The Generation And Propagation Of The Intense Relativistic Sheet Electron Beam

High-power microwave generators with sheet electron beams are promised to have high beam-wave conversion efficiency with low beam current density while keeping compact, and to be a new approach for the development of the high-power microwave generators. During the process of investigating the sheet-electron-beam high-power microwave generators, the generation and propagation of the intense relativistic sheet electron beam in vacumm are the key issues, and could be very difficult, but few reports could be found. To overcome the difficulties, the following problems should be resolved including the theoretical analysis of the physical model in three dimensions, generation of the sheet electron beam using a cold cathode, beam-matching focusing with stable propagation, assembling the periodic cusped magnets safely and precisely, the measurement of the sheet electron beam.In this paper, the generation and propagation of the intense relativistic sheet electron beam have been investigated using theoretical analysis, numerical calculations, particle-in-cell simulations, and experiments. The following results have been obtained.1. The sheet electron beam with the cross section of a quasi-rectangle, composed by a rectangle and two halves of an ellipse connected to the shorter sides of the rectangle, respectively, has been proposed. It has been mentioned that the sheet electron beam with rectangular or elliptical cross section could not be focused well enough by the periodic cusped permanent magnets or could not be well generated by the cold cathode with explosive emission process.2. The expression of the space-charge limiting current of a relativistic sheet electron beam propagating in a rippled rectangular waveguide has been derived. Using numerical computation, interesting results of the space-charge limiting current are provided. The magnetic fields excited by the periodic cusped permanent magnets used for focusing the sheet electron beams in the vertical direction have been approximately expressed in two different forms for the convenience of future numerical calculations and theoretical analyses, respectively. Firstly, the surface-current-sheet and the two-magnetic-charge-surface models have been used to approximate the periodic cusped permanent magnet, and two equivalent accurate expressions have been obtained. These expressions would rather be applied to numerical calculations than theoretical analyses because of the complication. Secondly, to obtain simple expressions of the periodic cusped magnetic fields for the convenience of future theoretical analyses, the method of undetermined coefficient has been used, and validation by numerical calculations shows that the expressions are accurate if the number of the periodic magnetic fields harmonics is sufficient large. The magnetic fields excited by the four side magnets used for focusing the sheet electron beam in the horizontal direction have also been approximately expressed using the two-magnetic-charge-surface model with better precision than that reported before by other researchers. In addition, using the two-magnetic-charge-surface model, the four side magnets have been optimized for the better beam focusing by rotating the four magnets.3. The focusing magnets, including the periodic cusped magnets and four-side magnets, have been designed according to the given space-charge electric fields for the beam matching. To verify the theoretical analysis, the particle-in-cell simulations have been performed, showing that the 300keV, 3kA sheet electron beam can be well focused by the 0.15T periodic cusped magnetic fields and the 0.009T quadrupole magnetic fields excited by the designed focusing magnets. More than 98% of the total current has been propagated through the distance of 300.0mm. For the sheet electron beam propagating in the combined magnetic fields including 0.4T solenoidal field, the periodic cusped magnetic feilds and four-side magnetic feilds, the particle-in-cell simulations have also been performed. The simulation results show that the 300keV, 3kA sheet electron beam can be well focused and more than 90% of the total current has been propagated through the distance of 200.0mm.4. The experiments of the generation and propagation of the intense relativistic sheet electron beam have been carried out. In 0.5T solenoid magnetic fields with a full width at half maximum of 50.0mm, the 325keV, 2.60kA sheet electron beam has been generated with good current distribution, and more than 80% of the total current has been propagated through the distance of 100.0mm in the magnetic fields which are combined by the 0.5T solenoid magnetic fields, the 10×10.0mm, 0.12T periodic cusped magnetic fields, and 0.009T side focusing magnetic fields.These results show that the idea of sheet electron beam could be used in field of the genenration and propagation of the intense relativistic electron beams, and the intense relativistic sheet electron beam could be well generated by the cold cathode and well focused by the periodic cusped magnetic fields. These results are of great interest to the investigation of the high-power microwave generators with intense relativistic sheet electron beams.