By V. Kulish

This can be the second one of a two-volume set for complicated scholars in actual digital, plasma, and radio physics, optical and digital engineering, utilized mechanics, and area applied sciences. It deals a hierarchical remedy of undulative electrodynamic structures and describes structures akin to EH-accelerators, EH-formers, EH-coolers, the klystron, and multi-harmonic two-stream superheterodyne unfastened electron lasers. unique realization is paid to phenomena reminiscent of explosive instability, section and polarization discrimination, and nonlinear new release of electrical and magnetic fields.

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**Extra info for Hierarchical Methods: Undulative Electrodynamical Systems**

**Sample text**

The general structure of both these fields, at the first sight, is similar. Indeed, they both consist of a crossed transverse vortex electric field and a magnetic field, respectively. However, the real differences are more essential than this resemblance. The point is that the field of any electromagnetic wave propagating along the EH-ACCELERATORS 15 is a ‘moving’ one, whereas an EH-undulated field is represented by the superposition of two (E-undulatory and H-undulatory) ‘standing’ quasi-stationary waves.

However, as the calculation for the first approximation shows (curve 1 in Fig. 4), this result really is ‘virtual’ because the capture effect develops earlier on the system length (curve 1 in Fig. 4). Or, in other words, the acceleration process breaks before owing to the capture effect rather than the high levels of the particle acceleration will be attained. Thus the non-stationary EH-accelerators really have some fundamental limitation for magnitude of maximum particle averaged kinetic energy The relevant analytical expression for this maximal energy can be obtained in the form: 32 HIERARCHICAL METHODS where Physically this limitation is determined by the capture effect, and it can be regarded, in principle, as an essential disadvantage of the nonstationary models discussed.

Let as come back to the input reflection again. 12), there is a possibility of obtaining the expression for the critical angle of flight of a particle, where it is reflected from the input (see the area of reflection angles in Fig. 1): where is the magnitude of the induction vector of the transversal component of the input magnetic field for the time of particle leaves the input region, is the magnitude of initial particle momentum. This angle, analogously to ‘ordinary’ optics, is interpreted as the ‘angle of complete internal reflection’.

### Hierarchical Methods: Undulative Electrodynamical Systems by V. Kulish

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