The Ribbon Electronic Note Diocotron Instability

Sheet electron beam play a vital role for a number of applications,such as: microwave tube, gas laser excitation and plasma chemistry reaction.There are obviously virtues, when it was used in microwave tubes. Firstly,we can extend it wide. That is means; we can improve the tube's powerinfinitely in theory, if we need. Ring or cylindrical electron beam wasneeded to rise voltage and enhance density if we went improve power of tube,while the density can't increase infinitely because of space charge force.So, ring and cylindrical electron beam have some disadvantages comparingwith sheet electron beam. In the second place, the more high frequency weneed the more small of the SWS section. We can use sheet electron beam inmicrometer microwave device, while ring or cylindrical electron beamcan't be used in such device. In the third place, sheet electron beam couldput close to SWS(slow wave structure), that make the tubes more efficientlythan ring or cylindrical electron beam tubes. Fourthly, rectangularstructure using sheet electron beam is easier machining and remodel. Thelast, it is small that make it can be used in spaceflight and aviation.However, the ring and cylindrical electron beam tubes always were themainstream of scientific research for past 50 years, because sheet electronbeam was difficult to focusing. Without focusing leads to discollect.Diocotron mode was appeared in uniform solenoid focusing magnetic field.This paper is begin with space charge wave theory and get surface wave inhalf infinite sheet electron beam. Than we assume sheet electron beam waslayered and deduce the Diocotron mode.Copying ring electron beam tube used PPM focusing, closePCM(periodically cusped magnetic) was used in sheet electron beam tube.Electron move in close PCM and be integrated for one periodicity. That isa equilibrium potential, and we can arrive a equilibrium force. If it wasput in Diocotron mode theory, we get the conditions for sheet electron beam transmitted without Diocotron mode.Close PCM can focus sheet electron beam in horizontal direction, whileit can't focus sheet electron beam in vertical direction. We develop closePCM to open PCM. Open PCM can focus sheet electron beam in horizontal andvertical directions.MAGIC, 3D(three dimensional) PIC(particle in cell) code, was used tosimulate electron behave. In case of z=u₀t (u₀ as the velocity of electronis confirmed, "t" means the section of position "z" in 2D simulations),Diocotron mode was simulated with infinitely wide sheet electron beam andsheet beam in wave guide focusing by uniform solenoid magnetic field. Weobserve the influence of Diocotron mode by each parameters.We use MAGIC for 3D simulations and proof the result of 2D simulations.Then the behaves of infinitely wide sheet electron beam and sheet beam inwave guide focusing by close PCM was simulation. The result show, PCM canrestrain Diocotron mode.