Particle current, time structure

TOWARDS THE HYDRODYNAMIC LIMIT STRUCTURE FACTORS AND SOUND DISPERSION. The collective motions of water molecules give rise to many hydrodynamical phenomena observable in the laboratories. They are most conveniently studied in terms of the spatial Fourier ( ) components of the density, particle currents, stress, and energy fluxes. The time correlation function of those Fourier components detail the decay of density, current, and fluctuation on the length scale of the Ijk. 

Of special interest is the time structure of the particle current illustrated in Fig. 4. The duration of the puls Tp depends on the length and the velocity of the bunch. At the... 

The beams coming from cyclic and linear accelerators consist of short pulses of particles, that is, their beam has a time structure as shown in Fig. 50.25. The repetition frequency of the bunches ( microstructure ) is determinedbytheRFsystem, while the macrostructure can be varied by switching on and off the acceleration process. Taking into account the duty factor, which is the fraction of time when there is current, the peak current is much higher than the measured average current of the beam. 

The vanishing of this matrix element is, in fact, independent of the assumption of current conservation, and can be proved using the transformation properties of the current operator and one-partic e states under space and time inversion, together with the hermiticity of jn(0). By actually generating the states q,<>, from the states in which the particle is at rest, by a Lorentz transformation along the 3 axis, and the use of the transformation properties of the current operator, essentially the entire kinematical structure of the matrix element of on q, can be obtained.15 We shall, however, not do so here. Bather, we note that the right-hand side of Eq. (11-529) implies that... 

These curves show four kinds of structures which are dependent on the current particle concentrations and the oscillation phases of the reaction rate K(t). The moment of time t = 295.0 corresponds to the K(t) maximum whose concentration Na(t) is close to its minimum value. The behaviour of the correlation functions reminds that shown in Fig. 8.5 but the function for the dissimilar particles has now maximum. After a short time interval, at t = 296.0, despite very small change of concentrations and the correlation functions for similar particles, the maximum in the correlation functions for dissimilar particles completely disappeared (K(t) has a minimum). 

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