Showing papers on "Momentum published in 1978"

Stimulated emission from relativistic electrons passing through a spatially periodic transverse magnetic field

Abstract: Stimulated emission from a relativistic beam of electrons passing through a spatially periodic right-hand circularly polarized magnetic field is considered. The amplification is found to be due to a ponderomotive bunching of the electrons. The effect is completely classical and for an infinite interaction distance a dispersion relation, which takes into account space-charge effects, describing the scattered field is derived. Conditions on the pump field amplitude, beam density, and momentum spread of the beam for emission from individual electrons to occur or for emission from plasma oscillations to occur are examined. Also, emission from individual electrons over a finite interaction distance is considered and gain is determined for distances less than an $e$-folding length.

Intermittency and preferential transport of heat in a round jet

Abstract: The temperature and velocity fields in a round heated jet were investigated in detail. Both conventional measurements and conditional measurements (zone averages and point averages) were performed. The probability density functions of the lengths of turbulent and non-turbulent durations were also measured. Filtered correlation measurements show that large-scale turbulent motions were responsible for the bulk of momentum and heat transport, and also that small scales were more efficient in transporting heat than in transporting momentum. In no case was heat transported further or more than momentum, however. These results are discussed in detail, particularly with regard to the entrainment. Conservation equations for turbulent-zone variables and the intermittency factor are derived and a model for some of the resulting higher-order correlations is suggested. An exact equation for the intermittency function is presented.

Numerical simulation of helical magnetohydrodynamic turbulence

Abstract: The three-dimensional incompressible magnetohydrodynamic (MHD) equations for rectangular geometry and periodic boundary conditions are solved numerically using the spectral method of Orszag & Patterson (1972). The calculations are restricted to a magnetic Prandtl number of one and to Gaussian random initial conditions with zero mean magnetic and momentum fields. We permit non-mirror-symmetric (helical) flows. In all cases, there is a continuous transfer of energy from the momentum field to the magnetic field. A proposed mechanism for this transfer involves the cascading of energy from the large scales of the momentum field to the small scales, thence a redistribution of energy between the momentum and magnetic fields by Alfven waves, and, finally, an inverse cascade of energy from the small scales of the magnetic field to the large scales. This inverse cascade is found when magnetic helicity (〈a. b〉, where b = curl a is the magnetic induction) is present in the flow.

Mass divergences in annihilation processes. I. Origin and nature of divergences in cut vacuum polarization diagrams

Abstract: The origin of mass divergences in internal loop momentum integrals of cut vacuum polarization diagrams is investigated. It is found that loop momentum configurations which can give rise to mass divergences are of a severely limited form and have a direct interpretation in terms of physically realizable processes. A power-counting procedure suitable for estimating the nature of mass divergences is developed, and it is found that in a large class of field theories, cross sections smeared over a small region of phase space are at worst logarithmically divergent.

Engineering Mechanics: Statics and Dynamics

Abstract: 1. Introduction. Engineering and Mechanics. Learning Mechanics. Fundamental Concepts. Units. Newtonian Gravitation. 2. Vectors. Vector Operations and Definitions. Scalars and Vectors. Rules for Manipulating Vectors. Cartesian Components. Components in Two Dimensions. Components in Three Dimensions. Products of Vectors. Dot Products. Cross Products. Mixed Triple Products. 3. Forces. Types of Forces. Equilibrium and Free-Body Diagrams. Two-Dimensional Force Systems. Three-Dimensional Force Systems. 4. Systems of Forces and Moments. Two-Dimensional Description of the Moment. The Moment Vector. Moment of a Force About a Line. Couples. Equivalent Systems. Representing Systems by Equivalent Systems. 5. Objects in Equilibrium. The Equilibrium Equations. Two-Dimensional Applications. Statically Indeterminate Objects. Three-Dimensional Applications. Two-Force and Three-Force. 6. Structures in Equilibrium. Trusses. The Method of Joints. The Method of Sections. Space Trusses. Frames and Machines. 7. Centroids and Centers of Mass 316. Centroids. Centroids of Areas. Centroids of Composite Areas. Distributed Loads. Centroids of Volumes and Lines. The Pappus-Guldinus Theorems. Centers of Mass. Definition of the Center of Mass. Centers of Mass of Objects. Centers of Mass of Composite Objects. 8. Moments of Inertia. Areas. Definitions. Parallel-Axis Theorems. Rotated and Principal Axes. Masses. Simple Objects. Parallel-Axis Theorem. 9. Friction. Theory of Dry Friction. Applications. 10. Internal Forces and Moments. Beams. Axial Force, Shear Force, and Bending Moment. Shear Force and Bending Moment Diagrams. Relations Between Distributed Load, Shear Force, and Bending Moment. Cables. Loads Distributed Uniformly Along Straight Lines. Loads Distributed Uniformly Along Cables. Discrete Loads. Liquids and Gasses. Pressure and the Center of Pressure. Pressure in a Stationary Liquid. 11. Virtual Work and Potential Energy. Virtual Work. Potential Energy. Appendix A. Review of Mathematics. Algebra. Trigonometry. Derivatives. Integrals. Taylor Series. Vector Analysis. Appendix B. Properties of Areas and Lines. Areas. Lines. Properties of Volumes and Homogeneous Objects. Answers to Even-Numbered Problems. 12. Engineering and Mechanics. Engineering and Mechanics. Learning Mechanics. Fundamental Concepts. Units. Newtonian Gravitation. 13. Motion of a Point. Position, Velocity, and Acceleration. Straight-Line Motion. Curvilinear Motion. 14. Force, Mass, and Acceleration. Newton's Second Law. Equation of Motion for the Center of Mass. Inertial Reference Frames. Applications. Orbital Mechanics. Numerical Solutions. 15. Energy Methods. Work and Kinetic Energy. Principle of Work and Energy. Work and Power. Work Done by Particular Forces. Potential Energy. Conservation of Energy. Conservative Forces. Relationship between Force and Potential Energy. 16. Momentum Methods. Principle of Impulse and Momentum. Conservation of Linear Momentum. Impacts. Angular Momentum. Mass Flows. 17. Planar Kinematics of Rigid Bodies. Rigid Bodies and Types of Motion. Rotation about a Fixed Axis. General Motions: Velocities. General Motions: Accelerations. Sliding Contacts. Moving Reference Frames. 18. Planar Dynamics of Rigid Bodies. Preview of the Equations of Motion. Momentum Principles for a System of Particles. Derivation of the Equations of Motion. Applications. Numerical Solutions. Appendix: Moments of Inertia. 19. Energy and Momentum in Rigid-Body Dynamics. Principle of Work and Energy. Kinetic Energy. Work and Potential Energy. Power. Principles of Impulse and Momentum. Impacts. 20. Three-Dimensional Kinematics and Dynamics of Rigid Bodies. Kinematics. Euler's Equations. The Euler Angles. Appendix: Moments and Products of Inertia. 21. Vibrations 506 Conservative Systems. Damped Vibrations. Forced Vibrations. Appendix A. Review of Mathematics. Appendix B. Properties of Areas and Lines. Appendix C. Properties of Volumes and Homogeneous Objects. Appendix D. Spherical Coordinates. Appendix E. D'Alembert's Principle. Index.

What the electromagnetic vector potential describes

Abstract: An explicit physical interpretation of the electromagnetic vector potential is here pointed out—as field momentum available for exchange with kinetic momenta of charged matter. It is shown that the vector potential can be quite as directly measurable, without recourse to only quantum‐mechanical effects, as are scalar potential differences and the force fields E, B. This suggests, in keeping with quantum electrodynamics, that the equations for potentials may be regarded as more ’’basic’’ than the Maxwell equations—but only because the potentials most directly represent interaction energy‐momenta through which fields and charges become observable.

Clean tests of quantum chromodynamics in μp scattering

Abstract: Hard gluon bremsstrahlung in μp scattering produces final-state hadrons with a large component of momentum transverse to the virtual-photon direction. Quantum chromodynamics can be used to predict not only the absolute value of the transverse momentum, but also its angular distribution relative to the muon scattering plane. The angular correlations should be insensitive to nonperturbative effects.

Mass divergences in two-particle inelastic scattering

Abstract: Feynman integrals for two-particle inelastic scattering are studied in the limit that the ratio of particle masses to all relevant invariants vanishes. The discussion applies to renormalizable field theories including quantum chromodynamics. Dominant contributions arise from momentum configurations which recall the parton model. The results can be applied to cross sections for single-particle or multiparticle inclusive reactions and to cross sections averaged over small regions of phase space.

Role of the two-roton bound state in neutron scattering on superfluid 4He

Abstract: It is shown that due to the hybridisation between the one-particle excitation and the two-roton states in superfluid 4He the interaction between the rotons is characterised by an affective roton-roton coupling g4eff instead of the bare roton-roton coupling. The magnitude of this interaction, estimated from the neutron scattering measurements at momentum transfer between 2.4 AA-1 and 3.5 AA-1, is g4eff approximately=-1*10-38 erg cm3 and therefore the neutron scattering measurements show the existence of the two-roton bound state even at large momentum values.

Effect of instantons on the short-distance structure of hadronic currents

Abstract: The influence of the nonperturbative structure of the quantum-chromodynamic vacuum on the short-distance behavior of hadronic currents is discussed. The dilute-gas approximation is systematically used. We show how to calculate in this approximation arbitrary Green's functions and that the effects of tunneling (instantons) are summarized by an appropriate effective Lagrangian. These methods are applied to the two-point current correlation function, which is explicitly calculated in the dilute-gas approximation. We estimate the numerical size of the instanton effects for e/sup +/e/sup -/ annihilation and find them to be strongly momentum dependent and large. The qualitative features of these corrections suggest an explanation of precocious scaling.

A second‐order theory for k∥B0 electromagnetic instabilities

Abstract: Electromagnetic instabilities which propagate parallel to an external magnetic field in an infinite, homogeneous Vlasov plasma are considered. Linear theory is used to construct second‐order expressions for the time rates of change of momentum, as well as perpendicular, parallel, and total energies of each plasma species. The results are expressed in a concise form appropriate for many instabilities of this type. The ion cyclotron (T⊥i≳T∥i) and firehose (T∥i≳T⊥i) instabilities are considered as examples.

Theory of draw resonance: Part I. Newtonian fluids

Abstract: Draw resonance in isothermal spinning is explained by using kinematic wave theory. The throughput wave equation and the expression for the throughput wave velocity are derived from the governing equations of the system, that is, the continuity, momentum, and constitutive equations. A comparison is made between twice the wave residence time and the threadline residence time from the spinneret to the take-up in order to find the stable and draw resonance regions in terms of the drawdown ratio. For Newtonian fluids, the critical drawdown ratio to cause the onset of draw resonance is 19.744. Part II will deal with draw resonance in the spinning of power law fluids and Maxwell fluids using the same wave theory. Calculation of the draw resonance amplitude when the drawdown ratio exceeds the critical values for Newtonian, power law, and Maxwell fluids will be explained in Part III.

Structure of the energy tensor in the classical electrodynamics of point particles

Abstract: Classical electromagnetic theory provides an energy tensor defined off the particles's world line. The definition is extended to a distribution valid ''everywhere.'' The extended definition is essentially unique. The Lorentz-Dirac equation follows immediately without the appearance of infinities at any stage. In the distribution theory formulation momentum integrals over spacelike planes exist and are finite. The planes are not restricted to be orthogonal to the particles' world lines, and consequently a finite, conserved momentum integral exists for a system of charged particles. ''Self-momentum'' (the ''momentum'' due to the strongest singularities in the energy tensor) is conserved differentially for each particle separately, and the associated integral over a spacelike plane is zero. It may therefore be omitted. This justifies and generalizes the ad hoc procedure of dropping self-energy terms in electrostatics.

The effect of symmetry on electron momentum distributions in solids

Abstract: A group-theoretical treatment of the symmetry properties of electron momentum distributions in cubic crystals is given. The contribution to the momentum density from a band not belonging to the totally symmetric representation possesses nodes in certain directions. A selection rule allows the location of these nodes. Tables are presented which summarise the consequences of the selection rule for simple cubic, FCC and BCC lattices, and some examples are discussed.

Shear instability: Auroral arc deformation and anomalous momentum transport

Abstract: Temporal evolution of a two-dimensional electrostatic shear instability is numerically studied with special attention to rotational deformation of auroral arcs and momentum transport across the magnetospheric boundary. It is found that the spatial structure of the growing vortex is in good agreement with the small-scale auroral deformation called ‘curl.’ An anomalous viscosity arising from the shear instability is found to be given approximately by 0.08 aV0, where a is the characteristic distance over which the flow velocity changes by V0. If we assume that a = 200 km and V0 = 250 km/s at the magnetospheric boundary, the anomalous viscosity becomes 4 × 1013 cm² s−1, which is comparable to, or even larger than, the value estimated by Axford (1964) from energy requirements of a typical magnetic storm. Spectral energies of fully developed electrostatic turbulence are also studied. It is found that the observed power spectral energies can well be represented by a power law of the form k−4.

The integral equations for round buoyant jets in stratified flows

Abstract: The basic integral equations governing the behavior of a round, buoyant momentum jet discharged into an infinite, stratified, turbulent, flowing ambient fluid are derived. The analysis is based on the fundamental partial differential equations for conservation of mass. momentum, concentration and heat energy, transformed by vector operations into a natural coordinate system and integrated in the angular and radial directions using symmetry and similarity assumptions. The common Boussinesq-assumption has not been used. The resulting set of non-linear first-order differential equations differs from previous systems similarly based on integral methods, and which are presently used to model spreading and dilution of chimney gases in the atmosphere or of waste water in the ocean. The differences caused by mathematical errors and methodological inconsistencies in the previous approaches are pointed out and discussed.

On the Momentum, Vorticity and Mass Balance on the Oregon Shelf

Abstract: Velocity measurements from the continental shelf off Oregon taken during the Coastal Upwelling Experiment CUE-2 in the summer of 1973 are utilized to investigate momentum, vorticity and mass balance relationships for subinertial frequency (ω < 0.6 cpd) current fluctuations. Measurements from stations in water of depths of 54, 100 and 200 m are utilized. By a comparison of the magnitude of terms involving horizontal velocities in the linear momentum and in the nonlinear, depth-integrated momentum equations, support is found for the linear geostrophic balance of the alongshore velocity in the onshore-offshore momentum equation and, in the depth range 100 m ≤ H ≤ 200 m, for a linear ageostrophic balance in the alongshore momentum equation. Evidence is also found to support the validity of a linear depth-integrated vorticity balance, again for depths 100 m ≤ H ≤ 200 m. In this balance, which is similar to that in the theory for continental shelf waves, the interaction of the onshore velocity with the...

Momentum dependence of the ion-ion potential in a microscopic theory

Abstract: A momentum-dependent real potential for ion-ion scattering is calculated, from Reid's soft-core potential, with Brueckner's theory. The densities of the two nuclei are kept fixed and the Pauli principle is obeyed by rearrangement in momentum space. The calculated potential is increasingly attractive up to 2 fm/sup -1/ relative momentum per particle. At this relative momentum, the attraction does not decrease at small distances; for larger momenta, the potential finally becomes repulsive.

A note on the conservation of the axial momentum of a turbulent jet

Abstract: The conservation law for the flux of axial momentum in a turbulent jet is examined. The examination discloses that for a plane jet out of a wall the momentum flux is reduced appreciably because the induced flow towards the jet has a component in the direction opposite to the main jet flow and because of the pressure field generated in the ambient fluid. Existing experimental results confirm this conclusion.

Multipole expansions of electromagnetic fields using Debye potentials

Abstract: The Debye potentials are introduced by giving new derivations of the multipole expansions of the magnetostatic and electrostatic fields. Simplified derivations of the multipole expansions of the electrodynamic fields are then given. The radiated energy, momentum, and angular momentum are all calculated in the same manner, i.e., using the proper transport equations. The questions of uniqueness and completeness of the Debye potential representations of the fields are discussed. In the Appendices are collected together some useful vector field theorems and operator identities involving the angular momentum operator, and also simplified derivations of the spherical harmonic expansions of the static and dynamic Green functions.

A study of the Efimov states and binding energies of the helium trimer through the Faddeev‐coordinate–momentum approach

Abstract: A thorough bound state analysis of the helium trimer is made using the Faddeev equations with form factors generated by a modified Kowalski–Feldman approach. The presence of Efimov states is manifested by each of the realistic potentials considered.

Thermonuclear fusion system

Abstract: This invention discloses apparatus and methods to produce nuclear fusion utilizing fusible material in the form of high energy ion beams confined in magnetic fields. For example, beams of deuterons and tritons are injected in the same direction relative to the machine axis, but the deuteron velocity is sufficiently greater than the triton velocity so that the deuterons overtake the tritons at a relative velocity which produces a high fusion reaction cross section. The momentum of the deuterons is approximately equal to the momentum of the tritons so that both types of ions follow essentially the same path. Thus, the deuteron and triton beams, together with electrons for space charge neutralization, constitute a "moving-plasma", in which fusion reactions occur. Various alternative magnetic field configurations are described for confinement of the high energy ion beams. Methods are given for the starting and steady-state operation of the invention, based on change-of-charge-state trapping of injected material.

Position and momentum distributions do not determine the quantum mechanical state

Abstract: Publisher Summary This chapter presents examples that are constructed to show that the state of an elementary quantum mechanical system need not be uniquely determined by the associated position distribution and the associated momentum distribution. It explains that pure states are not distinguishable by their position statistics or by their momentum statistics in the quantum mechanical state. The position statistics and the momentum statistics play very different roles in quantum mechanics from their roles in classical mechanics. The chapter explains that distinct pure states exist that not only have the same position and momentum distributions but also the same distributions with respect to other significant observables, including, under certain circumstances, the energy.