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

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!

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

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’

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.

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

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

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

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

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

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