Overview of XOOPIC code

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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

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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.
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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
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Maxwells Equations for Electromagnetic Field
Maxwells equations in integral form
C-1, L-1 coupling matrices with the
dimemsionality of capacitance and inductance.
Nonuniform orthogonal Yee mesh
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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.
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Velocity Advance
Relativistic Boris advance

• Half acceleration

• Rotation

• Half acceleration

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Charge Conserving Current Weighting Algorithm
Charge conserving current weighting

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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
• Maxwells 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 Cylindrica
l 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 Elect
rostatic 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

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Method and Noise
Leapfrog time integration scheme
Well-centering

• Particle-induced noise is introduced through the
  current term in Maxwells equations.

Transverse particle noise
Longitudinal particle noise

• Spatial fluctuations in space charge and
• the Gausss law constraint
• The slow, self-heating instability
• Charge allocation algorithm

• Propagating, wave-like, electromagnetic nose
• Large curl derivatives
• Time-biased and high-Q algorithms

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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
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Charge Conservation Scheme
Langdon-Marder correction
Boris-DADI correction
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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 Rin2300 ?, R20 ?, f7.69 GHz
• Output port R47.124 ?

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Example of Klystron Simulation
Phase space
Density
Kinetic energy
uz
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Simulation Results at 0.5 ns
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Simulation Results at 2.5 ns
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Simulation Results at 10 ns
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Simulation Results at 20 ns
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Simulation Results at 6 us
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KE as a Function of Beam Current
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KE as a Function of Beam Energy
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Klystron
3 cm
2 cm
Phase space
Density
Kinetic energy
uz
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Simulation Results at 0.5 ns and 2.5 ns
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Simulation Results at 10 ns and 20 ns
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Simulation Results at 6 us