Signatures of the self-modulation instability of relativistic proton bunches in the AWAKE experiment

We investigate numerically the detection of the self-modulation instability in a virtual detector located downstream from the plasma in the context of AWAKE. We show that the density structures, appearing in the temporally resolving virtual detector, map the transverse beam phase space distribution at the plasma exit. As a result, the proton bunch radius that appears to grow along the bunch in the detector results from the divergence increase along the bunch, related with the spatial growth of the self-modulated wakefields. In addition, asymmetric bunch structures in the detector are a result of asymmetries of the bunch divergence, and do not necessarily reflect asymmetric beam density distributions in the plasma.Comment: Accepted for publication in NIM-A for the proceedings of the 3rd European Advanced Accelerator Workshop. 5 pages, 2 figure

Chaos in Periodically Perturbed Monopole + Quadrupole Like Potentials

The motion of a particle that suffers the influence of simple inner (outer) periodic perturbations when it evolves around a center of attraction modeled by an inverse square law plus a quadrupole-like term is studied. The equations of motion are used to reduce the Melnikov method to the study of simple graphics.Comment: 12 pages, 6 Postscript figure

Exponential Distributions in a Mechanical Model for Earthquakes

We study statistical distributions in a mechanical model for an earthquake fault introduced by Burridge and Knopoff [R. Burridge and L. Knopoff, {\sl Bull. Seismol. Soc. Am.} {\bf 57}, 341 (1967)]. Our investigations on the size (moment), time duration and number of blocks involved in an event show that exponential distributions are found in a given range of the paramenter space. This occurs when the two kinds of springs present in the model have the same, or approximately the same, value for the elastic constants. Exponential distributions have also been seen recently in an experimental system to model earthquake-like dynamics [M. A. Rubio and J. Galeano, {\sl Phys. Rev. E} {\bf 50}, 1000 (1994)].Comment: 11 pages, uuencoded (submitted to Phys. Rev. E

A simple deterministic self-organized critical system

We introduce a new continuous cellular automaton that presents self-organized criticality. It is one-dimensional, totally deterministic, without any kind of embedded randomness, not even in the initial conditions. This system is in the same universality class as the Oslo rice pile system, boundary driven interface depinning and the train model for earthquakes. Although the system is chaotic, in the thermodynamic limit chaos occurs only in a microscopic level.Comment: System slightly modified. New results on Liapunov exponents. Submitted for publication (8 pages

Stabilized jellium model and structural relaxation effects on the fragmentation energies of ionized silver clusters

Using the stabilized jellium model in two schemes of `relaxed' and `rigid', we have calculated the dissociation energies and the fission barrier heights for the binary fragmentations of singly-ionized and doubly-ionized Ag clusters. In the calculations, we have assumed spherical geometries for the clusters. Comparison of the fragmentation energies in the two schemes show differences which are significant in some cases. This result reveals the advantages of the relaxed SJM over the rigid SJM in dynamical processes such as fragmentation. Comparing the relaxed SJM results and axperimental data on fragmentation energies, it is possible to predict the sizes of the clusters just before their fragmentations.Comment: 9 pages, 12 JPG figure

Chaos and Synchronized Chaos in an Earthquake Model

We show that chaos is present in the symmetric two-block Burridge-Knopoff model for earthquakes. This is in contrast with previous numerical studies, but in agreement with experimental results. In this system, we have found a rich dynamical behavior with an unusual route to chaos. In the three-block system, we see the appearance of synchronized chaos, showing that this concept can have potential applications in the field of seismology.Comment: To appear in Physical Review Letters (13 pages, 6 figures