Dynamics of a magnetized relativistic electron beam in composite drift tubes with virtual cathodes

Spontaneous and induced radiation by electrons/positrons in natural and photonic crystals. Volume free electron lasers (VFELs): From microwave and optical to X-ray range

“…From (169) follows that the growth of the wavelength (reduction of k) makes n ′ → 0, and n ′ can even become negative. However, it should be reminded that (169) is valid only when |n ′ − 1| ≪ 1 (i.e 2π dydzk 2 |ReA 0( ) | ≪ 1).…”

“…From (169) follows that the growth of the wavelength (reduction of k) makes n ′ → 0, and n ′ can even become negative. However, it should be reminded that (169) is valid only when |n ′ − 1| ≪ 1 (i.e 2π dydzk 2 |ReA 0( ) | ≪ 1). It is interesting to compare n ′ calculated by formulas (164) and (169): in the range of large wavelength they yield different results because the condition |n ′ − 1| ≪ 1 is violated.…”

“…where m and e are the mass and the charge of an electron, c is the speed of light, γ is the Lorentz factor of the electron beam and G depends on the geometry [167,169]. For example, for an annular electron beam in a cylindrical drift tube G reads as follows [169]:…”

“…This means that the hybrid system "vircator + grid TWT (grid VFEL)" arise by analogy with the system described in [174], where several vircators could appear due to the presence of several anode grids (see also [169]). But in contrast to the system [169], the hybrid system "vircator + grid TWT (grid VFEL)" uses periodically placed grids with either constant [112,175,176] or variable period [177].…”

“…In vircator systems, a grid cathode and anode (or anodes) are commonly used [169,170,171,173]. The electron beam oscillates, making electrons periodically cross the grid anodes and cathode (see, for example [171]).…”