The present invention pertains to an electron gun that generates an electron flow and the application of this gun to produce rf energy or for injectors. The electron gun comprises an electrostatic cavity having a first stage with emitting faces and multiple stages with emitting sections. The gun is also comprised of a mechanism for producing an electrostatic force which encompasses the emitting faces and the multiple emitting sections so electrons are directed from the emitting faces toward the emitting sections to contact the emitting sections and generate additional electrons and to further contact other emitting sections to generate additional electrons and so on then finally to escape the end of the cavity. The emitting sections preferably provide the cavity with an accelerating force for electrons inside the cavity. The multiple sections preferably include thin forward emitting surfaces. The forward emitting surfaces can be of an annular shape, or of a circular shape, or of a rhombohedron shape. The mechanism preferably includes a mechanism for producing an electrostatic electric field that provides the force and which has a radial component that prevents the electrons from straying out of the region between the first stage with emitting faces and the multiple emitting sections. Additionally, the gun includes a mechanism for producing a magnetic field to contain the electrons anywhere from the first stage with emitting faces or any emitting section and to the end of the cavity. The present invention pertains to a method for producing a flow of electrons. The method comprises the steps of moving at least a first electron in a first direction at one location. Next there is the step of striking a first area with the first electron. Then there is the step of producing additional electrons at the first area due to the first electron. Next there is the step of moving electrons from the first area to a second area and transmitting electrons through the second area and creating more electrons due to electrons from the first area striking the second area. These newly created electrons from the second area move in the first direction then strike the third area, fourth area, etc. Each area creates even more electrons in a repeating manner by moving in the first direction to multiple areas. This process is also repeated at different locations. The mechanism preferably includes a mechanism for accelerating the electrons inside the electrostatic cavity to allow the electron multiplication to continue. The mechanism preferably includes a control grid for bunching the electron flow. The present invention pertains to an electron gun. The electron gun comprises an electrostatic cavity having a first stage with electron emitting faces and multiple stages with electron emitting sections. The electron gun also comprises a mechanism for producing an electrostatic force which encompasses the electron emitting faces and the multiple electron emitting sections so electrons from the electron emitting faces and sections are directed from the emitting faces toward the emitting sections to contact the emitting sections and generate additional electrons on the opposite sides of the emitting sections and to further contact other emitting sections. The present invention pertains to a method for producing electrons. The method comprises the steps of moving at least a first electron in a first direction from a first location. Then, there is the step of striking a first area with the first electron. Next, there is the step of producing additional electrons at the first area due to the first electrons on the opposite side of the first area which was struck by the first electron. Next, there is the step of moving electrons from the first area to a second area. Then, there is the step of transmitting electrons to the second area and creating more electrons due to electrons from the first area striking the second area.