International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012...

International Workshop on Plasma Science and Applications

(IWPSA2012) 4 – 5 October 2012 University of Chulalongkorn

INTI International University, Nilai, MalaysiaInstitute for Plasma Focus Studies, Melbourne Australia





Parameters of a PFNumerical Experiments – an example PF1000 Step I - Fit Computed Current (CC) to Measured Current(MC)Obtain all parameters and a Measured CurrentConfigure the codeAdd Measured Current Fire, compare Computed Current(CC) to MC

Vary parameters until CC fits MCStep II – PF1000 Yn vs PConfigure code at 27kV, 3.5 Torr D using parameters fitted in Part IRun at various P for D gasCollect Computed data and current waveformsInterpret results and notesVarious NE ProjectsConclusion





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:Steps I: Obtain all parameters of PF1000Obtain all parameters of PF1000

1.1.Require a measured current waveform - obtain this current Require a measured current waveform - obtain this current waveform and record the parameters which are givenwaveform and record the parameters which are given2.2.Configure the code as the PF1000 using given parameters; note Configure the code as the PF1000 using given parameters; note those parameters that are not certain or guessedthose parameters that are not certain or guessed3.3.Fire the PF1000, compare computed current waveform with Fire the PF1000, compare computed current waveform with measured current waveformmeasured current waveform4.4.Fit computed waveform to measured waveformFit computed waveform to measured waveforma) Fit current rise slope, adjust static inductance La) Fit current rise slope, adjust static inductance L0 0 where necessarywhere necessary

b) Fit position of start of dip adjusting fb) Fit position of start of dip adjusting fmm and f and fcc as necessary as necessaryc) Fit slope of dip, adjusting fc) Fit slope of dip, adjusting fmrmr, f, fcrcr as necessary as necessary





1. 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 columnsIn the case of PF1000 we do not have a digital file, but there is a published waveform in a published paperWe had digitised the waveform using a freeware digitising software called Engauge





PF1000:published waveform and digitised waveform





Start Configuration

Given: L0 (nH) C0 (µF) b (cm) a (cm) z0 (cm) r0 (mΩ)

20 1332 16 11.55 60 6

fm fc fmr fcr

0.1 0.7 0.2 0.7

V0 (kV) P0 (Torr) MW A Atom-molecule

27 3.5 4 1 2





Fire the PF1000, Fire the PF1000,

compare Computed Current waveform with compare Computed Current waveform with

Measured Current waveformMeasured Current waveform





Fitting PF1000 27kV-adjusting model parameters Fitting PF1000 27kV-adjusting model parameters until computed current waveform matches until computed current waveform matches measured (after getting Lmeasured (after getting L00 correct) correct)





PF1000 fitted resultsPF1000 fitted results





a) Fit current rise slope, adjust static inductance La) Fit current rise slope, adjust static inductance L0 0 where where necessary necessary

b) Fit position of start of dip adjusting fb) Fit position of start of dip adjusting fmm and f and fcc as as necessarynecessary

c) Fit slope of dip, adjusting fc) Fit slope of dip, adjusting fmrmr, f, fcrcr as necessary as 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.]





Steps: II Run PF1000 at 27 kV at various pressure in D; Collect data

1. Collect current waveforms2. 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





Steps: III Interpret results of experiments 1. Show a set of current waveform at various pressures2. 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 Yn vs P0 in terms of behaviour of Ipinch and pinch ion density.





1) Pressure increases, Ipeak increases2) Ipinch increases, peaks just before 5 Torr, then dropsEINP follows roughly trend of Ipinchni, not plotted, seen from table to increase continuously with presssureYn peaks not where Ipinch peaks, but at higher P due to increase in niAll Competing effects need to be consideredThe effects, all regulated by the physics, are automatically included in the model





Different machines- including your own and othersDifferent gases- D-T mixture for neutronsNeon for neon SXRAr, 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 Yn vs P0 curve to the published curves for several machines including PF-400J and FN-II.

yy.






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International Workshop on Plasma Science and Applications (IWPSA2012) 4 – 5 October 2012...

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