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Scaling investigation for the dynamics of charged particles in an electric field accelerator
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10.1063/1.4772997
/content/aip/journal/chaos/22/4/10.1063/1.4772997
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/4/10.1063/1.4772997
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Pieces of two possible orbits in the proposed model. The upper trajectory illustrates a situation where the particle enters into and leaves from the electric field region at x = 0. The lower trajectory illustrates a situation where the particle enters into the electric field at the left side and leaves this region at x = d.

Image of FIG. 2.
FIG. 2.

These plots display the phase space of the system for different control parameters: (a) and , (b) and , (c) and and (d) and .

Image of FIG. 3.
FIG. 3.

These plots illustrate the average Lyapunov exponent as function of: (a) for constant and; (b) as function of for fixed .

Image of FIG. 4.
FIG. 4.

This figure shows the position of the lowest energy invariant KAM curves for different values of and considering: (a) ; (b) ; and (c) .

Image of FIG. 5.
FIG. 5.

The figure shows the average of the absolute values of the velocity of the KAM curves as function of for three different values of . The best fits furnish with .

Image of FIG. 6.
FIG. 6.

(a) shows the plot of the normalized number of escaping orbits at the iteration n for different values of and fixed . (b) displays the overlap of all curves shown in (a) onto a single plot, after a suitable rescaling of the axis.

Image of FIG. 7.
FIG. 7.

(a) illustrates the crossover as function of . The best fit furnishes with z = −0.98 ± 0.02. (b) illustrates the maximum values of h as function of . The best fit furnishes with .

Image of FIG. 8.
FIG. 8.

(a) displays the normalized number of remaining orbits (do not escape) as function of n and different values of ; (b) illustrates the decay of the quantity showing evidently two regimes.

Image of FIG. 9.
FIG. 9.

(a) shows the numerical data of crossover of . The best fit furnishes with . Appropriate scaling transformation overlaps the curves onto a single plot, as displayed in (b).

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/content/aip/journal/chaos/22/4/10.1063/1.4772997
2012-12-28
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Scaling investigation for the dynamics of charged particles in an electric field accelerator
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/4/10.1063/1.4772997
10.1063/1.4772997
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