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Analytical theory of low-frequency space charge oscillations in gyrotrons
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10.1063/1.2990024
/content/aip/journal/pop/15/10/10.1063/1.2990024
http://aip.metastore.ingenta.com/content/aip/journal/pop/15/10/10.1063/1.2990024

Figures

Image of FIG. 1.
FIG. 1.

Trapped electrons in the region between electron gun and the cavity.

Image of FIG. 2.
FIG. 2.

The model of three beam components in the trap region.

Image of FIG. 3.
FIG. 3.

Comparison of the real parts [(a) and (c)] and imaginary parts [(b) and (d)] of the normalized propagation constant calculated by using approximation (12)–(14) with those obtained from the sixth-order dispersion relation (9). [(a) and (b)] The dependence of these propagation constants on the trap fraction ratio . [(c) and (d)] The dependence of these propagation constants on the ratio of the current to the limited current ratio. Calculations are done for the following set of parameters: , , , for (a) and (b), and for (c) and (d).

Image of FIG. 4.
FIG. 4.

Determinant of the matrix showing three solutions: modes A, B, and C (, , , , ).

Image of FIG. 5.
FIG. 5.

Dependence of oscillation frequencies on the trap length for the simplified and accurate models of the lowest three modes. Dashed line shows the oscillation frequency determined by Eq. (15), solid line shows the frequency defined by an accurate model (, , , ).

Image of FIG. 6.
FIG. 6.

Dependence of oscillation frequency on the trap fraction (a) and on the ratio of the current to the limited current ratio; , , ; for (a) and for (b).

Image of FIG. 7.
FIG. 7.

Contours of equal growth rates and oscillation frequencies of the mode A and mode B in the plane of parameters and (, , ).

Image of FIG. 8.
FIG. 8.

Axial dependences of the amplitude (a) and phase (b) of the perturbed potential for several values of the trap fraction (, , , ).

Image of FIG. 9.
FIG. 9.

Coefficient of reflection as the function of the beam voltage (a) and the pitch-factor (b) for different values of the transverse velocity spread .

Tables

Generic image for table
Table I.

The beam density coefficients corresponding to the main beam, trap forward, and trap backward partial waves of mode A [, , , , , ].

Generic image for table
Table II.

The coefficients corresponding to the main beam, trap forward, and trap backward partial waves of mode B [, , , , , ].

Generic image for table
Table III.

The coefficients corresponding to the main beam, trap forward, and trap backward partial waves of mode C [, , , , , ].

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/content/aip/journal/pop/15/10/10.1063/1.2990024
2008-10-01
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Analytical theory of low-frequency space charge oscillations in gyrotrons
http://aip.metastore.ingenta.com/content/aip/journal/pop/15/10/10.1063/1.2990024
10.1063/1.2990024
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