charge the electrostatic potential φ d can be estimated as well. Here we report the first measurement of the electrostatic potential of E ring particles. Particles detected inside the orbit of Saturn's moon Rhea were always found to be negatively charged, whereas grains outside Rhea's orbit were on a positive potential of about 3 V. Our results are in good agreement with measurements of the spacecraft potential by Cassini's radio and plasma wave science (RPWS) investigation [Wahlund et al., 2005. The inner magnetosphere of Saturn: Cassini RPWS cold plasma results from the first encounter. Geophys. Res. Lett. 32]. Our analysis implies that the CDA dust analyser (DA) mass calibration by Göller and Grün [1998. Calibration of the Galileo/Ulysses dust detectors with different projectile materials and at varying impact angles. Planet. Space Sci. 37, 1197–1206] is applicable for ice particles. We achieved a good match between our findings and the model calculations of the grain potential when using new Cassini measurements of plasma properties within Saturn's inner plasma sphere. Based on this we provide a realistic description for the grain potential needed for modelling the dynamics of Saturn's E ring.

The moving boundary problem in the presence of a dipole magnetic field

An exact analytic solution is obtained for a uniformly expanding, neutral, infinitely conducting plasma sphere in an external dipole magnetic field. The electrodynamical aspects related to the radiation and transformation of energy were considered as well. The results obtained can be used in analyzing the recent experimental and simulation data.

Cluster explosion investigated by linearly chirped spectral scattering of an expanding plasma sphere

Femtosecond explosive processes of argon clusters irradiated by linearly chirped ultraintense laser pulses have been investigated by 90 degrees side spectral scattering. The spectral redshift and blueshift, which correlate with the cluster explosion processes have been measured for negatively and positively chirped driving laser pulses, respectively. The evolution of the heated-cluster polarizability indicates that the core of the cluster is shielded from the laser field in the beginning of the explosion and enhanced scattering occurs after the fast explosion initiates. Evidence of resonant heating is found from the coincidence of enhanced scattering with enhanced absorption measured using the transmitted spectra. Anomalously large-size clusters with very low gas density have been observed in this way and can be used as clean and important cluster targets.

Continuum model for the breathing oscillation of a spherical complex plasma

A nonlinear equation of motion for the breathing oscillation of a spherical complex plasma is derived. A spherical complex plasma, or “dust ball,” is a three-dimensional arrangement of n identical charged particles interacting through a shielded Coulomb force (i.e., a Yukawa potential) with a Debye length λ and confined by a three-dimensional, isotropic, parabolic potential well for which the single-particle oscillation frequency is ω0. The dependence of the equilibrium radius R0 and small-amplitude breathing frequency ωbr on λ is computed. Exact analytical results are given for the continuum limit n→∞ (i.e., a spherical Yukawa fluid). The squared breathing frequency (ωbr∕ω0)2=3 for the unshielded Coulomb interaction (1∕λ→0), irrespective of n, and increases to (ωbr∕ω0)2=5 as 1∕λ→∞. The effects of a finite number of particles are modeled by assuming an inner cutoff for the Yukawa potential a distance a from any point in the complex plasma sphere. Three physical regimes are identified: a Coulomb regime where λ⪢R0 and corrections to the infinite-λ case are small, a nearest-neighbor regime, where R0⪢a>λ and nearest-neighbor interactions dominate, and a plasma regime where R0⪢λ≳a and continuum plasma theory is applicable. For 1∕λ→∞, (ωbr∕ω0)2∼a∕λ in the nearest-neighbor regime, while (ωbr∕ω0)2∼5 in the plasma regime.

Experimental Observation of a Periodically Oscillating Plasma Sphere in a Gridded Inertial Electrostatic Confinement Device

The periodically oscillating plasma sphere (POPS) [D. C. Barnes and R. A. Nebel, Phys. Plasmas 5, 2498 (1998).] oscillation has been observed in a gridded inertial electrostatic confinement device. In these experiments, ions in the virtual cathode exhibit resonant behavior when driven at the POPS frequency. Excellent agreement between the observed POPS resonance frequency and theoretical predictions has been observed for a wide range of potential well depths and for three different ion species. The results provide the first experimental validation of the POPS concept proposed by Barnes and Nebel [R. A. Nebel and D. C. Barnes, Fusion Technol. 34, 28 (1998).].

Terahertz sensing of non-equilibrium microplasmas

The characterization of plasma by microwaves has been performed for decades. Generally, all known microwave approaches can be classified as analysis of either the wave interference within a quasi-transparent plasma or the absorption near the so-called critical point. These approaches can be generalized for the study of media containing absorbing space-localized irregularities. Essentially, the problem is to identify the power transmittance dependence on the shape, size and refraction or absorption of these irregularities. Moreover, the probing field should have a duration sufficiently short compared to the time scale of the irregularity evolution in order to clearly image the medium. The generalized analysis involves a diffraction theory development for typical plasma formations. The Khizhnyak method of integral equations is exploited here for this purpose. Solutions are obtained in a robust analytical form that allows constructive inversion to determine the particular plasma properties that produce the observed diffraction pattern. The specific cases of a flat plasma layer, plasma cylinder and plasma sphere are described in this manner. The proposed analysis can be implemented experimentally with a compact, tunable, pulsed terahertz source. This development is discussed as well.

Periodically oscillating plasma sphere

The periodically oscillating plasma sphere, or POPS, is a novel fusion concept first proposed by D. C. Barnes and R. A. Nebel [Fusion Technol. 38, 28 (1998)]. POPS utilizes the self-similar collapse of an oscillating ion cloud in a spherical harmonic oscillator potential well formed by electron injection. Once the ions have been phase-locked, their coherent motion simultaneously produces very high densities and temperatures during the collapse phase of the oscillation. A requirement for POPS is that the electron injection produces a stable harmonic oscillator potential. This has been demonstrated in a gridded inertial electrostatic confinement device and verified by particle simulation. Also, the POPS oscillation has been confirmed experimentally through observation that the ions in the potential well exhibit resonance behavior when driven at the POPS frequency. Excellent agreement between the observed POPS frequencies and the theoretical predictions has been observed for a wide range of potential well depths and three different ion species. Practical applications of POPS require large plasma compressions. These large compressions have been observed in particle simulations, although space charge neutralization remains a major issue.

An observation of synthetic ball lightning

Ball lightning has been extensively researched for many centuries. Here, in this paper, we present one form of ball lightning where plasma spheres several centimeters in diameter were produced in atmospheric pressure air. These spheres persisted for up to a half second after the power supply was turned off. A mathematical theory was derived that predicts the observed lifetime. The theory predicts that the sphere lifetime should scale as the sphere radius squared, which means that large spheres should persist for many seconds.

Dipole resonances of an ionized cluster

We study the resonance properties of an ionized spherical cluster that interacts with an optical radiation field in terms of linear hot-plasma polarizability models. Based on a generalization that includes spatial dispersion in the well-known Mie problem of the diffraction of a plane wave by a small-size plasma sphere, we calculate the eigenfrequencies, the radiative and collisional damping constants, and the resonance amplitudes of the cluster surface and bulk plasmon fields. The role of collisionless dissipation processes is analyzed in terms of a one-dimensional kinetic model. The latter allows the corresponding damping constants for both types of plasmons to be determined as functions of the characteristic electron-plasma boundary collision frequency. We show that both types of plasmons in certain domains of cluster and external-radiation parameters can undergo a strong resonance that causes both the amplitude of the scattered wave and the absorbed power and the field inside the cluster to increase significantly.

An Experimental Study of Ball Lightning

This paper presents a study of one possible form of ball lightning. Plasma spheres several centimeters in diameter were produced in atmospheric pressure air. These spheres persisted for up to a half-second after the power supply was turned off. A mathematical theory was derived that predicts the observed lifetime. The theory predicts that the sphere lifetime should scale as the sphere radius squared, which means that large spheres should persist for many seconds.

Estimates on the mean current in a sphere of plasma

Several turbulent dynamo models predict the concentration of the magnetic field in chaotic plasmas in sheets with the field vector pointing alternatively in opposite directions, which should produce strong current sheets. It is proved that if the plasma is contained in a rigid sphere with perfectly conducting boundary the geometry of these sheets must be balanced so that the mean current remains essentially bounded by the Coulomb gauged mean vector potential of the field. This magnitude remains regular even for the sharp field variations expected in a chaotic flow. For resistive plasmas the same arguments imply that the contribution to the total current of the regions near the boundary compensates the current of the central part of the sphere.

Equilibrium and low-frequency stability of a uniform density, collisionless, spherical Vlasov system

Equilibrium and stability of a collisionless, spherical Vlasov system with uniform density are considered. Such an electron system is useful for the Periodically Oscillating Plasma Sphere (POPS) fusion system. In POPS the space charge of a uniform-density spherical electron cloud provides a harmonic well for an under-dense thermal ion population. Previous special solutions [D. C. Barnes, Phys. Plasmas 6, 4472 (1999)] are extended to arbitrary energy dependence. These equilibrium distribution functions and their first derivatives may be made nonsingular, in contrast to the previous solutions. Linear stability of general spherical equilibria is considered, and reduced to a one-dimensional calculation by the introduction of a spherical harmonic decomposition. All azimuthal mode numbers are degenerate. Using this formalism, the low-frequency stability of a collisionless, spherical Vlasov electron system coupled to a minority ion cloud is studied for the class of uniform-density electron equilibria found. In the low-frequency (adiabatic) limit, the general kinetic stability formalism can be integrated to find a closed form for the response of electron number density. The adiabatic response operator is shown to be self-adjoint. Computation of its eigenvalues proves the constant-density electrons/thermal ions system in POPS to be mostly stable to ion-electron electrostatic modes. Unstable modes are avoided unless central electrons have an extremely small energy spread. These results may also be useful for the consideration of gravitational and beam systems.

Fluid and kinetic stability of virtual cathodes for the periodically oscillating plasma sphere

Recent theoretical work [R. A. Nebel and D. C. Barnes, Fusion Technol. 38, 28 (1998); D. C. Barnes and R. A. Nebel, Phys. Plasmas 5, 2498 (1998)] has suggested that a tiny oscillating ion cloud (referred to as the periodically oscillating plasma sphere or POPS) may undergo a self-similar collapse that can result in the periodic and simultaneous attainment of ultrahigh densities and temperatures. However, a major uncertainty in this plasma system is the behavior of the electron cloud that forms a virtual cathode. Here it is demonstrated that the required electron cloud (which forms a harmonic oscillator potential) is susceptible to an instability related to buoyancy-driven modes present in compressible fluids. Although it is demonstrated that no absolutely stable profiles with uniform electron density exist, stable profiles that are close to the required harmonic oscillator potential are found. A simple two-stream analysis indicates that kinetic effects lead to a critical limit in λD/a above which the virtual cathodes are stable. This result is consistent with previous experimental observations.

Collective modes in neutrino “beam” electron-positron plasma interactions

We derive semiclassical neutrino-electron transport equations in the collisionless (Vlasov) limit from the coupled Dirac equations, incorporating the charged and neutral weak current-current as well as electromagnetic interactions. A corresponding linear response theory is derived. In particular, we calculate the response functions for a variety of beam-plasma geometries, which are of interest in a supernova scenario. We apply this to the study of plasmons and to a new class of collective pharon resonance modes, which are characterized by $\ensuremath{\omega}<q.$ We find that the growth rates of the unstable modes correspond to a strongly temperature $(\ensuremath{\propto}{T}_{\ensuremath{\nu}}^{2}{T}_{e}^{3})$ and linearly momentum dependent e-folding length of about ${10}^{10} \mathrm{km}$ under typical conditions for type II supernovas. This appears to rule out such long-wavelength collective modes as an efficient means of depositing neutrino energy into the plasma sphere.