An electron-coupled transformer for generating a high voltage output pulse as an amplified version of an input pulse, comprising: a) a cylindrical triode electron tube with a central solid anode along the main axis of the tube, a high voltage insulator , a grid , a phase-matching network , a cathode radially spaced from the anode a glass vacuum envelope that encloses the anode, grid and cathode, a grid feedthrough and a cathode feedthrough ; the anode having a first end directly grounded and a second end insulated from a direct connection to ground by the high voltage insulator; the cathode is configured to receive said input pulse via the cathode feedthrough and forming a primary of the transformer, and the second end of the anode forming a secondary of the transformer, the grid being coupled to the phase-matching network via the grid feedthrough through the vacuum envelope via which the grid is configured to be selectively biased relative to the cathode; b) the cathode and the grid forming a traveling wave electron gun; the traveling wave electron gun forming a circular waveguide structure; the traveling wave electron gun being configured to produce, when the grid is switched from a voltage relative to the cathode to ground through the phase-matching network , a radially symmetrical collapsing traveling wave of ground potential in the Transverse Electromagnetic mode, whereby the radially symmetrical collapsing traveling wave of ground potential causes a beam of electrons to flow from the cathode to the anode and causes a voltage output pulse to be produced on the second end of the anode, whose magnitude is an amplified version of said input pulse applied to the cathode ; and c) the cathode and the grid being configured so that at least the energy contained in distributed interelectrode capacitance of the cathode and the grid linearly pumps the energy in the electron-coupled transformer. a) a cylindrical triode electron tube with a central solid anode along the main axis of the tube, a high voltage insulator , a grid , a phase-matching network , a cathode radially spaced from the anode a glass vacuum envelope that encloses the anode, grid and cathode, a grid feedthrough and a cathode feedthrough ; the anode having a first end directly grounded and a second end insulated from a direct connection to ground by the high voltage insulator; the cathode is configured to receive said input pulse via the cathode feedthrough and forming a primary of the transformer, and the second end of the anode forming a secondary of the transformer, the grid being coupled to the phase-matching network via the grid feedthrough through the vacuum envelope via which the grid is configured to be selectively biased relative to the cathode; b) the cathode and the grid forming a traveling wave electron gun; the traveling wave electron gun forming a circular waveguide structure; the traveling wave electron gun being configured to produce, when the grid is switched from a voltage relative to the cathode to ground through the phase-matching network , a radially symmetrical collapsing traveling wave of ground potential in the Transverse Electromagnetic mode, whereby the radially symmetrical collapsing traveling wave of ground potential causes a beam of electrons to flow from the cathode to the anode and causes a voltage output pulse to be produced on the second end of the anode, whose magnitude is an amplified version of said input pulse applied to the cathode ; and c) the cathode and the grid being configured so that at least the energy contained in distributed interelectrode capacitance of the cathode and the grid linearly pumps the energy in the electron-coupled transformer. <EOS>