International Conference on Plasma Science & Applications ICPSA2013 Singapore 3-6 December 2013

1. International Conference on Plasma Science & Applications ICPSA2013Singapore 3-6 December 2013 Developing a Plasma Focus Research Training System for the Fusion Energy Age S Lee Institute for Plasma Focus Studies, Melbourne Australia. INTI International University, 71800 Nilai, Malaysia University of Malaya, Kuala Lumpur, Malaysia leesing@optusnet.com.au

2. Summary • Background- AAAPT and the UNU/ICTP PFF as outstanding example of plasma training • The Lee Model code • A fundamental new result: optimising energy transfer into the plasma focus- The question of a matching bank inductance! (?) • A training system for the Fusion Energy Age

3. Background • From the mid-Eighties the AAAPT assisted in the starting and strengthening of several laboratories on plasma focus studies. • We developed a 3 kJ plasma focus the UNU/ICTP PFF, specially designed as a reliable research system. • More than 20 scientists were trained to build, use and maintain this plasma focus through intensive hands-on programmes sponsored by UNU, ICTP, UNESCO and TWAS and the AAAPT. • Several trainees are now at the forefront of the PF community. • The UNU ICTP PFF is now in 7 countries. Research on it has produced more than 22 PhD theses, 50 Masters theses and 200 peer reviewed research papers. (at last count) • It has developed into several modern variants (notably the KSU PF (USA), the AECS PF2 (Syria), the USofia PF (Bulgaria). Many devices have been built based on its design

4. 3 kJ plasma focus designed for international collaboration

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

6. UNU/ICTP PFF- narrow trolley to fit ICTP lift

7. Good Training, hard work, mutual help, support & follow-up

8. High standard maintained 1985/86 Training Programme: 11 research papers written; including the following standard paper for plasma focus design; one of 3 top-cited plasma focus papers.

9. As we move inevitably into the Age of Nuclear Fusion, the AAAPT experience is an outstanding one in providing small research groups access to fusion research • This was underscored when towards the end of 2010 an approach was made by a Luxembourg project development consultant company, EXECO Consulting, based on their internet search on the plasma focus. • Representing a group of wealthy investors one of their proposed projects was the building of infrastructures in preparation for the fusion age; including a centre for plasma research in an Asian or Middle Eastern country • They proposed to utilise the UNU/ICTP PFF experience towards this end. • Despite the GFC affecting their original objective there was a series of meetings culminating with an IPFS Conference in Bangkok where a small group of PF experts met with an EXECO team of financial, legal and engineering consultants for 3 days of intensive discussions.

10. 3 points from this experience • The AAAPT has an outstanding impact on the concept of plasma training, within and beyond the world of plasma physics • As the world moves into the fusion energy age interest in plasma training will increase and extend beyond academic circles. • At some point of time our academic interest will converge with commercial interest.

11. The Model Code • From beginning of our plasma focus 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 and variants • It now includes thermodynamics data so the code can be operated in H, D, D-T, N, O, He, Ne, Ar, Kr,Xe. • We have used it to simulate a wide range of PF devices including: 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); and the large MJ PF1000 (Poland). • An Iranian Group has modified the model code, calling it the Lee model, to simulate Filippov type plasma focus .

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

13. 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

14. Priority of Results • Applicable to all PF machines, existing and hypothetical • Current Waveform accuracy; anomalous resistance • 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; High Voltage, & Current-Step • Design of new experiments: Radiative cooling, radiative collapse, IFMIF scale PF and larger, Thermonuclear PF

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

16. A good code can continue to deliver fresh research perspectives • A good machine like the UNU ICTP PFF continues to provide fresh research areas proportionate to the efforts put in by the researchers • New research perspectives ideas and results continue to come out of the code, proportionate to the efforts put in by the numerical experiments researchers. To illustrate this second point we try now to establish a fresh perspective

17. Optimisation of Plasma Focus At least 4 separate effects/mechanisms need to be differentiated: (a) Optimising power (energy) transfer; (b) Current and yield limitations as static bank inductance L0 is reduced and (c) Current, neutron and yield scaling deterioration with increase of bank energy E0. (d) real effects: speed requirements, temperature windows M. Trunk had discussed (1975) an optimum L0 for the pinch properties of the Stuttgart machines. Krishnan (2012) has reviewed optimising processes. A clear picture has emerged regarding (b) (c) and (d) due to our systematic numerical experiments in the past few years. However for (a) a consistent perspective has yet to emerge.

18. Energy Transfers of the axial and radial phases of the plasma focus • Misconception of impedance ‘matching’ in the Maximum Power Transfer Theorem sense.

19. The Maximum Power Transfer (MPT) Theorem • applicable to a generator with a fixed resistance Rgen. With the generator at a given voltage, maximum power is delivered when Rload = Rgen. This is said to be the matched condition for Maximum Power Transfer.

20. The situation of the plasma focus is the converse • The question here is: with a fixed (though time-varying; averaged if you like) load, how do you arrange the generator to give MPT? • For the plasma focus we are not at liberty to fix the load resistance or impedance. There are speed requirements. • At an axial speed of 10 cm/ms the typical PF has a ‘dynamic resistance’ Rdyn of some 5 mW, with little variation among plasma focus, large and small. • A small capacitor bank like the UNU ICTP PFF has a surge impedance (Z0=(L0/C0)1/2) some 10 times Rdyn. A large bank like that of PF1000 has Z0~Rdyn. A super-large multi-MJ bank will have its Z0<<Rdyn.

21. Case of ‘fixed’ load impedance • In this situation we have little control over the ‘fixed’ resistance and impedance of the load. The question is to optimise power transfer by variation of the generator impedance. • In such a case MPT theorem does not apply. The energy transfer to the load (taking the plasma focus as a whole) will keep increasing towards 100% when the generator impedance is reduced towards zero subject to conditions other than impedances. • We will now test this concept

22. Generalised Situation:Equations to determine speed during axial phase: • Rate of change of momentum at current sheath, position z, is • Magnetic force on current sheath is fm = fraction of mass swept down the tube in axial direction fc = fraction of current flowing in piston

23. Equation of motion: (applying Newton’s 2nd Law) equating rate of change of momentum to force:Hence: Equation I

24. Equation of motion: (applying Newton’s 2nd Law) equating rate of change of momentum to force:Hence: Equation I

25. Circuit representation of Axial Phase of Plasma Focus (consider just the outside mesh only) Ignore r(t), plasma resistance. This is the approximation generally used for electromagnetic drive.

26. Circuit (current) Equation: (Applying Kirchhoff’s voltage law) Last line is Equation II

27. Equations (I) and II) are the generating equations of the model for the axial phase. They contain the physics built into the model. They are coupled equations. (2 coupled equations with two unknowns, z and I)- dz/dt is integrated from d2z/dt2; and z from dz/dt by linear approximations; I is integrated from dI/dt; and integral I dt from I by linear approximations. The equation of motion is affected by the electric current I. The circuit equation is affected by the current sheath motion and position z. This is the basis of the axial phase.

28. Normalise the equations to obtain scaling parameters Replace each variable by normalised dimensionless variable as follows: z=z/z0; i=I/I0; t=t/t0 • z0 is the length of the anode • I0=V0/(L0/C0)1/2 • t0= (L0C0)1/2

29. Non-dimensionalised equation of motion α = (t0/ta) – first scaling parameter; ratio of characteristic times of capacitor bank & axial transit

30. Non-Dimensionalised Circuit Equation • b=La/L0 second scaling parameter, ratio of tube inductance to bank (static) inductance where La= inductance of axial phase when CS reaches z = z0. • The third scaling parameter d=r0/(L0/C0)1/2 : ratio of circuit stray resistance to surge impedance. Summary: • 3 scaling parameters: time matching α, inductance ratio b, anddamping ratio d .

31. Numerical experiments quickly establish that good transfer is achieved when d =0 and a =1.5; Using these we vary b and obtain the following:

32. The larger b = La/L0 is, the better the energy transfer • ie the smaller L0 the better the energy transfer • Above b=7 the transfer curves level off with Eelec ~90%, Wpiston just over 50%; plasma KE~23% In practice b=4 is good enough, with negligible gain with further reduction of L0 below ¼ La Conclusion:There is no matching inductance condition for optimising energy transfer into axial phase plasma stream

33. We apply this non-dimensional analysis to the radial phase •  = t/t0,  = I/I0 as in axial phase but with: • s = rs/a, p = rp/a, f = zf/a • ie. distances are normalized to anode radius ‘a’.

34. The radial phase yields the following non-dimensionalised equations

35. Scaling parameters of Radial Phase where the 3 scaling parameters are • 1 = /(Flnc), ratio of inductances with dependance on modified aspect ratio • Flnc = (zo/a) ln(b/a), anode aspect ratio modified weakly by cathode/anode radius ratio. Radial scaling parameter1 is ta/tr ; ratio of characteristic transit times of axial and radial phases

36. Radial Phase controlling parameter • Radial phase scaling parameters a1 and b1 are fixed once F is specified. F is controlling parameter. • Numerical experiments found the following set of scaling parameters with good energy transfer for radial phase: (a=3.4, b=0.8, d=0.06 [fixed]) with small values of F. We use a typical value of c=2, and g=1.667 for deuterium plasma.

37. For (a=3.4, b=0.8, d=0.06) we fine-tune the variation of energy transfers as a function of F • At F=0.2 radial Wpiston peaks at 61% E0; & Eelec is at near peak value of 93% . • La ~ <L0and Lpinch~15 L0. [can show Lpinch~3/F]

38. Conclusions • Time-Matching is most important: t0, ta, tr • For given C0 & V0; small values of L0 increases discharge currents and reduces t0. To match ta requires reducing z0. • To optimise energy transfer into radial phase requires adjusting a1= ta /tr; ie F. • For this set of parameters, optimum is F=0.2 • Anode radius is 5 times anode length. • As a result the value of a1= 0.22 with tr = 4.6 ta. Thus ta needs to be considerably smaller than t0, to allow tr to end whilst there is still considerable current. This explains the large value of a=3.4.

39. Consequential requirements on inductance ratios • La ~ <L0and • Lpinch~15 L0.

40. These results are for maximising energy transfers. • For optimising plasma focus performance (a) these results should be considered together with: (b) optimising pinch current (c) a consideration of pinch current scaling deterioration at large storage energies and (d) real [unscaled] effects.

41. Real (other than scaled) effects are important For neutron yield: (a) beam-gas target: speed considerations are important; (b) thermonuclear: temperatures are important. • For soft x-rays: temperature window for each group of characteristic soft x-rays. • For materials deposition: uniform large area fast plasma streams FPS may be important; the above non-dimensionalised method may be most pertinent: good energy transfer with large anode radius (i.e. small values of F=z0/a)

42. Role and scope of numerical experiments • These new results on energy transfers show that fresh perspectives at fundamental level may be generated by numerical experiments when required for research, training or applications.

43. Is there a demand for such training? • Sept-Oct 2013: Initiative of Deepak Subedi of Kathmandu University a workshop was held at KU, Dhulikhel, Nepal • 30 participants immersed in plasma focus numerical experiments for a whole course-lively discussions and great interaction. Results: • 30 participants trained in PF NE 2. A paper was jointly written from work done at the WS; it is planned to be submitted for publication. 3. KU is planning to build a PF 4. A PhD project based on plasma focus numerical experiment is being planned in Tribhuvan University

45. Research Paper from NEW PF Kathmandu 2013 to be submitted to IEEE Trans Plasma Sci

46. NEW PF- Kathmandu 2013 • Shows what can be done for one part of a training programme- the NEW part • The other part- the PF part- requires a place where dedicated training experiments can be carried out

47. Developing the most powerful training and research system for the dawning of the Fusion Age: Plasma focus for training/Research a) Experimental facility: TRPF 1 kJ focus: 10 kV 20 mF 80 nH b) The proven most effective and comprehensive Model code c) The proven tradition and spirit of AAAPT collaboration

48. 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 which may be advantageously operated in slow pinch (barely pinching) mode

49. Slow Pinch mode- larger and more uniform deposition footprint

50. b) The proven most effective and comprehensive Model code • Firmly grounded in Physics • Connected to reality • The discharge phases of any PF-from its electric birth to its final plasma streaming • Useful and comprehensive outputs • Diagnostic reference-many properties, design, scaling & scaling laws, insights & innovations