By Levi Schächter
This article is essentially eager about the interplay of electrons with electromagnetic waves for the new release and amplification of radiation. It dicusses a few of the equipment of electron-beam new release and propagation and the elemental electron-wave interplay schemes, then it offers an idealized photo of the beam-wave interplay in a dielectric loaded waveguide. steadily the complexity of the research is elevated by way of featuring the impact of mirrored waves and additional by way of contemplating the beam as an ensemble of macro-particles. The e-book additionally dicusses the interplay in periodic and in quasi-periodic steel buildings and the basics of the beam-wave interplay in a periodic box, concluding with a short dialogue of particle acceleration, together with novel acceleration schemes.
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Extra info for Beam-Wave Interaction in Periodic and Quasi-Periodic Structures (Accelerator Physics)
42) which is shown in Fig. 18 for the particular case of ω0 = π/3. 18. 42) for the particular case of ω 0 = π /3 Discrete-time signals and systems 29 It can be easily checked that this sequence cannot be absolutely summed, but has finite energy. 42). 43) is a real function, which means that the phase of the frequency response is nil for every value of ω. 43), shown in Fig. 19 in the case of ω0 = π/3, it can be noted that it is the same as the frequency response of an ideal low-pass filter. 42) is not absolutely summable, a digital system acting as an ideal low-pass filter is not stable.
19 in the case of ω0 = π/3, it can be noted that it is the same as the frequency response of an ideal low-pass filter. 42) is not absolutely summable, a digital system acting as an ideal low-pass filter is not stable. 19. 43) for ω 0 = π /3 The Fourier transform of a sequence. In the last paragraph, the Fourier transform of the sequence obtained as the response to the unit sample sequence of a linear, shift-invariant system has been derived by analysing the response of such a system to the generalized sinusoid sequence.
26) is concerned, these relationships can be further on simplified, removing the limit operation. 28) are equal to zero, for any value of |k| ≤ N. 30) which confirms that the Fourier components of a sequence are periodic in the frequency domain. 22) are satisfied. 29); otherwise, the original information cannot be retrieved any longer from the discrete-time signal. From a very intuitive point of view, this conclusion is explained, in a graphical way, by Fig. 8 a and b. Fig. 8 a) shows the sequence of samples obtained by sampling a sinewave with 20 samples/period, in a synchronous way (T = 20Ts).
Beam-Wave Interaction in Periodic and Quasi-Periodic Structures (Accelerator Physics) by Levi Schächter