Global View of the Lee Model code

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Global View of the Lee Model code

• S H Saw
• INTI International University, Nilai, Malaysia

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3 kJ Plasma Focus Designed for International
Collaboration
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Design of the UNU/ICTP PFF- 3kJ Plasma Focus
System??
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UNU/ICTP PFF- narrow trolley to fit ICTP lift???
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The 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 1984
• 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 .

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Philosophy of our Modelling

• 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.

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Priority of Basis

• Energy consistent for the total process and each
  part of the process
• Mass consistent
• Charge consistent
• Connected to the reality of experiments

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Priority of Results

• 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 in
  conformity with experiments
• Widest Scaling of the yields
• Insightful definition of scaling properties
• Design of new devices e.g. Hi V C-S
• Design of new experiments

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Philosophy, modelling, results and applications
of the Lee Model code
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Numerical Experiments

• Range of activities using the code is so wide
• Not theoretical
• Not simulation
• The only correct description is
• Numerical Experiments

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PF1000

• Lo nH Co uF b cm a cm z0 ro mW
• 33.5 1332 16 11.6 60 6.1
• fm fc fmr fcr
• 0.13 0.7 0.35 0.65
• Vo Po Mw A At/Molecular
• 27 3.5 4 1 2

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Firing the PF1000
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Fitting PF1000 27kV-adjusting model parameters
until computed current waveform matches measured
(after getting L0 correct)
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PF1000 fitted results
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PF1000 Yn Focus Pinch Properties as functions
of Pressure
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Plasma Focus- Numerical Experiments leading
Technology

• 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

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NE showing the way for experiments and technology

• 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 their L0 33 nH
• that their L0 was already at optimum
• that lowering their L0 would be a waste of
  effort and resources

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New General Insight- For every PF there is a
minimum L0 below which yield no longer increase

• It was thought that the lower L0 is the better
  would be the current and the yield
• Our NE showed that on the contrary every PF
  system has a minimum L0 no point trying to go
  below that- very expensive and will not increase
  yield
• This was a surprising result- and changes one
  frontier area of plasma focus technology

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Determination of Pinch Current- by fitting a
measured current trace with reliable neutron
yield to the computed current trace.

• by fitting a measured current trace with reliable
  neutron yield to the computed current trace.

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Results from Numerical Experiments with PF1000
- For decreasing L0- from 100 nH to 5 nH

• As L0 was 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.
• Yn also had a maximum value of 3.2x1011 at 35 nH.

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Pinch Current Limitation Effect - (1/3)

• L0 decreases? higher Ipeak ?bigger a ?longer zp
  ?bigger Lp
• L0 decreases ?shorter rise time? shorter zo?
  smaller La
• L0 decreases, Ipinch/Ipeak decreases

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Pinch Current Limitation Effect - (2/3)

• 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
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Pinch Current Limitation Effect - (3/3)

• 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

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Neutron yield scaling laws and neutron saturation
problem

• One of most exciting properties of plasma focus
  is
• Early experiments show YnE02
• 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

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Global Scaling LawScaling 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

• 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

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Scaling for large Plasma Focus

• 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)

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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

• IPFS numerical Experiments

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Fast capacitor bank 10x PF1000-Fully modelled-
1.5x1015 D-T neutrons per shot

• Operating Parameters 35kV, 14 Torr D-T
• Bank Parameters L033.5nH, C013320uF, r00.19mW
  
• E08.2 MJ
• Tube Parameters b35.1 cm, a25.3 cm z0220cm
• Ipeak7.3 MA, Ipinch3.0 MA
• Model parameters 0.13, 0.65, 0.35, 0.65

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Ongoing IPFS numerical experiments of Multi-MJ
Plasma Focus
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50 kV modelled- 1.2x1015 D-T neutrons per shot

• Operating Parameters 50kV, 40 Torr D-T
• Bank Parameters L033.5nH, C02000uF, r00.45mW
• E02.5 MJ
• Tube Parameters b20.9 cm, a15 cm z070cm
• Ipeak6.7 MA, Ipinch2.8 MA
• Model parameters 0.14, 0.7, 0.35, 0.7
• Improved performance going from 35 kV to 50 kV

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IFMIF-scale device

• 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

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Scaling further- possibilities

• 1. Increase E0, however note scaling
  deteriorated already below YnE0
• 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

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Scaling Plasma Focus from Ipinch using present
predominantly beam-target in Lee Model code
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SXR Scaling Laws

• First systematic studies in the world done in
  neon as a collaborative effort of IPFS, INTI IU
  CPR and NIE Plasma Radiation Lab
• Scaling laws extended to Argon by AECS

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Special characteristics of SXR-for applications

• 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

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Compression- and Yield- Enhancement methods

• Suitable design optimize compression
• Role of high voltage
• Role of special circuits e.g current-steps
• Role of radiative cooling and collapse

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Latest development

• Modelling
• Ion beam fluence
• Post focus axial shock waves
• Plasma streams
• Anode sputtered material

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Ion beam post-pinch plasma stream
calculationsSome preliminary Results- INTI
IU-IAEA collaboration
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6. Developing the most powerful training and
research system for the dawning of the Fusion Age.

• Integrate
• 6a the proven most effective hardware system
  of the UNU/ICTP PFF with
• 6b the proven most effective numerical
  experiment system Lee Model code
• with emphasis on dynamics, radiation and
  materials applications.

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Into the fusion era Plasma focus for
training/Research

• (a) Experimental facility TRPF
• 1 kJ focus 10 kV 20 uF 80 nH
• Measurements
• current, voltage sufficient to deduce dynamics
  and estimate temperatures
• Fibre-optics, pin diodes magnetic probes
  directly measure speeds, ns imaging
• SXR spectrometry, neutron counters TOF, ion
  collectors for radiation particle measurements
• Simple materials processing experiments

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Into the fusion era Plasma focus for research
training

• (b) Numerical Experiments code
• To complement TRPF
• Computes dynamics and energy distributions
• Plasma pinch evolution, size and life time
• Post focus Ion Beam, plasma stream and anode
  sputtered material
• Connection with reality through fitting computed
  current to measured current trace
• Behaviour of plasma focus and yields as functions
  of pressure, gases, storage energies, circuit
  currents and pinch currents.
• Carry out above experiments with any plasma
  focus.
• Optimization of planned plasma focus

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(a) The proven most effective 3 kJ PF system
The trolley based UNU/ICTP PFF 3 kJ plasma focus
training and research system will be updated as
a 1 kJ system
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(b) The proven most effective and comprehensive
Model code

• Firmly grounded in Physics
• Connected to reality
• From birth to death of the PF
• Useful and comprehensive outputs
• Diagnostic reference-many properties, design,
  scaling scaling laws, insights innovations

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(b) Philosophy, modelling, results and
applications of the Lee Model code