Observation of Poincaré-Andronov-Hopf Bifurcation in Cyclotron Maser Emission from a Magnetic Plasma Trap

We report the first experimental evidence of a controlled transition from the generation of periodic bursts of electromagnetic radiation into the continuous-wave regime of a cyclotron maser formed in magnetically confined nonequilibrium plasma. The kinetic cyclotron instability of the extraordinary wave of weakly inhomogeneous magnetized plasma is driven by the anisotropic electron population resulting from electron cyclotron plasma heating in a MHD-stable minimum-$B$ open magnetic trap.

Figure 1

(a) Solution of the characteristic equation (4), (b),(d) the characteristic phase trajectories, and (c),(e) the time evolution of $E$ and $f_1$ from Eqs. (2) in the cw regime (b),(c) and limit cycle regime (d),(e). The wave energy and number of particles in the ${\varphi }_1$ mode are normalized over their stationary values (3). The parameters $J_0{k}_1/{\nu }^2=0.01$ and ${\kappa }_{\mathrm{c}}=0.39$ are chosen to fit the experimental data; the first six modes are taken into account in the numerical calculations. The Hopf bifurcation occurs at ${\kappa }_t=0.82$.

Figure 2

Schematic of the experimental setup. Microwaves are launched through a WR-62 waveguide port, while the plasma emission is measured through a WR-75 waveguide port. The transmission line to the oscilloscope (Keysight DSOV334A, $80\mathrm{Gs}/\mathrm{s}$ sampling rate and 33 GHz bandwidth) includes high voltage break, waveguide-to-coaxial transition, power limiter, and tunable attenuator; the frequency response of the line is constant in the range of 8–15 GHz. The mirror ratios are $B_{\max }/B_{\min }=4.7–6.8$ and 2.4–3, correspondingly, in the injection (left) and extraction (right) mirrors.

Figure 3

Dynamic spectra of the plasma emission in the 8–12 GHz range in the (a) pulsed regime at $B_{\min }/B_{\mathrm{ECR}}=0.935$, and the (b) cw regime at $B_{\min }/B_{\mathrm{ECR}}=0.947$. The spectrograms were calculated off-line by short-time Fourier transform with a Hamming window. The horizontal line at 11.8 GHz corresponds to the stray radiation at the TWT amplifier frequency.

Figure 4

Intensity of microwave emission in 8–12 GHz band referred to the generation of (a) periodic bursts, (b) cw emission, and (c) spontaneous transition from quasiperiodic bursts to cw and back. Stray radiation of the heating TWT amplifier at 11.8 GHz is shown with a red line. Three regimes differ only by the value of the magnetic field: $B_{\min }/B_{\mathrm{ECR}}=0.935$ for the burst, 0.947 for the cw, and 0.98 for the transient regimes, correspondingly.

Figure 5

Waveforms of the electron precipitation through the axial (extraction) mirror with energies of (a) $51.2\pm 0.25\mathrm{keV}$ and (b) $201.6\pm 0.25\mathrm{keV}$; the microwave emission in the 8–15 GHz range is denoted with red lines. (c) Energy distributions of escaping electrons averaged over 100 s in the stable, burst, and cw regimes; the distributions are reduced to a unit square by dividing by the total number of detected particles. The measurements are performed using a magnetostatic energy spectrometer with 500 eV resolution [48].