tube (TWT) [@Pierce; @Gilmour] extensively used to mimic beam plasma interaction [@Tsunoda; @Dimonte] and recently to observe resonance overlap responsible for Hamiltonian chaos  [@Macor1]. The TWT sketched in Fig. \[fig:twt\] is made up of three main elements: an electron gun, a slow wave structure (SWS) formed by a helix with axially movable antennas, and an electron velocity analyzer. The electron gun creates a beam which propagates along the axis of the SWS and is confined by a strong axial magnetic field with a typical amplitude of $0.05
{\,\rm T}$ which does not affect the axial motion of the electrons. The central part of the gun consists of the grid-cathode subassembly of a ceramic microwave triode and the anode is replaced by a Cu plate with an on-axis hole whose aperture defines the beam diameter equal to $1 {\,\rm mm}$. Beam currents, $I_b < 1 {\,\rm mA}$, and maximal cathode voltages, $|V_c| < 200 {\,\rm V}$, can be set independently; an example of typical velocity distribution functions is given in Figs. \[fig:085\] and \[fig:127\] (panel (a)). Two correction coils provide perpendicular magnetic fields to control the tilt of the electron beam with respect to the axis of the helix. For the 