International Workshop on Plasma Science Applications 27 28

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International Workshop on Plasma Science & Applications, 27 & 28 October, Tehran, Iran Review

International Workshop on Plasma Science & Applications, 27 & 28 October, Tehran, Iran Review of Plasma Focus Numerical Experiments Scaling and Compression Enhancement S H Saw and S Lee INTI International University, 71800 Nilai, Malaysia Institute for Plasma Focus Studies, Chadstone VIC 3148 Australia e-mail: [email protected] com. au sorheoh. [email protected] edu. my The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Plasma Focus- Scaling Properties and Scaling Laws Outline 1. Lee Model code- relates to

Plasma Focus- Scaling Properties and Scaling Laws Outline 1. Lee Model code- relates to physical reality through measured current trace; results are reference points for diagnostics 2. Axial phase scaling properties axial speed, speed factor, energy density 3. Radial phase scaling properties -same speeds, temperatures, densities -pinched plasma dimensions, lifetimes 4. Scaling Laws: Neutrons and SXR Global Scaling Laws for neutrons 5. New developments: instability phase modelling, current-stepping, radiative collapse, The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

The Plasma Focus Plasma focus: small fusion device, complements international efforts to build fusion

The Plasma Focus Plasma focus: small fusion device, complements international efforts to build fusion reactor Multi-radiation device - x-rays, particle beams and fusion neutrons Neutrons for fusion studies Soft XR applications include microelectronics lithography and micro-machining Large range of device-from J to thousands of k. J Experiments-dynamics, radiation, instabilities and nonlinear phenomena The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

The 5 phases of Lee Model code Includes electrodynamical and radiation-coupled equations to portray

The 5 phases of Lee Model code Includes electrodynamical and radiation-coupled equations to portray the REGULAR mechanisms of the: • axial (phase 1) • radial inward shock (phase 2) • radial RS (phase 3) • slow compression radiation phase (phase 4) • the expanded axial post-pinch phase (phase 5) • Extension to phase 4 a- instability-induced resistive phase Crucial technique of the code: Current Fitting The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

The Plasma Dynamics in Focus Radial Phase Axial Accelaration Phase Inverse Pinch Phase HV

The Plasma Dynamics in Focus Radial Phase Axial Accelaration Phase Inverse Pinch Phase HV 30 F, 15 k. V

The Lee Model Code Realistic simulation properties of all gross focus Couples the electrical

The Lee Model Code Realistic simulation properties of all gross focus Couples the electrical circuit with plasma focus dynamics, thermodynamics and radiation (1984, 1990) 5 -phase model; axial & radial phases Includes plasma self-absorption for SXR yield (2000) Includes neutron yield, Yn, using a beam– target mechanism(2007) The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

The Plasma Focus Axial Phase Radial Phases The 4 th International Workshop on Plasma

The Plasma Focus Axial Phase Radial Phases The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Philosophy of Current fittings • • • (1/3) The current trace of the focus

Philosophy of Current fittings • • • (1/3) The current trace of the focus is the best indicators of gross performance. The exact time profile of the current trace is governed by the bank parameters, the focus tube geometry and the operational parameters. It depends on the mass swept-up and drive current fractions and their variations. These parameters determine the dynamics, specifically the axial and radial speeds which in turn affect the profile and magnitudes of the current. There are many underlying mechanisms (see following 2 slides) which are not simply modeled. The detailed current profile is influenced by these effects and during the pinch phase also reflects the Joule heating and radiative yields. At the end of the pinch phase the profile reflects the sudden transition from a constricted pinch to a large column flow. Thus the current powers all dynamic, electrodynamic, thermodynamic and radiation processes in the various phases. Conversely all dynamic, electrodynamic, thermodynamic and radiation processes in the various phases affect the current. The current waveform contains information on all the dynamic, electrodynamic, thermodynamic and radiation processes that occur in the various phases. This explains the importance attached to matching the computed total current trace to the measured total current trace in the procedure adopted by the Lee model code. Once matched, the fitted model parameters assure that computation proceeds with all physical mechanisms accounted for, in the gross energy & mass balance sense. The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Philosophy of Current fittings (2/3) • So we relate to reality through a measured

Philosophy of Current fittings (2/3) • So we relate to reality through a measured current trace • computed current waveform is adjusted to fit measured current waveform • Adjustment by model parameters fm, fc, fmr, fcr; account for all factors affecting mass flow and force field flows not specifically modelled including all KNOWN and UNKNOWN effects. • When adjustments are completed so that the computed waveform fit the measured waveform, the computed system is energetically and mass-wise equivalent to the real system. The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Philosophy of Current fittings (3/3) All inaccurate model effects are accounted for by the

Philosophy of Current fittings (3/3) All inaccurate model effects are accounted for by the fitting: Known effects that might deviate from our modelling include: 1. 2. 3. 4. 5. 6. 7. Geometrical, including our assumed geometry Our assumed structures and distributions Mass shedding & current sheet CS porosity Current shedding, fragmenting, leakage & inclination Non uniformity & inhomogeneity of CS and plasma; boundary layer effects Radiation & thermodynamics Ejection of mass caused by necking curvatures Once current-fitted, all unspecified even unknown effect are also accounted for in terms of energy and mass The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

From Measured Current Waveform to Modelling for Diagnostics (1/4) Procedure to operate the code:

From Measured Current Waveform to Modelling for Diagnostics (1/4) Procedure to operate the code: Step 1: Configure the specific plasma focus, Input: • Bank parameters, L 0, C 0 and stray circuit resistance r 0 • Tube parameters b, a and z 0 and • Operational parameters V 0 and P 0 and the fill gas The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Step 2: Fitting the computed current waveform to the measured waveform – (connecting with

Step 2: Fitting the computed current waveform to the measured waveform – (connecting with reality) (2/4) • • A measured discharge current Itotal waveform for the specific plasma focus is required The code is run successively. At each run the computed Itotal waveform is fitted to the measured Itotal waveform by varying model parameters fm, fc, fmr and fcr one by one, one step for each run, until computed waveform agrees with measured waveform. The 5 -Point Fit: • First, the axial model factors fm, fc are adjusted (fitted) until – (1) computed rising slope of the Itotal trace and – (2) the rounding off of the peak current as well as – (3) the peak current itself • are in reasonable (typically very good) fit with the measured Itotal trace. Next, adjust (fit) the radial phase model factors fmr and fcr until - (4) the computed slope and (5) the depth of the dip agree with the measured Itotal waveform. The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Fitting computed Itotal wafeform to measured Itotal twaveform: the 5 -point fit (3/4) The

Fitting computed Itotal wafeform to measured Itotal twaveform: the 5 -point fit (3/4) The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Once fitted: model is energy-wise & masswise equivalent to the physical situation (4/4) •

Once fitted: model is energy-wise & masswise equivalent to the physical situation (4/4) • All dynamics, electrodynamics, radiation, plasma properties and neutron yields are realistically simulated; so that the code output of these quantities may be used as reference points for diagnostics The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Numerical Diagnostics- Example of NX 2 Time histories of dynamics, energies and plasma properties

Numerical Diagnostics- Example of NX 2 Time histories of dynamics, energies and plasma properties computed by the code 1/3 Last adjustment, when the computed Itotal trace is judged to be reasonably well fitted in all 5 features, computed times histories are presented (NX 2 operated at 11 k. V, 2. 6 Torr neon) Computed Itotal waveform fitted to measured Computed Tube voltage Computed Itotal & Iplasma Computed axial trajectory & speed The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Numerical Diagnostics- Example of NX 2 The 4 th International Workshop on Plasma Science

Numerical Diagnostics- Example of NX 2 The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee 2/3

Numerical Diagnostics- Example of NX 2 The 4 th International Workshop on Plasma Science

Numerical Diagnostics- Example of NX 2 The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee 3/3

Scaling Properties 3 k. J machine Small Plasma Focus 1000 k. J machine Big

Scaling Properties 3 k. J machine Small Plasma Focus 1000 k. J machine Big Plasma Focus The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Comparison (Scaling) - 1/2 Important machine properties: UNU ICTP PFF PF 1000 E 0

Comparison (Scaling) - 1/2 Important machine properties: UNU ICTP PFF PF 1000 E 0 3 k. J at 15 k. V 600 k. J at 30 k. V I 0 170 k. A 2 MA ‘a’ 1 cm 11. 6 cm The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Comparison (Scaling) - 2/2 Important Compressed Plasma Properties • Density of plasma • Temperature

Comparison (Scaling) - 2/2 Important Compressed Plasma Properties • Density of plasma • Temperature of plasma These two properties determine radiation intensity energy radiated per unit volume per unit lifetime of plasma) • Size of plasma • Lifetime of plasma These two properties together with the above two determine total yield. The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Compare Temperatures UNU ICTP PFF PF 1000 (from LS lecture) (this estimate) Axial speed

Compare Temperatures UNU ICTP PFF PF 1000 (from LS lecture) (this estimate) Axial speed 10 12 cm/us Radial speed 25 20 cm/us Temperature 1. 5 x 106 1 x 106 K Reflected S 3 x 106 2 x 106 K After RS comes pinch phase which may increase T a little more in each case Comparative T: about same; several million K The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Compare Number Density – 1/2 • During shock propagation phase, density is controlled by

Compare Number Density – 1/2 • During shock propagation phase, density is controlled by the initial density and by the shock-’jump’ density • Shock density ratio=4 (for high T deuterium) • RS density ratio=3 times • On-axis density ratio=12 • Initial at 3 torr n=2 x 1023 atoms m-3 • RS density ni=2. 4 x 1024 m-3 or 2. 4 x 1018 per cc • Further compression at pinch; raises no. density higher typically to just under 1019 per cc. The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Compare Number Density – 2/2 • Big or small PF initial density small range

Compare Number Density – 2/2 • Big or small PF initial density small range of several torr • Similar shock processes • Similar final density The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Big PF and small PF Same density, same temperature • Over a range of

Big PF and small PF Same density, same temperature • Over a range of PFs smallest 0. 1 J to largest 1 MJ; over the remarkable range of 7 orders of magnitude- same initial pressure, same speeds • • This leads to conclusion that all PF’s: Same T, hence same energy (density) per unit mass same n, hence same energy (density) per unit volume Hence same radiation intensity The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Next question: How does yield vary? • Yield is Intensity x Volume x Lifetime

Next question: How does yield vary? • Yield is Intensity x Volume x Lifetime • Dimensions and lifetime of the focus will determine radiation and particle yields. • How do dimensions and lifetime of compressed plasma vary from PF to PF? • Look at experimental observations The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Comparing large and small PF’s- Dimensions and lifetimesputting shadowgraphs side-by-side, same scale Anode radius

Comparing large and small PF’s- Dimensions and lifetimesputting shadowgraphs side-by-side, same scale Anode radius 1 cm 11. 6 cm Pinch Radius: 1 mm 12 mm Pinch length: 8 mm 90 mm Lifetime ~10 ns order of ~100 ns The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Comparing small (sub k. J) and large (thousand k. J) Plasma Focus Scaling Properties:

Comparing small (sub k. J) and large (thousand k. J) Plasma Focus Scaling Properties: size (energy) , current, speed and yield Scaling properties-mainly axial phase Table 1 Plasma Focus Devices E 0 a Z 0 V 0 P 0 Ipeak va ID SF Yn k. J cm cm k. V Torr k. A cm/ s k. A/cm (k. A/cm)/Torr 0. 5 10 8 PF 1000 486 11. 6 60 27 4 1850 11 160 85 1100 UNU ICTP PFF PF 400 J 2. 7 1. 0 15. 5 14 3 164 9 173 100 0. 20 0. 4 0. 6 1. 7 28 7 126 9 210 82 0. 01 The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Scaling of anode radius ‘a’ with current (I) and storage energy (E 0) Scaling

Scaling of anode radius ‘a’ with current (I) and storage energy (E 0) Scaling properties-machine properties • Peak current Ipeak increases with E 0. • Anode radius ‘a’ increases with E 0. • Current per cm of anode radius (ID) Ipeak /a : narrow range 160 to 210 k. A/cm for all machines The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Speeds, Speed Factor SF and Yn • Observed Peak axial speed va : 9

Speeds, Speed Factor SF and Yn • Observed Peak axial speed va : 9 to 11 cm/us. • SF (speed factor) (Ipeak /a)/r 0. 5 : narrow range 82 to 100 (k. A/cm) per Torr 0. 5 D • Fusion neutron yield Yn : 106 for PF 400 -J to 1011 for PF 1000 (Yn 5 orders of magnitude for storage energy of 3 orders of magnitude) The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Scaling properties-mainly radial phase The 4 th International Workshop on Plasma Science and Application

Scaling properties-mainly radial phase The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

 • Moreover number densities are also the same for big and small focus,

• Moreover number densities are also the same for big and small focus, in the pinch compressed plasma around 1019/cc The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Focus Pinch T, dimensions & lifetime with anode radius ‘a’ Scaling properties-mainly radial phase

Focus Pinch T, dimensions & lifetime with anode radius ‘a’ Scaling properties-mainly radial phase • Dimensions and lifetime scales as the anode radius ‘a’. • rmin/a (almost constant at 0. 14 -0. 17) • zmax/a (almost constant at 1. 5) • Pinch duration narrow range 8 -14 ns/cm of ‘a’ • Tpinch is measure of energy per unit mass. Quite remarkable that this energy density varies so little (factor of 5) over such a large range of device energy (factor of 1000). The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Rule-of-thumb scaling properties, (subject to minor variations caused primarily by the variation in c=b/a)

Rule-of-thumb scaling properties, (subject to minor variations caused primarily by the variation in c=b/a) over whole range of device • Axial phase energy density (per unit mass) constant • Radial phase energy density (per unit mass) constant • Pinch radius ratio constant • Pinch length ratio constant • Pinch duration per unit anode radius constant The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Further equivalent Scaling Properties • Constant axial phase energy density (Speed Factor (I/a)/r 0.

Further equivalent Scaling Properties • Constant axial phase energy density (Speed Factor (I/a)/r 0. 5, speed) equivalent to constant dynamic resistance • I/a approx constant since r has only a relatively small range for each gas The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Scaling Conclusions Energy Storage in Plasma Focus spans 7 orders of magnitudes We discussed

Scaling Conclusions Energy Storage in Plasma Focus spans 7 orders of magnitudes We discussed the scaling of properties 1. Machine properties - Ipeak, anode radius ‘a’, storage energy; (Ipeak/a)=constant 2. Axial phase scaling properties - axial speed, speed factor, energy density; constant 3. Radial phase scaling properties -same speeds, temperatures, densities; constant hence same radiation intensities and 4. Radiation/particle yields depend only on -pinched plasma dimensions, lifetimes: depend on ‘a’, on I The current dominates Plasma Focus Yields The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Insights Ground-breaking Insights published • Limitation to Pinch Current and Yields- Appl Phys Letts.

Insights Ground-breaking Insights published • Limitation to Pinch Current and Yields- Appl Phys Letts. 92 (2008) S Lee & S H Saw: an unexpected, important result • Neutron Yield Scaling-sub k. J to 1 MJ-J Fusion Energy 27 (2008) S Lee & S H Saw- multi-MJ- PPCF 50 (2008) S Lee • Neon Soft x-ray Scaling- PPCF 51 (2009) S Lee, S H Saw, P Lee, R S Rawat • Neutron Yield Saturation- Appl Phys Letts. 95 (2009) S Lee Simple explanation of major obstruction to progress The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Summary-Scaling Laws (1/2) The scaling laws obtained (at optimized condition) for Neutrons: Yn~E 02.

Summary-Scaling Laws (1/2) The scaling laws obtained (at optimized condition) for Neutrons: Yn~E 02. 0 at tens of k. J to Yn~E 00. 84 at the highest energies (up to 25 MJ) Yn =3. 2 x 1011 Ipinch 4. 5 (0. 2 -2. 4 MA) Yn=1. 8 x 1010 Ipeak 3. 8 (0. 3 -5. 7 MA) The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Summary-Scaling Laws (2/2) The scaling laws obtained (at optimized condition) for neon SXR: Ysxr~E

Summary-Scaling Laws (2/2) The scaling laws obtained (at optimized condition) for neon SXR: Ysxr~E 01. 6 at low energies Ysxr~E 00. 8 towards 1 MJ Ysxr~Ipeak 3. 2 (0. 1– 2. 4 MA) and Ysxr~Ipinch 3. 6 (0. 07 -1. 3 MA) The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Global scaling law, combining experimental and numerical data- Yn scaling , numerical experiments from

Global scaling law, combining experimental and numerical data- Yn scaling , numerical experiments from 0. 4 k. J to 25 MJ (solid line), compared to measurements compiled from publications (squares) from 0. 4 k. J to 1 MJ. What causes the deterioration of Yield scaling? The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

What causes current scaling deterioration and eventual saturation? 1/2 • The axial speed loads

What causes current scaling deterioration and eventual saturation? 1/2 • The axial speed loads the discharge circuit with a dynamic resistance • The same axial speed over the range of devices means the same dynamic resistance constituting a load impedance DR 0 • Small PF’s : have larger generator impedance Z 0=[L 0/C 0]^0. 5 than DR 0 • As energy is increased by increasing C 0, generator impedance Z 0 drops The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

What causes current scaling deterioration and eventual saturation? 2/2 • At E 0 of

What causes current scaling deterioration and eventual saturation? 2/2 • At E 0 of k. J and tens of k. J the discharge circuit is dominated by Z 0 • Hence as E 0 increases, I~C 0 -0. 5 • At the level typically of 100 k. J, Z 0 has dropped to the level of DR 0; circuit is now no longer dominated by Z 0; and current scaling deviates from I~C 0 -0. 5, beginning of current scaling deterioration. • At MJ levels and above, the circuit becomes dominated by DR 0, current saturates The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Into the Future • Anomalous Resistive Modelling • Current Stepping • Radiative Collapse The

Into the Future • Anomalous Resistive Modelling • Current Stepping • Radiative Collapse The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Current-Step method to enhance compressions The 4 th International Workshop on Plasma Science and

Current-Step method to enhance compressions The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Ongoing IPFS numerical experiments of Multi-MJ, High voltage MJ and Current-step Plasma Focus The

Ongoing IPFS numerical experiments of Multi-MJ, High voltage MJ and Current-step Plasma Focus The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Current step increases compression The 4 th International Workshop on Plasma Science and Application

Current step increases compression The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Comparison Deuterium PF Case Study: • 50 k. V 777 u. F stepped with

Comparison Deuterium PF Case Study: • 50 k. V 777 u. F stepped with 200 k. V 20 u. F total energy=1. 37 MJ produces 1013 D-D neutrons • Compared with 90 k. V 777 u. F energy 3 MJ Produces 1013 D-D neutrons • Current-step has improved compression and the yield per unit input energy The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Radiative Cooling and Collapse In Kr and Xe, intense line radiation reduces pinch plasma

Radiative Cooling and Collapse In Kr and Xe, intense line radiation reduces pinch plasma pressure allowing magnetic piston to compress further. Numerical experiments show that a complete column collapse to very small radii is possible. • Thus radiative cooling/collapse can enhance compression • This mechanism may be instrumental in the observed neutron enhancement of Kr-doped deuterium PF • Numerical Experiments will be carried out to understand use this mechanism better

 Numerical Experiments on 3 k. J PF demonstrating Kr pinch column undergoing radiative

Numerical Experiments on 3 k. J PF demonstrating Kr pinch column undergoing radiative collapse of whole column 0. 1 Torr 0. 5 Torr

Conclusion • Numerical experiments have played a significant role in the understanding of scaling

Conclusion • Numerical experiments have played a significant role in the understanding of scaling properties and scaling laws of the plasma focus • We continue to push the boundaries of this understanding upwards by studying yield enhancement methods developed within the numerical experiments. The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

International Workshop on Plasma Science & Applications, 27 & 28 October, Tehran, Iran Review

International Workshop on Plasma Science & Applications, 27 & 28 October, Tehran, Iran Review of Plasma Focus Numerical Experiments Scaling and Compression Enhancement S H Saw and S Lee INTI International University, 71800 Nilai, Malaysia Institute for Plasma Focus Studies, Chadstone VIC 3148 Australia e-mail: [email protected] com. au sorheoh. [email protected] edu. my The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

The Lee Model Code • Institute for Plasma Focus Studies – http: //www. plasmafocus.

The Lee Model Code • Institute for Plasma Focus Studies – http: //www. plasmafocus. net/ • Internet Workshop on Plasma Focus Numerical Experiments (IPFS-IBC 1) 14 April 19 May 2008 – http: //www. plasmafocus. net/IPFS/Papers/IWPCAk eynote 2 Resultsof. Internet-based. Workshop. doc • Lee S Radiative Dense Plasma Focus Computation Package: RADPF o o http: //www. intimal. edu. my/school/fas/UFLF/File 1 R ADPF. htm http: //www. plasmafocus. net/IPFS/modelpackage/F ile 1 RADPF. htm The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Papers from Lee model code 13 S Lee and S H Saw, “Pinch current

Papers from Lee model code 13 S Lee and S H Saw, “Pinch current limitation effect in plasma focus, ” Appl. Phys. Lett. 92, 2008, 021503. S Lee and S H Saw, “Neutron scaling laws from numerical experiments, ” J Fusion Energy 27, 2008, pp. 292 -295. S Lee, P Lee, S H Saw and R S Rawat, “Numerical experiments on plasma focus pinch current limitation, ” Plasma Phys. Control. Fusion 50, 2008, 065012 (8 pp). S Lee, S H Saw, P C K Lee, R S Rawat and H Schmidt, “Computing plasma focus pinch current from total current measurement, ” Appl. Phys. Lett. 92 , 2008, 111501. S Lee, “Current and neutron scaling for megajoule plasma focus machine, ” Plasma Phys. Control. Fusion 50, 2008, 105005, (14 pp). S Lee and S H Saw, “Response to “Comments on ‘Pinch current limitation effect in plasma focus’”[Appl. Phys. Lett. 94, 076101 (2009)], ” Appl. Phys. Leet. 94, 2009, 076102. S Lee, S H Saw, L Soto, S V Springham and S P Moo, “Numerical experiments on plasma focus neutron yield versus pressure compared with laboratory experiments, ” Plasma Phys. Control. Fusion 51, 2009, 075006 (11 pp). S H Saw, P C K Lee, R S Rawat and S Lee, “Optimizing UNU/ICTP PFF Plasma Focus for Neon Soft X-ray Operation, ” IEEE Trans Plasma Sci, VOL. 37, NO. 7, JULY (2009) Lee S, Rawat R S, Lee P and Saw S H. “Soft x-ray yield from NX 2 plasma focus- correlation with plasma pinch parameters” JOURNAL OF APPLIED PHYSICS 106, 023309 (2009) S Lee, S H Saw, P Lee and R S Rawat, “Numerical experiments on plasma focus neon soft x-ray scaling”, Plasma Physics and Controlled Fusion 51, 105013 (8 pp) (2009) M Akel, S Hawat, S Lee, Numerical Experiments on Soft X-Ray Emission Optimization of Nitrogen Plasma in 3 k. J Plasma Focus Using Modified Lee Model, J Fusion Energy DOI 10. 1007/s 10894 -0099203 -4 First online Tuesday, May 19, 2009 M Akel, S Hawat, S Lee, Pinch Current and Soft x-ray yield limitation by numerical experiments on Nitrogen Plasma Focus, J Fusion Energy DOI 10. 1007/s 10894 -009 -9238 first online 21 August 2009 The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Papers from Lee model code 23 • S. Lee. Neutron Yield Saturation in Plasma

Papers from Lee model code 23 • S. Lee. Neutron Yield Saturation in Plasma Focus-A fundamental cause. Appl Phys Letts (2009) 95, 151503 93. . • M. Akel, Sh. Al-Hawat, S. H. Saw and S. Lee. Numerical Experiments on Oxygen Soft X- Ray Emissions from Low Energy Plasma Focus Using Lee Model J Fusion Energy DOI 10. 1007/s 10894 -009 -9262 -6 First online 22 November 2009 • Sing Lee and Sor Heoh Saw Numerical Experiments providing new Insights into Plasma Focus Fusion Devices-Invited Review Paper: for Energy: special edition on “Fusion Energy” Energies 2010, 3, 711 -737; doi: 10. 3390/en 3040711 -Published online 12 April 2010 • S H Saw, S Lee, F Roy, PL Chong, V Vengadeswaran, ASM Sidik, YW Leong & A Singh. In-situ determination of the static inductance and resistance of a plasma focus capacitor bank –Rev Sci Instruments (2010) 81, 053505 • S H Saw and S Lee, Scaling the Plasma Focus for Fusion Energy Considerations- Int. J. Energy Res. (2010) View this article online at wileyonlinelibrary. com. DOI: 10. 1002/er. 1758 • S H Saw and S Lee- Scaling laws for plasma focus machines from numerical experiments Energy and Power Engineering, 2010, 65 -72 doi: 10. 4236/epe. 2010. 21010, Published online February 2010 (http: //www. scirp. org/journal/epe) • S H Saw and S Lee, Scaling the Plasma Focus for Fusion Energy Considerations, International J of Energy Research (2010) View at wileyonlinelibrary. com DOI: 10. 1002/er. 1758. 8 pages • S Lee and S H Saw, Numerical Experiments providing new Insights into Plasma Focus Fusion Devices, Invited Review Paper for Energies: special edition on “Fusion Energy” Energies 2010, 3, 711 -737; doi: 10. 3390/en 3040711 -Published online 12 April 2010 • In-situ determination of the static inductance and resistance of a plasma focus capacitor bank The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee

Papers from Lee model code • • 33 S H Saw, S Lee, F

Papers from Lee model code • • 33 S H Saw, S Lee, F Roy, PL Chong, V Vengadeswaran, ASM Sidik, YW Leong and A Singh, Review Sci Instruments (2010) 81, 053505 S Lee, S H Saw, A E Abdou and H Torreblanca, Characterising Plasma Focus Devices– Role of Static Inductance– Instability Phase Fitted by Anomalous Resistance, J Fusion Energy DOI 10. 1007/s/10894 -010 -9372 -1, Published online: 25 December 2010, Journal of Fusion Energy: Volume 30, Issue 4 (2011), Page 277 -282 http: //www. springerlink. com/openurl. asp? genre=article&id=doi: 10. 1007/s 10894 -010 -9372 -1 S Lee and S H Saw, Nuclear Fusion Energy – Mankind’s Giant Step Forward, J Fusion Energy DOI 10. 1007/s 10894 -011 -9390 -7 online first TM 10 February 2011 S Lee and S H Saw, The Plasma Focus – Trending into the Future, Accepted for publication: International J Energy Research, 11 July 2011 S Lee, S H Saw, R S Rawat, P Lee, A. Talebitaher, P L Chong, F Roy, A Singh, D Wong and K Devi, Correlation of soft-x-ray pulses with modeled dynamics of the plasma focus, Submitted to IEEE Trans on Plasma Science for publication Sh Al-Hawat, M. Akel , S. Lee, S. H. Saw, Model Parameters Versus Gas Pressure in Two Different Plasma Focus Devices Operated in Argon and Neon J Fusion Energy DOI 10. 1007/s 10894 -011 -9414 -3, Published online: 22 April 2011 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, Measurement and Processing of Fast Pulsed Discharge Current in Plamsa Focus Machines, J Fusion Energy DOI 10. 1007/s 10894 -011 -9456 -6, Published online: 28 July 2011 The 4 th International Workshop on Plasma Science and Application 27 th and 28 th October 2011, Tehran, Iran S H Saw & S Lee