POWER AND PARTICLE BALANCE
Results for Reduced Problem with L&K Cross Sections:
The diagnostics were gathered after the simulation reached a
steady-state.
The time interval during which the diagnostics
were gathered was about 1 microsecond.
In the previous calculation, the Jr(r) diagnostic was
incorrect and gave us a sumjdote which was larger
than the power input. This has been corrected. The
problem was two-fold:
- The ion Jr(r) was incorrectly divided by the subcycling factor.
- The other problem was that e- Jr(r) is inherently noisy.
The way we compute flux diagnostics currently does not
take into account that some particles will be crossing
cell boundaries.
For the ion Jr(r) this is no problem, since for a typical timestep,
the ions barely move. Hence, our ion flux diagnostics are very accurate.
However, for the e- J(r), a large number of electrons cross cell
boundaries for a typical timestep.
Fortunately, Jr(r) is only calculated if you run with Xgrafix (diagnostics
turned on), and
NOT when you are doing the actual physics run to get to equilibrium.
Also, in our discharges, most of the current is
in the axial direction. Net current in the r direction is
typically small. This implies that ion J(r) and e- J(r) are
very close.
To get accurate electron Jr(r) and
JdotE(r) diagnostics, reduce the time step so that barely
any electrons cross a cell boundary in a timestep.
However, for all the other diagnostics and to do the actual run
to equilibrium, it is NOT necessary to reduce the timestep.
The following link shows the effect of varying the timestep dt on
th e- Jr(r):
Jr(r) for diff. dt
Mathematica Input file to calculate Power and Particle Balance:
Input File.
CollLoss = the power loss due to inelastic and elastic collisions.
WallLoss = the power loss due to particles striking the wall.
PowInput = the volume integral of jz.Ez, or the power input from both e- and ions.
sumjdote = the volume integral of jr.Er for electrons.
sumijdote = the volume integral of jr.Er for ions.
pcreated = the number of ionization events.
pelost = the number of electrons lost to the wall.
pilost = the number of ions lost to the wall.
Below are the results. Note that as expected:
- PowInput = CollLoss + WallLoss
- pcreated = pilost = pelost
CollLoss = 0.113759 Watts
WallLoss = 0.17149 Watts
(e- WallLoss = 0.0651154 Watts; ion WallLoss = 0.106375 Watts)
CollLoss+WallLoss = 0.285249 Watts
PowInput = 0.285357 Watts
pcreated = 55051
pelost = 55082
pilost = 55196
sumjdote = -0.122507 Watts
sumijdote = 0.117928 Watts
sumjdote + sumijdote = -0.00457855 Watts
Before, I thought that there should be a match between
sumjdote and WallLoss, but that is not the case.