and is slowed down by three retarding electrodes. Then the electrons having the correct drift energy determined by the potential difference on two parallel deflector plates are collected after passing through an off-axis hole at the back of the analyzer. The time averaged collected current is measured by means of a pico-ampermeter. Retarding potential and measured current are computer controlled, allowing an easy acquisition and treatment with an energy resolution lower than $0.5 {\,\rm eV}$. In the absence of any emitted wave, after propagating along the helix, the beam exhibits a sharp velocity distribution function with a velocity width mainly limited by the analyzer resolution as shown in Figs. \[fig:085\] and \[fig:127\] (panel (a)). For Fig. \[fig:085\]a, the beam with radius 3mm is diffracted by passing through the three grounded grids of a spreader [@spreader] just after leaving the gun while for Fig. \[fig:127\]a, the beam radius is $1
{\,\rm mm}$ and the spreader has beem removed for the sake of simplicity.

![Sketch of the Travelling Wave Tube: (1) helix, (2) electron gun, (3) trochoidal analyzer, (4) antenna, (5) glass vacuum tube, (6) slotted rf ground cylinder, and (7) magnetic coil.[]{data-label="fig:twt"}](Fig8.eps){width="7.5cm" height="4.9cm"}

![Beam velocity distribution functions at the output of 