This chapter is devoted to a discussion of CMs with uniform magnetic fields. This is usually the case for laboratory CMs. The nonlinear theory of laboratory plasma devices has been developed over many years, and has received excellent experimental confirmation (Gaponov-Grekhov and Petelin, 1981). Space CMs differ from their laboratory analogues, even for the homogeneous magnetic field situation. The main difference concerns the smooth charged particle distribution function and various wave spectral features in space plasmas in comparison with the mono-energetic beams and high Q resonators, with waves in a narrow frequency band, in laboratory devices. However, many important nonlinear effects are similar in both laboratory and space CMs, and the experience of laboratory CM investigations can be relevant to importing their results to the nonlinear theory of CMs in space.

In particular, we are concerned with the nonlinear theory of the cyclotron generation of electromagnetic quasi-monochromatic waves by a beam of electrons, rotating about a homogeneous magnetic field. Pioneering investigations of this problem were performed by Yulpatov (1965) and Gaponov et al. (1967). The modern nonlinear theory of laboratory electron generators includes many features which are important for space CMs. The so-called backward wave oscillator (Kuznetsov and Trubetskov, 1977; Ginzburg and Kuznetsov, 1981), which seems to be very important for an explanation of a wide range of discrete ELF/VLF signals in the magnetosphere, especially the so-called chorus emissions, is discussed here and also in Chapter 11.