Global View of the Lee Model code

1. Global View of the Lee Model code S H Saw INTI International University, Nilai, Malaysia

2. 3 kJ Plasma Focus Designed for International Collaboration

3. Design of the UNU/ICTP PFF- 3kJ Plasma Focus System??

4. UNU/ICTP PFF- narrow trolley to fit ICTP lift???

5. The Code • From beginning of that program it was realized that the laboratory work should be complemented by computer simulation. • A 2-phase model was developed in 1984 • We are continually developing the model to its present form • It now includes thermodynamics data so the code can be operated in H2, D2, D-T, N2, O2, He, Ne, Ar, Kr,Xe. • We have used it to simulate a wide range of plasma focus devices from the sub-kJ PF400 (Chile) , the small 3kJ UNU/ICTP PFF (Network countries), the NX2 3kJ Hi Rep focus (Singapore), medium size tens of kJ DPF78 & Poseidon (Germany) to the MJ PF1000, the largest in the world. • An Iranian Group has modified the model, calling it the Lee model, to simulate Filippov type plasma focus .

6. Philosophy of our Modelling • Experimental based • Utility prioritised • To cover the whole process- from lift-off, to axial, to all the radial sub-phases; and recently to post-focussed phase which is important for advanced materials deposition and damage simulation.

7. Priority of Basis • Energy consistent for the total process and each part of the process • Mass consistent • Charge consistent • Connected to the reality of experiments

8. Priority of Results • Applicable to all PF machines, existing and hypothetical • Current Waveform accuracy • Dynamics in agreement with experiments • Consistency of Energy distribution • Realistic Yields of neutrons, SXR, other radiations; Ions and Plasma Stream; in conformity with experiments • Widest Scaling of the yields • Insightful definition of scaling properties • Design of new devices; e.g. Hi V & C-S • Design of new experiments

9. Philosophy, modelling, results and applications of the Lee Model code

10. Numerical Experiments • Range of activities using the code is so wide • Not theoretical • Not simulation • The only correct description is: Numerical Experiments

11. PF1000 Lo nH Co uF b cm a cm z0 ro mW 33.5 1332 16 11.6 60 6.1 fm fc fmr fcr 0.13 0.7 0.35 0.65 Vo Po Mw A At/Molecular 27 3.5 4 1 2

12. Firing the PF1000

13. Fitting PF1000 27kV-adjusting model parameters until computed current waveform matches measured (after getting L0 correct)

14. PF1000 fitted results

15. PF1000: Yn Focus & Pinch Properties as functions of Pressure

16. Plasma Focus- Numerical Experiments leading Technology • Numerical Experiments- For any problem, plan matrix, perform experiments, get results- sometimes surprising, leading to new insights • In this way, the Numerical Experiments have pointed the way for technology to follow

17. NE showing the way for experiments and technology • PF1000 (largest PF in world): 1997 was planning to reduce static inductance so as to increase current and neutron yield Yn. They published their L0 as 20 nH • Using their published current waveform and parameters we showed their L0 =33 nH that their L0 was already at optimum that lowering their L0 would be a waste of effort and resources

18. New General Insight- For every PF there is a minimum L0 below which yield no longer increase • It was thought that the lower L0 is the better would be the current and the yield • Our NE showed that on the contrary every PF system has a minimum L0; no point trying to go below that- very expensive and will not increase yield • This was a surprising result- and changes one frontier area of plasma focus technology

19. Determination of Pinch Current- by fitting a measured current trace with reliable neutron yield to the computed current trace. • by fitting a measured current trace with reliable neutron yield to the computed current trace.

20. Results from Numerical Experiments with PF1000 - For decreasing L0- from 100 nH to 5 nH • As L0was reduced from 100 to 35 nH - As expected • Ipeak increased from 1.66 to 3.5 MA • Ipinch also increased, from 0.96 to 1.05 MA • Further reduction from 35 to 5 nH • Ipeak continue to increase from 3.5 to 4.4 MA • Ipinch decreasing slightly to - Unexpected  1.03 MA at 20 nH,  1.0 MA at10 nH, and  0.97 MA at 5 nH. • Ynalso had a maximum value of 3.2x1011 at 35 nH.

21. Pinch Current Limitation Effect - (1/3) • L0 decreases higher Ipeakbigger a longer zp bigger Lp • L0 decreases shorter rise time shorter zo smaller La L0 decreases, Ipinch/Ipeak decreases

22. Pinch Current Limitation Effect - (2/3) • L0 decreases, L-C interaction time of capacitor decreases • L0 decreases, duration of current drop increases due to bigger a Capacitor bank is more and more coupled to the inductive energy transfer  Effect is more pronounced at lower L0

23. Pinch Current Limitation Effect - (3/3) • A combination of two complex effects • Interplay of various inductances • Increasing coupling of C0 to the inductive energetic processes as L0 is reduced Leads to this Limitation Effect Two basic circuit rules: lead to such complex interplay of factors which was not foreseen; revealed only by extensive numerical experiments

24. Neutron yield scaling laws and neutron saturation problem • One of most exciting properties of plasma focus is • Early experiments show: Yn~E02 • Prospect was raised in those early research years that, breakeven could be attained at several tens of MJ . • However quickly shown that as E0 approaches 1 MJ, a neutron saturation effect was observed; Yn does not increase as much as expected, as E0 was progressively raised towards 1 MJ. • Question: Is there a fundamental reason for Yn

25. S Lee & S H Saw, J Fusion Energy, 27 292-295 (2008) S Lee, Plasma Phys. Control. Fusion, 50 (2008) 105005 S H Saw&S Lee.. Nuclear & Renewable Energy Sources Ankara, Turkey, 28 & 29 Sepr 2009. S Lee Appl Phys Lett 95, 151503 (2009) Cause: Due to constant dynamic resistance relative to decreasing generator impedance Global Scaling LawScaling deterioration observed in numerical experiments (small black crosses) compared to measurements on various machines (larger coloured crosses) Neutron ‘saturation’ is more aptly portrayed as a scaling deterioration-Conclusion of IPFS-INTI UC research

26. Scaling for large Plasma Focus Targets: • IFMIF (International fusion materials irradiation facility)-level fusion wall materials testing (a major test facility for the international programme to build a fusion reactor)

27. Fusion Wall materials testing at the mid-level of IFMIF: 1015 D-T neutrons per shot, 1 Hz, 1 year for 0.1-1 dpa- Gribkov IPFS numerical Experiments:

28. Fast capacitor bank 10x PF1000-Fully modelled- 1.5x1015 D-T neutrons per shot • Operating Parameters: 35kV, 14 Torr D-T • Bank Parameters: L0=33.5nH, C0=13320uF, r0=0.19mW • E0=8.2 MJ • Tube Parameters: b=35.1 cm, a=25.3 cm z0=220cm • Ipeak=7.3 MA, Ipinch=3.0 MA • Model parameters 0.13, 0.65, 0.35, 0.65

29. Ongoing IPFS numerical experiments of Multi-MJ Plasma Focus

30. 50 kV modelled- 1.2x1015 D-T neutrons per shot • Operating Parameters: 50kV, 40 Torr D-T • Bank Parameters: L0=33.5nH, C0=2000uF, r0=0.45mW • E0=2.5 MJ • Tube Parameters: b=20.9 cm, a=15 cm z0=70cm • Ipeak=6.7 MA, Ipinch=2.8 MA • Model parameters 0.14, 0.7, 0.35, 0.7 Improved performance going from 35 kV to 50 kV

31. IFMIF-scale device • Numerical Experiments suggests the possibility of scaling the PF up to IFMIF mid-scale with a PF1000-like device at 50kV and 2.5 MJ at pinch current of 2.8MA

32. Scaling further- possibilities • 1. Increase E0, however note: scaling deteriorated already below Yn~E0 • 2. Increase voltage, at 50 kV beam energy ~150kV already past fusion x-section peak; further increase in voltage, x-section decreases, so gain is marginal • Need technological advancement to increase current per unit E0 and per unit V0. • We next extrapolate from point of view of Ipinch

33. Scaling Plasma Focus from Ipinch using present predominantly beam-target in Lee Model code

34. SXR Scaling Laws • First systematic studies in the world done in neon as a collaborative effort of IPFS, INTI IU CPR and NIE Plasma Radiation Lab • Scaling laws extended to Argon by AECS

35. Special characteristics of SXR-for applications • Not penetrating; for example neon SXR only penetrates microns of most surfaces • Energy carried by the radiation is delivered at surface • Suitable for lithography and micro-machining • At low intensity - applications for surface sterilisation or treatment of food • at high levels of energy intensity, Surface hammering effect;, production of ultra-strong shock waves to punch through backing material

36. Compression- and Yield- Enhancement methods • Suitable design optimize compression • Role of high voltage • Role of special circuits e.g current-steps • Role of radiative cooling and collapse

37. Latest development Modelling Ion beam fluence Post focus axial shock waves Plasma streams Anode sputtered material

38. Ion beam post-pinch plasma stream calculationsSome preliminary Results- INTI IU-IAEA collaboration

39. 6. Developing the most powerful training and research system for the dawning of the Fusion Age. Integrate: 6a the proven most effective hardware system of the UNU/ICTP PFF with 6b the proven most effective numerical experiment system Lee Model code with emphasis on dynamics, radiation and materials applications.

40. Into the fusion era: Plasma focus for training/Research (a) Experimental facility: TRPF 1 kJ focus: 10 kV 20 uF 80 nH Measurements: • current, voltage sufficient to deduce dynamics and estimate temperatures • Fibre-optics, pin diodes; magnetic probes directly measure speeds, ns imaging • SXR spectrometry, neutron counters & TOF, ion collectors for radiation & particle measurements Simple materials processing experiments

41. Into the fusion era: Plasma focus for research training (b) Numerical Experiments code To complement TRPF • Computes dynamics and energy distributions • Plasma pinch evolution, size and life time • Post focus Ion Beam, plasma stream and anode sputtered material Connection with reality: through fitting computed current to measured current trace Behaviour of plasma focus and yields as functions of pressure, gases, storage energies, circuit currents and pinch currents. Carry out above experiments with any plasma focus. Optimization of planned plasma focus

42. (a) The proven most effective 3 kJ PF system The trolley based UNU/ICTP PFF 3 kJ plasma focus training and research system will be updated as a 1 kJ system

43. (b) The proven most effective and comprehensive Model code • Firmly grounded in Physics • Connected to reality • From birth to death of the PF • Useful and comprehensive outputs • Diagnostic reference-many properties, design, scaling & scaling laws, insights & innovations

44. (b) Philosophy, modelling, results and applications of the Lee Model code