By Griffith Conrad Evans

An Unabridged Printing, With textual content And All Figures Digitally Enlarged - half considered one of : Functionals And Their functions, And chosen subject matters together with fundamental Equations. integrated on the finish Of The e-book Is The Author's Preface And desk Of Contents From The Cambridge Colloquium, half , research SITUS, by means of Oswald Veblen.

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1 EH-ACCELERATOR AS A HIERARCHICAL OSCILLATIVE SYSTEM Oscillations and Quasi-Resonances Let us give the hierarchical interpretation of the class of undulative electrodynamic systems considered. A simplest transversely homogeneous model will be chosen the longitudinal component influence of the undulating magnetic and electric fields are neglected. Also it is assumed in the general case that the polarization of the EH-field can be arbitrary and a longitudinal homogeneous (quasi-homogeneous) magnetic field is applied along the The H-ubitron field has been assumed to have stationary and non-stationary forms.

Undulatory) fields: 12 HIERARCHICAL METHODS are the harmonic numbers of the wave fields, are the wave numbers, and the are the spatial field periods. 2), we be can sure that in the general case the EH-accelerator can be regarded as a special wave resonant hierarchical system (the concept of ‘resonance’ see in Volume I). Let us discuss this affirmation in more detail by following the general theory of hierarchical oscillation systems described earlier in the preceding Volume. Correspondingly, the formation the vectors of slow variables and fast varying (rotating) phases should be accomplished at the first stage of our analysis.

The dynamics of the considered process is clearly shown in Fig. 2, where the motion paths of three typical particles with different input times into the system are shown. It is clearly seen that the captured particles 2 and 3 in Fig. 2 in the case in which the channel width (along the is more than 12 cm, became stuck in the accelerating channel volume. These particles strike the channel lateral walls in the opposite case. 8 in the case illustrated by Fig. 2 is limited, in fact, by the coordinate So, particles 2 and 3 in such situation strike the walls of the accelerating channel (see also item 4 in Fig.