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Analytical theory of low-frequency space charge oscillations in gyrotrons
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10.1063/1.2990024
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Affiliations:
1 University of Electronic Science and Technology of China, ChengDu, SiChuan 610054, People's Republic of China
2 University of Maryland, College Park, Maryland 20742, USA
Phys. Plasmas 15, 103102 (2008)
/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

FIG. 1.

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

FIG. 2.

The model of three beam components in the trap region.

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).

FIG. 4.

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

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 (, , , ).

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).

FIG. 7.

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

FIG. 8.

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

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

Table I.

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

Table II.

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

Table III.

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

/content/aip/journal/pop/15/10/10.1063/1.2990024
2008-10-01
2014-04-18

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