Multipacting

Problem Description

Multipacting, which is the resonant build up of secondary electrons, is often a concern in radio frequency structures. Anytime a there is an oscillating electromagnetic field across a gap between two surfaces there exists the possibility that for the right field amplitude across the gap a resonance condition will exist allowing the exponential build up of secondary electrons. A coaxial waveguide is such structure where these conditions can exist.

Input File Features

The simulation setup consists of a coaxial waveguide where an electromagnetic wave is launched at one end and then propagates down the waveguide leaving the simulation at an open boundary. The Yee electromagnetic model, along with the Dey-Mittra cut-cell algorithm, are used to model the electromagnetics in the simulation. Typically the simulation is run once without particles to determine a normalization amplitude for the wave launcher. This allows following simulations to run where it is easy to specify a specific wave amplitude.

After the wave has been established in the waveguide, we seed a ring of electrons in the center of the waveguide with electrons. We a special particle species available in VORPAL called field scale particles which allow each electron to carry a parameter that scales the electromagnetic field it sees. This allows a single simulation to sample multiple power or voltage levels letting us search multipacting resonances. This special electron species is variable weight and tagged so the electron’s trajectory as well as the population growth along that trajectory can be tracked. Using the secondary electron routines in VORPAL, every time an electron impacts the waveguide walls with an energy in the correct range, they will produce at least one secondary electron. Instead of producing more macro particles in the simulation, the electron is reemitted with its particle weight multiplied by the secondary electron yield. The field scale species does not act as a current or charge source for the electromagnetic fields so space charge effects will not be modeled with this simulation.

Several histories are used in this simulation. The power launched at the one end of the coaxial waveguide is measured with a Poynting flux history and the voltage across the coax gap is measured with a pseudo potential history. We also track the trajectories for a few electrons associated with each resonance we will identify with this simulation.

Running the Simulation

Start VorpalComposer and select File -> Clone Example. Highlight Solving Classical Physics Problems and then select Next. Highlight Multipacting Resonances and then select Choose. Create a new folder and then select Choose.

Alternativley, save the VORPAL input file, multipacting01.pre, and open in VorpalComposer.

The file should be displayed in the right pane of the Setup window. Click on the Save and Process Setup button in the lower right corner. Proceed to the run window as instructed. To run the file, click on the Run button in the lower left corner of the window. You can see the real time output of the run in the right pane.

Viewing the Output

Once instructed after the run has completed, proceed to the Visualize window to view the results. Load in the data files as instructed.

To view the multipacting resonances, click on Phase Space and then select electrons_7 for the X-axis and electrons_8 for the Y-axis. Then click on Draw.

Results

The output of the run shows the growth in the particle weight, which corresponds the electron growth for that trajectory, versus the scaling parameter, which corresponds to the voltage experienced by that electron. The plot clearly shows bands of voltage where multipacting occurs and band where it does not.

The growth in the electron population versus the voltage across the coax gap.

Further Experiments

In addition searching for multipacting resonances, it is worth investigating the generation of multiple secondary electrons at a particular voltage. This will allow for simulations of self-consistent effects such the reflection of the wave from the growing electron plasma.

Several changes need to be made to the input file to do this simulation. First the voltage level needs to be changed from 1 Volt/meter to the value for the particular resonance we are interested in. Int this case we will use 5000 Volts/meter.

$ NORM_AMP = 5000.0/75. # Produces gap voltage of 5 kV

Now we need to switch to using the standard particle species in VORPAL that is self-consistent. Then we switch the secondary electron model that produces multiple secondary electrons.

<Species electrons>

  kind   = relBoris # Uses standard self-consistent particles
  charge = ELECCHARGE
  mass   = ELECMASS
  emField = myYeeEmField

  ...
</Species>

To modify the current input file to be able to handle opposite charges requires changing only one block in the input file. The potential on the surface is currently defined by the following space-time function block.

# The secondary electron emitter
  <ParticleSource mySecondaryEmitter>
    kind = secElec   # This is the only model that generates multiple secondaries
    material = stainless
    ptclCountType = emitCounting  # Emit multiple secondaries after impacts
    ptclAbsorber = gbAbsorber
    gridBoundary = coax
  </ParticleSource>

We also need to replace the velocity generator that set the tags and scaling parameters for the previous run.

# Empty velocity generator since all velocities start at zero
<VelocityGenerator velGen>
  kind = funcVelGen
</VelocityGenerator>

Finally we add a history that tracks the total number of electrons in the simulation.

<History numElectrons>
  kind = speciesNumberOf
  species = electrons
</History>

Now if we run the simulation again as above except with these new blocks which can be found in the input file, multipacting02.pre, we get the following results.

The growth in the number electrons in the simulation.