TY - JOUR

T1 - The radiative kicked oscillator

T2 - A stochastic web or chaotic attractor?

AU - Ashkenazy, Y.

AU - Horwitz, L. P.

PY - 2002/9

Y1 - 2002/9

N2 - A relativistic charged particle moving in a uniform magnetic field and kicked by an electric field is considered. Under the assumption of small magnetic field, an iterative map is developed. We consider both the case in which no radiation is assumed and the radiative case, using the Lorentz-Dirac equation to describe the motion. Comparison between the non-radiative case and the radiative case shows that in both cases, one can observe a stochastic web structure for weak magnetic fields, and although there are global differences in the result of the map, that both cases are qualitatively similar in their small scale behavior. We also develop an iterative map for strong magnetic fields. In that case, the web structure no longer exists; it is replaced by a rich chaotic behavior. It is shown that the particle does not diffuse to infinite energy; it is limited by the boundaries of an attractor (the boundaries are generally much smaller than light velocity). Bifurcation occurs, converging rapidly to Feigenbaum's universal constant. The chaotic behavior appears to be robust. For intermediate magnetic fields, it is more difficult to observe the web structure, and the influence of the unstable fixed point is weaker.

AB - A relativistic charged particle moving in a uniform magnetic field and kicked by an electric field is considered. Under the assumption of small magnetic field, an iterative map is developed. We consider both the case in which no radiation is assumed and the radiative case, using the Lorentz-Dirac equation to describe the motion. Comparison between the non-radiative case and the radiative case shows that in both cases, one can observe a stochastic web structure for weak magnetic fields, and although there are global differences in the result of the map, that both cases are qualitatively similar in their small scale behavior. We also develop an iterative map for strong magnetic fields. In that case, the web structure no longer exists; it is replaced by a rich chaotic behavior. It is shown that the particle does not diffuse to infinite energy; it is limited by the boundaries of an attractor (the boundaries are generally much smaller than light velocity). Bifurcation occurs, converging rapidly to Feigenbaum's universal constant. The chaotic behavior appears to be robust. For intermediate magnetic fields, it is more difficult to observe the web structure, and the influence of the unstable fixed point is weaker.

KW - Chaos

KW - Relativity

KW - Stochastic Web

UR - http://www.scopus.com/inward/record.url?scp=0036759410&partnerID=8YFLogxK

U2 - 10.1142/S0218348X02001099

DO - 10.1142/S0218348X02001099

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AN - SCOPUS:0036759410

SN - 0218-348X

VL - 10

SP - 353

EP - 371

JO - Fractals

JF - Fractals

IS - 3

ER -