Search Results (5 total)

A novel, single shot, nondestructive scheme to measure the bunch length of submillimeter relativistic electron bunches using the electro-optical method is described. In this scheme, the birefringence induced by the electric field of the electrons converts the temporal characteristics of the bunch to a spatial intensity distribution of an optical pulse. Electric field characteristics, induced birefringence, and retardation are calculated for a few typical electron beam parameters and criteria limiting the resolution are established.

A Comment on the Letter by Henning Struchtrup and Wolf Weiss, Phys. Rev. Lett. 80, 5048 (1998). The authors of the Letter offer a Reply.

Computer simulations of a compressible fluid, convecting heat in two dimensions, suggest that, within a range of Rayleigh numbers, two distinctly different, but stable, time-dependent flow morphologies are possible. The simpler of the flows has two characteristic frequencies: the rotation frequency of the convecting rolls, and the vertical oscillation frequency of the rolls. Observables, such as the heat flux, have a simple-periodic (harmonic) time dependence. The more complex flow has at least one additional characteristic frequency—the horizontal frequency of the cold, downward- and the warm, upward-flowing plumes. Observables of this latter flow have a broadband frequency distribution. The two flow morphologies, at the same Rayleigh number, have different rates of entropy production and different Lyapunov exponents. The simpler “harmonic” flow transports more heat (produces entropy at a greater rate), whereas the more complex “chaotic” flow has a larger maximum Lyapunov exponent (corresponding to a larger rate of phase-space information loss). A linear combination of these two rates is invariant for the two flow morphologies over the entire range of Rayleigh numbers for which the flows coexist, suggesting a relation between the two rates near the onset of convective turbulence.

Numerical simulations of the fully compressible Navier-Stokes equations are used to study the transition from simple-periodic “harmonic” thermal convection to chaotic thermal convection as the Rayleigh number Ra is increased. The simulations suggest that a sharp discontinuity in the relationship between the Nusselt number Nu (the ratio of the total heat flux to the Fourier heat flux) and the Rayleigh number is associated with this transition in flow morphology. This drop in the Nusselt number is also seen in the data reported in independent experiments involving the convection of two characteristically different fluids—liquid mercury [Phys. Rev. E 56, R1302 (1997)] (a nearly incompressible fluid with Prandtl number Pr=0.024) and gaseous helium [Phys. Rev. A 36, 5870 (1987)] (a compressible fluid with unit Pr). The harmonic flow generates a dual-maximum (quasiharmonic) temperature histogram, while the chaotic flow generates a single-maximum histogram at the center point in the simulated cell. This is consistent with the temperature distributions reported for the convecting mercury before and after the drop in Nu. Our simulations also suggest a hysteresis in the Nu-Ra curve linking the two distinctly different flow morphologies, heat fluxes, and temperature-fluctuation histograms at the same Rayleigh number.

We demonstrate that precise solutions of the convective flow equations for a compressible conducting viscous fluid can give degenerate stationary states. That is, two or more completely different stable flows can result for fixed stationary boundary conditions. We characterize these complex flows with finite-difference, smooth-particle methods, and high-order implicit methods. The fluids treated here are viscous conducting gases, enclosed by thermal boundaries in a gravitational field—the ``Rayleigh-Bénard problem.'' Degenerate solutions occur in both two- and three-dimensional simulations. This coexistence of solutions is a macroscopic manifestation of the strange attractors seen in atomistic systems far from equilibrium.