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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Pulsars as cosmic ray particle accelerators: Proton orbits

Proton orbits are calculated in the electromagnetic vacuum field of a magnetic point dipole rotating with its angular velocity omega perpendicular to its dipole moment mu by numerical integration of the Lorentz-Dirac equation. Trajectories are shown and discussed for various initial conditions. A critical surface is shown separating initial positions of protons which finally hit the pulsar in the polar region from those which finally recede to infinity.

Thielheim, K. O.↗
NASA NTRS1985

Pulsars as cosmic ray accelerators: Energy development of protons

Results of numerical integrations of the Lorentz-Dirac-equation with Landau approximation for protons in the electromagnetic vacuum field of a magnetic dipole rotating with its angular velocity omega perpendicular to its magnetic moment mu will be discussed with special attention to the energy development of protons.

Thielheim, K. O.↗
NASA NTRS1985

Pulsars as cosmic ray particle accelerators: Dynamics of electrons

The Lorentz-Dirac-equation with Landau approximation has been solved numerically for electrons in the electromagnetic field of a magnetic dipole rotating with the angular velocity omega perpendicular to its magnetic moment mu. Results are discussed with respect to electron orbits and energy development.

Thielheim, K. O.↗
NASA NTRS1986

On the fine-structure constant in a plasma model of the fluctuating vacuum substratum

The existence of an intimate connection between the quivering motion of electrons and positrons (Zitterbewegung), predicted by the Dirac equation, and the zero-point fluctuations of the vacuum is suggested. The nature of the proposed connection is discussed quantitatively, and an approximate self-consistency relation is derived, supplying a purely mathematical expression that relates the dimensionless coupling strengths (fine-structure constants) alpha sub e and alpha sub g of electromagnetism and gravity. These considerations provide a tentative explanation for the heretofore puzzling number 1/alpha sub e of about 137.036 and suggest that attempts to unify gravity with the electroweak and strong interactions will ultimately prove successful.

Cragin, B. L.↗
NASA NTRS1991

Synchrotron radiation with radiation reaction

A rigorous discussion is presented of the classical motion of a relativistic electron in a magnetic field and the resulting electromagnetic radiation when radiation reaction is important. In particular, for an electron injected with initial energy gamma(0), a systematic perturbative solution to the Lorentz-Dirac equation of motion is developed for field strengths satisfying gamma(0) B much less than 6 x 10 to the 15th G. A particularly accurate solution to the electron orbital motion in this regime is found and it is demonstrated how lowest-order corrections can be calculated. It is shown that the total energy-loss rate corresponds to what would be found using the exact Larmor power formula without including radiation reaction. Provided that the particle energy and field strength satisfy the same contraint, it is explicitly demonstrated that the intuitive prescription for calculating the time-integrated radiation spectrum described above is correct.

Nelson, Robert W.↗
NASA NTRS1993

Mass spectra of the particle-antiparticle system with a Dirac oscillator interaction

The present view about the structure of mesons is that they are a quark-antiquark system. The mass spectrum corresponding to this system should, in principle, be given by chromodynamics, but this turns out to be a complex affair. Thus it is of some interest to consider relativistic systems of particle-antiparticle, with a simple type of interaction, which could give some insight on the spectra we can expect for mesons. This analysis is carried out when the interaction is of the Dirac oscillator type. It is shown that the Dirac equation of the antiparticle can be obtained from that of the particle by just changing the frequency omega into -omega. Following a procedure suggested by Barut, the equation for the particle-antiparticle system is derived and it is solved by a perturbation procedure. Thus, explicit expressions for the square of the mass spectra are obtained and its implications in the meson case is discussed.

Moshinsky, M.↗
NASA NTRS1993

Second quantization in bit-string physics

Using a new fundamental theory based on bit-strings, a finite and discrete version of the solutions of the free one particle Dirac equation as segmented trajectories with steps of length h/mc along the forward and backward light cones executed at velocity +/- c are derived. Interpreting the statistical fluctuations which cause the bends in these segmented trajectories as emission and absorption of radiation, these solutions are analogous to a fermion propagator in a second quantized theory. This allows us to interpret the mass parameter in the step length as the physical mass of the free particle. The radiation in interaction with it has the usual harmonic oscillator structure of a second quantized theory. How these free particle masses can be generated gravitationally using the combinatorial hierarchy sequence (3,10,137,2(sup 127) + 136), and some of the predictive consequences are sketched.

Noyes, H. Pierre↗
NASA NTRS1994

On the physics of waves in the solar atmosphere: Wave heating and wind acceleration

This paper presents work performed on the generation and physics of acoustic waves in the solar atmosphere. The investigators have incorporated spatial and temporal turbulent energy spectra in a newly corrected version of the Lighthill-Stein theory of acoustic wave generation in order to calculate the acoustic wave energy fluxes generated in the solar convective zone. The investigators have also revised and improved the treatment of the generation of magnetic flux tube waves, which can carry energy along the tubes far away from the region of their origin, and have calculated the tube wave energy fluxes for the sun. They also examine the transfer of the wave energy originated in the solar convective zone to the outer atmospheric layers through computation of wave propagation and dissipation in highly nonhomogeneous solar atmosphere. These waves may efficiently heat the solar atmosphere and the heating will be especially significant in the chromospheric network. It is also shown that the role played by Alfven waves in solar wind acceleration and coronal hole heating is dominant. The second part of the project concerned investigation of wave propagation in highly inhomogeneous stellar atmospheres using an approach based on an analytic tool developed by Musielak, Fontenla, and Moore. In addition, a new technique based on Dirac equations has been developed to investigate coupling between different MHD waves propagating in stratified stellar atmospheres.

Musielak, Z. E.↗
NASA NTRS1993

On the physics of waves in the solar atmosphere: Wave heating and wind acceleration

This paper presents work performed on the generation and physics of acoustic waves in the solar atmosphere. The investigators have incorporated spatial and temporal turbulent energy spectra in a newly corrected version of the Lighthill-Stein theory of acoustic wave generation in order to calculate the acoustic wave energy fluxes generated in the solar convective zone. The investigators have also revised and improved the treatment of the generation of magnetic flux tube waves, which can carry energy along the tubes far away from the region of their origin, and have calculated the tube energy fluxes for the sun. They also examine the transfer of the wave energy originated in the solar convective zone to the outer atmospheric layers through computation of wave propagation and dissipation in highly nonhomogeneous solar atmosphere. These waves may efficiently heat the solar atmosphere and the heating will be especially significant in the chromospheric network. It is also shown that the role played by Alfven waves in solar wind acceleration and coronal hole heating is dominant. The second part of the project concerned investigation of wave propagation in highly inhomogeneous stellar atmospheres using an approach based on an analytic tool developed by Musielak, Fontenla, and Moore. In addition, a new technique based on Dirac equations has been developed to investigate coupling between different MHD waves propagating in stratified stellar atmospheres.

Musielak, Z. E.↗
NASA NTRS1997

Interfacing Relativistic and Nonrelativistic Methods: A Systematic Sequence of Approximations

A systematic sequence of approximations for the introduction of relativistic effects into nonrelativistic molecular finite-basis set calculations is described. The theoretical basis for the approximations is the normalized elimination of the small component (ESC) within the matrix representation of the modified Dirac equation. The key features of the normalized method are the retention of the relativistic metric and the ability to define a single matrix U relating the pseudo-large and large component coefficient matrices. This matrix is used to define a modified set of one- and two-electron integrals which have the same appearance as the integrals of the Breit-Pauli Hamiltonian. The first approximation fixes the ratios of the large and pseudo-large components to their atomic values, producing an expansion in atomic 4-spinors. The second approximation defines a local fine-structure constant on each atomic centre, which has the physical value for centres considered to be relativistic and zero for nonrelativistic centres. In the latter case, the 4-spinors are the positive-energy kinetic al ly-balanced solutions of the Levy-Leblond equation, and the integrals involving pseudo-large component basis functions on these centres, are set to zero. Some results are presented for test systems to illustrate the various approximations.

Dyall, Ken↗
NASA NTRS1966

Four-fermion interaction Lagrangians

Pauli exclusion principle and Fierz rearrangement theorem shown to limit arbitrariness of Lorentz invariant interaction Lagrangian for self-coupled Dirac field

LAGRANGE EQUATION↗
NASA NTRS1994

Particle localization, spinor two-valuedness, and Fermi quantization of tensor systems

Recent studies of particle localization shows that square-integrable positive energy bispinor fields in a Minkowski space-time cannot be physically distinguished from constrained tensor fields. In this paper we generalize this result by characterizing all classical tensor systems, which admit Fermi quantization, as those having unitary Lie-Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form.

Reifler, Frank↗
NASA NTRS1976

On the equation of state for an electron gas in an intense magnetic field

In this paper we derive the equation of state for a relativistic electron gas imbedded in a static homogeneous magnetic field of arbitrary strength. The derivation is based on the evaluation of the energy-momentum tensor and the use of Dirac's equation for such a problem. Contrary to a derivation presented several years ago, the present derivation is completely gauge-invariant. We also show how to recover, in an exact manner, the perfect gas law for the case of weak magnetic fields.

Canuto, V.↗
NASA NTRS1983

Statistical mechanics of light elements at high pressure. V Three-dimensional Thomas-Fermi-Dirac theory

A numerical technique for solving the Thomas-Fermi-Dirac (TED) equation in three dimensions, for an array of ions obeying periodic boundary conditions, is presented. The technique is then used to calculate deviations from ideal mixing for an alloy of hydrogen and helium at zero temperature and high presures. Results are compared with alternative models which apply perturbation theory to calculation of the electron distribution, based upon the assumption of weak response of the electron gas to the ions. The TFD theory, which permits strong electron response, always predicts smaller deviations from ideal mixing than would be predicted by perturbation theory. The results indicate that predicted phase separation curves for hydrogen-helium alloys under conditions prevailing in the metallic zones of Jupiter and Saturn are very model dependent.

Macfarlane, J. J.↗