By R. Martini

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**Extra info for Geometrical approaches to differential equations**

**Example text**

Or, in other words, the longitudinal mechanical particle momentum increases after passing by particle the EH-field jump in the system output. Up to now only the dynamics of the longitudinal component of particle mechanical particle momentum during the input reflection process have been discussed. But the question arises: what is happening to its transversal components? Let us shortly discuss this problem also. The appropriate calculation shows that transversal momentum components also undergo some changes.

Firstly, the action of the force (see Fig. 3) leads to some decreasing amplitude of the transversal oscillations of an accelerated particle, as shown in Fig. 4. But let us explain this effect in more detail. The point is that the action of the force simultaneously causes the appearance of a transversal dynamical drift of the accelerated electron (see Fig. 5, curve 1). As follows from elementary qualitative analysis (see diagram in Fig. 4), this circumstance is responsible for the EH-ACCELERATORS 45 decreasing mentioned of the amplitude of electron oscillations.

4. But let us explain this effect in more detail. The point is that the action of the force simultaneously causes the appearance of a transversal dynamical drift of the accelerated electron (see Fig. 5, curve 1). As follows from elementary qualitative analysis (see diagram in Fig. 4), this circumstance is responsible for the EH-ACCELERATORS 45 decreasing mentioned of the amplitude of electron oscillations. The sequence is somewhat unexpected: the presence of additional longitudinal acceleration (owing to the horizontal component of the force actually leads to decreasing the current rate of electron acceleration (owing to both its components).