1. Seminar on Plasma Focus Experiments SPFE2010 Use of current measurements to interpret plasma focus properties and mechanisms S Lee, S H Saw INTI International University, Nilai, Malaysia Institute for Plasma Focus Studies, Melbourne, Malaysia, Singapore Nanyang Technological University, NIE, Singapore

2. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Outline The Lee model code and its contributions to landmark plasma focus understanding The Lee model code and its contributions to landmark plasma focus understanding Use of the code to reference diagnostics Use of the code to reference diagnostics Current waveforms show necessity to classify PF’s into T1 and T2 Current waveforms show necessity to classify PF’s into T1 and T2 T2 shows necessity to model 6 th phase ie Phase 4a T2 shows necessity to model 6 th phase ie Phase 4a Product of this fitting is the magnitude and temporal form of anomalous resistance. Product of this fitting is the magnitude and temporal form of anomalous resistance.

3. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Insights 1/3 The Lee model code has produced ground-breaking insights no other plasma focus codes has been able to produce The Lee model code has produced ground-breaking insights no other plasma focus codes has been able to produce

4. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 For Example: Ground-breaking Insights published 2/3 Limitation to Pinch Current and Yields- Appl Phys Letts. 92 (2008) S Lee & S H Saw: an unexpected, important result Limitation to Pinch Current and Yields- Appl Phys Letts. 92 (2008) S Lee & S H Saw: an unexpected, important result Neutron Yield Scaling-sub kJ to 1 MJ- J Fusion Energy 27 (2008) S Lee & S H Saw- multi-MJ - PPCF 50 (2008) S Lee Neutron Yield Scaling-sub kJ to 1 MJ- J Fusion Energy 27 (2008) S Lee & S H Saw- multi-MJ - PPCF 50 (2008) S Lee Neon Soft x-ray Scaling- PPCF 51 (2009) S Lee, S H Saw, P Lee, R S Rawat Neon Soft x-ray Scaling- PPCF 51 (2009) S Lee, S H Saw, P Lee, R S Rawat Neutron Yield Saturation- Appl Phys Letts. 95 (2009) S Lee Neutron Yield Saturation- Appl Phys Letts. 95 (2009) S Lee simple explanation of major obstruction to progress for a generation simple explanation of major obstruction to progress for a generation

5. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Others papers we published using the Lee model code numerical experiments 3/3 Techniques: of Pinch current from total current measurements, in-situ determination of bank parameters (2 papers 2008, 2010) ; numerical experiments applied to specific machines (3 papers 2009); soft x-rays from nitrogen and oxygen (4 papers with Syrian AEC 2009, 2010)

6. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 The 5-phase Lee Model code 1/4 Includes electrodynamical- and radiation- coupled equations to portray the REGULAR mechanisms of the axial (phase 1), radial inward shock (phase 2), radial RS (phase 3), slow compression radiation phase (phase 4) & the expanded axial post-pinch phase (phase 5) Includes electrodynamical- and radiation- coupled equations to portray the REGULAR mechanisms of the axial (phase 1), radial inward shock (phase 2), radial RS (phase 3), slow compression radiation phase (phase 4) & the expanded axial post-pinch phase (phase 5) Relates to physical reality through a measured current trace Relates to physical reality through a measured current trace

7. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Given any plasma focus machine: e.g. PF1000 (biggest PF in the world) 2/4 Bank parameters: L 0 =33nH; C 0 =1332uF; r 0 =6 m  Bank parameters: L 0 =33nH; C 0 =1332uF; r 0 =6 m  Tube parameters: b=16 cm, a=11.55 cm, z 0 =60cm Tube parameters: b=16 cm, a=11.55 cm, z 0 =60cm Operation parameters: V 0 =27kV, P 0 =3.5 Torr in D2 Operation parameters: V 0 =27kV, P 0 =3.5 Torr in D2 The UPFLF (Lee code) is configured (by keying figures into the configuration panel on the EXCEL sheet) as the PF1000 Output of code: PF1000 current waveform PF1000 dynamics & electrodynamics PF1000 dynamics & electrodynamics PF1000 plasma pinch dimensions & characteristics PF1000 plasma pinch dimensions & characteristics PF1000 neutron & Radiation yields PF1000 neutron & Radiation yields

8. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 1997 ICDMP (International Centre for Dense Magnetised Plasmas) established in Warsaw-now operates one of biggest plasma focus in the world, the PF1000 1997 ICDMP (International Centre for Dense Magnetised Plasmas) established in Warsaw-now operates one of biggest plasma focus in the world, the PF1000

9. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Connection of model with Reality is by means of a measured current waveform 3/4 The computed current waveform is fitted to the measured current waveform by adjusting 4 physical parameters: The computed current waveform is fitted to the measured current waveform by adjusting 4 physical parameters: f m & f c : mass swept up & current factor; axial phase f m & f c : mass swept up & current factor; axial phase f mr & f cr : mass swept up & current factors : radial phase f mr & f cr : mass swept up & current factors : radial phase 5-point fit: rising slope, topping profile, peak value, slope of dip, depth of dip

10. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Once fitted: model is energy-wise & mass-wise & equivalent to the physical situation 4/4 All dynamics, electrodynamics, radiation, plasma properties and neutron yields are realistically simulated; so that the code output of these quantities may be used as reference points for diagnostics All dynamics, electrodynamics, radiation, plasma properties and neutron yields are realistically simulated; so that the code output of these quantities may be used as reference points for diagnostics

11. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Diagnostics-Time histories of dynamics, energies and plasma properties computed by the code Last adjustment, when the computed I total trace is judged to be reasonably well fitted in all 5 features, computed times histories are presented (NX2 operated at 11 kV, 2.6 Torr neon) Computed Itotal waveform fitted to measured Computed Tube voltage Computed Itotal & Iplasma Computed axial trajectory & speed

12. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010

13. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 piston

14. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 All well-published PF machines are well-fitted: see following examples and many others; note: the fit for the axial phase, and for the radial phase 1/4

15. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Except one 2/4 UNU ICTP PFF- famed low-cost sharing network; current signal noisy and dip is small; difficult to judge the fitting-suspected ill-fit UNU ICTP PFF- famed low-cost sharing network; current signal noisy and dip is small; difficult to judge the fitting-suspected ill-fit Low cost- necessitates single capacitor- hence high inductance L 0 Low cost- necessitates single capacitor- hence high inductance L 0

16. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Recently KSU commissioned a machine; a modernised version of the UNU ICTP PFF 3/4 A good Rogowski system was developed to measure dI/dt; which was then numerically integrated resulting in a clean current signal- A good Rogowski system was developed to measure dI/dt; which was then numerically integrated resulting in a clean current signal- Best fit nowhere near the fit of the well-published machines- in fact clearly could only fit a small portion of the radial phase

17. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 A study followed; resulting in classifying plasma focus devices into T1 & T2 4/4 Differentiator: L 0 Better Differentiators: R L =(L 0 +L a )/L p R EL =(E L0 +E La )/ ELPinch

18. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Physical explanation 1/2 RD mechanism for pinch purely compressive RD mechanism for pinch purely compressive At end of RD (call this REGULAR DIP), expts show other effects eg instabilities leading to anomalous resistance- these mechanisms not modelled by 5-phase Lee code At end of RD (call this REGULAR DIP), expts show other effects eg instabilities leading to anomalous resistance- these mechanisms not modelled by 5-phase Lee code These anomalous resistive effects will absorb further energy from pinch; will result in further current dips- called EXTENDED DIP, ED These anomalous resistive effects will absorb further energy from pinch; will result in further current dips- called EXTENDED DIP, ED

19. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Our studies further concluded 2/2 T1: Small L 0 lead to big RD and relatively small ED T1: Small L 0 lead to big RD and relatively small ED T2: Big L 0 lead to small RD and relatively big ED T2: Big L 0 lead to small RD and relatively big ED This explains why the 5-phase model: For T1: the model parameters can be stretched for the RD to ‘absorb’ the ED For T2: the model parameters, stretch how one likes, the RD cannot ‘absorb’ the ED

20. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Need to develop 6 th phase ie Phase 4a 1/2 We have simulated using anomalous resistance of following form: We have simulated using anomalous resistance of following form: Where R 0 is of order of 1 Ohm, t 1 controls rise time of the anomalous resistance and t 2 controls the fall time (rate) Use one term to fit one feature; terminate the term Then use a 2nd term to fit a 2 nd feature and so on

21. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Simulated Anomalous Resistance Term 2/2

22. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Result of Phase 4a fitting applied to KSU Current Trace 1/3

23. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Result of Phase 4a fitting applied to KSU Current Trace 2/3

24. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Features 3/3 Current ED now fitted very well Current ED now fitted very well Fig also shows the form of the fitted anomalous resistance (3 terms) Fig also shows the form of the fitted anomalous resistance (3 terms) Figure shows that the computed tube voltage waveform also shows features in agreement with the measured tube voltage waveform Figure shows that the computed tube voltage waveform also shows features in agreement with the measured tube voltage waveform The product of this Phase 4a fitting is the magnitude and temporal form of the anomalous resistance. This is an important experimental result. The information is useful to elaborate further on the instability mechanisms. The product of this Phase 4a fitting is the magnitude and temporal form of the anomalous resistance. This is an important experimental result. The information is useful to elaborate further on the instability mechanisms. Moreover even for the T1 current waveforms, we should fit by first just fitting the RD using the 5-phase model; ie the part that fits well with the computed is the RD; the rest of the dip is then fitted using phase 4a. Moreover even for the T1 current waveforms, we should fit by first just fitting the RD using the 5-phase model; ie the part that fits well with the computed is the RD; the rest of the dip is then fitted using phase 4a.

25. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 UNU ICTP PFF (INTI) 6-Phase Fit

26. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 Conclusion In this paper we have discussed: The Lee model code and its contributions to landmark plasma focus understanding The Lee model code and its contributions to landmark plasma focus understanding Use of the code to reference diagnostics Use of the code to reference diagnostics Current waveforms show necessity to classify PF’s into T1 and T2 Current waveforms show necessity to classify PF’s into T1 and T2 T2 shows necessity to model 6 th phase ie Phase 4a T2 shows necessity to model 6 th phase ie Phase 4a Product of this fitting is the magnitude and temporal form of anomalous resistance. Product of this fitting is the magnitude and temporal form of anomalous resistance.

27. Seminar on Plasma Focus Experiments(SPFE 2010) – Use of current measurements to interpret plasma focus properties and mechanisms S Lee & SH Saw 27 August 2010 A Paper has been submitted:

28. Use of current measurements to interpret plasma focus properties and mechanisms S Lee, S H Saw INTI International University, Nilai, Malaysia Institute for Plasma Focus Studies, Melbourne, Malaysia, Singapore Nanyang Technological University, NIE, Singapore

29. Remembering Abdus Salam- Thank You