S H Saw 1,2, S Lee 1,2,3

Transcription

1 Review of Plasma Focus Numerical Experiments S H Saw 1,2, S Lee 1,2,3 1 Nilai University, Nilai, Malaysia 2 Institute for Plasma Focus Studies, Melbourne, Australia 3 University of Malaya, Kuala Lumpur, Malaysia

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, radiative collapse and HED, throughput scaling to breakeven

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 It was realized that the laboratory work should be complemented by computer simulation. A 2-phase model was developed in 1983 We continually developed the code to its 5-phase form It now includes thermodynamics data so the code can be operated in H 2, D 2, D-T, N 2, O 2, 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 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 Lee Code Plasma Focus Numerical Experiments Intro code The code 10 couples the electrical circuit with PF dynamics, thermodynamics and radiation. Using standard circuit equations and equations of motion adapted for the axial and radial phases, the code is consistent in (a) energy, (b) charge and (c) mass.

8 Development of the code Intro code It was described in and used in the design and interpretation of experiments This evolved into a 5-phase code incorporating finite small disturbance speed 16, radiation and radiationcoupled dynamics 17-19, It was web-published 20 in 2000 and Plasma self- absorption was included 20 in 2007

9 Axial Phase- snow plough type Axial Phase: Snow- plow type equation of motion coupled to circuit equation

10 Inward radial shock phase - 4 coupled equations namely: inward radial shock, elongation, inward radial piston and circuit, respectively as follows: p o s r I dt dr 4 f f 1) ( mr c 2 1 dt dr dt dz s f f 2 2 f dt p s p s p p s p s p s p r r dz r r z r dt di r r I r dt dr r r dt dr f p c o c o p p f c f p c o o o z r b f z c f L dt dr I r z f dt dz I r b f I r C Idt V dt di ln 2 ) (ln 2 2 ln 2

11 Reflected Shock RS phase Reflected shock radial phase- RS moving out, piston moving in and column elongation coupled to circuit equationtotal of 4 coupled equations

12 Pinch Phase Key equation: radiation- coupled dynamics Piston dynamics depends on di/dt, dzf/dt and dq/dt. di/dt is computed with coupled circuit equation; dq/dt is calculated with the various components being the bremsstrahlung, recombination and line radiation and Joule heating. dr p dt r I p di dt 1 1 r z p f dzf dt z f f r 2 c p I 2 dq dt

13 Usage Intro code It has been used extensively as a complementary facility in several machines, for example: UNU/ICTP PFF 12,14,15,17-19, NX2 19,22, NX1 19, DENA 23, AECS It has also been used in other machines for design and interpretation including Chile s sub-kj PF and other machines 24, Mexico s FNII 25 and the Argentinian UBA hard x-ray source 26. More recently KSU PF (US), NX3 (Singapore), FoFu I (US) and several Iranian machines APF, Tehran U, AZAD U

14 Information derived Intro code Information computed includes axial and radial dynamics 11,17-23, pinch properties SXR emission characteristics and yield 17-19, 22, 27-33, design of machines 10,12,24,26, optimization of machines 10,22, 24,30 and adaptation to Filippov-type DENA 23. Speed-enhanced PF 17 was facilitated.

15 Information Derived Intro code Scaling Properties; Constancy of energy density (per unit mass) across range of machines 14 Hence same temperature and density 14 Constancy of drive current density I/a relating to the speed factor 14 (I/a)/ 0.5 Scaling of pinch dimensions & lifetime 14 with anode radius a : pinch radius ratio pinch length ratio r p /a =constant z p /a=constant pinch duration ratio t p /a=constant

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

17 Recent development and Insights Intro code PF neutron yield calculations 34 Current & neutron yield limitations 35 with reducing L 0 Wide-ranging neutron scaling laws Wide-ranging soft x-ray scaling laws in various gases Neutron saturation 36,37 - cause and Global Scaling Law Radiative collapse 38 Current-stepped PF 39 Extraction of diagnostic data 33,40-42 Anomalous resistance data 43,44 from current signals Benchmarks for Ion Beams- scaling with E 0.

18 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.

19 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

20 Priority of Results Philosophy 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 (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

21 Philosophy, modelling, results & applications of the Lee Model code Philosophy

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

23 UPFLF-The Code Control Panel- configured for PF1000 Demo L 0 nh C 0 F b cm a cm z 0 r 0 mw f m f c f mr f cr V 0 P 0 M.W. A At/Molecular

24 PF1000, ICDMP Poland, the biggest plasma focus in the world Firing the PF1000 Demo

25 Fitting: 1. L 0 fitted from current rise profile 2. Adjust model parameters (mass and current factors f m, f c, f mr, f cr ) until computed current waveform matches measured current waveform (sequential processes shown below) Demo

26 PF1000 fitted results Demo

27 PF1000: Y n Focus & Pinch Properties as functions of Pressure Demo

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

29 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 Y n. They published their L 0 as 20 nh Using their published current waveform and parameters we showed a. their L 0 =33 nh b. their L 0 was already at optimum c. that lowering their L 0 would be a waste of effort and resources

30 Results from Numerical Experiments with PF For decreasing L 0 - from 100 nh to 5 nh Insights 1 As L 0 was reduced from 100 to 35 nh - As expected I peak increased from 1.66 to 3.5 MA I pinch also increased, from 0.96 to 1.05 MA Further reduction from 35 to 5 nh I peak continue to increase from 3.5 to 4.4 MA I pinch decreasing slightly to - Unexpected 1.03 MA at 20 nh, 1.0 MA at10 nh, and 0.97 MA at 5 nh. Y n also had a maximum value of 3.2x10 11 at 35 nh.

31 Pinch Current Limitation Effect - Insights 1 L 0 decreases higher I peak bigger a longer z p bigger L p L 0 decreases shorter rise time shorter z o smaller L a L 0 decreases, I pinch /I peak decreases

32 Pinch Current Limitation Effect Insights 1 L 0 decreases, L-C interaction time of capacitor decreases L 0 decreases, duration of current drop increases due to bigger a Capacitor bank is more and more coupled to the inductive energy transfer

33 Pinch Current Limitation Effect Insights 1 A combination of two complex effects Interplay of various inductances Increasing coupling of C 0 to the inductive energetic processes as L 0 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

34 Neutron yield scaling laws and neutron saturation problem Insights 2 One of most exciting properties of plasma focus is Early experiments show: Y n ~E 0 2 Prospect was raised in those early research years that, breakeven could be attained at several tens of MJ. However quickly shown that as E 0 approaches 1 MJ, a neutron saturation effect was observed; Y n does not increase as much as expected, as E 0 was progressively raised towards 1 MJ. Question: Is there a fundamental reason for Y n

35 Global Scaling Law Insights 2 Scaling 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 LogYn, Yn in 10^ y = 0.001x 2 LogYn vs LogEo y = 0.5x 0.8 Hig h E0 (Lo w Eo ) M id Eo c o m pile e xpts 0 8 c o m pile d da ta Log Eo, Eo in kj S Lee & S H Saw, J Fusion Energy, (2008) S Lee, Plasma Phys. Control. Fusion, 50 (2008) S H Saw & S Lee.. Nuclear & Renewable Energy Sources Ankara, Turkey, 28 & 29 Sepr S Lee Appl Phys Lett 95, (2009) Cause: Due to constant dynamic resistance relative to decreasing generator impedance

36 Scaling for large Plasma Focus Scaling 1 Targets: 1. 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

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

38 Possible PF configuration: Fast capacitor bank 10x PF1000- Fully modelled- 1.5x10 15 D-T neutrons per shot Scaling 1 Operating Parameters: 35kV, 14 Torr D-T Bank Parameters: L 0 =33.5nH, C 0 =13320uF, r 0 =0.19mW E 0 =8.2 MJ Tube Parameters: b=35.1 cm, a=25.3 cm z 0 =220cm I peak =7.3 MA, I pinch =3.0 MA Model parameters 0.13, 0.65, 0.35, 0.65

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

40 50 kv modelled- 1.2x10 15 D-T neutrons per shot Scaling 1 Operating Parameters: 50kV, 40 Torr D-T Bank Parameters: L 0 =33.5nH, C 0 =2000uF, r 0 =0.45mW E 0 =2.5 MJ Tube Parameters: b=20.9 cm, a=15 cm z 0 =70cm I peak =6.7 MA, I pinch =2.8 MA Model parameters 0.14, 0.7, 0.35, 0.7 Improved performance going from 35 kv to 50 kv

41 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

42 Scaling further- possibilities Scaling 2 1. Increase E 0, however note: scaling deteriorated already below Y n ~E 0 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 E 0 and per unit V 0. We next extrapolate from point of view of I pinch

43 Scaling from I pinch using present predominantly beam-target : Y n =1.8x10 10 I peak 3.8 ; Y n =3.2x10 11 I pinch 4.4 (I in MA) Scaling 2

44 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: Y sxr = 8300 I pinch 3.6 Y sxr = 600 I peak 3.2 in J (I in MA). Scaling laws extended to Argon, N and O by M Akel AEC, Syria in collaboration.

45 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

46 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

47 A more dramatic example: radiative collapse in Kr, measured in the INTI PF on the basis of a current measurement Fig 1. Fitting the computed current trace to the measured current trace of INTI PF at 12 kv 0.5 Torr Kr (shot 631). (Note the two curves have a close fit. Without radiation, the current (not shown) has a much smaller dip.

48 Expanding the current trace to show the region of the dip Fig 1a Expanded view of the fitting

49 The fitting to the measured current waveform gives the radial trajectory revealing strong radiative collapse to very small radius Having fitted the computed current trace to the measured current trace, the resulting radial trajectory indicates strong radiative collapse to very small radius, as shown in the following Figure. The radial trajectory hypothetically without radiation is also computed and shown for comparison.

50 Comparing radial trajectory with radiation (purple) and (hypothetically) without radiation (black)

51 Expanding the time scale to show details of radiative collapse region

52 From a measured current waveform, the parameters of the radiative collapse are derived. The peak compression region is magnified and shown in the above figure. The current values are normalized by 145 ka, the P line is normalized by 3.7x10 12 W and the radius ratio k p =r p /a is multiplied by 20. The pinch compresses to a radius of cm corresponding to a radius ratio (pinch radius normalized to anode radius) of T The radiative collapse is ended when plasma self-absorption attenuates the intense line radiation. The rebound of the pinch radius is also evident in Fig 3. The line radiation leaving the plasma is also plotted (in normalized unit) to show its correlation to the trajectory in order to show the effect of the radiation on the compression. This intense compression, despite the low mass swept in factor of f mr = 0.11, reaches 3.7 x ions m -3, which is 15 times atmospheric density (starting from less than 1/1000 of an atmospheric pressure). The energy pumped into the pinch is 250 J whilst 41 J are radiated away in several ns, most of the radiation occurring in in a tremendous burst of 50 ps at peak compression with a peak radiation power of almost 4 x10 12 W. The energy density at peak compression is 4 x J m -3 or 40 kj mm -3. Thus from a measured current waveform in this Kr discharge, the parameters of this intense HED is measured showing the high density achieved.

53 All this information from just one measured current waveform

54 Recent developments Modelling of: Ion beam fluence Post focus axial shock waves Plasma streams Anode sputtered material Radiatively enhanced compressions Energy Throughput scaling

55 Plasma Focus Pinch Latest photo taken by Paul Lee on INTI PF

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

57 Sequence of shadowgraphs of PF Pinch- M Shahid Rafique PhD Thesis NTU/NIE Singapore 2000 Latest Highest post-pinch axial shock waves speed ~50cm/us M500

58 Much later Sequence of shadowgraphics of post-pinch copper jet S Lee et al J Fiz Mal 6, 33 (1985) Latest

59

60 Extracted from V A Gribkov presentation: IAEA Dec 2012

61 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

62 Modelling the flux Latest Ion beam number fluence is derived from beam-plasma target considerations as: F ib t = C n I pinch2 z p [ln(b/r p )]/ (r p 2 U 1/2 ) ions m -2 All SI units:calibration constant C n =8.5x10 8 ; calibrated against experimental point at 0.5MA I pinch =pinch current z p =pinch length b=outer electrode, cathode radius r p =pinch radius U=beam energy in ev where in this model U=3x V max (max dynamic induced voltage) These values are computed by our code

63 Table 1: Parameters of a range of Plasma Focus and computed Ion Beam characteristics Latest Machine PF1000 DPF78 NX3 INTIPF NX2 PF-5M PF400J E 0 (kj) L 0 (nh) V 0 (kv) 'a' (cm) c=b/a I peak (ka) I pinch (ka) z p (cm) r p (cm) t (ns) V max (kv)

64 Machine IB Ion Fluence (x10 20 m -2 ) PF DPF NX3 5.7 INTI 3.6 NX2 3.4 PF5M 2.4 Latest IB Ion Flux (x10 27 m -2 s -1 ) Mean Ion Energy (kev) IB Energy Fluence (x10 6 J m -2 ) IB Energy Flux (x10 13 W m -2 ) Ion Number (x10 14 ) IB Energy (J) (% E 0 ) (2.5) (4.1) (3.3) (0.7) (4.1) (2.8) (1.3) IB current (ka) IB Damage Ftr (x10 10 Wm -2 s 0.5 ) Ion Speed (cm/ms) Ion Number per kj (x10 14 ) Plasma Stream Energy (J) (% E 0 ) (8.1) (1.3) (12.0) (7.4) (13.7) (4.5) (4.5) Plasma Stream Speed (cm/s) PF400J 2.6

65 Plasma Focus Numerical Experiments- Conclusions: We have covered Development, usage and results Basis and philosophy Reference for Diagnostics Insights and frontiers Continuing development- Ion beam modelling, radiative collapse for HED and energy throughput scaling.

66 References 10 S Lee, Radiative Dense Plasma Focus Computation Package: RADPF. websites) 11 S Lee in Radiation in Plasmas Vol II, Ed B McNamara, Procs of Spring College in Plasma Physics (1983) ICTP, Trieste, p , ISBN , Published byworld Scientific Publishing Co, Singapore (1984) 12 S Lee, T.Y. Tou, S.P. Moo, M.A. Elissa, A.V. Gholap, K.H. Kwek, S. Mulyodrono, A.J. Smith, Suryadi, W.Usala & M. Zakaullah. Amer J Phys 56, 62 (1988) 13 T.Y.Tou, S.Lee & K.H.Kwek. IEEE Trans Plasma Sci 17, (1989) 14 S Lee & A Serban, IEEE Trans Plasma Sci 24, (1996) 15 SP Moo, CK Chakrabarty, S Lee - IEEE Trans Plasma Sci 19, (1991) 16 D E Potter, Phys Fluids 14, 1911 (1971) 17 A Serban and S Lee, Plasma Sources Sci and Tehnology, 6, 78 (1997) 18 M H Liu, X P Feng, SV Springham & S Lee, IEEE Trans Plasma Sci. 26, 135 (1998) 19 S Lee, P.Lee, G.Zhang, X.Feng, V.A.Gribkov, M.Liu, A.Serban & T.Wong. IEEE Trans Plasma Sci, 26, 1119 (1998) 20 S.Lee in (archival website) (2012) 21 S. Lee in ICTP Open Access Archive: (2005) 22 D.Wong, P.Lee, T.Zhang, A.Patran, T.L.Tan, R.S.Rawat & S.Lee. Plasma Sources, Sci & Tech 16, 116 (2007) 23 V. Siahpoush, M.A.Tafreshi, S. Sobhanian, & S. Khorram. Plasma Phys & Controlled Fusion 47, 1065 (2005)

67 References 24 L. Soto, P. Silva, J. Moreno, G. Silvester, M. Zambra, C. Pavez, L. Altamirano, H. Bruzzone, M. Barbaglia, Y. Sidelnikov & W. Kies. Brazilian J Phys 34, 1814 (2004) 25 H.Acuna, F.Castillo, J.Herrera & A.Postal. International conf on Plasma Sci, 3-5 June 1996, conf record Pg C.Moreno, V.Raspa, L.Sigaut & R.Vieytes, Applied Phys Letters 89(2006) 27 S. Lee, R S Rawat, P Lee and S H Saw, J. Appl. Phys. 106, (2009) 28 S. H. Saw and S. Lee, Energy and Power Engineering, 2 (1), (2010) 29 M. Akel, Sh Al-Hawat, S H Saw and S Lee, J Fusion Energy, 29, 3, (2010) 30 S H Saw, P C K Lee, R S Rawat, S Lee, IEEE Trans Plasma Sci, 37, (2009) 31 Sh. Al-Hawat, M. Akel, S H Saw, S Lee, J Fusion Energy, 31, 13 20, (2012) 32 Sh Al-Hawat, M. Akel, S. Lee, S. H. Saw, J Fusio Energy 31, (2012) 33 S Lee, S H Saw, R S Rawat, P Lee, A.Talebitaher, A E Abdou, P L Chong, F Roy, A Singh, D Wong and K Devi, IEEE Trans Plasma Sci 39, (2011) 34 S Lee and S H Saw, J Fusion Energy, 27, (2008) 35 S. Lee and S H Saw, Appl. Phys. Lett., 92, (2008) 36 S Lee. Plasma Physics Controlled Fusion, (2008) 37 S Lee. Appl. Phys. Lett (2009)

68 References 38 S Lee, S. H. Saw and Jalil Ali, J Fusion Energy DOI: /s First Online 26 Feb (2012) 39 S Lee and S H Saw, J Fusion Energy DOI: /s First Online 31 January (2012) 40 S Lee, S H Saw, P C K Lee, R S Rawat and H Schmidt, Appl Phys Lett 92, (2008) 41 S H Saw, S Lee, F Roy, PL Chong, V Vengadeswaran, ASM Sidik, YW Leong & A Singh, Rev Sci Instruments, 81, (2010) 42 S Lee, S H Saw, R S Rawat, P Lee, R Verma, A.Talebitaher, S M Hassan, A E Abdou, Mohamed Ismail, Amgad Mohamed, H Torreblanca, Sh Al Hawat, M Akel, P L Chong, F Roy, A Singh, D Wong and K Devi, J Fusion Energy 31, (2012) 43 S Lee, S H Saw, A E Abdou and H Torreblanca, J Fusion Energy 30, (2011) 44 F M Aghamir and R A Behbahani, J. Plasma Physics: doi: /s in press (2012) 45 S.Lee, S.H.Saw, L..Soto, S V Springham, S P Moo, Plasma Phys and Control. Fusion, (11pp) (2009) 46 S.P. Chow, S. Lee and B.C. Tan, J Plasma Phys, (1972).