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Teaching the Lee model code - Institute for Plasma Focus Studies

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									             Review of (UPFLF) Plasma Focus
               Numerical Experiments


                        S Lee1,2,3 &  H Saw1,2
         1
        INTI International University, Nilai, Malaysia
2
  Institute for Plasma Focus Studies, Melbourne, Australia
      3
       University of Malaya, Kuala Lumpur, Malaysia




International Workshop on Plasma Science and Applications, 4 & 5 October 2012, Bangkok, Thailand
    Plasma Focus Numerical Experiments-
             Outline of Lecture

•   Development, usage and results
•   Basis and philosophy
•   Reference for Diagnostics
•   Insights and frontiers
•   Continuing development- Ion beam modelling



             Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                         S H Saw
UNU ICTP PFF- 3 kJ Plasma Focus Designed for
  International Collaboration within AAAPT Background




         Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                     S H Saw
Design of the UNU/ICTP PFF- 3kJ Plasma Focus System                                   Background




               Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                           S H Saw
UNU/ICTP PFF- placed at ICTP, 1988                                                      Background




                                                                                Network: Malaysia,
                                                                                Singapore, Thailand,
                                                                                Pakistan, India,
                                                                                Egypt,

                                                                                Similar machines
                                                                                with designs based
                                                                                on or upgraded:
                                                                                Zimbabwe, Syria,
                                                                                USA, Bulgaria, Iran




         Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                     S H Saw
                             The Code                                                Intro 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 1983
• 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 .
              Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                          S H Saw
  Review of UPFLF Plasma Focus Numerical
               Experiments                                                            Intro code




• The code10 couples the electrical circuit with PF 
  dynamics, thermodynamics and radiation.  
• Using standard circuit equations and Newtonian equations 
  of motion adapted for the plasma focus:
   the code is consistent in 
        (a) energy, 
        (b) charge and 
            (c) mass. 


               Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                           S H Saw
    Development of the code                                                          Intro code




• It was described in 198311 and used in the design and 
  interpretation of  experiments12-15.  
• An improved 5-phase code incorporating finite small 
  disturbance speed16, radiation and radiation-coupled 
  dynamics was used17-19, 
• It was web-published20 in 2000 and 200521. 
• Plasma self- absorption was included20 in 2007




              Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                          S H Saw
                                     Usage                                          Intro code




• It has been used extensively as a complementary 
  facility in several machines, for example: UNU/ICTP 
  PFF12,14,15,17-19,  NX219,22, NX119, DENA23, AECS
• It has also been used in other machines for design
  and interpretation including Chile’s sub-kJ PF
  and other machines24, Mexico’s FNII25 and the
  Argentinian UBA hard x-ray source26.
• More recently KSU PF (US), NX3 (Singapore), FoFu 
  I (US) and several Iranian machines APF, Tehran U, 
  AZAD U
             Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                         S H Saw
              Information derived                                                     Intro code




Information computed includes 
•axial and radial dynamics11,17-23, pinch properties
•SXR emission characteristics and  yield17-19, 22, 27-33, 
•design of machines10,12,24,26, 
•optimization of machines10,22, 24,30 and adaptation to 
Filippov-type DENA23. 
•Speed-enhanced PF17 was facilitated.




               Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                           S H Saw
             Information Derived                                                          Intro code



Scaling Properties; 
•Constancy of energy density (per unit mass) across range of 
machines14
•Hence same temperature and density14
•Constancy of drive current density I/a relating to the speed factor14
• (I/a)/r0.5
•Scaling of pinch dimensions & lifetime14  with anode radius ‘a’: 
        pinch radius ratio  rp/a =constant
        pinch length ratio  zp/a=constant
        pinch duration ratio  tp/a=constant

                   Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                               S H Saw
        Recent development and Insights                                               Intro code



•   PF neutron yield calculations34 
•   Current & neutron yield limitations35 with reducing L0
•   Wide-ranging neutron scaling laws
•   Wide-ranging soft x-ray scaling laws in various gases
•   Neutron saturation36,37- cause and Global Scaling Law
•   Radiative collapse 38
•   Current-stepped PF39
•   Extraction of diagnostic data33,40-42
•   Anomalous resistance data43,44 from current signals
•   Benchmarks for Ion Beams- scaling with E0.
               Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                           S H Saw
     Philosophy of our Modelling                                                  Philosophy




• 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.

           Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                       S H Saw
          Priority of Basis                                                                Philosophy




Correct choice of Circuit equations coupled to equations of motion ensures:

•Energy consistent for the total process and 
each part of the process
•Charge consistent 
•Mass consistent
Fitting computed current waveform to measured current waveform
ensures:

•Connected to the reality of experiments

                    Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                                S H Saw
        Priority of Results                                                         Philosophy




• 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 (latest-Benchmarks); in
  conformity with experiments
• Widest Scaling of the yields
• Insightful definition of scaling properties
• Design of new devices; e.g. Hi V & Current-Step
• Design new experiments-Radiative cooling & collapse
             Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                         S H Saw
Philosophy, modelling, results &
applications of the Lee Model code                                           Philosophy




      Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                  S H Saw
  Numerical Experiments                                                           Philosophy




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

           Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                       S H Saw
              UPFLF-The Code
    Control Panel- configured for PF1000                                         Demo




L0 nH   C0 mF b cm a cm z0 r0 mW
33.5    1332 16     11.6 60   6.1
fm       fc   fmr   fcr
0.13     0.7   0.35 0.65
V0      P0   M.W.       A At/Molecular
27       3.5    4      1   2

          Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                      S H Saw
PF1000, ICDMP Poland, the biggest plasma focus in the world
                  Firing the PF1000                                                   Demo




               Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                           S H Saw
Fitting: 1. L0 fitted from current rise profile
2. Adjust model parameters (mass and current factors fm, fc, fmr, fcr) until computed current
waveform matches measured current waveform (sequential processes shown below)                      Demo




                            Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                                        S H Saw
PF1000 fitted results                                                    Demo




  Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                              S H Saw
PF1000: Yn Focus & Pinch Properties as
      functions of Pressure                                                     Demo




         Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                     S H Saw
Plasma Focus- Numerical Experiments
     leading Technology                                                          Insights




• 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


          Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                      S H Saw
NE showing the way for experiments
      and technology                                                                 Insights




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

              Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                          S H Saw
Results from Numerical Experiments with PF1000
  - For decreasing L0- from 100 nH to 5 nH Insights 1



•  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 
       à 1.03 MA at 20 nH,
       à 1.0 MA at10 nH, and 
       à 0.97 MA at 5 nH. 
                                                                                       11
• Yn also had a maximum value of 3.2x10  at 35 nH.



                Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                            S H Saw
    Pinch Current Limitation Effect -                                                  Insights 1




§ L0 decreasesà higher Ipeak àbigger a àlonger zp
  àbigger Lp

§ L0 decreases àshorter rise timeà shorter zoà smaller
  La

            L0 decreases, Ipinch/Ipeak decreases


                Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                            S H Saw
  Pinch Current Limitation Effect                                                     Insights 1




• L0 decreases, L-C interaction time of capacitor decreases
• L0 decreases, duration of current drop increases due to
  bigger a

àCapacitor bank is more and more coupled to the inductive
  energy transfer
à




               Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                           S H Saw
    Pinch Current Limitation Effect                                                      Insights 1




• 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



                  Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                              S H Saw
    Neutron yield scaling laws and neutron
         saturation problem                                                                 Insights 2




•   One of most exciting properties of plasma focus is
                                                                2
•   Early experiments show: Yn~E0
•   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




                     Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                                 S H Saw
                                    Global Scaling Law                                                    Insights 2

Scaling 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
                     Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                                 S H Saw
   Scaling for large Plasma Focus                                                  Scaling 1




Targets:
1. IFMIF (International fusion materials 
   irradiation facility)-level fusion wall 
   materials testing
(a major test facility for the international 
   programme to build a fusion reactor)- 
   essentially an ion accelerator

            Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                        S H Saw
 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               Scaling 1




IPFS numerical Experiments:




              Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                          S H Saw
Possible PF configuration: Fast capacitor bank 10x PF1000-
  Fully modelled- 1.5x1015 D-T neutrons per shot Scaling 1

• Operating Parameters: 35kV, 14 Torr D-T
• Bank Parameters: L0=33.5nH, C0=13320uF, r0=0.19mW 
• E0=8.2 MJ
• Tube Parameters: b=35.1 cm, a=25.3 cm z0=220cm
• Ipeak=7.3 MA, Ipinch=3.0 MA
• Model parameters 0.13, 0.65, 0.35, 0.65


              Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                          S H Saw
Ongoing IPFS numerical experiments of Multi-MJ Plasma Focus                            Scaling 1




                Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                            S H Saw
50 kV modelled- 1.2x1015 D-T neutrons per shot                                         Scaling 1




•   Operating Parameters: 50kV, 40 Torr D-T
•   Bank Parameters: L0=33.5nH, C0=2000uF, r0=0.45mW 
•   E0=2.5 MJ
•   Tube Parameters: b=20.9 cm, a=15 cm z0=70cm
•   Ipeak=6.7 MA, Ipinch=2.8 MA
•   Model parameters 0.14, 0.7, 0.35, 0.7

Improved performance going from 35 kV to 50 kV




                Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                            S H Saw
        IFMIF-scale device                                                        Scaling 1




• 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
• Such a system would cost only a few %
  of the planned IFMIF

           Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                       S H Saw
        Scaling further- possibilities                                              Scaling 2




• 1. Increase E0, however note: scaling 
  deteriorated already below Yn~E0
• 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
             Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                         S H Saw
Scaling from Ipinch using present predominantly beam-target :
Yn=1.8x1010Ipeak3.8; Yn=3.2x1011Ipinch4.4 (I in MA)                                  Scaling 2




              Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                          S H Saw
            SXR Scaling Laws                                                         Scaling 3




• First systematic studies in the world done in neon as a 
  collaborative effort of IPFS, INTI IU CPR and NIE 
  Plasma Radiation Lab:
  Ysxr = 8300× Ipinch3.6  
  Ysxr =  600 × Ipeak3.2     in J  (I in MA).

• Scaling laws extended to Argon, N and O by M Akel 
  AEC, Syria in collaboration.

              Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                          S H Saw
Special characteristics of SXR-for applications                                         Scaling 3




• 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; or as high intensity compression 
  drivers in fusion scenarios




                 Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                             S H Saw
Compression- and Yield- Enhancement methods                                         Scaling 4




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




             Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                         S H Saw
    Latest development                                                          Latest




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



         Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                     S H Saw
Plasma Focus Pinch                   Latest

photo taken by Paul Lee on INTI PF
Emissions from the PF Pinch region          Latest




                            +Mach500 Plasma stream
                            +Mach20 anode material jet
   Sequence of shadowgraphs of PF Pinch-
     M Shahid Rafique PhD Thesis NTU/NIE Singapore 2000                                  Latest




                              Highest post-pinch axial shock waves speed ~50cm/us M500
Much later…Sequence of shadowgraphics of post-pinch copper jet
               S Lee et al J Fiz Mal 6, 33 (1985)       Latest
Extracted from V A Gribkov presentation: IAEA Dec 2012




           Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                       S H Saw
Comparing large and small PF’s- Dimensions and lifetimes
    - putting shadowgraphs side-by-side, same scale




                 Anode radius 1 cm    11.6 cm

                 Pinch Radius: 1mm     12mm

                 Pinch length: 8mm     90mm



            Lifetime ~10ns           order of ~100 ns
    Flux out of Plasma Focus

Charged particle beams
Neutron emission when operating with D
Radiation including Bremsstrahlung, line radiation, SXR and 
  HXR
Plasma stream
Anode sputtered material
  Plasma Focus Ion Beam Fluence and
Flux –Scaling with Stored Energy E0                                                    Latest



• Many Measurements on plasma focus ion beams have been 
  published
• Include various advanced techniques producing a bewildering 
  variety of data using variety of units 
• Yet to produce benchmark numbers. 
• Our latest work uses the Lee Model code, integrated with 
  experimental measurements to provide the basis for reference 
  numbers and the scaling of deuteron beams versus E0




                Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                            S H Saw
Basic Definition of Ion Beam characteristics                                       Latest




• Beam number fluence Fib defines (ions m-2) 
• Beam energy fluence defines (J m-2)

Flux =fluence x pulse duration
• Beam number flux Fib/t defines (ions m-2s-1)
• Beam energy flux defines (W m-2)



            Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                        S H Saw
               Modelling the flux                                                        Latest




Ion beam number fluence is derived from beam-plasma target considerations as:

Fibt = Cn Ipinch2zp[ln(b/rp)]/ (prp2 U1/2)
                                                                         ions m-2
All SI units:calibration constant Cn =8.5x108; calibrated against experimental point at 0.5MA
    Ipinch=pinch current
    zp=pinch length
    b=outer electrode, cathode radius
    rp=pinch radius
    U=beam energy in eV where in this model U=3x Vmax 
         (max dynamic induced voltage)
These values are computed by our code
Example: Numerical Experiment for PF1000 based on following
fitted parameters:                                  Latest



L0=33 nH, C0=1332 uF, r0=6.3 mW
b=16 cm, a= 11.6 cm, z0=60 cm
fm=0.14, fc=0.7, fmr=0.35, fcr=0.7 V0=27 kV,
P0= 3.5 Torr MW=4, A=1, At=2 for deuterium


Results are extracted from dataline after shot:
Ipinch=8.63x105 A,
zp=0.188 m, b/rp=16 cm/2.23 cm, ln(b/rp)=1.97,
U=3Vmax=3x4.21x104 =1.26x105 V
From the above; estimate ions/m2 per shot
For PF1000 (at 500 kJ) we obtained

      Jbt =4.3x1020 ions/m2 per shot

       =4.3x1016 ions/cm2 per shot     at 126 keV

Computing for various plasma focus we obtain the
following table:
     Table 1: Parameters of a range of Plasma Focus and 
             computed Ion Beam characteristics Latest
Machine                                 PF1000              DPF78 NX3                    INTIPF NX2    PF-5M PF400J

E0 (kJ)                                 486                31.0               14.5       3.4    2.7    2.0    0.4

L0 (nH)                                 33                 55                 50         110    20     33     40

V0 (kV)                                 27                 60                 17         15     14     16     28
'a' (cm)                                11.50              4.00               2.60       0.95   1.90   1.50   0.60
c=b/a                                   1.4                1.3                2          3.4    2.2    1.7    2.7
Ipeak (kA)                              1846               961                582        180    382    258    129
Ipinch (kA)                               862              444                348        122    220    165    84
zp (cm)                                 18.8               5.5                3.8        1.4    2.8    2.3    0.8
rp (cm)                                 2.23               0.62                 0.4      0.13   0.31   0.22   0.09
t (ns)                                  255                41.0               36.5       7.6    30.0   12.2   5.1
Vmax (kV)                               42                 68.3               35         25     22     32.3   18


                  Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                              S H Saw
                                                                                                                            Latest

Machine                                           PF1000              DPF78              NX3       INTI    NX2      PF5M        PF400J
IB Ion Fluence (x1020m-2)                         3.9                 3.2                5.7       3.6     3.4      2.4         2.6
IB Ion Flux (x1027m-2s-1)                         1.5                 7.8                15.6      46.7    11.5     19.6        50.4
Mean Ion Energy (keV)                             126                 205                105       75      66       97          54
IB Energy Fluence (x106 J m-2)                    7.8                 10.6               9.6       4.3     3.6      3.7         2.2

IB Energy Flux (x1013 W m-2)                      3.1                 25.8               26.3      56.4    12.0     30.6        43.2

Ion Number (x1014)                                6100                390                280       19      110      37          5.9
IB Energy (J)                                     12248               1284               479       23      111      58          5.1

(% E0)                                            (2.5)               (4.1)              (3.3)     (0.7)   (4.1)    (2.8)       (1.3)
IB current (kA)                                   380.0               152.4              124.8     40.0    56.7     49.1        18.6
IB Damage Ftr (x1010 Wm-2s0.5)                    1.6                 5.2                5.0       4.9     2.1      3.4         3.1
Ion Speed (cm/ms)                                 347                 443                317       269     250      305         226
Ion Number per kJ (x1014)                         12.6                12.7               19.4      5.6     40.1     18.1        15.1
Plasma Stream Energy (J)                          39120               394                1707      249     369      92          17
(% E0)                                            (8.1)               (1.3)              (12.0)    (7.4)   (13.7)   (4.5)       (4.5)
Plasma Stream Speed (cm/ms)                       18.2                23.1               24.2      47.4    20.1     48.6        35.7

                            Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                                        S H Saw
     Table 2: Summary of Range of Ion beam properties and suggested scaling

Ion Beam Property                Units (multiplier)                              Range              Suggested Scaling

Fluence                          Ions m-2 ( x1020)                               2.4 – 7.8          independent of E0

Average ion energy               keV                                             55 - 300           independent of E0

Energy Fluence                   J m-2 (x106)                                    2 - 33             independent of E0

Beam exit radius                 fraction of radius 'a'                          0.14 - 0.19        scales with 'a'

Beam Ion number                  Ions  per kJ ( x1014)                           12 - 40*           scales with E0

Beam energy                      % of E0                                         1.3 – 5.4+         scales with E0

Beam charge                      mC per kJ                                       0.2 - 0.4#         scales with E0

Beam duration                    ns per cm of ‘a’                                8 – 20             scales with ‘a’

Flux                             ions m-2 s-1   (x1027)                          1.5 – 50           independent of E0

Energy flux                      W m-2 (x1013)                                   3 – 56             independent of E0

Beam current                     % of Ipeak                                      14 – 23            scales with Ipeak


Damage Factor                    (x1010 Wm-2s0.5)                                1.6 – 11           independent of E0

*= 6 for INTI PF                                                                                     

+
    = 0.7 for INTI PF                                                                                

#
    = 0.1 for INTI PF                                                                                
                             Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                                         S H Saw
(b) Philosophy, modelling, results and
  applications of the Lee Model code                                            TR Package




         Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                     S H Saw
    Plasma Focus Numerical Experiments-
        Conclusions: We have covered

•   Development, usage and results
•   Basis and philosophy
•   Reference for Diagnostics
•   Insights and frontiers
•   Continuing development- Ion beam modelling



             Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                         S H Saw
                                               References
•10S Lee, Radiative Dense Plasma Focus Computation Package: RADPF.
http://www.plasmafocus.net; http://www.intimal.edu.my/school/fas/UFLF/(archival websites)
•11 S Lee in  Radiation in Plasmas Vol II, Ed B McNamara, Procs of Spring College in Plasma 
Physics (1983) ICTP, Trieste,  p. 978-987, ISBN 9971-966-37-9, Published byWorld Scientific 
Publishing Co, Singapore (1984)
•12S  Lee, T.Y. Tou, S.P. Moo, M.A. Elissa, A.V. Gholap, K.H.  Kwek, S. Mulyodrono, A.J. 
Smith, Suryadi, W.Usala & M. Zakaullah.  Amer J Phys 56, 62 (1988)
•13T.Y.Tou, S.Lee & K.H.Kwek. IEEE Trans Plasma Sci 17, 311-315 (1989)
•14S Lee & A Serban, IEEE Trans Plasma Sci 24, 1101-1105 (1996)
•15 SP Moo, CK Chakrabarty, S Lee - IEEE Trans Plasma Sci 19, 515-519 (1991)
•16D E Potter, Phys Fluids 14, 1911 (1971)
•17A Serban and S Lee, Plasma Sources Sci and Tehnology, 6, 78 (1997)
•18M H Liu, X P Feng, SV Springham & S Lee, IEEE Trans Plasma Sci. 26, 135 (1998)
•19S Lee, P.Lee, G.Zhang, X.Feng, V.A.Gribkov, M.Liu, A.Serban & T.Wong. IEEE Trans Plasma 
Sci, 26, 1119 (1998)
•20S.Lee in http://ckplee.home.nie.edu.sg/plasmaphysics/ (archival website)  (2012) 
•21S. Lee in ICTP Open Access Archive: http://eprints.ictp.it/85/ (2005)
•22D.Wong, P.Lee, T.Zhang, A.Patran, T.L.Tan, R.S.Rawat & S.Lee. Plasma Sources, Sci & Tech 
16, 116 (2007)
•23V. Siahpoush, M.A.Tafreshi, S. Sobhanian, & S. Khorram. Plasma Phys & Controlled Fusion 
47, 1065 (2005)

                       Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                                   S H Saw
                                              References
•24L. Soto, P. Silva, J. Moreno, G. Silvester, M. Zambra, C. Pavez, L. Altamirano, H. Bruzzone, 
M. Barbaglia, Y. Sidelnikov & W. Kies. Brazilian J Phys 34, 1814 (2004)
•25H.Acuna, F.Castillo, J.Herrera & A.Postal. International conf on Plasma Sci, 3-5 June 1996, 
conf record Pg127 
•26C.Moreno, V.Raspa, L.Sigaut & R.Vieytes, Applied Phys Letters 89(2006)
•27S. Lee, R S Rawat, P Lee and S H Saw, J. Appl. Phys. 106, 023309 (2009)
• 28S. H. Saw and S. Lee, Energy and Power Engineering, 2 (1), 65-72 (2010)
• 29M. Akel, Sh Al-Hawat, S H Saw and S Lee, J Fusion Energy, 29, 3, 223-231 (2010)
• 30S H Saw, P C K Lee, R S Rawat, S Lee, IEEE Trans Plasma Sci, 37, 1276-1282 (2009)
•31Sh. Al-Hawat, M. Akel, S H Saw, S Lee, J Fusion Energy, 31, 13 – 20, (2012)
• 32Sh Al-Hawat, M. Akel , S. Lee, S. H. Saw, J Fusio Energy 31, 13-20 (2012)
• 33S Lee, S H Saw, R S Rawat, P Lee, A.Talebitaher, A E Abdou, P L Chong, F Roy, 
     A Singh, D Wong and K Devi, IEEE Trans Plasma Sci  39, 3196-3202 (2011)
• 34S Lee and S H Saw, J Fusion Energy, 27, 292-295 (2008)
• 35S. Lee and S H Saw, Appl. Phys. Lett., 92, 021503 (2008)
• 36S Lee. Plasma Physics Controlled Fusion, 50 10500 (2008)                                                               
•37S Lee. Appl. Phys. Lett. 95 151503 (2009) 



                              Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                                          S H Saw
                                        References
•38S Lee, S. H. Saw and Jalil Ali, J Fusion Energy DOI: 10.1007/s10894-012-9522- 8 First Online   
26 Feb (2012) 
• 39S Lee and S H Saw, J Fusion Energy DOI: 10.1007/s10894-012-9506-8 First Online 31 
January (2012) 
•40 S Lee, S H Saw, P C K  Lee, R S Rawat and H Schmidt, Appl Phys Lett 92, 111501 (2008)
• 41S H Saw, S Lee, F Roy, PL Chong, V Vengadeswaran, ASM Sidik, YW Leong & A 
   Singh, Rev Sci Instruments, 81, 053505 (2010)
• 42 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, J Fusion Energy 31,198–204 (2012)
• 43S Lee, S H Saw, A E Abdou and H Torreblanca, J Fusion Energy 30, 277-282 (2011)
• 44F M Aghamir and R A Behbahani, J. Plasma Physics: doi:10.1017/S0022377812000438 in 
press (2012)
• 45 S.Lee, S.H.Saw, L..Soto, S V Springham, S P Moo, Plasma Phys and Control. Fusion, 51
075006 (11pp) (2009)
•46 S.P. Chow, S. Lee and B.C. Tan, J Plasma Phys,  8 21-31 (1972).




                        Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                                    S H Saw
             Review of (UPFLF) Plasma Focus
               Numerical Experiments


                        S Lee1,2,3 &  H Saw1,2
         1
        INTI International University, Nilai, Malaysia
2
  Institute for Plasma Focus Studies, Melbourne, Australia
      3
       University of Malaya, Kuala Lumpur, Malaysia




International Workshop on Plasma Science and Applications, 4 & 5 October 2012, Bangkok, Thailand
Developing the most powerful training and research
   system for the dawning of the Fusion Age    TR Package




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

              Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                          S H Saw
       Into the fusion era: Plasma focus for
training/Research- A complete package integrating
     Experiment and Numerical Experiment TR Package

(a)  Experimental facility: TRPF (repetitive)
    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



              Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                          S H Saw
  Into the fusion era: Plasma focus
       for research training                                                              TR Package



(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




                   Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                               S H Saw
(a) The proven most effective 3 kJ PF system                                              TR Package




The trolley based UNU/ICTP PFF 3 kJ plasma focus training
and research system will be updated as a 1 kJ system
                   Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                               S H Saw
(b) The proven most effective and comprehensive
                 Model code                                                            TR Package




 •   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




                Seminar on Plasma Focus Experiments 2012,(SPFE2012), 12 th July 2012
                                            S H Saw

								
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