Observation of Scattering of Ion-Acoustic Cylindrical Solitons

Abstract

tation mechanism via inner-shell vacancies for the Pb + Pb and Pb + U systems. These calculations and the extrapolation for the U+ U system, which does not include effects from the spreading of the lsa state in the negative-energy continuum, reproduce the absolute positron yield as well as its dependence on Z and on the distances of closest approach within the limits of error.We would like to acknowledge the achievements of the UNILAC crew in making excellent U beams, P. Maier-Komor and E. Kellner for fabricating the delicate U targets, M. Richter, R. Hadsell, and F. Weik for their computational assistance, and H. Stettmeier and L. Richter for helping us during the initial phase of the work. We thank A large-amplitude ion-acoustic cylindrical soliton launched in an axisymetric cylindrical system collapses at the center of the cylinder. The highly nonlinear nature of the interaction is observed after the collapse, showing that many isolated pulses are emitted abruptly and propagate out without clear evolution of their wave forms.

Nonlinear cylindrical or spherical converging ion-acoustic pulses

“…It should be noted that the trajectory for a compressive initial pulse is approximately straight between r = 50 and 250, whereas the amplitude varies significantly in that range. This means that the velocity-amplitude relationship v/c s = 1 + a.rjr with a being a constant is not valid in contrast to what was assumed in previous experimental works (Hershkowitz & Romesser 1974;Nishida et al 1978). For example, a varies from 1-0 to 0-55 between r = 200 and 70 in figure 2.…”

“…This is in agreement with previous results for diverging cylindrical waves (Chen & Schott 1977 6). In experiments, the width of the soliton-like pulses is mentioned (Nishida et al 1978). Unfortunately, the width of the soliton-like pulses is not well defined for our initial conditions because a completely isolated pulse is not found and consequently the measured width always contains an uncertainty.…”

“…Recently, non-planar ion-acoustic solitons have been studied extensively. Cylindrical or spherical converging solitons have been investigated by several workers (Maxon & Viecelli 1974a, b;Hershkowitz & Romesser 1974;Ogino & Takeda 1976;Chen & Schott 1977a, b;Nishida, Nagasawa & Kawamata 1978Hershkowitz, Glanz & Lonngren 1979). In the theoretical works, a planar soliton is assumed as an initial condition (Maxon & Viecelli 1974 a, 6;Ogino & Takeda 1976).…”

“…In the theoretical works, a planar soliton is assumed as an initial condition (Maxon & Viecelli 1974 a, 6;Ogino & Takeda 1976). However, in experiments, it is difficult to excite solitons initially and the evolution of soliton-like structures from a compressive broad pulse is observed (Hershkowitz & Romesser 1974;Nishida et al 1978Nishida et al , 1979.…”

“…In this paper, the Korteweg-de Vries equation for cylindrical or spherical converging waves is solved numerically for various initial pulse shapes including rarefactive or mixed ones, and it will be shown that the soliton-like structures can be generated from such pulses. We treat also the generation process of a 2 E. Olcvisu soliton-like structure from a broad compressive initial pulse, which is usually observed in experiments, and we will solve the apparent paradox that the velocity of the experimentally observed' cylindrical solitons' is different from case to case (Hershkowitz & Romesser 1974;Nishida et al 1978).…”