Study Of Time-dependent Theories And Generalized Nonlinear Simulation Techniques For Beam And Wave Interaction In Traveling Wave Tubes

Being a branch of important microwave vacuum devices, traveling wave tubes(TWTs) become an indispensable key part in the defense and communicationequipments because of their compatibility with wide bandth and high powercharacteristics. Accordingly, nonlinear theories for simulating the beam and waveinteraction (BWI) of TWTs have been developed to improve their performances. Sincemost of the exsiting nonlinear theories are mainly in frequency domain to analyze theBWI in steady state, the time-dependent nonlinear theories are in lackage to study thetransient BWI situations in TWTs. Meanwhile, as the demand of devices with higherfrequency and higher power increases, new types of TWTs, such as folded waveguide(FWG) TWTs have been designed and manfactured. As a result, nonlinear theories forsimulating the BWI of these TWTs are needed. So it can be concluded that the study oftime-dependent theories and generalized nonlinear simulation techniques for the BWI ofTWTs is essentially important.A nonlinear BWI theory in a TWT should include a system of at least three typesof basic equations. These include1) the radio frequency (RF) field equations describingthe energy transformation between the RF signals and the electron beam,2) the spacecharge (SC) fields describing the coulomb forces among electrons, and3) the dynamicelectron equations describing the motion of the electrons. To develop nonlinear BWItheories and models in TWTs, the main work of this dissertation is focused on thesethree types of equations as follows. Firstly, the variation of time is included in the radiofrequency (RF) and space charge (SC) field equations to develop the time-dependentnonlinear theory. Secondly, the digitized RF field profiles have been applied toconstruct the generalized nonlinear BWI simulation model for various types of TWTs.Therefore, the main work and innovations of this dissertation are concluded below.1. The nonlinear time-dependent BWI theory for helix TWTs is presented. Thedispersion relationship of the helix TWTs is obtained based on the sheath helix model.Based on the dispersion relationship and the analytical RF field expressions, thetime-dependent RF field equations are developed. The SC fields are modeled by SC waves and the corresponding SC field equations are discussed. On combining the RFfield equations and the SC field models with the dynamic electron equations which aredescribed using the relativistic Lorentz equations, the nonlinear time-dependent BWItheory for helix TWTs is developed.2. A practical helix TWT is modeled to validate the time-denpendent theory.Firstly, the initial conditions for simulation, including the grid settings, the initial RFfields along frids, as well as the initial distribution of electrons are given. Meanwhile,the MacCormack method, which can be used to simulaously step the time and position,is discussed and applied in the numerial model. Secondly, as an example, the dispersionrelationship of a C band helix TWT is obtained. The BWI of this helix TWT is thenmodeled within the dispersion relationship and the initial conditions. The simulationresults, including the propagation of RF signals, the RF power varied with axial positionor time, and the scan of power are shown and discussed to prove the validation of thistime-dependent BWI theory in helix TWTs.3. To increase the simulation accuracy, as well to simulate the multisiganalnonlinear charactistics, such as harmonic generation and intermodulations, the nonlineartime-dependent BWI theory has been improved. Firstly, the parameters obtained fromhigh frequency electromagnetic simulation software (e.g. HFSS), such as the couplingimpedence and so on, are applied in the RF field expressions to improve the simulationpracticiticy and accutacy. Secondly for the stimulus sources of the RF and SC fieldequations, the axial average over RF wavelength is replaced by the average over thecommon time period among RF signals. Hence the BWI grids are simplified andmultifrequency signals can be simulated.4. The nonlinear time-dependent BWI model for the FWG TWTs has beendeveloped. Firstly, with the digitized RF fields in a single period from HFSS, the RFfield profile in the whole BWI scale can obtained by means of the Floquet theorem tosolve the RF field equations. Secondly, the SC fields in the FWG TWTs are calculatedby the combination of the Possion’s equations with the Particle-In-Cell (PIC) method.The one-dimensional (1-D) code based on this time dependent BWI theory is compiledto simulate a practical FWG TWT. The consistency between the simulation and testresults proves the validation of the BWI theory in FWG TWTs. 5. The generalized nonlinear BWI simulation technique has been developed forvarious types of TWTs in a unified way. Firstly, the RF field equations are developedfrom the Law of Energy Conservation between the RF signals and the electron beam.Accordingly, the digitized RF fields obtained from HFSS can be applied to solve thegeneralized RF field equations. The Fourier series of the SC wave have been applied inthe generalized SC model where the SC fields in TWTs are solved by the finitedifference method. The1-D code has been constructed to simulate a helix TWT, a CCTWT and a FWG TWT. The consistency between the simulation and test results showsthe feasibility of this generalized BWI model.