Observation of Dynamic Interactions between Fundamental and Second-Harmonic Modes in a High-Power Sub-Terahertz Gyrotron Operating in Regimes of Soft and Hard Self-Excitation

Dynamic mode interaction between fundamental and second-harmonic modes has been observed in high-power sub-terahertz gyrotrons [T. Notake et al., Phys. Rev. Lett. 103, 225002 (2009); T. Saito et al. Phys. Plasmas 19, 063106 (2012)]. Interaction takes place between a parasitic fundamental or first-harmonic (FH) mode and an operating second-harmonic (SH) mode, as well as among SH modes. In particular, nonlinear excitation of the parasitic FH mode in the hard self-excitation regime with assistance of a SH mode in the soft self-excitation regime was clearly observed. Moreover, both cases of stable two-mode oscillation and oscillation of the FH mode only were observed. These observations and theoretical analyses of the dynamic behavior of the mode interaction verify the nonlinear hard self-excitation of the FH mode.

Figure 1

Start oscillation currents $I_s$ plotted as functions of the cavity field for $V_k=60\mathrm{kV}$, $R_b=1.97\mathrm{mm}$, and $\alpha =1.3$. Labels near each curve indicate the oscillation mode. For each mode, $I_s$ of either corotating or counterrotating mode with lower current is plotted to avoid unnecessary complication.

Figure 2

Oscillation intensities for (a) $V_k=50\mathrm{kV}$ and (b) $V_k=60\mathrm{kV}$ are plotted as functions of the cavity field. Solid lines represent signals with the high-pass filter; dashed lines are those without the high-pass filter.

Figure 3

Transmission signals through a Fabry-Perot interferometer plotted as functions of distance between the reflecting meshes: (a) $B_c=7.6\mathrm{T}$ and (b) $B_c=7.68\mathrm{T}$. The beam voltage $V_k$ was 60 kV; the beam current $I_b$ was 10 A.

Figure 4

Frequency spectra for the intermediate frequency signal from the harmonic mixer of the heterodyne receiver system: (a) $R_b=1.97\mathrm{mm}$ and (b) $R_b=2.05\mathrm{mm}$. The abscissa is converted to a rf scale.

Figure 5

Mode interaction calculations: (a) the relevant four SH modes are taken into account; (b) only the FH ${\mathrm{TE}}_{4,3}$ mode is included in the calculation ($V_k=60\mathrm{kV}$, $R_b=1.97\mathrm{mm}$, $\alpha =1.33$).

Figure 6

Temporal evolution of the ${\mathrm{TE}}_{4,3}$ mode and the ${\mathrm{TE}}_{17,2}$ mode at $B_c=7.69\mathrm{T}$ is plotted on the mode interaction calculation ($V_k=60\mathrm{kV}$, $R_b=1.97\mathrm{mm}$, $\alpha =1.33$). The inset displays the start-up phase.

Figure 7

Perpendicular efficiency is plotted as a function of the normalized current for different values of the frequency detuning parameter $\Delta$. The inset gives the same calculation for various $\Delta >0.6$.