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Numerical Experiments on Plasma Focus S H Saw & S Lee

Numerical Experiments on Plasma Focus S H Saw & S Lee. INTI International University, Nilai , Malaysia Institute for Plasma Focus Studies, Melbourne Australia. Numerical Experiments on Plasma Focus Contents. Parameters of a PF Numerical Experiments – an example PF1000

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Numerical Experiments on Plasma Focus S H Saw & S Lee

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  1. Numerical Experiments on Plasma FocusS H Saw & S Lee INTI International University, Nilai, Malaysia Institute for Plasma Focus Studies, Melbourne Australia

  2. Numerical Experiments on Plasma Focus Contents • Parameters of a PF • Numerical Experiments – an example PF1000 • Step I - Fit Computed Current (CC) to Measured Current(MC) • Obtain all parameters and a Measured Current • Configure the code • Add Measured Current • Fire, compare Computed Current(CC) to MC • Vary parameters until CC fits MC • Step II – PF1000 Yn vs P • Configure code at 27kV, 3.5 Torr D using parameters fitted in Part I • Run at various P for D gas • Collect Computed data and current waveforms • Interpret results and notes • Various NE Projects • Conclusion

  3. Parameters of a Plasma Focus • Bank: L0 (static inductance),C0(capacitance), r0(resistance) • Tube: b (cathode radius), a (anode radius), z0 (anode length) • Model:fm (axial mass), fc(axial curr), fmr(radial mass), fcr(radial current factor) Note: In yellow: typically not given, to be fitted from measured current waveform International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

  4. Numerical Experiment – An Example:To obtain neutron yield Ynof PF1000 as function of pressure P, and relate to pinch data Steps I:Obtain all parameters of PF1000 • Require a measured current waveform - obtain this current waveform and record the parameters which are given • Configure the code as the PF1000 using given parameters; note those parameters that are not certain or guessed • Fire the PF1000, compare computed current waveform with measured current waveform • Fit computed waveform to measured waveform a) Fit current rise slope, adjust static inductance L0 where necessary b) Fit position of start of dip adjusting fm and fc as necessary c) Fit slope of dip, adjusting fmr, fcr as necessary

  5. Step I.1: Measured current waveform • Require a measured current waveform - obtain this current waveform and record the parameters which are given • Usually digital file (from DSO) is available in two columns • In the case of PF1000 we do not have a digital file, but there is a published waveform in a published paper • We had digitised the waveform using a freeware digitising software called Engauge

  6. Step I.1: Measured current waveform • PF1000:published waveform and digitised waveform

  7. Step I.2. Configure the code as the PF1000 using given parameters; note those parameters that are not certain are guessed.

  8. Step I.3. To do that, first import the PF1000 current data into the code, say Sheet3 of Excel Fire the PF1000, compare Computed Current waveform with Measured Current waveform

  9. Step I.3. To do that, first import the PF1000 current data into the code, say Sheet3 of Excel Fire the PF1000, compare Computed Current waveform with Measured Current waveform

  10. 1. Use typical trial values of fm, fc, tmr, fcr; use given value of L0 and guess value of r0;Result: computed current risetime too short; need to increase L0 - risetime~L00.5

  11. 2. Increase L0 to 25 nH, computed risetime increases, fits better; but not enough- Need to increase Lo further

  12. 3. Increase Lo to 30 nH, fits better. Next note computed current too high; that suggests to increase r0

  13. 4. Increase r0 to 3 mΩ, that drops the current and the fit is better. Try increase r0 further

  14. 5. Increase r0 to 5 mΩ; fit of current rise slope is now quite good. For the moment fit of L0 and r0 looks OK; although may need to come back later.Next note radial phase comes far too early; that means axial speed too fast.To reduce axial speed, increase axial mass factor fm

  15. 6. Increase axial fm to 0.1; note improvement to fit; but axial speed still too fast. Need to increase fm further. Note, also that reducing the speed increases the current International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

  16. 7. Increase fm to 0.13, note that computed radial phase starts later and fit is better; but still not enough. Note that current has gone higher- due to the reduced loading because of lower speed.. Lower speed leads to higher current. Suggest increase fm, which will slow axial speed and increase current further; so at same time need to increase r0

  17. 8. Increase fm to 0.14 at same time increase r0 to 6 mΩ; fit is now better but current still too high; the computed radial start point is still slightly early; but if we increase r0 the current will drop and the speed will reduce. So suggest increase r0 slightly.

  18. 9. Increase r0 to 6.3 mΩ. Note that the computed current has dropped enough for the rising slope (particularly the top part of the rising slope) and the flattened top to agree very well. Also the computed current dip start (roll off) agrees very well with the measured current dip start. Thus L0 and r0 fitted; also fm is fitted.

  19. 10 Next, to fit the radial phase. Note last slide computed slope of dip is much too steep than measured dip slope.This means that the computed speed is too high. To reduce the radial speed, increase fmr; try 0.25. Note improvement; the computed slope is now less steep and agrees better with the measured; need to increase fmr further.

  20. 11. Increase fmr to 0.34; Note that the average slope of the computed current dip is now very close to the average slope of the measured current dip. Note 5 points of agreement: 1. Rising slope 2. Topping profile 3. Top and Ipeak 4.start of current dip 5.slope of dip and 6. Bottom of dip. The fit is good overall.

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

  22. PF1000 fitted results

  23. Step I.4 Fit computed waveform to measured waveform • a) Fit current rise slope, adjust static inductance L0 where necessary • b) Fit position of start of dip adjusting fmand fcas necessary • c) Fit slope of dip, adjusting fmr, fcras necessary

  24. Example 1: Variation of current waveforms as a function of pressure • The Universal PF code: RADPFV5.15de • Configure: for PF1000: 27 kV 3.5 Torr D2 (published and fitted)

  25. Example 1: Variation of current waveforms as a function of pressure • The Universal PF code: RADPFV5.15de • Configure: for PF1000: 27 kV 3.5 Torr D2 (published and fitted) [run 100000 Torr, 19, 10, 7, 5, 2, 1 Torr; at 7 Torr show how to collect cols A and B (for curr waveform) and how to collect dataline.]

  26. Example 1: Variation of current waveforms as a function of pressure • The Universal PF code: RADPFV5.15de • Configure: for PF1000: 27 kV 3.5 Torr D2 (published and fitted) [run 100000 Torr, 19, 10, 7, 5, 2, 1 Torr; at 7 Torr show how to collect cols A and B (for curr waveform) and how to collect dataline.]

  27. Steps: II Run PF1000 at 27 kV at various pressure in D; Collect data 1. Collect current waveforms 2. Collect data of dynamics and pinch properties and neutron yield

  28. Fire the PF1000 • RADPFV5.15de • Look at results: Sheet 1 figures Sheet 3 dataline Sheet 3 (1) figures

  29. Fire the PF1000 • RADPFV5.15de • Look at results: Sheet 1 figures Sheet 3 dataline Sheet 3 (1) figures

  30. PF1000 fitted results

  31. Collect current waveform 3.5 Torr(copy columns A & B and paste on another sheet)

  32. Collect data PF1000 3.5 Torr(copy dataline and paste on another sheet; select data)

  33. SF1000: Current Waveforms as functions of Pressure(toggle to elena file to show pg of collected waveforms and selected data)

  34. PF1000: A Selection of data

  35. PF1000: Ynvs Pressure

  36. PF1000: Neutron Yield vs Pressure; and physics involved

  37. Steps: III Interpret results of experiments 1. Show a set of current waveform at various pressures 2. Show a set of pinch properties as a function of data • Discuss decrease of Ipeak as operation pressure P0 is decreased in terms of dynamic resistance • Observe behaviour of Ipinch as pressure is decreased • Observe neutron yield Yn as function of pressure • Discuss the behaviour of Ynvs P0 in terms of behaviour of Ipinch and pinch ion density.

  38. Notes: • 1) Pressure increases, Ipeak increases • 2) Ipinch increases, peaks just before 5 Torr, then drops • EINP follows roughly trend of Ipinch • ni, not plotted, seen from table to increase continuously with presssure • Yn peaks not where Ipinch peaks, but at higher P due to increase in ni • All Competing effects need to be considered • The effects, all regulated by the physics, are automatically included in the model

  39. Variations of Project • Different machines- including your own and others • Different gases- D-T mixture for neutrons Neon for neon SXR Ar, N2, O2 for SXR Compare with experimental results- see examples below

  40. PF-400J: AEC Chile 1.Fit computed to measured current waveforms to get model parameters 2.Use these fitted model parameters for PF400J to get Yn at various pressures 3. Compare computed with measured Yn (agreement is state-of-the-art)

  41. FN-II: U of Mexico 1.fit computed to measured current waveforms to get model parameters 2.Use these fitted model parameters for FN-II to get Yn at various pressures 3. Compare computed with measured Yn (agreement is state-of-the-art)

  42. Conclusions We carried out a Numerical Experiment – To obtain neutron yield Yn of PF1000 as function of pressure, and relate to pinch data We started with a published current waveform of the PF1000 at 27 kV. We carried out a typical fitting (of computed to measured current waveform) to obtain L0 and the model parameters for the PF1000. With the complete parameters of the PF1000 we ran experiments for the PF1000 at 27 kV varying the pressure from 19 Torr down to 1 Torr deuterium. We collected the current waveforms and pinch parameters; at various pressures and obtained the neutron yield Yn with pressure P0 curve. The shape of the neutron yield curve was correlated to the behaviour of the pinch current and pinch density. We noted that the peak neutron yield at 2x1011 is consistent with the measured range of neutrons as published. As an extension to the experiment, we compared the computed Ynvs P0 curve to the published curves for several machines including PF-400J and FN-II. y. International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

  43. THANK YOU Profound Simple Research Projects developed from Plasma Focus Numerical Experiments

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