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NASA NTRS1991

A fully Galerkin method for the recovery of stiffness and damping parameters in Euler-Bernoulli beam models

A fully Sinc-Galerkin method for recovering the spatially varying stiffness and damping parameters in Euler-Bernoulli beam models is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which converges exponentially and is valid on the infinite time interval. Hence the method avoids the time-stepping which is characteristic of many of the forward schemes which are used in parameter recovery algorithms. Tikhonov regularization is used to stabilize the resulting inverse problem, and the L-curve method for determining an appropriate value of the regularization parameter is briefly discussed. Numerical examples are given which demonstrate the applicability of the method for both individual and simultaneous recovery of the material parameters.

Smith, R. C.↗

NASA NTRS1984

Constraints on continuous beam models of the jet in 3C 273

The one-sidedness, 'superluminal' motion, and detailed spectra observed for 3C 273 put significant constraints on continuous beam models for the source of the extended emission in 3C 273 A. The one-sidedness of the extended emission implies that the age of the radio-frequency cloud is probably about 3-5 Myr. The 'superluminal' motion observed with VLBI constrains the bulk Lorentz factor of the jet to be more than about 10. Finally, the observed X-ray emission from the jet provides a method for deciding the question of beam composition: for a given beam power, an electron-positron beam would produce a much higher (beamed) inverse-Compton X-ray flux off extended-jet optical photons than an electron-proton beam would, thus making the observed weak jet X-ray flux a strong indicator of a proton positive component to the jet. Remaining experimental uncertainties in the case of 3C 273 make it impossible to decide the question of beam composition at present, but the next generation of experiments may make this possible for 3C 273 and other 'superluminal' objects. The above arguments have the advantage of not depending on the details of the mechanism for producing the high-energy radio-cloud electrons.

Roberts, D.↗

NASA NTRS1991

Laser beam modeling in optical storage systems

A computer model has been developed that simulates light propagating through an optical data storage system. A model of a laser beam that originates at a laser diode, propagates through an optical system, interacts with a optical disk, reflects back from the optical disk into the system, and propagates to data and servo detectors is discussed.

Treptau, J. P.↗

NASA NTRS1976

Pulsar average wave forms and hollow-cone beam models

Pulsar wave forms have been analyzed from observations conducted over a wide radio-frequency range to assess the wave-form morphologies and to measure wave-form widths. The results of the analysis compare favorably with the predictions of a model with a hollow-cone beam of fixed dimensions and with random orientation of both the observer and the cone axis with respect to the pulsar spin axis. A class of three-component wave forms is included in the model by adding a central pencil beam to the hollow-cone hypothesis. The consequences of a number of discrepancies between observations and quantitative predictions of the model are discussed.

Backer, D. C.↗

NASA NTRS1990

Simplified truss-beam modeling - Dynamic analysis

A model of the truss-beam has been developed and a set of algorithms provided to determine the flexibility matrix. Using lumped masses at the panel juncture, and applying the flexibility matrix in the equation of motion for the system, the dynamic characteristics are readily determined. An interactive computer program has been developed both in Basic and in Fortran for the IMB PC and other compatible micro-computers. This method is used to determine the lower natural frequencies of two truss-beams, and the results compared with those found by others.

Abu-Saba, Elias G.↗

DOE OSTI2024

Enhanced beam-beam modeling to include longitudinal variation during weak-strong simulation

Beam-beam interactions pose substantial challenges in the design and operation of circular colliders, significantly affecting their performance. In particular, the weak-strong simulation approach is pivotal for investigating single-particle dynamics during the collider design phase. This paper evaluates the limitations of existing models in weak-strong simulations, noting that while they accurately account for energy changes due to slingshot effects, they fail to incorporate longitudinal coordinate changes ( z variation). To address this gap, we introduce two novel transformations that enhance Hirata’s original framework by including both z variation and slingshot effect-induced energy changes. Through rigorous mathematical analysis and extensive weak-strong simulation studies, we validate the efficacy of these enhancements in achieving a more precise simulation of beam-beam interactions. Our results reveal that although z variation constitutes a higher-order effect and does not substantially affect the emittance growth rate within the specific design parameters of the Electron-Ion Collider, the refined model offers improved accuracy, particularly in scenarios involving the interaction between beam-beam effects and other random diffusion processes, as well as in simulations incorporating realistic lattice models. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1972

Gamma-ray absorption for a beam model of NP0532.

The model involves an assessment of the effect of beaming as indicated by the pulsations themselves rather than by assuming gamma-ray absorption by interaction with an isotropic photon field. The chief absorption process to be taken into account is that of pair production in the intense photon field. Most important is the pair production in the intense photon field which occurs during the pulse.

Stecker, F. W.↗

NASA NTRS1976

Considerations for the application of finite element beam modeling to vibration analysis of flight vehicle structures

The manner of representing a flight vehicle structure as an assembly of beam, spring, and rigid-body components for vibration analysis is described. The development is couched in terms of a substructures methodology which is based on the finite-element stiffness method. The particular manner of employing beam, spring, and rigid-body components to model such items as wing structures, external stores, pylons supporting engines or external stores, and sprung masses associated with launch vehicle fuel slosh is described by means of several simple qualitative examples. A detailed numerical example consisting of a tilt-rotor VTOL aircraft is included to provide a unified illustration of the procedure for representing a structure as an equivalent system of beams, springs, and rigid bodies, the manner of forming the substructure mass and stiffness matrices, and the mechanics of writing the equations of constraint which enforce deflection compatibility at the junctions of the substructures. Since many structures, or selected components of structures, can be represented in this manner for vibration analysis, the modeling concepts described and their application in the numerical example shown should prove generally useful to the dynamicist.

Kvaternik, R. G.↗

NASA NTRS1975

Pulsar average waveforms and hollow cone beam models

An analysis of pulsar average waveforms at radio frequencies from 40 MHz to 15 GHz is presented. The analysis is based on the hypothesis that the observer sees one cut of a hollow-cone beam pattern and that stationary properties of the emission vary over the cone. The distributions of apparent cone widths for different observed forms of the average pulse profiles (single, double/unresolved, double/resolved, triple and multiple) are in modest agreement with a model of a circular hollow-cone beam with random observer-spin axis orientation, a random cone axis-spin axis alignment, and a small range of physical hollow-cone parameters for all objects.

Backer, D. C.↗

NASA NTRS1971

Gamma-ray absorption for a beam model of the Crab nebula pulsar NP0532

A model is discussed for determining gamma ray absorption from NP0532 by estimating the effect of beaming as indicated by the pulsations. The main absorption process is considered to be that of pair production in the intense photon field which occurs during the pulse. The results indicate that for this model, absorption does not occur below 10 GeV.

Stecker, F. W.↗

DOE OSTI2024

Modelling Beam Loss Within the LANSCE Proton Storage Ring

Several upgrades are being considered for the proton storage ring (PSR) at the Los Alamos Neutron Science Center (LANSCE) to reduce beam loss and thereby reduce the cooldown period of the PSR following a beam run. First, we have considered an increased beam pipe diameter would reduce beam loss due to beam scraping caused by misalignments and tuning errors. However, this would require increased pole-to-pole gap height within the dipoles and quadrupoles, which would change their effective length and alter their fringe fields. The effect of different magnet gaps on the beam optical parameters and on beam loss was studied using the simulation codes MAD-X and PyORBIT. Second, we are developing a detailed particle tracking model within the framework of the simulation package General Particle Tracer (GPT) for the PSR H - stripping system. This model will be used to study the effect of the stripper foil parameters (position, composition, areal density, depth, etc.) on first-turn losses, where most of the observed beam loss and emittance growth occurs due to foil scattering, foil stripping, and Lorentz stripping. The model implements C++ custom elements created to model foil scattering, foil stripping, and Lorentz stripping, as these are not built-in features of GPT. The preliminary results of the MAD-X and PyORBIT simulations, as well as the GPT simulation model, is described in this tech note.

43 PARTICLE ACCELERATORS↗

NASA NTRS1987

Equivalent beam modeling using numerical reduction techniques

Numerical procedures that can accomplish model reductions for space trusses were developed. Three techniques are presented that can be implemented using current capabilities within NASTRAN. The proposed techniques accomplish their model reductions numerically through use of NASTRAN structural analyses and as such are termed numerical in contrast to the previously developed analytical techniques. Numerical procedures are developed that permit reductions of large truss models containing full modeling detail of the truss and its joints. Three techniques are presented that accomplish these model reductions with various levels of structural accuracy. These numerical techniques are designated as equivalent beam, truss element reduction, and post-assembly reduction methods. These techniques are discussed in detail.

Chapman, J. M.↗

NASA NTRS1978

A beaming model of the Io-independent Jovian decameter radiation based on multipole models of the Jovian magnetic field

A geometrical model is presented in which the apparent source locations of the Io-independent decameter radiation are computed. The calculations assume that the radiation is produced by stably trapped electrons radiating near the electron gyrofrequency and that the emission is then beamed onto a conical surface. The maximum occurrence probability of noise storms is associated with regions in the Jovian magnetosphere where the axis of the emission cone is most inclined toward the Jovian equatorial plane. The calculations utilize and compare two of the octupole spherical harmonic expansions of the Jovian magnetic field constructed from data accumulated by the fluxgate and vector helium magnetometers on board Pioneer 11.

Goldstein, M. L.↗

NASA NTRS1979

A beaming model of the Io-independent Jovian decameter radiation based on multipole models of the Jovian magnetic field

A geometrical model is presented in which the apparent source locations of the Io-independent decameter radiation are computed. The calculations assume that the radiation is produced by stably trapped electrons radiating near the local electron gyrofrequency and that the emission is then beamed onto a conical surface. The maximum occurrence probability of noise storms is associated with regions in the Jovian magnetosphere where the axis of the emission cone is most inclined toward the Jovian equatorial plane. The calculations utilize and compare two of the octopole spherical harmonic expansions of the Jovian magnetic field constructed from data accumulated by the fluxgate and vector helium magnetometers on board Pioneer 11.

Goldstein, M. L.↗

DOE OSTI2021

Validating pyORBIT for Modeling Beam Dynamics in the IOTA Ring

The Integrable Optics Test Accelerator (IOTA) ring is a new Fermilab facility dedicated to beam physics experiments, currently operating with 150 MeV electrons. Space charge effects are expected to be significant when it operates with 2.5 MeV protons. In this contribution, we present results of a suite of validation tests of PyORBIT, a PICstyle space charge code. Single particle dynamics of quasiintegrable optics using an octupole string in IOTA is compared with MADX, and shown to be in good agreement. Requirements for the convergence of space charge computations are systematically established and when possible, tests involving space charge are compared with theoretical predictions.

Li, Runze↗

NASA NTRS1988

Estimation of Boltzmann damping coefficients in beam models

A distributed parameter model of a flexible structure with Boltzmann type viscoelastic damping is discussed. A computational method for the estimation of the damping parameters is developed, and theoretical convergence results are given. An example is presented in which actual experimental data is used, demonstrating the efficacy of the computational method and the plausibility of the model for predicting response in damped structures.

Banks, H. T.↗

NASA NTRS1990

A fully Sinc-Galerkin method for Euler-Bernoulli beam models

A fully Sinc-Galerkin method in both space and time is presented for fourth-order time-dependent partial differential equations with fixed and cantilever boundary conditions. The Sinc discretizations for the second-order temporal problem and the fourth-order spatial problems are presented. Alternate formulations for variable parameter fourth-order problems are given which prove to be especially useful when applying the forward techniques to parameter recovery problems. The discrete system which corresponds to the time-dependent partial differential equations of interest are then formulated. Computational issues are discussed and a robust and efficient algorithm for solving the resulting matrix system is outlined. Numerical results which highlight the method are given for problems with both analytic and singular solutions as well as fixed and cantilever boundary conditions.

Smith, R. C.↗

NASA NTRS1991

Numerical recovery of material parameters in Euler-Bernoulli beam models

A fully Sinc-Galerkin method for recovering the spatially varying stiffness parameter in fourth-order time-dependence problems with fixed and cantilever boundary conditions is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains. This yields an approximation solution which converges exponentially and is valid on the infinite time interval. When the forward methods are applied to parameter recovery problems, the resulting inverse problems are ill-posed. Tikhonov regularization is applied and the resulting minimization problems are solved via a quasi-Newton/trust region algorithm. The L-curve method is used to determine an appropriate value of the regularization parameter. Numerical results which highlight the method are given for problems with both fixed and cantilever boundary conditions.

Smith, R. C.↗