New plasma systems are expensive to create and operate.  Therefore, modeling of plasma systems by computer simulation is increasingly required in order to demonstrate that a proposed system is likely to succeed before it is ever funded to be built.  Until now, the level of approximation of simulated plasma systems due to the limits of computer power were such that the interactions of the plasma with the walls of its container were small enough to be ignored.  However, we have reached a point with plasma models that in order to improve any further we must consider interactions with the walls as well as interactions between particles within the bulk of the plasma.  Fortunately, computer power has increased enough to begin to make such simulations possible.

For a plasma contained within a vessel, the surfaces of the inner wall that interact with the plasma are called plasma-facing components (PFCs).  The product of this thesis will be a model that predicts erosion rates of PFCs.  Additionally, the model will be used as a tool to explore whether material emitted from PFCs in vapor form can act as a shielding barrier that is able to partially protect the PFC from heat related damage.

In a plasma, some or all of the constituent particles are charged.  The motions of the charged particles are affected by electric and magnetic fields.  The changing positions of the particles also change the electric field itself.  Simulating the interaction of each particle with every other particle would be impractical, so we will instead track the electric potential in a grid and the particles will affect and will be affected by the electric potentials of the grid.  This type of simulation is called a particle-in-cell (PIC).  We will track position in only a single spatial dimension, however we will track velocities in three dimensions (1D3V PIC).

In the plasmas that we will simulate only a small fraction of a neutral gas is ionized.  The ions are tracked individually, however the neutral particles are modeled only as a constant density background.  In some simulations electrons are also tracked individually.  However, we will instead treat the locations of electrons as a Boltzmann distribution that is created in response to the corresponding distribution of the ions.

A collision my occur between any pair of particles.  Since fraction of the gas that is ionized is small, the fraction of collisions that are electron-electron, electron-ion or ion-ion are small enough to be ignored.  Only collisions involving neutral particles will be considered.  For a collision of an ion into a neutral, the position of the neutrals are not tracked.  Therefore, a determination of how many collisions should occur within a unit of  time is calculated and then that many ions are selected at random to have been the ones that collided.  A similar process occurs for a collision of an electron into a neutral, however neither particle position is tracked, so only the collective properties such as temperature are affected.  When particles collide, one of a set of interactions occurs.  Each interaction has a probability of occurring and the interaction which does occur is random based on the probabilities.  The method of handling collisions that we will use is called a Monte Carlo collision operator (MCC) with null collision method.  When used with the 1D3V PIC, the system is called a 1D3V PIC MCC.

Others have already created 1D3V PIC MCC simulations, so we will compare our implementation to published results [Turner].  Ion and electron collisions will depend on published cross-sections that are dependent on the energy of the incoming particle (actually based on the relative velocities of the colliding particles, but the kinetic energy of the neutral target is negligible).

Particle interactions with the wall surface are similar in behavior to interactions that occur within the plasma, however the surface interactions depend on the temperature of the wall in addition to the properties of the incoming particle.  The temperature of the wall depends on the previous interactions of the plasma with the wall, therefore the wall requires its own model for the heat transport.  We will rely on published emission behaviors of surfaces in this work rather than repeating that time-consuming work.

Particles that leave the surface of the wall become impurities in the plasma.  Impurities tend to cool a plasma.  In the central bulk of the plasma, impurities can quickly interfere with the processes that maintain the plasma state.  However, if the impurities remain close to the surface, the same impurities and processes may instead protect the wall surface from damage by reducing the heat flux from the plasma.  There is already evidence that vapor shielding may occur, however the amount of shielding provided by particular combinations of wall material and plasma fuel remains a topic for exploration.  This work intends to provide predictions of the amount of heat flux reduction in conditions as would be seen at a divertor.