childLangmuirVelGen

childLangmuirVelGen

Velocity generator that determines the weight of the particles (and therefore the current) based on the Child-Langmuir Law. The current is simply calculated to vary linearly with the normal \(E\) field. Ampere’s law is solved, recognising that this represents the case where at the nearby virtual cathode surface \(E=0\), as this represents the potential minimum.

childLangmuirVelGen Parameters

reduction (option)

The factor by which emitted current is reduced. e.g. if reduction = 0.1 then you emit 1/10 the child-langmuir current. Reduction = 1.0 is the full child-langmuir current

STFunc (block, option)

STFunc Block with function name specifying component#, where ‘#’ is the component number (0,1,2, …) for each velocity component you wish to specify.

The component# space-time function blocks are specified like any other Vorpal space-time function block, and the value of this function (depending on the position and time of the particle’s placement at load or emission time) is used to determine the value of the specified component of the velocity.

useChildLangmuirLaw (option)

True/False option to allow for space charge limited emission. If false the emitted current will be eps0*E_normal/dt, while if true the emitted current is 4/9*epsilon0*sqrt(2*q/m)*(E_normal*dx)^(3/2)/(dx^2) where dx is the distance between the zeroth node and first node from the emitter. This limits space charge as if the potential on each side of the cell were fixed, and will proivde a higher accuracy density, potential and current density. Without this an oscillation can be seen in the emitted current

childLangmuirVelGen Example Block

<VelocityGenerator emitVelGen>
  kind = childLangmuirVelGen
  reduction = 0.1 #1.0e-3

  # Optionally set individual components of the velocity with STFunc blocks
  <STFunc component0>
    kind = expression
    expression = -2.0e5
  </STFunc>
</VelocityGenerator>