1. PIC Code-to-Code Benchmarking Efforts
Helga Timkó
In collaboration with Sandia National Laboratories
Helga Timkó

2. Background
Paul Crozier and Matt Hopkins from Sandia National Labs contacted me 1.5 years ago to start a collaboration on PIC plasma modelling of vacuum arcs
Their motivation: ignition mechanisms; interest in:
Full current-voltage-characteristic
Long-term evolution of arcs
Not necessarily UHV arcs
Their experiments: Te and ne measurements of the plasma via laser-induced excitation
We could only profit by a collaboration on experiments!

3. Codes used for comparison
1D Arc-PIC (IPP); serial 1d3v electrostatic PIC/MCC
Poisson solver: tridiagonal matrix Thomas algorithm, FDM
Particle pusher: Boris method
Cloud-in-cell field interpolation and charge assignment
Collisions based on the direct Monte Carlo algorithm
Aleph (Sandia); 2D/3D parallel electromagnetic PIC/DSMC, run in 2D mode
Unstructured triangular mesh
Dynamic particle weighting (not used for this comparison)
Solver: FEM, pusher: velocity Verlet
Both 0th and 1st order field interpolation/charge assignment

4. Comparison problem
Konstantin’s simple model with constant e- and Cu injection fluxes  reaches a ‘steady-state’ after breakdown
Main comparison quantity: time-to-breakdown, which we define as
‘the first time when the saturated current density is reached’

5. Results: Influence of ionisation collisions
1D Arc-PIC: modified null-collision method
Linear interpolation of cross-section data
Aleph: no-time-counter method
Linear or logarithmic interpolation of cross-section data
Unveiled a bug in the Aleph NTC implementation
Realised that the details of the ionisation collision can influence the tBRD significantly (> 10 %)
Interpolation of cross-section data
Extrapolation outside measurement data
Threshold energy
Etc.

6. Results: Influence of PIC methodology
Made some seemingly controversial observations;
Aleph results did not converge with decreasing weighting
Simple ionisation rate tests agreed perfectly
It turned out that Paul used the 0th order field interpolation and charge assignment scheme
Poorly resolved E-field causes incorrect acceleration
Incorrect acceleration leads to incorrect relative velocities during collisions
Ionisation rates deviate
Time-to-breakdown altered

7. Some messages... No. 1
Overall behaviour is the same

8. Some messages... No. 2
Perfect match in current densities when 1D field solver is used in Aleph

9. Some messages... No. 3
Long-term average densities deviate (due to inlet schemes?)

10. Some messages... No. 4
Time-to- breakdown is influenced by almost all the PIC methodology...

11. Conclusions and outlook
The biggest profit for us was to realise that it is practically impossible to get quantitative predictions;
Independent of the physics model, the time-to-breakdown depends on the choice of methods, which should not influence the results at all!
As for the future,
Sandia would like to continue comparison with a more realistic physics model (to be taken over by my successor)
They offered help in implementing dynamic particle weighting in 2D Arc-PIC; could be of much use for us
We might want to establish a collaboration on experiments