Abstract

A single relativistic electron may exhibit large hysteresis and bistability in its cyclotron resonance at the main frequency (Ω ≈ Ω₀, where Ω₀ = eH₀/m₀c is the cyclotron frequency with H₀ being a dc magnetic field).¹ The microwave cyclotron motion of an electron can also be excited by an optical laser using either biharmonic driving with the optical frequencies ω₁ and ω₂ so that ω₁– ω₂ = nΩ, where n is an integer (the so-called cyclo-Raman excitation) or higher-order subharmonics with ω = nΩ.¹ So far, only steady-state regimes of oscillations for all these processes have been analyzed in detail. Here we report the results of our study on the dynamic behavior of the electron in large using a phase portrait technique for all the relativistic-related nonlinear effects mentioned above. These results confirm our previously reported results as to the small-perturbation stability of all the steady states and reveal topology of phase portraits of the system for large perturbations very much similar to that of classical anharmonic oscillators.² The phase portrait for main frequency oscillation consists of two (stable) focal points and one saddle point. The phase portrait for subharmonic oscillation shows the similarity to that for other physical nonlinear systems.² In biharmonically excited cyclotron oscillations, the phase portrait for the first-order process (n = 1) is qualitatively similar to that for the main frequency, and the higher-order processes have phase portraits essentially similar to those of subharmonic cyclotron excitation.

© 1988 Optical Society of America