Overview of XOOPIC code Overview of MAGIC code Klystron simulation using XOOPIC codeContentsXOOPIC and MAGIC Codes for Electromagnetic Field S.J. Kim and J.K. Lee
Overview of XOOPIC Code Two dimension and three velocity Cartesian (x-y) or cylindrical (r-z) coordinates Electrostatic or full electromagnetic field Discrete model (Finite-Difference Method) : uniform or non-uniform mesh Boltzmann and inertial electrons Immobile and inertial ions Monte-Carlo collision model Complex boundaries : conductor, cylindrical axis, wave ports, absorption, transmission, emission.XOOPIC Features* Values of gridded quantities can be approximated at intermediate points by interpolation.
Program FlowDefined region of the discrete modelElectromagnetic fields on the meshDiscretization meshGroup of similar particlesIndividual particle (position, momentum, mass, charging, numerical weight)
Maxwells Equations for Electromagnetic FieldMaxwells equations in integral formC-1, L-1: coupling matrices withthe dimemsionality of capacitanceand inductance.Nonuniform orthogonal Yee mesh
Maxwell Curl EquationsTransverse magnetic (TM) setTransverse electric (TE) setThe TM and TE field equations are advanced in time using a leap frog advance.The currents result from charged particle motion.
Velocity Advance Half acceleration: Rotation: Half acceleration: Relativistic Boris advance
Charge Conserving Current Weighting AlgorithmCharge conserving current weighting =
Overview of MAGIC CodeUniform gridManual gridAppended regionsPolynomial smoothly varying gridPade smoothly varying gridResistiveDielectricConductorsScattering foilPolarizer sheetHelix elementGeneral current sourceAir chemistrySemiconductorCartesian coordinatesPolar coordinatesCylindrical coordinatesSpherical coordinatesMirror symmetry boundaryPeriodic symmetry boundaryAbsorbing boundaryOutgoing wave boundaryApplied voltage boundaryExternal circuit voltage sourceParticle and field importStandard leapfrogTime-reversible leapfrogSemi-implicitStandard noise filteringHigh-Q noise filteringQuasistaticElectrostatic ADIElectrostatic SORExternally specified magnet fieldRestricted TE or TM modes GridMaterialsGeometryField algorithm Application fields : microwave amplifiers, antennas, sensors, fiber optics, lasers, accelerator components, beam propagation, pulsed power, plasma switches, microwave plasma heating, ion sources, field emitter arrays, semiconductor devices, wave scattering, and coupling analyses Particle-in-cell (PIC) approach Maxwells equations on a finite-difference grid for electromagnetic fieldElectromagnetic computational processing cycleMAGIC code
Method and NoiseLeapfrog time integration schemeWell-centering Particle-induced noise is introduced through the current term in Maxwells equations. Propagating, wave-like, electromagnetic nose Large curl derivatives Time-biased and high-Q algorithms Spatial fluctuations in space charge and the Gausss law constraint The slow, self-heating instability Charge allocation algorithmTransverse particle noiseLongitudinal particle noise
Time-Biased AlgorithmTime-biased algorithm : semi-implicit schemea1, a2, and a3 determine the degree of spatial filtering and the time-centering.i : iteration coefficient=k/kmax : normalized eigenmodekmax : maximum spatially-resolvable Fourier wave number
Charge Conservation SchemeBoris-DADI correctionLangdon-Marder correction
Simulation Domain of KlystronRF input portRF output portE-beamCylindrical Axis10.05 cm13.07 cm9.55 cm37.2 cm7.569 cm6.66 cm Simulation condition: Beam emitter: I= 12 kA, ud =2.48e8 m/s Input port : Rin=2300 , R=20 , f=7.69 GHz Output port : R=47.124
Example of Klystron Simulation Phase spaceDensityKinetic energyuz
Simulation Results at 0.5 ns
Simulation Results at 2.5 ns
Simulation Results at 10 ns
Simulation Results at 20 ns
Simulation Results at 6 us
KE as a Function of Beam Current
KE as a Function of Beam Energy
Klystron Phase spaceDensityKinetic energyuz2 cm3 cm
Simulation Results at 0.5 ns and 2.5 ns
Simulation Results at 10 ns and 20 ns
Simulation Results at 6 us
