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Review of (UPFLF) Plasma Focus Numerical Experiments

Review of (UPFLF) Plasma Focus Numerical Experiments. S Lee 1,2,3 & H Saw 1,2 1 INTI International University, Nilai, Malaysia 2 Institute for Plasma Focus Studies, Melbourne, Australia 3 University of Malaya, Kuala Lumpur, Malaysia

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Review of (UPFLF) Plasma Focus Numerical Experiments

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  1. Review of (UPFLF) Plasma Focus Numerical Experiments S Lee1,2,3 & H Saw1,2 1INTI International University, Nilai, Malaysia 2Institute for Plasma Focus Studies, Melbourne, Australia 3University of Malaya, Kuala Lumpur, Malaysia International Workshop on Plasma Science and Applications, 4 & 5 October 2012, Bangkok, Thailand

  2. Plasma Focus Numerical Experiments- Outline of Lecture • Development, usage and results • Basis and philosophy • Reference for Diagnostics • Insights and frontiers • Continuing development- Ion beam modelling

  3. UNU ICTP PFF- 3 kJ Plasma Focus Designed for International Collaboration within AAAPT Background

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

  5. UNU/ICTP PFF- placed at ICTP, 1988 Background Network: Malaysia, Singapore, Thailand, Pakistan, India, Egypt, Similar machines with designs based on or upgraded: Zimbabwe, Syria, USA, Bulgaria, Iran

  6. The Code Intro 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 1983 • 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 .

  7. Review of UPFLF Plasma Focus Numerical Experiments Intro code • The code10 couples the electrical circuit with PF dynamics, thermodynamics and radiation. • Using standard circuit equations and Newtonian equations of motion adapted for the plasma focus: the code is consistent in (a) energy, (b) charge and (c) mass.

  8. Development of the code Intro code • It was described in 198311 and used in the design and interpretation of experiments12-15. • An improved 5-phase code incorporating finite small disturbance speed16, radiation and radiation-coupled dynamics was used17-19, • It was web-published20 in 2000 and 200521. • Plasma self- absorption was included20 in 2007

  9. Usage Intro code • It has been used extensively as a complementary facility in several machines, for example: UNU/ICTP PFF12,14,15,17-19, NX219,22, NX119, DENA23, AECS • It has also been used in other machines for design and interpretation including Chile’s sub-kJ PF and other machines24, Mexico’s FNII25 and the Argentinian UBA hard x-ray source26. • More recently KSU PF (US), NX3 (Singapore), FoFu I (US) and several Iranian machines APF, Tehran U, AZAD U

  10. Information derived Intro code Information computed includes • axial and radial dynamics11,17-23, pinch properties • SXR emission characteristics and yield17-19, 22, 27-33, • design of machines10,12,24,26, • optimization of machines10,22, 24,30 and adaptation to Filippov-type DENA23. • Speed-enhanced PF17 was facilitated.

  11. Information Derived Intro code Scaling Properties; • Constancy of energy density (per unit mass) across range of machines14 • Hence same temperature and density14 • Constancy of drive current density I/a relating to the speed factor14 • (I/a)/r0.5 • Scaling of pinch dimensions & lifetime14 with anode radius ‘a’: pinch radius ratio rp/a =constant pinch length ratio zp/a=constant pinch duration ratio tp/a=constant

  12. Recent development and Insights Intro code • PF neutron yield calculations34 • Current & neutron yield limitations35 with reducing L0 • Wide-ranging neutron scaling laws • Wide-ranging soft x-ray scaling laws in various gases • Neutron saturation36,37- cause and Global Scaling Law • Radiative collapse 38 • Current-stepped PF39 • Extraction of diagnostic data33,40-42 • Anomalous resistance data43,44 from current signals • Benchmarks for Ion Beams- scaling with E0.

  13. Philosophy of our Modelling Philosophy • 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.

  14. Priority of Basis Philosophy Correct choice of Circuit equations coupled to equations of motion ensures: • Energy consistent for the total process and each part of the process • Charge consistent • Mass consistent Fitting computed current waveform to measured current waveform ensures: • Connected to the reality of experiments

  15. Priority of Results Philosophy • Applicable to all PF machines, existing and hypothetical • Current Waveform accuracy • Dynamicsin agreement with experiments • Consistency of Energy distribution • Realistic Yields of neutrons, SXR, other radiations; Ions and Plasma Stream (latest-Benchmarks); in conformity with experiments • Widest Scaling of the yields • Insightful definition of scaling properties • Design of new devices; e.g. Hi V & Current-Step • Design new experiments-Radiative cooling & collapse

  16. Philosophy, modelling, results & applications of the Lee Model code Philosophy

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

  18. UPFLF-The CodeControl Panel- configured for PF1000 Demo L0 nH C0mF b cm a cm z0 r0 mW 33.5 1332 16 11.6 60 6.1 fm fc fmr fcr 0.13 0.7 0.35 0.65 V0 P0 M.W. A At/Molecular 27 3.5 4 1 2

  19. PF1000, ICDMP Poland, the biggest plasma focus in the worldFiring the PF1000Demo

  20. Fitting: 1. L0 fitted from current rise profile 2. Adjust model parameters (mass and current factors fm, fc, fmr, fcr) until computed current waveform matches measured current waveform (sequential processes shown below) Demo

  21. PF1000 fitted results Demo

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

  23. Plasma Focus- Numerical Experiments leading Technology Insights • 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

  24. NE showing the way for experiments and technology Insights • 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 a. their L0 =33 nH b. their L0 was already at optimum c. that lowering their L0 would be a waste of effort and resources

  25. Results from Numerical Experiments with PF1000 - For decreasing L0- from 100 nH to 5 nH Insights 1 • 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.

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

  27. Pinch Current Limitation Effect Insights 1 • 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

  28. Pinch Current Limitation Effect Insights 1 • 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

  29. Neutron yield scaling laws and neutron saturation problem Insights 2 • 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

  30. 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 Law Insights 2Scaling 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

  31. Scaling for large Plasma Focus Scaling 1 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)- essentially an ion accelerator

  32. 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 Scaling 1 IPFS numerical Experiments:

  33. Possible PF configuration: Fast capacitor bank 10x PF1000-Fully modelled- 1.5x1015 D-T neutrons per shot Scaling 1 • 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

  34. Ongoing IPFS numerical experiments of Multi-MJ Plasma Focus Scaling 1

  35. 50 kV modelled- 1.2x1015 D-T neutrons per shot Scaling 1 • 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

  36. IFMIF-scale device Scaling 1 • 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 • Such a system would cost only a few % of the planned IFMIF

  37. Scaling further- possibilities Scaling 2 • 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

  38. Scaling from Ipinch using present predominantly beam-target : Yn=1.8x1010Ipeak3.8; Yn=3.2x1011Ipinch4.4 (I in MA) Scaling 2

  39. SXR Scaling Laws Scaling 3 • First systematic studies in the world done in neon as a collaborative effort of IPFS, INTI IU CPR and NIE Plasma Radiation Lab: Ysxr= 8300× Ipinch3.6 Ysxr= 600 × Ipeak3.2 in J (I in MA). • Scaling laws extended to Argon, N and O by M Akel AEC, Syria in collaboration.

  40. Special characteristics of SXR-for applications Scaling 3 • 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; or as high intensity compression drivers in fusion scenarios

  41. Compression- and Yield- Enhancement methods Scaling 4 • Suitable design optimize compression • Role of high voltage • Role of special circuits e.g current-steps • Role of radiative cooling and collapse

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

  43. Plasma Focus PinchLatest photo taken by Paul Lee on INTI PF

  44. Emissions from the PF Pinch region Latest +Mach500 Plasma stream +Mach20 anode material jet

  45. Sequence of shadowgraphs of PF Pinch- M ShahidRafique PhD Thesis NTU/NIE Singapore 2000 Latest Highest post-pinch axial shock waves speed ~50cm/us M500 Highest pre-pinch radial speed>25cm/us M250

  46. Much later…Sequence of shadowgraphics of post-pinch copper jetS Lee et al J Fiz Mal 6, 33 (1985) Latest Slow Copper plasma jet 2cm/us M20

  47. Extracted from V A Gribkov presentation: IAEA Dec 2012

  48. Comparing large and small PF’s- Dimensions and lifetimes- putting shadowgraphs side-by-side, same scale Anode radius 1 cm 11.6 cm Pinch Radius: 1mm 12mm Pinch length: 8mm 90mm Lifetime ~10ns order of ~100 ns

  49. Flux out of Plasma Focus Charged particle beams Neutron emission when operating with D Radiation including Bremsstrahlung, line radiation, SXR and HXR Plasma stream Anode sputtered material

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