ECE490O: Special Topics in EM-Plasma Simulations JK LEE (Spring, 2006)

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

3. Computational Eng./Sci.

4. ECE490O: PIC & FEMJK LEE (Spring, 2006)

6. PIC Overview • PIC Codes 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.

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

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

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

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

14. 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

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

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

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

18. Plasma Application Modeling, POSTECH Simulation Domain of Klystron RF output port RF input port 9.55 cm 10.05 cm 13.07 cm E-beam 7.569 cm 6.66 cm Cylindrical Axis 37.2 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 

19. Plasma Application Modeling, POSTECH Example of Klystron Simulation Phase space Density uz Kinetic energy

20. Plasma Application Modeling, POSTECH Simulation Results at 0.5 ns

21. Plasma Application Modeling, POSTECH Simulation Results at 2.5 ns

22. Plasma Application Modeling, POSTECH Simulation Results at 10 ns

23. Plasma Application Modeling, POSTECH Simulation Results at 20 ns

24. Plasma Application Modeling, POSTECH Simulation Results at 6 us

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

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

27. Plasma Application Modeling, POSTECH Overview of XOOPIC Code XOOPIC Features • 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. * Values of gridded quantities can be approximated at intermediate points by interpolation.

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

29. 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

30. Plasma Application Modeling, POSTECH Maxwell Curl Equations Transverse magnetic (TM) set Transverse 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.

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

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

33. Plasma Application Modeling, POSTECH Overview of MAGIC Code MAGIC code Grid Materials Resistive Dielectric Conductors Scattering foil Polarizer sheet Helix element General current source Air chemistry Semiconductor • Particle-in-cell (PIC) approach • Maxwell’s equations on a finite-difference • grid for electromagnetic field Uniform grid Manual grid Appended regions Polynomial smoothly varying grid Pade smoothly varying grid Electromagnetic computational processing cycle Geometry Field algorithm 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 • 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

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

35. Plasma Application Modeling, POSTECH Time-Biased Algorithm Time-biased algorithm : semi-implicit scheme a1, a2, and a3 determine the degree of spatial filtering and the time-centering. i : iteration coefficient =k/kmax : normalized eigenmode kmax : maximum spatially-resolvable Fourier wave number

36. Charge Conservation Scheme Langdon-Marder correction Boris-DADI correction

37. Plasma Application Modeling, POSTECH Klystron 3 cm 2 cm Phase space Density uz Kinetic energy

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

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

40. Plasma Application Modeling, POSTECH Simulation Results at 6 us