1. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn INTI International University, Nilai, Malaysia Institute for Plasma Focus Studies, Melbourne Australia

2. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn Parameters of a PF Numerical Experiments – an example PF1000 Step I - Fit Computed Current (CC) to Measured Current(MC) Obtain all parameters and a Measured Current Configure the code Add Measured Current Fire, compare Computed Current(CC) to MC Vary parameters until CC fits MC Step II – PF1000 Y n vs P Configure code at 27kV, 3.5 Torr D using parameters fitted in Part I Run at various P for D gas Collect Computed data and current waveforms Interpret results and notes Various NE Projects Conclusion

3. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn Bank: L 0 (static inductance), C 0 (capacitance), r 0 (resistance) Tube: b (cathode radius), a (anode radius), z 0 (anode length) Model: f m (axial mass), f c (axial curr), f mr (radial mass), f cr (radial current factor) Note: In yellow: typically not given, to be fitted from measured current waveform International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

4. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn Steps I: Obtain all parameters of PF1000 1.Require a measured current waveform - obtain this current waveform and record the parameters which are given 2.Configure the code as the PF1000 using given parameters; note those parameters that are not certain or guessed 3.Fire the PF1000, compare computed current waveform with measured current waveform 4.Fit computed waveform to measured waveform a) Fit current rise slope, adjust static inductance L 0 where necessary b) Fit position of start of dip adjusting f m and f c as necessary c) Fit slope of dip, adjusting f mr, f cr as necessary

5. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn 1.Require a measured current waveform - obtain this current waveform and record the parameters which are given Usually digital file (from DSO) is available in two columns In the case of PF1000 we do not have a digital file, but there is a published waveform in a published paperpublished waveform We had digitised the waveform using a freeware digitising software called EngaugeEngauge

6. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn PF1000:published waveform and digitised waveform

7. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn Start Configuration Given:L 0 (nH)C 0 (µF)b (cm)a (cm)z 0 (cm)r 0 (mΩ) 2013321611.55606 fmfcfmrfcr 0.10.70.20.7 V 0 (kV)P 0 (Torr)MWAAtom-molecule 273.5412

8. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn Fire the PF1000, compare Computed Current waveform with Measured Current waveform

9. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn ( toggle to radpf5.15de to show published waveform, digitised waveform Import PF1000data) Initial configuration set to published value of 20nH, guesses r0=6 mΩ Set model parameters at guessed values 0.1, 0.7, 0.2, 0.7 Fit: L0 from slope and top of current profile fm from start of dip, without changing fc from 0.7 if possible fm from start of dip, without changing fc from 0.7 if possible fmr from downward slope of dip and depth of dip) fmr from downward slope of dip and depth of dip) Fire the PF1000, compare computed current waveform with measured current waveform

10. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn Fire the PF1000, compare Computed Current waveform with Measured Current waveform

11. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

12. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

13. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

14. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

15. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

16. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

17. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

18. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

19. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

20. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

21. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

22. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn Fitting PF1000 27kV-adjusting model parameters until computed current waveform matches measured (after getting L 0 correct)

23. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn PF1000 fitted results

24. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn Step I.4 Fit computed waveform to measured waveform a) Fit current rise slope, adjust static inductance L 0 where necessary b) Fit position of start of dip adjusting f m and f c as necessary c) Fit slope of dip, adjusting f mr, f cr as necessary

25. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn The Universal PF code: RADPFV5.15deRADPFV5.15de Configure: for PF1000: 27 kV 3.5 Torr D 2 (published and fitted)

26. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn The Universal PF code: RADPFV5.15deRADPFV5.15de Configure: for PF1000: 27 kV 3.5 Torr D 2 (published and fitted) [ run 100000 Torr, 19, 10, 7, 5, 2, 1 Torr; at 7 Torr show how to collect cols A and B (for curr waveform) and how to collect dataline.]

27. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn The Universal PF code: RADPFV5.15deRADPFV5.15de Configure: for PF1000: 27 kV 3.5 Torr D 2 (published and fitted) [ run 100000 Torr, 19, 10, 7, 5, 2, 1 Torr; at 7 Torr show how to collect cols A and B (for curr waveform) and how to collect dataline.]

28. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn Steps: II Run PF1000 at 27 kV at various pressure in D; Collect data 1. Collect current waveforms 2. Collect data of dynamics and pinch properties and neutron yield

29. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn RADPFV5.15de Look at results: Sheet 1 figures Sheet 3 dataline Sheet 3 (1) figures

30. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn RADPFV5.15de Look at results: Sheet 1 figures Sheet 3 dataline Sheet 3 (1) figures

31. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

32. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

33. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

34. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

35. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

36. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

37. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

38. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn Steps: III Interpret results of experiments 1. Show a set of current waveform at various pressures 2. Show a set of pinch properties as a function of data Discuss decrease of I peak as operation pressure P 0 is decreased in terms of dynamic resistance Observe behaviour of I pinch as pressure is decreased Observe neutron yield Y n as function of pressure Discuss the behaviour of Y n vs P 0 in terms of behaviour of I pinch and pinch ion density.

39. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn 1) Pressure increases, Ipeak increases 2) Ipinch increases, peaks just before 5 Torr, then drops EINP follows roughly trend of Ipinch ni, not plotted, seen from table to increase continuously with presssure Yn peaks not where Ipinch peaks, but at higher P due to increase in ni All Competing effects need to be considered The effects, all regulated by the physics, are automatically included in the model

40. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn Different machines- including your own and others Different gases- D-T mixture for neutrons Neon for neon SXR Ar, N 2, O 2 for SXR Compare with experimental results- see examples below

41. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn 1.Fit computed to measured current waveforms to get model parameters 2. Use these fitted model parameters for PF400J to get Y n at various pressures 3. Compare computed with measured Y n (agreement is state-of-the-art)

42. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn 1.fit computed to measured current waveforms to get model parameters 2. Use these fitted model parameters for FN-II to get Y n at various pressures 3. Compare computed with measured Y n (agreement is state-of-the-art)

43. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn We carried out a Numerical Experiment – To obtain neutron yield Yn of PF1000 as function of pressure, and relate to pinch data We started with a published current waveform of the PF1000 at 27 kV. We carried out a typical fitting (of computed to measured current waveform) to obtain L0 and the model parameters for the PF1000. With the complete parameters of the PF1000 we ran experiments for the PF1000 at 27 kV varying the pressure from 19 Torr down to 1 Torr deuterium. We collected the current waveforms and pinch parameters; at various pressures and obtained the neutron yield Yn with pressure P0 curve. The shape of the neutron yield curve was correlated to the behaviour of the pinch current and pinch density. We noted that the peak neutron yield at 2x1011 is consistent with the measured range of neutrons as published. As an extension to the experiment, we compared the computed Yn vs P0 curve to the published curves for several machines including PF-400J and FN-II. y y. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

44. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn THANK YOU Simple Profound Research Projects developed from Plasma Focus Numerical Experiments