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Analytical model for electromagnetic cascades in rotating electric field
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10.1063/1.3624481
/content/aip/journal/pop/18/8/10.1063/1.3624481
http://aip.metastore.ingenta.com/content/aip/journal/pop/18/8/10.1063/1.3624481
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) The trajectories in p − ψ space for (a) electrons, (b) positrons, and (c) photons moving in the rotating electric field. Photon emission and pair production are not taken into account. The bold lines correspond to the trajectories which separate bounded and open trajectories. Here p is the particle momentum normalized to mca 0.

Image of FIG. 2.
FIG. 2.

(Color online) The distribution functions of (a) the electrons and (b) the photons of the electromagnetic cascade developing in the rotating electric field with the normalized amplitude a 0 = 1.6 × 105 and λ l  = 0.8 μm. The DFs are plotted some time after the cascade start when the shapes of the DFs cease to evolve (however, the amplitude of the functions grows exponentially with time).

Image of FIG. 3.
FIG. 3.

(Color online) The growth rate of the electromagnetic cascade in the rotating electric field as a function of and λ l  = 2πc/ωl . Here, E 0 is the amplitude of the electric field, ωl if the cyclic frequency of the field rotation, I 25 = 1025 W/cm2.

Image of FIG. 4.
FIG. 4.

(Color online) The dependence of the growth rate on λ l : the numerical data (dots) and the fits for the data (lines). The amplitude A is chosen such that the RMS deviation from the numerical data is minimal. The error bars show the dispersion of the numerical data for 7 runs of the simulation. Line 1 corresponds to the data obtained for I = 1029 W/cm2, line 2 corresponds to I = 1027 W/cm2, and line 3 corresponds to I = 1025 W/cm2.

Image of FIG. 5.
FIG. 5.

(Color online) The dependence of the growth rate on μ = E 0/αEcr . The numerical results are presented by the solid black dots. The error bars show the dispersion of the numerical data for 7 runs of the simulation. The solid lines represent fits Γ =  1/4. The amplitude A is chosen such that the RMS deviation from the numerical data is minimal. Line 1 corresponds to numerical data for λ l  = 10 μm (squares), line 2 corresponds to λ l  = 5 μm (triangles), and line 3 corresponds to λ l  = 1 μm (circles).

Image of FIG. 6.
FIG. 6.

(Color online) The electron (line 1) and the photon (line 2) distribution functions obtained by the numerical simulation of the electromagnetic cascade developing in the rotating electromagnetic field with a 0 = 8 × 105 and λ l  = 0.8 μm for γ: γ/a 0 = 0.05 (a) and γ/a 0 = 0.15 (b). Line 3 corresponds to the analytical expression for the PhDF (Eq. (68)). All plotted functions are normalized to their maximal values.

Image of FIG. 7.
FIG. 7.

(Color online) The electron (line 1) and the photon (line 2) distribution functions at γ/a 0 = 0.1 obtained by the numerical simulations of the electromagnetic cascade developing in the rotating electromagnetic field with λ l  = 0.8 μm and (a) a 0 = 3.2 × 104, (b) a 0 = 1.6 × 105, and (c) a 0 = 8 × 105. Line 3 corresponds to the analytical expression for the PhDF (Eq. (68)). All plotted functions are normalized to their maximal values.

Image of FIG. 8.
FIG. 8.

(Color online) The electron (upper lines) and the photon (lower lines) energy spectra for the electromagnetic cascade developing in the rotating electric field with λ l  = 0.8 μm and (a) a 0 = 3.2 × 104, (b) a 0 = 1.6 × 105, and (c) a 0 = 8 × 105. Solid lines correspond to the numerical results and the dash-dotted lines correspond to the analytical expressions (63) and (70).

Image of FIG. 9.
FIG. 9.

(Color online) The ratio of the growth rate, Γ, to the fit Eq. (71) (dots) and unity level (line). Γ is computed for the intensity range I = 1025 − 1029 W/cm2 and the range of wavelengths λ = 1 − 10 μm with the step 1 μm.

Image of FIG. 10.
FIG. 10.

(Color online) The electron (upper solid lines) and the photon (lower solid lines) energy spectra obtained by the numerical simulations of the electromagnetic cascade developed in the field characterized by λ = 0.8 μm and a 0 = 3.2 × 104 (plate (a)), a 0 = 1.6 × 105 (plate (b)), and a 0 = 8 × 105 (plate (c)). The corresponding asymptotic expressions (75) and (77) are shown by the dash-dotted lines.

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/content/aip/journal/pop/18/8/10.1063/1.3624481
2011-08-22
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Analytical model for electromagnetic cascades in rotating electric field
http://aip.metastore.ingenta.com/content/aip/journal/pop/18/8/10.1063/1.3624481
10.1063/1.3624481
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