two_stream_ee_es
{

This is the classic electron/electron two-stream instability, with counter-propagating electron beams
having velocities much larger than their thermal velocity.

We work in pseudo-1D geometry.  It's 2D Cartesian geometry, but the y-direction is only
2 cells across with periodic BC's.  The x-direction is long.

The field solve is electrostatic.  Hence, there is also a background distribution of ions to provide
charge neutrality.

For the theory, see Sections 5-6 and 5-7 of the classic reference
  C.K. Birdsall and A.B. Langdon
  Plasma Physics via Computer Simulation
  McGraw-Hill, 1985
}

Variables
{
// General numerical parameters
  PI = 3.14159

// **********************************************************************
// General physical parameters
// **********************************************************************
  electronMassMKS = 9.1094e-31 
  electronCharge  = -1.6022e-19
  speedLight      = 2.9979e8

  unitMassMKS     = electronMassMKS / 5.48579903e-04
  HeMassNum       = 4.0026
  HeMassMKS       = unitMassMKS * HeMassNum

  ionDensityMKS      = 1.0e+24
  electronDensityMKS = 0.5 * ionDensityMKS
  plasmaFrequency = 2.*PI*9000.*sqrt(2.e-06*electronDensityMKS)
  ds              = 0.005 * speedLight / plasmaFrequency

// **********************************************************************
// Grid parameters
// **********************************************************************
  Nx = 256
  Ny =   2
  dx =  ds
  dy =  dx
  Lx =  Nx * dx
  Ly =  Ny * dy

  simulationVolume = Lx * Ly
  numCells         = Nx * Ny

//
// streaming electrons
//
  totalNumElectrons    = electronDensityMKS * simulationVolume
  numElectronsPerCell  = 4
  numElectronPtcls     = numElectronsPerCell * numCells
  electronNumRatio     = totalNumElectrons / numElectronPtcls
  rmsElectronSpeedMKS  = 3.e+04
  electronVelocityMKS  = 1.e+07
  peakCurrentElectrons = electronCharge * electronDensityMKS * Ly * electronVelocityMKS

//
// background ions
//
  totalNumIons   = ionDensityMKS * simulationVolume
  numIonsPerCell = 4
  numIonPtcls    = numIonsPerCell * numCells
  ionNumRatio    = totalNumIons / numIonPtcls
  ionMassMKS     = HeMassMKS
  ionCharge      = -electronCharge
  rmsIonSpeedMKS = 3000.

  d = 1. / sqrt( 1./(dx*dx) + 1./(dy*dy) )
  timeStep = 0.3 * d / electronVelocityMKS
}

Region
{

Grid
{
  J = Nx 
  x1s = 0.0
  x1f = Lx 
  n1 = 1.0 
  K = Ny 
  x2s = 0.0
  x2f = Ly 
  n2 = 1.0

  Geometry = 1         // 2D (x-y) slab geometry
  PeriodicFlagX1 = 1   // periodic in x1 (x)
  PeriodicFlagX2 = 1   // periodic in x2 (y)
}

Control
{
  dt = timeStep

// Use the multigrid electrostatic field solve
  ElectrostaticFlag = 4
}

Species
{
  name = electrons
  m = electronMassMKS
  q = electronCharge 
}

Species
{
  name = ions
  m    = ionMassMKS
  q    = ionCharge

  subcycle = 10
}

// Load the cold, background ions over the entire simulation region
Load
{
  speciesName = ions
  density = ionDensityMKS
  x1MinMKS = 0.0
  x1MaxMKS = Lx
  x2MinMKS = 0.0
  x2MaxMKS = Ly
  np2c = ionNumRatio

// specify MKS units for all velocities
  units = MKS
  v1thermal = rmsIonSpeedMKS
  v2thermal = 0.
  v3thermal = 0.
}

// Load the right-going plasma electrons over the entire simulation region
Load
{
  speciesName = electrons
  density = electronDensityMKS
  x1MinMKS = 0.0
  x1MaxMKS = Lx
  x2MinMKS = 0.0
  x2MaxMKS = Ly
  np2c = electronNumRatio

// specify MKS units for all velocities
  units = MKS
  v1drift   = electronVelocityMKS
  v1thermal = rmsElectronSpeedMKS
  v2thermal = 0.
  v3thermal = 0.
}

// Load the left-going plasma electrons over the entire simulation region
Load
{
  speciesName = electrons
  density = electronDensityMKS
  x1MinMKS = 0.0
  x1MaxMKS = Lx
  x2MinMKS = 0.0
  x2MaxMKS = Ly
  np2c = electronNumRatio

// specify MKS units for all velocities
  units = MKS
  v1drift   = -electronVelocityMKS
  v1thermal = rmsElectronSpeedMKS
  v2thermal = 0.
  v3thermal = 0.
}

}