  In contemporary sub-stellar model atmospheres, dust growth occurs through
neutral gas-phase surface chemistry. Recently, there has been a growing body of
theoretical and observational evidence suggesting that ionisation processes can
also occur. As a result, atmospheres are populated by regions composed of
plasma, gas and dust, and the consequent influence of plasma processes on dust
evolution is enhanced. This paper aims to introduce a new model of dust growth
and destruction in sub-stellar atmospheres via plasma deposition and plasma
sputtering. Using example sub-stellar atmospheres from Drift-Phoenix, we have
compared plasma deposition and sputtering timescales to those from neutral
gas-phase surface chemistry to ascertain their regimes of influence. We
calculated the plasma sputtering yield and discuss the circumstances where
plasma sputtering dominates over deposition. Within the highest dust density
cloud regions, plasma deposition and sputtering dominates over neutral
gas-phase surface chemistry if the degree of ionisation is $\gtrsim10^{-4}$.
Loosely bound grains with surface binding energies of the order of $0.1-1$ eV
are susceptible to destruction through plasma sputtering for feasible degrees
of ionisation and electron temperatures; whereas, strong crystalline grains
with binding energies of the order $10$ eV are resistant to sputtering. The
mathematical framework outlined sets the foundation for the inclusion of plasma
deposition and plasma sputtering in global dust cloud formation models of
sub-stellar atmospheres.
