ECE490O: Special Topics in EM-Plasma Simulations JK LEE (Spring, 2006) ODE Solvers PIC-MCC PDE Solvers (FEM and FDM) Linear & NL Eq. Solvers

Computational Eng./Sci.

ECE490O: PIC & FEM JK LEE (Spring, 2006)

PIC Overview PIC codes simulate plasma behavior of a large number of charges particles using a few representative “super particles”. These type of codes solve the Newton-Lorentz equation of motion to move particles in conjunction with Maxwell’s equations (or a subset). Boundary conditions are applied to the particles and the fields to solve the set of equations. PIC codes are quite successful in simulating kinetic and nonlinear plasma phenomenon like ECR, stochastic heating, etc.  PIC Codes Overview

삼성 낸드플래시 대추격 … 일본 이어 미국까지 뛴다 인텔 등 2 조원 설비투자

– – – –– – – + + – + ~ Sheath j = 1, , N ~ 1D Asymmetric Dual-Freq. Voltage-Driven System Plasma Application Modeling POSTECH Capacitively Coupled Plasma – 1D PIC-MCC MCC (Monte-Carlo Collision) Processes - Electron-Neutral Collisions (Ionization, Scattering, Excitation) - Ion-Neutral Collisions (Charge-exchange, Scattering) Bulk Plasma Substrate

PIC-MCC Flow Chart Fig: Flow chart for an explicit PIC-MCC scheme Particles in continuum space Fields at discrete mesh locations in space Coupling between particles and fields III IIIIV V

I. Particle Equations of Motion  Newton-Lorentz equations of motion  In finite difference form, the leapfrog method Fig: Schematic leapfrog integration

III. Electrostatic Field Model  Possion’s equation Finite difference form in 1D planar geometry  Boundary condition : External circuit Fig: Schematic one-dimensional bounded plasma with external circuit

PDP Structure Dielectric Layer Bus Electrode Protection Layer Barrier Rib Address Electrode Sustain Electrode Phosphor(R,G,B) Front Glass Substrate Visible Light Rear Glass Substrate Discharge Address Electrode Phosphor Barrier MgO Bus Electrode Dielectric layer UV 90 rotation o Sustain Electrode AC PDP Discharge in PDP Plasma Application Modeling POSTECH

Striation Profiles in PDP – 2D PIC/MCC Plasma Application Modeling POSTECH 100Torr 200Torr 500Torr Pressure dependence of striations : Number of peaks depend on the pressure and electrode size. AnodeCathode

Plasma Application Modeling, POSTECH Overview of XOOPIC code Overview of MAGIC code Klystron simulation using XOOPIC code Contents XOOPIC and MAGIC Codes for Electromagnetic Field S.J. Kim and J.K. Lee

Plasma Application Modeling, POSTECH Simulation Domain of Klystron RF input port RF output port E-beam Cylindrical Axis cm13.07 cm 9.55 cm 37.2 cm cm 6.66 cm Simulation condition: Beam emitter: I= 12 kA, u d =2.48e8 m/s Input port : Rin=2300 , R=20 , f=7.69 GHz Output port : R= 

Plasma Application Modeling, POSTECH Example of Klystron Simulation Phase spaceDensity Kinetic energy uz

Plasma Application Modeling, POSTECH Simulation Results at 0.5 ns

Plasma Application Modeling, POSTECH Simulation Results at 2.5 ns

Plasma Application Modeling, POSTECH Simulation Results at 10 ns

Plasma Application Modeling, POSTECH Simulation Results at 20 ns

Plasma Application Modeling, POSTECH Simulation Results at 6 us

Plasma Application Modeling, POSTECH KE as a Function of Beam Current

Plasma Application Modeling, POSTECH KE as a Function of Beam Energy

Plasma Application Modeling, POSTECH 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.

Plasma Application Modeling, POSTECH Program Flow Defined region of the discrete model Electromagnetic fields on the meshDiscretization mesh Group of similar particles Individual particle (position, momentum, mass, charging, numerical weight)

Plasma Application Modeling, POSTECH Maxwell’s Equations for Electromagnetic Field Maxwell’s equations in integral form C -1, L -1 : coupling matrices with the dimemsionality of capacitance and inductance. Nonuniform orthogonal Yee mesh

Plasma Application Modeling, POSTECH Maxwell Curl Equations Transverse magnetic (TM) setTransverse electric (TE) set The TM and TE field equations are advanced in time using a leap frog advance. The currents result from charged particle motion.

Plasma Application Modeling, POSTECH Velocity Advance Half acceleration: Rotation: Half acceleration: Relativistic Boris advance

Plasma Application Modeling, POSTECH Charge Conserving Current Weighting Algorithm Charge conserving current weighting =

Plasma Application Modeling, POSTECH Overview of MAGIC Code Uniform grid Manual grid Appended regions Polynomial smoothly varying grid Pade smoothly varying grid Resistive Dielectric Conductors Scattering foil Polarizer sheet Helix element General current source Air chemistry Semiconductor Cartesian coordinates Polar coordinates Cylindrical coordinates Spherical coordinates Mirror symmetry boundary Periodic symmetry boundary Absorbing boundary Outgoing wave boundary Applied voltage boundary External circuit voltage source Particle and field import Standard leapfrog Time-reversible leapfrog Semi-implicit Standard noise filtering High-Q noise filtering Quasistatic Electrostatic ADI Electrostatic SOR Externally specified magnet field Restricted TE or TM modes GridMaterials GeometryField 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 Maxwell’s equations on a finite-difference grid for electromagnetic field Electromagnetic computational processing cycle MAGIC code

Plasma Application Modeling, POSTECH Method and Noise Leapfrog time integration schemeWell-centering Particle-induced noise is introduced through the current term in Maxwell’s equations. Propagating, wave-like, electromagnetic nose Large curl derivatives Time-biased and high-Q algorithms Spatial fluctuations in space charge and the Gauss’s law constraint The slow, self-heating instability Charge allocation algorithm Transverse particle noiseLongitudinal particle noise

Plasma Application Modeling, POSTECH Time-Biased Algorithm Time-biased algorithm : semi-implicit scheme a 1, a 2, and a 3 determine the degree of spatial filtering and the time-centering.  i : iteration coefficient  =k/k max : normalized eigenmode k max : maximum spatially-resolvable Fourier wave number

Charge Conservation Scheme Boris-DADI correction Langdon-Marder correction

Plasma Application Modeling, POSTECH Klystron Phase spaceDensity Kinetic energy uz 2 cm 3 cm

Plasma Application Modeling, POSTECH Simulation Results at 0.5 ns and 2.5 ns

Plasma Application Modeling, POSTECH Simulation Results at 10 ns and 20 ns

Plasma Application Modeling, POSTECH Simulation Results at 6 us