Space-Charge Limit in Atmospheric Plasma
Wes Faler
current density in plasma at normal atmospheric density?
For typical plasma work, there are several assumptions that prevent
the standard sheath equations from being used. First is the
assumption that the electron temperature is very large compared to the
local voltage (q*Voltage << k*TempElectron). The Debye length is
based on this assumption and is used in the general, non-analytical
form of the sheath equations I've seen. For high densities of ions
and neutrals, such as in air, electrons do not accumulate very large
velocities in response to fields and do not react as quickly to charge
imbalances, thus changing the typical Debye shielding behavior.
The second assumption made is that the plasma is collisionless. With
this assumption, it is possible to relate velocity, through kinetic
energy, to the change in voltage for a sheath. That is: charge*
VoltageDifference = (1/2)*mass*velocity^2. This relation is the
foundation for the Child-Langmuir equation that gives the maximum
current density as a function of geometry, voltage, and ion density.
As we know from our lifter work, plasma at atmospheric conditions is
far from collisionless and velocity is a statistical average, the
"drift velocity", and a nearly-linear relationship to the local
electric field. It's a shame too because the Child-Langmuir equation
works where q*Voltage >> k*TempElectron.
I've tried following the Child-Langmuir methodology, altering the
differential equation to reflect the new voltage/velocity relation but
so far haven't found a solvable equation.
Any suggestions? I'm going to build a device for testing of course,
but would like some equations to know what to expect should the device
not work upon first powerup.
-Wes