Author details

more difficult than usage of the result of the initial and boundary problems (in spite of presented approach gives incomparably more data). In this sense, the approach can be used instead of the problems. It could seem that the procedure is a bit more difficult. However, this

44 Plasma Science and Technology - Basic Fundamentals and Modern Applications

The general character of presented approach should be emphasized once more. It is based on very general assumptions and does not refer on any particular model. The approach transforms the general form of the DR to an equation for SVA of the developing wave train. For a large class of beam-plasma instabilities (Cherenkov, cyclotron, etc.), the equation for SVA is actually the same. Its solution gives analytical expression describing evolution of initial perturbation. Various SI evolve in similar manner. This emphasizes identity of their physical nature (induced radiation of the system proper waves by the beam electrons). For given instability, one should specify two parameters only: the resonant growth rate and the group velocity of the resonant wave. Obtained expression gives detailed information on the instability. The information is: the shape of developing wave train (envelope), velocities of unstable perturbations, the type of given instability (absolute or convective), location of the peak and the character of its movement, the rate of field's growth in the peak, temporal and spatial growth rates, the rate of growth for perturbation moving at given velocity. Most of these data

Validity limitations also should be mentioned. Obtained results may not be applied to the systems where beam instability is caused by finite longitudinal dimension, for example, Pierce

Presented approach has neither inner contradictions, no contradictions to previous results of the beam-plasma interaction theory. Its results fully coincide to those obtained by direct analysis of the DR. In some cases, (e.g., for overlimiting e-beam instability and the instability in spatially separated beam-plasma system) obvious analysis is possible due to comparatively simple contribution of the beam in the DR (namely when the contribution has first (but not

The results of presented approach actually are continuation and further development of the results of the initial and boundary problems. In its turn, the results of the problems have been repeatedly tested and rechecked experimentally. This actually can serve as confirmation of

In [19, 20] the nonlinear dynamics of the beam-plasma instability was investigated numerically at no stationary beam injection into plasma-filled systems. The results show that at the initial stage of instability development the field has a shape matching reasonably to presented

Obtained results on SI evolution help to understand how the instability transforms given equilibrium of background plasma, estimate the level and/or scale of originated irregularities clear up how the nonlinear stage arises and predict saturation mechanisms. The systems, to which this may be applied are numerous, as the SI are the most common instabilities: from the Earth ionosphere to current carrying plasma (where the Buneman instability plays important

role). Not to mention relativistic microwave electronics etc.

difficulty only seems.

are unavailable by other methods.

instability.

results.

second) order pole).

validity of the approach.

Eduard V. Rostomyan

Address all correspondence to: eduard\_rostomyan@mail.ru

Institute of Radiophysics and Electronics Armenian National Academy of Sciences, Astarack, Armenia
