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Numerical Experiments on Plasma Focus S H Saw & S Lee

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Numerical Experiments on Plasma FocusS H Saw & S Lee

INTI International University, Nilai, Malaysia

Institute for Plasma Focus Studies, Melbourne Australia

- 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

- 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

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

- 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

- PF1000:published waveform and digitised waveform

Fire the PF1000,

compare Computed Current waveform with Measured Current waveform

Fire the PF1000,

compare Computed Current waveform with Measured Current waveform

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

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

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

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

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.

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.

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.

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.

- 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

- The Universal PF code: RADPFV5.15de
- Configure: for PF1000: 27 kV 3.5 Torr D2 (published and fitted)

- 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.]

- 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.]

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

- RADPFV5.15de
- Look at results: Sheet 1 figures
Sheet 3 dataline

Sheet 3 (1) figures

- RADPFV5.15de
- Look at results: Sheet 1 figures
Sheet 3 dataline

Sheet 3 (1) figures

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.

- 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

- 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

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)

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)

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

THANK YOU

Profound

Simple

Research Projects developed from Plasma Focus Numerical Experiments