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NASA NTRS1984

Voyager 1 evidence for ion-cyclotron instability in the vicinity of the Io plasma Torus

The Voyager 1 traversal of the Io plasma torus was marked by pronounced enhancement in low frequency wave activity with especially strong wave intensification below the proton gyrofrequency, suggesting the excitation of ion-cyclotron waves over the same radial range in which the energetic ring current ions exhibit phase space density depletion due to strong pitch angle scattering loss to the atmosphere. If the more intense emissions observed intermittently by Voyager 1 are representative of waves in the high latitude source region, the resulting pitch angle scattering would be sufficiently rapid to explain the observed energetic ion losses and the excitation of intense Jovian auroral emissions of field lines passing through the torus.

Thorne, R. M.↗

NASA NTRS1982

Dynamic effects of combustion

The dynamic effects of combustion are due to the evolution of exothermic energy and its deposition in the compressible medium where the process takes place. The paper examines the dynamics of combustion phenomena, including ignition, turbulent flame propagation (inflammation), explosion, and detonation, with emphasis on their exothermic characteristics. Ignition and explosion are treated as problems of nonlinear mechanics, and their dynamic behavior is described in terms of phase space models and cinematographic laser shear interferograms. The results of a numerical random vortex model of turbulent flame propagation are confirmed in a combustion tunnel experiment, where it was observed that a fresh mixture of burnt and unburnt gases can sustain combustion with a relatively small expenditure of overall mass flow, due to the increasing specific volume of burnt gases inside the flame front. An isentropic pressure wave is found to precede the accelerating flame in the process of detonation, and components of this presssure wave are shown to propagate at local sonic velocities.

Oppenheim, A. K.↗

NASA NTRS1984

Pitch angle diffusion in the Jovian magnetodisc

Using a linear approximation to the field variation and a mathematical technique for distorting the orbit integration into the complex gyrophase plane, a formula is derived for the nonadiabatic change in magnetic moment. This change varies as the cosine of the particle gyrophase at the equator, so that if a particle traverses the equator several times with different values of this gyrophase, it suffers randomly correlated values for the nonadiabatic change in magnetic moment. The algebraic formula for this nonadiabatic change is found to be in excellent agreement with previous numerical computations. The phase space density, averaged over several bounce periods, is found to satisfy a diffusion equation in pitch angle. The diffusion coefficient is dependent on particle energy, pitch angle, and the field line along which the particles are moving.

Birmingham, T. J.↗

NASA NTRS1984

Solar-flare-induced Forbush decreases - Dependence on shock wave geometry

It is argued that the principal mechanism for the association of Forbush decreases with the passage of a solar flare shock wave is prolonged containment of cosmic ray particles behind the flare compression region, which acts as a semipermeable obstacle to particle motion along the field lines, leading to additional adiabatic cooling of the particles. Liouville's theorem is used to calculate the instantaneous distribution function at 1 AU for each particle arriving at the earth. By averaging over a large number of individual estimates, a representative estimate of the omnidirectional phase space density and the corresponding particle intensity is obtained. The energy change of individual particles at the shocks is found to be small in comparison to the energy lost by adiabatic cooling of the cosmic rays between the shock wave and the sun. The effects of particle rigidity, diffusion coefficient, and flare longitude on the magnitude of the Forbush decrease are quantitatively investigated.

Thomas, B. T.↗

NASA NTRS1984

Quenching of the beam-plasma instability by 3-D spectra of large scale density fluctuations

A model is presented to explain the highly variable yet low level of Langmuir waves measured in situ by spacecraft when electron beams associated with Type III solar bursts are passing by; the low level of excited waves allows the propagation of such streams from the Sun to well past 1 AU without catastrophic energy losses. The model is based, first, on the existence of large scale density fluctuations that are able to efficiently diffuse small k beam unstable Langmuir waves in phase space, and, second, on the presence of a significantly isotropic nonthermal tail in the distribution function of the background electron population, which is capable of stabilizing larger k modes. The strength of the model lies in its ability to predict various levels of Langmuir waves depending on the parameters. This feature is consistent with the high variability actually observed in the measurements.

Muschietti, L.↗

NASA NTRS1984

Antenna induced range smearing in MST radars

There is considerable interest in developing stratosphere troposphere (ST) and mesosphere stratosphere troposphere (MST) radars for higher resolution to study small-scale turbulent structures and waves. At present most ST and MST radars have resolutions of 150 meters or larger, and are not able to distinguish the thin (40 - 100 m) turbulent layers that are known to occur in the troposphere and stratosphere, and possibly in the mesosphere. However the antenna beam width and sidelobe level become important considerations for radars with superior height resolution. The objective of this paper is to point out that for radars with range resolutions of about 150 meters or less, there may be significant range smearing of the signals from mesospheric altitudes due to the finite beam width of the radar antenna. At both stratospheric and mesospheric heights the antenna sidelobe level for lear equally spaced phased arrays may also produce range aliased signals. To illustrate this effect the range smearing functions for two vertically directed antennas have been calculated, (1) an array of 32 coaxial-collinear strings each with 48 elements that simulates the vertical beam of the Poker Flat, Glaska, MST radar; and (2) a similar, but smaller, array of 16 coaxial-collinear strings each with 24 elements.

Watkins, B. J.↗

NASA NTRS1985

Evaluation of parameters for particles acceleration by the zero-point field of quantum electrodynamics

That particles may be accelerated by vacuum effects in quantum field theory has been repeatedly proposed in the last few years. A natural upshot of this is a mechanism for cosmic rays (CR) primaries acceleration. A mechanism for acceleration by the zero-point field (ZPE) when the ZPE is taken in a realistic sense (in opposition to a virtual field) was considered. Originally the idea was developed within a semiclassical context. The classical Einstein-Hopf model (EHM) was used to show that free isolated electromagnrtically interacting particles performed a random walk in phase space and more importantly in momentum space when submitted to the perennial action of the so called classical electromagnrtic ZPE.

Rueda, A.↗

NASA NTRS1984

Dynamic alignment and selective decay in MHD

Under some circumstances, incompressible magnetohydrodynamic turbulence will evolve toward a state in which the velocity fields and magnetic fields are aligned or anti-aligned. We propose a mechanism for this effect and illustrate with numerical computations. Under some other circumstances, the energy appears to decay selectively toward a minimum energy state in which the kinetic energy has disappeared. It has not been possible so far to identify a boundary in the phase space which divides the two regimes.

Matthaeus, W. H.↗

NASA NTRS1984

On the use of parametric differentiation to predict weak shock waves

The method of parametric differentiation is shown to be an effective means to transform both the time-linearized and the fully nonlinear transonic small disturbance potential flow equations to a linear system of equations. The globally linearized equations are then solved in phase space by finite difference methods and integral equation methods. The predicted birth, growth, and motion of weak shock waves in two-dimensional transonic flows are compared with existing theory and experiment.

Harris, W. L.↗

NASA NTRS1985

Simulation study of Type 2 counterstreaming electrons along auroral field lines

The production of counterstreaming electrons associated with parallel fields along auroral field lines is examined through the use of computer simulation. A 2 1/2-dimensional (two spatial and three velocity dimensions) electrostatic particle algorithm and auroral boundary conditions are used to set up a self-consistent V potential structure. The simulation produces signatures of counterstreaming electrons resembling those observed by the Dynamics Explorer 1 satellite. The main signatures are as follows: (1) the phase space contours of the electron distribution function are elongated along the V-parallel axis, and (2) the energy of electrons streaming in the upward direction is comparable to the energy of the accelerated electron beam. The simulation indicates that a portion of the accelerated electron beam is trapped by large amplitude electrostatic waves produced through the two-stream instability. Strong wave-particle interactions then thermalize the trapped electrons to produce suprathermal electrons streaming in the direction opposite to that of the accelerated electron beam. These results suggest a possible mechanism of producing counterstreaming electron fluxes through nonlinear processes of the two-stream instability.

Wagner, J. S.↗

NASA NTRS1985

Quenching of the beam-plasma instability by large-scale density fluctuations in 3 dimensions

The highly variable, yet low, level of Langmuir waves measured in situ by spacecraft when electron beams associated with type III solar bursts are passing by are addressed by a model based on the existence of large scale density fluctuations capable of sufficiently diffusing small-k beam-unstable Langmuir waves in phase space. The model is also informed by the presence of a significant isotropic nonthermal tail in the distribution function of the background electron population, which is capable of stabilizing larger k modes. The model is able to predict various levels of Langmuir waves, depending on the parameters; calculations indicate that, for realistic parameters, the most unstable small k modes are fully stabilized, while some oblique mode with higher k and lower growth rate may remain unstable.

Muschietti, L.↗

NASA NTRS1985

A perturbative treatment of motion near the 3/1 commensurability

A semianalytic perturbation theory for motion near the 3/1 commensurability in the planar elliptic restricted three-body problem is presented. The predictions of the theory are in good agreement with the features found on numerically generated surfaces of section; a global understanding of the phase space is achieved. The principal cause of the large chaotic zone near the 3/1 commensurability is identified, and a new criterion for the existence of large-scale chaotic behavior is presented.

Wisdom, J.↗

NASA NTRS1985

Markov-Tree model of intrinsic transport in Hamiltonian systems

A particle in a chaotic region of phase space can spend a long time near the boundary of a regular region since transport there is slow. This 'stickiness' of regular regions is thought to be responsible for previous observations in numerical experiments of a long-time algebraic decay of the particle survival probability, i.e., survival probability approximately t to the (-z) power for large t. This paper presents a global model for transport in such systems and demonstrates the essential role of the infinite hierarchy of small islands interspersed in the chaotic region. Results for z are discussed.

Meiss, J. D.↗

NASA NTRS1986

Non-existence of dynamical perturbations of Schwarzschild with vanishing self-dual part

A recent proposal of Ashtekar (1985) for the canonical quantisation of gravity involves a new choice of a (complex) polarisation on the (real) phase space of general relativity. In order for the 'four dimensional' version of Ashtekar's proposal to be viable, it is necessary that for an arbitrary (real) background solution there exist a sufficient number of (complex) solutions of the linearised Einstein equation with perturbed Weyl spinor having vanishing self-dual part. It is shown that this is not the case by explicitly demonstrating that for the Schwarzschild spacetime, aside from stationary perturbations, there are no such linearised solutions which can be expressed as superpositions of modes of real frequencies. The viability of the '3+1 version' of Ashtekar's proposal is not affected by these considerations.

Wald, R. M.↗

NASA NTRS1986

Electron-positron pair production by ultrarelativistic electrons in a soft photon field

The fully differential cross section for photon-electron pair production is integrated numerically over phase space. Results are obtained for the astrophysically interesting case in which the interaction between an ultrarelativistic electron and a soft photon results in electron-positron pair production. The positron spectrum is a function of the energies of both the photon and the electron, as well as the angle of interaction. It is found that the energy at which the positron distribution peaks is inversely proportional to the photon energy and independent of the electron energy. The positron spectrum is integrated once more over initial electron energies for a power-law energy distribution of primary electrons. The same procedure is repeated for the recoil particle; it is shown that the peak of the recoil energy distribution depends linearly on the energy of the primary electron. Finally, semianalytical expressions are obtained for the energy losses of the primary electrons.

Mastichiadis, A.↗

NASA NTRS1986

Limits on ion radial diffusion coefficients in Saturn's inner magnetosphere

The development of upper and lower limits for the rate of radial diffusion of energetic ions in Saturn's inner magnetosphere is discussed. Improved calculations of the satellite-sweeping rate and phase space density profiles for a wide range of ion invariants are utilized to determine the limits. The lower limit for the radial diffusion coefficient is established by requiring the rate of inward diffusion to be large enough to balance satellite sweeping losses; the upper limit is obtained by requiring the rate of inward diffusion to be less than the observable ultraviolet aurora on plasma torus L shell. It is concluded that the radial diffusion coefficient for ions in Saturn's inner magnetosphere is calculated to about two orders of magnitude.

Paonessa, M.↗

NASA NTRS1986

Chaos and nonlinear dynamics of single-particle orbits in a magnetotaillike magnetic field

The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.

Chen, J.↗

NASA NTRS1986

Low-energy electron-atom bremsstrahlung

This paper extends recent work providing an elementary calculation of bremsstrahlung and opacity associated with the scattering of low-energy electrons by neutral atoms and molecules. The method applies when the scattering potential is 'hard' or when the collision time is short, applying the classical soft-photon emission probability formula for arbitrary bremsstrahlung photon energy. However, now, in addition to correcting the probability factor for finite bremsstrahlung photon energy, another factor corrects for the reduced phase space available to the outgoing electron. The bremsstrahlung cross section and opacity are then computed directly from the elastic scattering cross section, determined experimentally or calculated; a small (approximately 10 percent) correction is computed from the anisotropic term in the elastic scattering cross section. The opacity is evaluated for electron scattering by H, He, and H2 using experimentally determined values for the elastic scattering cross section, and is compared with more elaborate calculations. The agreement is good (within 10 percent), indicating an accuracy for the general method comparable to variations among the results of different elaborate theoretical computations. The agreement seems to validate the basic approximation of short collision time even at large bremsstrahlung photon energy for electron energies and temperatures up to a few eV.

Gould, R. J.↗