Abstract:

A modeling code was developed to track the nonlinear, nonstationary time evolution of the fields in the gyroklystron cavities based on the fundamental pendulum coupled differential equations.

Work has begun on design of the gun cathode using the EGUN code.

Modeling code:

The modeling code, written in Fortran, solves the time evolution of the following coupled differential pendulum equations:

where “F” is related to the amplitude of the fields in cavity “n”.

In order to include the effects of velocity spread, these equations are solved using many particles of different initial conditions. The numbers of particles are divided into a specific number of velocity bins (typically 7) based on a Gaussian distribution of the transverse momentum. The initial phase of the electrons within each velocity bin is uniformly distributed. The phase of the electrons in different bins is distributed in such a way as to avoid overlapping of the various velocity classes in a phase evolution plot. Table 1 shows the preliminary operating parameters used to generate the plot in Figure 1.

Voltage	10 kV
Current	100 mA
Pitch Factor	1.4
Beam Radius	0.64 mm
Velocity Spread	4 %
Frequency	140.00 GHz
Magnetic Field	5.14 T
Input Power	1 mW
No. of Cavities	5
Operating Mode	TE (0,2,1)

Table 1: Preliminary design parameters.

Figure 1: The nonlinear time evolution of the F parameter in each cavity.

The saturated gain using these operating parameters along with a 4% perpendicular velocity spread is around 32 dB, which is probably the minimum acceptable gain for this project. The output power was 86 watts for an input of 50mW under these conditions. Increasing the voltage lowers gain significantly, while increasing current increases gain.

Electron Gun:

The design of a new electron gun now seems necessary. Although we had contemplated using an existing electron gun, this gyroklystron system seems to have unique requirements. Because Photonic Band Gap (PBG) didn’t seem to confine the TE₀₃ mode well and we needed higher gain, we moved down to TE₀₂. The TE₀₂ mode, however, requires a very small beam radius of only 0.64mm, compared to the 1.8mm on the 250GHz system. This small radius could require a compression of ~70 if used with the existing 250GHz gyrotron electron gun (designed for compression of 28), because the beam must be compressed to such a small size. Such a high compression is a problem as far as positioning the electron gun, so the aim is to design for a compression of around 25. The possibility of using other modes, such as TE₀₃ or TE₀₄ does not look promising in terms of gain. Designing such a small electron gun cathode is a difficult job, since all the problems with velocity spread, electron trajectory, beam alpha and current density uniformity could be worsened.