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Analytic theory for betatron radiation from relativistic electrons in ion plasma channels with magnetic field
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10.1063/1.3496983
/content/aip/journal/pop/17/11/10.1063/1.3496983
http://aip.metastore.ingenta.com/content/aip/journal/pop/17/11/10.1063/1.3496983

Figures

Image of FIG. 1.
FIG. 1.

Schematic diagram for an electron in an ion plasma channel subject to an electric field and a magnetic field.

Image of FIG. 2.
FIG. 2.

(a) Transverse trajectory and (b) longitudinal trajectory as a function of time calculated by the relativistic (abbreviated as R) and semiclassical (abbreviated as S) theories at incident energies (E) of 1 GeV (solid line for R, hollow triangle for S), 500 MeV (dashed line for R, hollow circle for S), and 100 MeV (dashed-dotted line for R, cross for S): and . The inset plots show the corresponding velocities and trajectories in the x-z plane for relativistic results only.

Image of FIG. 3.
FIG. 3.

(a) Transverse trajectory and (b) longitudinal trajectory as a function of time calculated by the relativistic theory at initial velocity ratios of (solid line), 5:5 (dashed line), and 3:7 (dashed-dotted line): and . The inset plots show the corresponding velocities and trajectory in the x-z plane.

Image of FIG. 4.
FIG. 4.

(a) Transverse trajectory and (b) longitudinal trajectory as a function of time in the presence of magnetic field calculated by the relativistic (solid line) and semiclassical (dashed line) theories: and . The inset plots show the corresponding velocities and trajectories in the x-z plane.

Image of FIG. 5.
FIG. 5.

(a) Critical magnetic field for cyclotron motion as a function of the incident energy calculated by the relativistic (R) and semiclassical (S) theories at three sets of conditions: (i) , (solid line for R, hollow triangle for S); (ii) , (dashed line for R, hollow circle for S); and (iii) , (dashed-dotted line for R, cross for S). (b) Peak-to-peak amplitude of x(t) and (c) oscillation period as a function of energy at with four sets of conditions: (i) , (solid line for R, hollow circle for S); (ii) , (dashed line for R, hollow triangle for S); (iii) , (dashed-dotted line for R, cross for S); and (iv) , (dotted line for R, hollow square for S).

Image of FIG. 6.
FIG. 6.

(a) Radiation intensity spectrum of the semiclassical trajectory at , , , , azimuth angle , polar angle , and oscillation number . (b) Radiation spectrum of the trajectory of Esarey et al. [z(t) with the second harmonic term] using the Gaussian quadrature method (triangle) and Jacobi–Anger expansion (solid line) with the same conditions as those in Fig. 6(a).

Image of FIG. 7.
FIG. 7.

Radiation intensity spectrum of the relativistic trajectory using (a) the Jacobi–Anger expansion and (b) the Gaussian quadrature method with the same conditions as those in Fig. 6(a).

Image of FIG. 8.
FIG. 8.

Radiation intensity spectrum of (a) the relativistic trajectory and (b) the trajectory of Esarey et al. at . Other conditions are the same as those in Fig. 6(a). The inset of (a) shows the enlarged diagram. The inset of (b) shows the semiclassical result.

Image of FIG. 9.
FIG. 9.

Radiation intensity spectrum of the relativistic trajectory (a) at and (b) at . Other conditions are the same as those in Fig. 6(a).

Image of FIG. 10.
FIG. 10.

Radiation intensity spectrum for the low initial velocity ratio of the relativistic trajectory (denoted by solid line) and the trajectory of Esarey et al. (hollow triangle) at (a) , (b) , and (c) . Other conditions are the same as those in Fig. 6(a). The inset plots show the radiation spectra of semiclassical trajectory.

Image of FIG. 11.
FIG. 11.

Effect of the magnetic field on the radiation intensity spectrum of the relativistic trajectory at (a) and (b) . The spectra with and without the magnetic field are denoted by solid triangle and hollow square, respectively; , , , , and . The inset plots show the results of semiclassical trajectory (with : solid line; without : dashed-dotted line) and the enlarged diagram.

Image of FIG. 12.
FIG. 12.

Radiation intensity spectrum (solid line) with (60 T) of the relativistic trajectory at for (a) and (b) . Other conditions are the same as those in Fig. 11(a). The inset plots show the enlarged diagrams. The results calculated using the twice integration accuracy better than that of solid line are denoted by solid square. A good agreement between them is demonstrated.

Image of FIG. 13.
FIG. 13.

Radiation intensity spectrum (solid line) with (60 T) of the relativistic trajectory at for (a) and (b) . Other conditions are the same as those in Fig. 11(a). The inset plots show the enlarged diagrams. The results calculated using the twice integration accuracy better than that of solid line are denoted by solid square. A good agreement between them is demonstrated.

Image of FIG. 14.
FIG. 14.

Radiation intensity spectrum (solid line) with (60 T) of the relativistic trajectory at for (a) and (b) . Other conditions are the same as those in Fig. 11(a). The inset plots show the enlarged diagrams. The results calculated using the twice integration accuracy better than that of solid line are denoted by solid square. A good agreement between them is demonstrated.

Image of FIG. 15.
FIG. 15.

Radiation intensity spectrum of the relativistic trajectory for low initial velocity ratio at (a), (b) , and (c) . Other conditions are the same as those in Fig. 11(a). The inset plots show the results of semiclassical trajectory.

Tables

Generic image for table
Table I.

Fourier components of relativistic trajectories at various initial velocity ratios . ; ; ; ; and . Dominant components are denoted by bold letters.

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/content/aip/journal/pop/17/11/10.1063/1.3496983
2010-11-10
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Analytic theory for betatron radiation from relativistic electrons in ion plasma channels with magnetic field
http://aip.metastore.ingenta.com/content/aip/journal/pop/17/11/10.1063/1.3496983
10.1063/1.3496983
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