Longitudinal Damping Research Articles

Change of the Energy Distribution in an Electron Storage Ring by a Dipole-Octupole Wiggler

A dipole-octupole wiggler is proposed to change the energy distribution of the electrons in a storage ring so that the peak current and the related collective effects are reduced. With a dipole-quadrupole wiggler the radiation damping partition can be changed and with a dipole-octupole wiggler this partition becomes dependent on the phase oscillation amplitude. These wigglers can be operated so that the longitudinal damping is negative for small amplitudes but increases for larger amplitudes. The particle distribution will peak around the amplitude which gives neither damping nor antidamping. This leads to a longitudinal blow-up of the bunch core without affecting very much the tails or the quantum lifetime. The distribution has been calculated analytically with an appropriate Fokker-Planck equation and by computer simulation. The results allow the optimization of the wiggler parameters. Due to the sum rule for the damping partitions this wiggler also affects the distribution in horizontal betatron amplitudes.

飽和層・乾燥層から成る層状地盤の動特性

The method of analysis of soil deposites with fluid saturated soil layer is proposed. Free vibration, frequency response and seismic response of a stratified ground which is composed of two layers-dry soil layer and water contended layer-, are presented and discussed. The ground considered, is assumed to be dry above the water tabel and saturated with water under the level. Eigenvalue analysis for such a ground by using the finite element method is carried out and transfer properties by the wave propagation method are obtained. The numerical results show that the water in the soil deposit deteriorate the ground stiffness and increase the damping properties in shear motion, whereas in the longitudinal motion, the stiffness and damping in the ground are increases. The seismic response analysis of the same soil layer gives the similiar properties in shear motion.

The effect of fibre diameter on the dynamic properties of glass-fibre-reinforced polyester resin

The effect of fibre diameter on the mechanical properties of unidirectional composites was investigated using a glass/polyester system. The specimens were vibrated in flexure and longitudinal shear, and finally tested to destruction in interlaminar shear.To allow for changes in fibre diameter at constant fibre volume fraction, the surface area of fibre per unit volume, Af, was defined.It was found that the fibre diameter had no significant effect on Young's modulus in flexure, nor on the longitudinal shear modulus and damping. However, there was a pronounced variation of flexural damping with fibre diameter and fibre volume fraction, and hence with Af. The interlaminar shear strength was low for small values of Af, but rapidly tended to an average of about 56 MN m−2.

Cell-Wall Dislocation Damping in Single-Crystal Cu

The dislocation substructure of 〈111〉 Cu single crystals has been controlled by varying crystal growth rates from 1.57 to 109 cm/h. Etch-pitting and x-ray studies reveal that the substructure consists of a random dislocation network, with density 1×106/cm1 independent of growth rate, and dislocation cells whose size and intercell misorientation angle increase with decreasing growth rate. Longitudinal resonance bar and ultrasonic pulse-echo damping measurements at frequencies from 25 kHz to 100 MHz show that the larger the cell size, the higher the damping over the entire frequency range. There is strong evidence that damping from cell-wall dislocations overshadows that due to the random network. The results are interpreted in terms of a modification of the Granato-Lücke damping theory, which treats cell walls as pseudomembranes vibrating under the action of the applied stress.

Parametric Torsional Stability of a Bar Under Axial Excitation

A study is made on the parametric torsional stability of an elastic cantilever of rectangular cross section under dynamic axial loading. The coupling between the longitudinal and torsional motions exists due to the “shortening effect.” The problem is so formulated that the stability of torsional vibrations is represented by a Mathieu equation, the stability of which is well known. The effect of longitudinal vibrations on the torsional stability is investigated. The steady-state torsional-vibrational response curves are given analytically, and the effect of longitudinal damping on the boundary of stability and the steady-state response curves is also determined.

Theory of Dynamical Behaviors of Ferromagnetic Spins

The dynamical behavior of ferromagnetic spins is studied on the basis of the statistical mechanics of irreversible processes. A macroscopic equation determining the change in time of an inhomogeneous magnetization is derived with explicit expressions for the frequency spectrum and damping constant. With the use of the general expressions thus obtained, the following problems are discussed on the basis of the Heisenberg model of ferromagnetic spins: (1) the pair correlation of spins, (2) the magnetic scattering cross section of neutrons, (3) the frequency spectrum and the damping constant of spin waves, (4) the damping of the longitudinal spin component above and below the Curie point. In the low temperature limit, a straightforward reduction of our expressions leads to the spin wave frequency and damping equivalent to Dyson's theory of spin wave interactions. A general expression is given for van Hove's parameters describing the asymptotic behavior of the spin pair correlation at large distances. It is shown that the longitudinal spin damping in the low temperature limit exhibits a variety of k dependences, depending upon the relative magnitudes of the spin wave energy Dk2, the effective magnetic field H coming from other than the exchange interaction and the thermal energy kBT; in particular, for gµBH ≪Dk2 ≪KBT, the longitudinal damping is proportional to k2, namely, the change in time of the longitudinal spin density obeys the diffusion equation. In the vicinity of the Curie point and in the paramagnetic region, the longitudinal damping is shown to obey the diffusion equation. The diffusion constant thus obtained vanishes at the Curie point and is in good agreement with the values observed by Ericson and Jacrot for iron above the Curie point.

Note on Nonstationary Slender-Body Theory

If we consider the quantity Jcc cos <XCL, which appears in the yawing equation of motion, as a yawing moment per unit pitch rate— i.e., Cnq—then the value of Cnq for one of the modern jet airplanes at low indicated air speeds is twice as large as Cnr. This is a definite indication of a sizeable coupling between the lateral and longitudinal modes of motion. This coupling, when included in the equations of motion, leads to the following general results: (a) an increase in the calculated lateral damping at low indicated air speeds; (b) a small decrease in the calculated longitudinal damping; (c) an insignificant change in the frequency of both modes; (d) small excitation of either mode when the other is disturbed—small enough, in fact, that a pilot seldom if ever notices it; (e) a small difference in the first few seconds of a calculated rolling time history. Fig. 3 shows the relative effects of coupling on the calculated damping for a modern jet airplane. Note on Nonstationary Slender-Body Theory J. D. Cole Guggenheim Aeronautical Laboratory, California Institute of Technology, Pasadena, Calif. July 14, 1953