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📄 afterb_li.inp

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afterB_Li.inp{High-energy electron bunch enters a quiet plasma in cylindrical geometry --Modeling the SLAC "afterburner" concept of Tom Katsouleas.Tunneling ionization effects are ignored..Collisional effects are ignored for both beam and plasma electrons.This simulation models a beam-plasma wake-field accelerator:a)  The background plasma is pre-ionized.  Ions are assumed stationary.b)  Beam density exceeds electron plasma density, so the beam "blows out"    plasma electrons near the symmetry axis.c)  The electron beam is Gaussian in z and r.d)  The electron beam is overfocussed by these fields and so executes    betatron oscillations;  however, the focussing force varies axially.Moving window:a)  Once the electron beam has entered the grid and is close to the far    edge of the simulation region, a moving window algorithm is invoked    so that the beam can be modeled for long times.Boundary conditions:a)  The simulation region must be bounded by either conductors or    insulators, in order to capture lost particles.b)  Conductors were chosen, to avoid any charge build up.c)  The choice of conducting boundary conditions means that electric    fields parallel to the boundaries are forced to zero;  however,    fields near the boundaries of the simulation must be small anyway    to accurately model a semi-infinite plasma, so this is OK.}// Define variables that can be used throughout this input file.Variables{// First, define some useful constants.  pi = 3.14159  speedOfLight = 2.998e+08  unitCharge = 1.602e-19  electronCharge = -1 * unitCharge  electronMass = 9.1095e-31  electronMassEV = electronMass * speedOfLight * speedOfLight / unitCharge  ionCharge = unitCharge  unitMassMKS = 1.6606e-27  lithiumMassNum = 6.942  lithiumMass = unitMassMKS * lithiumMassNum// Next, define the parameters of the high-energy electron beam.  beamEnergyEV = 50.0e+09  beamTempEV = 0.0  thermalBeamSpeedEV = 0.5 * beamTempEV  totalNumBeam = 2.0e+10  totalBeamCharge = totalNumBeam * electronCharge  rmsBeamRadius = 20.e-06  rmsBeamLength = 63.e-06  rmsBeamTime = rmsBeamLength / speedOfLight  radialCutoffFac = 3  axialCutoffFac = 3  totalBeamRadius = radialCutoffFac * rmsBeamRadius  totalBeamLength = 2 * axialCutoffFac * rmsBeamLength  beamAspectRatio = totalBeamLength / totalBeamRadius  totalBeamArea = pi * totalBeamRadius * totalBeamRadius  rmsBeamVolume = pi * rmsBeamRadius * rmsBeamRadius * rmsBeamLength//	rmsBeamEmittanceNormPiMRad = 1.25e-04// Define the number of grids in R and Z  lengthOverRadiusAspectRatio = 3  simRadiusOverBeamRadius = 8  numRgridsAcrossBeam = 8  numZgridsAcrossBeam = numRgridsAcrossBeam * beamAspectRatio  numRgrids = numRgridsAcrossBeam * simRadiusOverBeamRadius  numZgrids = numRgrids * lengthOverRadiusAspectRatio  numCells = numRgrids * numZgrids// Number of beam particles  numBeamPtclsPerCell = 100  numBeamCells = numRgridsAcrossBeam * numZgridsAcrossBeam  numBeamPtcls = numBeamPtclsPerCell * numBeamCells  beamNumRatio = totalNumBeam / numBeamPtcls// Intermediate calculations for modeling Gaussian shape of the beam.  invSigRsq = 1.0 / ( rmsBeamRadius * rmsBeamRadius )  invSigZsq = 0.5 / ( rmsBeamLength * rmsBeamLength )  invSigTsq = invSigZsq * speedOfLight * speedOfLight// Calculate the size of the simulation region, grid spacings, time step.// We are assuming the same grid size in both z and r	  maxRadiusMKS = simRadiusOverBeamRadius * totalBeamRadius  rGridSize = maxRadiusMKS / numRgrids  zGridSize = rGridSize  maxLengthMKS = numZgrids * zGridSize  timeStep = 0.5 * rGridSize / speedOfLight// This is the desired delay time before the moving window algorithm activates.  movingWindowDelay = 0.97 * maxLengthMKS / speedOfLight// Calculate peak currents for defining emission of the high-energy beam.  peakCurrentDensity=totalBeamCharge*speedOfLight/rmsBeamVolume/sqrt(2.*pi)  peakCurrent = peakCurrentDensity * totalBeamArea  pulseLengthSec = totalBeamLength / speedOfLight  oneHalfPulse = pulseLengthSec/2.  oneEighthPulse = pulseLengthSec/8.  threeEighthsPulse = 3.*oneEighthPulse  sevenEighthsPulse = 7.*oneEighthPulse// Define the plasma density, number of plasma electron macro-particles, etc.  plasmaDensityMKS = 1.8e+22  simulationVolume = pi * maxRadiusMKS * maxRadiusMKS * maxLengthMKS  totalNumPlasma = plasmaDensityMKS * simulationVolume  numPtclsPerCell = 8  numPlasmaPtcls = numPtclsPerCell * numCells  plasmaNumRatio = totalNumPlasma / numPlasmaPtcls}// This simulation has only one "region", which contains grid, all particles, etc.Region{// Define the grid for this region.Grid{// Define number of grids along Z-axis and physical coordinates.  J = numZgrids  x1s = 0.0  x1f = maxLengthMKS  n1 = 1.0// Define number of grids along R-axis and physical coordinates.  K = numRgrids  x2s = 0.0  x2f = maxRadiusMKS  n2 = 1.0}// Specify "control" parameters for this regionControl{// Specify the time step.  dt = timeStep// Turn on the moving window algorithm.  movingWindow = 1  shiftDelayTime = movingWindowDelay// Turn on damping for the high-frequency EM fields  emdamping = 0.49// Turn off the initial Poisson solve  initPoissonSolve = 0// Use bilinear current weighting  CurrentWeighting=1}// Define the plasma ions.Species{  name = lithium  m = lithiumMass  q = ionCharge// advance the ions only once every 100 steps, because they//   are essentially stationary  subcycle = 100// prevent out-of-control growth in # of ptcls  particleLimit = 8.e+05}// Define the plasma electrons.Species{  name = electrons  m = electronMass  q = electronCharge// prevent out-of-control growth in # of ptcls  particleLimit = 8.e+05}// Define the beam electrons.Species{  name = beam_electrons  m = electronMass  q = electronCharge//  collisionModel = 1}// Define the beam emitter, which introduces the high-energy beam into the// simulation.VarWeightBeamEmitter{  speciesName = beam_electrons  I = peakCurrent// Define the 2-D function F(x,t) that specifies beam emission profile.  xtFlag = 3  nIntervals = 32  F=exp(-invSigRsq*x*x)*exp(-invSigTsq*(t-oneHalfPulse)*(t-oneHalfPulse))*step(pulseLengthSec-t)// Macroparticles are emitted from the left boundary, close to the axis of symmetry.  j1 = 0  j2 = 0  k1 = 0  k2 = numRgridsAcrossBeam  normal = 1  np2c = beamNumRatio// Emit particles, directed along the Z-axis,  with specified energy and temperature.  units = EV  v1drift = beamEnergyEV}// Specify a perfect conductor along the left boundary.  This serves as a particle//   boundary condition (catches particles that leave the simulation) and as a//   field boundary condition (E_r is forced to vanish).Conductor{  j1 = 0  j2 = 0  k1 = 0  k2 = numRgrids  normal = 1}// Specify a perfect conductor along the radial boundary.  This serves as a//   particle boundary condition (catches particles that leave the simulation)//   and as a field boundary condition (E_z is forced to vanish).Conductor{  j1 = 0  j2 = numZgrids  k1 = numRgrids  k2 = numRgrids  normal = -1}// Specify a perfect conductor along the right boundary.  This serves as a//   particle boundary condition (catches particles that leave the simulation)//   and as a field boundary condition (E_r is forced to vanish).Conductor{  j1 = numZgrids  j2 = numZgrids  k1 = numRgrids  k2 = 0  normal = -1}// Define the cylindrical symmetry axis.CylindricalAxis{  j1 = 0  j2 = numZgrids  k1 = 0  k2 = 0  normal = 1}// Load the plasma ions over the entire simulation region.Load{  speciesName = lithium  density = plasmaDensityMKS  x1MinMKS = 0.5*maxLengthMKS  x1MaxMKS = maxLengthMKS  x2MinMKS = 0.0  x2MaxMKS = maxRadiusMKS// This specifies a static uniform background (no macro-particles).  np2c = 0}// Load the plasma electrons over the entire simulation region, but//   leave the last dz strip of cells empty, because this strip must//   be handled separately to accomodate the moving window algorithm.VarWeightLoad{  speciesName = electrons  density = plasmaDensityMKS  x1MinMKS = 0.5*maxLengthMKS  x1MaxMKS = maxLengthMKS - zGridSize  x2MinMKS = 0.0  x2MaxMKS = maxRadiusMKS  np2c = 2 * plasmaNumRatio// Specify loading that is more uniform than random  LoadMethodFlag = 1}// Load the plasma electrons into the last dz strip of cells, which was//   omitted by the load instruction above.VarWeightLoad{// Name this load group "shiftLoad" so that the moving window algorithm//   knows to invoke it every time the simulation window is shifted.  Name = shiftLoad  speciesName = electrons  density = plasmaDensityMKS  x1MinMKS = maxLengthMKS - zGridSize  x1MaxMKS = maxLengthMKS  x2MinMKS = 0.0  x2MaxMKS = maxRadiusMKS  np2c = 2 * plasmaNumRatio// Specify loading that is more uniform than random	LoadMethodFlag = 1}}

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