The Lorentz - Dirac equation
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چکیده
The Lorentz-Dirac equation (LDE) x 000 ? x 00 = d dx V (x) models the point limit of the Maxwell-Lorentz equation describing the interaction of a charged extended particle with the electromagnetic eld. Since (LDE) admits solutions which accelerate even if they are outside the zone of interaction, Dirac proposed to study so-called "non runaway" solutions satisfying the condition x 00 (t) ! 0 as t ! +1. We study the scattering of particles for a localized potential barrier V (x). We show, using global bifurcation techniques, that for every T > T 0 there exists a reeection solution with "returning time" T , and for every T > 0 there exists a transmission solution with "trans-mission time" T. Furthermore, some qualitative properties of the solutions are proved; in particular, it is shown that for increasing T , these solutions spend more and more time near the maximum point s 0 of V .
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تاریخ انتشار 2007