Description of Radiative Dense Plasma Focus Computation Package RADPFV5.011Abs&n and Downloads -  S Lee Model (incorporating Time Match Guard)



·       Numerical Experimental Facility

·       Simulate any Mathers-type plasma focus, computes dynamics

·       Design new plasma focus machines

·       Thermodynamics included; 4 gases: H2, D2, Ne, Ar, Xe and He

·       Model parameters to fit experimental axial, radial phase times

·       Radiative phase computes line radiation yield, may be modified to suit your needs e.g. compute recombination yield. Computes neutron yield for deuterium operation; based on a simplified inductive model and calibrated for the UNU/ICTP PFF with 10^8 neutrons at 15kV 4 torr. Also includes self absorption based on revised equations presented in File 3; appendix by N A D Khattak.


There are altogether 4 files in this package.

File1: PDF File "Description of Radiative Dense Plasma  Focus Computation Package": This file

File2: PDF File "Theory of Radiative Plasma Focus Model"                  

File3: PDF file "Appendix by N A D Khattak".


                        "Radiative Dense Plasma Focus Computation Code"


Hint for downloading the EXCEL FILE: Instead of left click to open the file; it is better to right click and select "save target as"; then choose a suitable location e.g. desktop. The saved EXCEL file will be only 950KB. (see last page for more hints on saving/copying )


These files may also be downloaded from the following URL:    (containing the latest revisions)        or     (containing an earlier version RADPFV5.008)


Files 4 & 5 contain earlier versions of the code.                                                       


Introductory description


A simple 2 phase (axial and radial) model was developed by S.Lee in 1985 as a component of a 3kJ plasma focus experimental package which became known as the UNU/ICTP PFF. This network of basically identical 3kJ PF machines, with different experimental and application emphases, is now operated by groups in countries including Singapore, Malaysia, Thailand, Indonesia, India, Pakistan,, Egypt and Zimbabwe.


The model was written as a 3 phase (non-radiative) model (in GWBASIC) for an experimental program at the 1991 Spring College in Plasma Physics at the ICTP.


The present 5-phase package (axial, radial inward shock, radial reflected shock, slow compression radiative and expanded large column phase) is re-written in Microsoft EXCEL VISUAL BASIC in order to make it available for wider usage.


The model may be adapted to any conventional Mather-type plasma focus by inputting machine perameters such as, inductance, capacitance, voltage, electrode radii and length.  The thermodynamics (specific heat ratio and charge number as functions of temperature) are included for 3 gases namely deuterium, neon and argon.  The gases may be selected by simply inputting atomic number, molecular weight and dissociation number (2 for deuterium, 1 for the others).


Fitting computed current trace to experimental current trace of existing machine:


The main model parameters are the tube current flow factor CURRF (known to be 0.7 for most machines) and the mass swept-up factor (MASSF, for axial & MASSFR, for radial).  These have been pre-selected in the model, but may be adjusted so that the time of focus, and the radial inward shock transit time, fit the experimentally observed times for each machine. The computed current trace may be compared with the experimental current trace.


Features for comparison include current risetime and rising shape, peak current, current 'roll off' and dip, both shape and amplitude. Absolute values may be compared.


The machine parameters and operating conditions should already have been determined and inputted into the active sheet. The model parameters are then adjusted, one by one, or in combination until best fit is obtained between the computed current trace and the experimental current trace.


Designing a new plasma focus


If a machine has not been built the model may be used to aid design. First use the following rule of thumb procedure [use SI units].


What capacitance ( C ) are you planning?

How low is the inductance (L) you expect to attain?

What maximum voltage (V) do you expect to operate?

Enter these values into the appropriate spaces for these machine parameters.


For the stray (circuit) resistance, take 1/4 the value of (L/C)1/2 .

Estimate the undamped peak current using the formula I=V/(L/C)1/2. 

Use (I/a)=250kA max undamped current per cm to assign the value of centre electrode radius 'a'.

Put in double this value for outer electrode radius 'b'.

The length of the electrode may be assigned as 5 times the value of 1.6(LC)1/2 . This length is in cm when the value of (LC)1/2 is expressed in microsecond.

 For pressure values assign as follows: D2: 4 torr;     neon: 1.5 torr;     Ar: 0.7 torr.


From the above rule of thumb design parameters, is your PF fat or thin? (according to the ratio length of the centre electrode divided by diameter; for NX2 this ratio is 1.2, fat; for UNU/ICTP PFF this ratio is 17, thin )

If it is fat use the model parameters suggested for the NX2 (These suggested values are tabulated at the top right of the active sheet which appears when you open RADPFV5.008).

If it is thin assign the model parameters closer to the UNU/ICTP PFF.


Run the computation and from results make adjustment to 'a', 'b', length (V may also easily be varied, especially reduced since we have started with max V; C also, use more or less capacitors; careful with L, normally make L as small as possible, but be realistic). Adjust parameters for best results over a range of pressures and gases. Best results could mean strong current dip or biggest line emission in the case of neon, which is useful for developing microlithography SXR sources.


Model may be adapted to suit requirements


The axial phase (trajectory) going into the radial phase (trajectories of shock front, current sheet and length of the focussing column) is portrayed reasonably well. As the radial inward shock goes on-axis, a reflected shock phase follows. The reflected shock moves outward until it hits the incoming radial piston which was moving behind the radial inward shock. Now follows the slow compression, radiative phase.


The radiative phase is the interesting phase, which is presented in the package in a form which gives reasonable results.  The slow piston motion is coupled to the rate of change of current, the elongation and power gain/loss due to joule heating, Bremsstrahlung and line emission losses.  Thus radiation collapse (critical current of 1.6 MA for deuterium, but much reduced to possibly below 100kA for neon and argon under certain conditions) is included into the modelling.  Reasonable line radiation yields (all lines) are computed for the UNU/ICTP PFF. One may wish to include recombination or emission in specific lines.


There is room for further interesting development.  For example, allowing the radiation collapse to couple to a ‘piston’ motion will lead to a huge voltage spike in a ‘high pressure’ regime which is not observed experimentally. In this model, this effect is ‘artificially’ restricted by ‘house keeping’ procedures in the package.  It should be looked into further.  Instabilities could be introduced into the package by insertion of a suitable ‘anomalous’ resistance time function. This should be coupled into the voltage and current equation; but not into the ‘piston’ equation. The current would rapidly diffuse as this ‘anomalous’ resistance kicks in, causing the necessary abandonment of the concept of a ‘piston’.


The radiative phase is followed by an expanded large column phase, in which the current flows in a large column with the radius of the centre electrode.


The theoretical basis (with all equations) is given in the next (separate) PDF file; File 2., with an appendix by N A D Khattak in PDF file 3..


Description of Programme Package


The package consists of an ACTIVE SHEET in EXCEL linked to a MACRO (where the basic programme is written).  The package may be operated from the sheet, without going into the MACRO.  The machine parameters may be inputted directly onto the sheet, as may the operating conditions and gas.  The model parameters (CURRF, MASSF and MASSFR), if required to be adjusted can also be directly inputted onto the sheet.


After downloading the programme, the EXCEL Sheet appears.  The first section, first 19 rows, contain essential information and inputted quantities.  Parameters which may be changed directly on the sheet are in bold underlined.


The programme (as downloaded) contains all machine parameters for the UNU/ICTP PFF. Thermodynamic data (for the 3 gases D, Ne and Ar) are also preloaded.  The pre-selected operational conditions and gas (neon) are shown.


 The programme may be operated directly from the sheet.  Just press “Ctrl + A”


The computation should take less than 1 minute (depending on speed of machine and input parameters).


Results are outputted on the sheet in columns as follows (starting row 20):




A                     time in microsecond

B                      current in kA

C                     tube voltage in kV

D                     axial position in cm

E                       axial speed in cm/ms

F                       time in microsecond (starting on row 20, radial phase)

G                      time in nanosecond, referenced to start of radial phase

H                      current in kA (radial phase data only)

I                        tube voltage in kV (radial phase data only)

J                       radial shock position, referenced to axis, in mm

K                      radial piston position, referenced to axis, in mm

L                       axial position of focus column, referenced to anode end, in mm

M                      radial shock speed in cm/ms

N                      radial piston speed in cm/ms

O                      elongation speed of column in cm/ms

P                       reflected shock radial position in mm

Q                      temperature in oK

R                       Joule heating power in watts

S                       Bremsstrahlung emission power in watts

T                       line emission power in watts

U                      sum of S & T

V                     sum of energy gain/loss, i.e. sum of W, X and Y (below)

W                    integrated Joule heating in Joules

X                     integrated Bremsstrahlung in Joules

Y                     time-integrated line emission in Joules

Z                      Total power i.e. sum of R, S & T (above)

AA                   specific heat ratio

AB                   charge number.


The number of data rows may go up to 7000.  The data is also presented near the top of the sheet in graphical forms.  The lines in each figure (identified by colour) plot the following data:


Series 1           dark blue

Series 2           pink

Series 3      yellow

Series 4           light blue


The horizontal axis (for Figs 1 & 2) is time in ms.  The other Figures display computed data of the radial phases. Radial phase time scale is in ns, referenced to the start of the radial phase’



series 1

series 2

series 3

series 4






Fig 1 (top left)





Fig 2 (top right)

axial position

axial speed



Fig 3

Radial shock position

radial piston position

axial focus length


Fig 4





Fig 5

Radial shock speed

radial piston speed

Elongation speed

line radiation energy

Fig 6

Plasma temperature




Fig 7

Joule heat energy

Bremsstrahlung energy

Line Radiation energy


Fig 8

Joule power

Bremstrahlung power

Line Emission Power

Total Radiation power

Inset                             Sp Heat Ratio        charge number


To get into the code (containing the programme lines)

(from top toolbar) click on 'Tools' 

(when menu appears) select 'Macro' and click on it

(when menu appears) seledt 'Macros' and click on it

(when Macro menu appears) select 'radpf005' by clicking on it

 On the right hand panel click on  'step into'

That gets you into the code. You may then modify the code as required.


When finished with the code

click 'red cross' on top right hand corner

click 'OK' when message "This command will stop the Debugger" appears

This gets you back to the active sheet.



Summary Steps


The complete computer package (active sheet and macro code) is provided as an EXCEL File RADPFV5.008

Open the file.

When the EXCEL Sheet appears, press ‘Ctrl + A”. The programme will run and present data in the 8 Figures and inset.



It is recommended that you keep a reference copy of RadPFV5.008, which you can refer to.  Editted programmes should be kept under another title such as RadPFTrialVersion.


The model has been tested for the UNU/ICTP PFF 3kJ plasma focus, in the following ranges, operating at 14kV.


            Deuterium         0.5 to 15 torr

            Neon                0.1 to 5.5 torr

            Argon               0.1 to 2.5 torr


Any plasma focus will only be able to operate properly within a range of parameters. For example if the parameters are such that the current sheet moves too slowly in the axial phase, by the time the radial phase starts the drive current may have dropped to too low a value and the radial phase cannot complete.


In other words there needs to be a matching between the sum of the characteristic axial & radial times and the characteristic capacitor discharge time.


The code has recently incorporated a Time Match Safeguard. Before axial phase computation is started the code checks that there is suitable matching within a suitable range. This is done by checking that the ratio ALT  in the code is LESS than a certain value. We have set the lower limit of ALT at 0.68 for D2 and 0.65 for neon and argon. If too large a pressure is set for selected capacitor voltage and the value of ALT falls below this set value an error message will appear recommending to set the pressure lower or the voltage higher.


If this happens click the 'red cross' on the upper right hand corner, click OK on the 'debugger' message, getting you back to the active sheet and adjust the pressure and or voltage accordingly.


(The value of ALT for each computation is shown in the active sheet.)


Furthermore if you have changed drastically the values of the parameters such as the capacitance C e.g. changing the value of C from 30 uF to 3 uF, you would have reduced the capacitor discharge time by 3 times (square root of 10), hence it may be difficult to match the axial transit time (by simply increasing voltage or reducing pressure) unless you also reduce the anode length by a similar factor. Likewise if you drastically alter the value of the circuit inductance L or the anode radius a you would have to adjust other parameters accordingly. Time matching is crucial for proper computation just as it is in actual operation in the laboratory.


If machines parameters of another machine are entered, keep in the middle (or lower end) of the pressure range.  If parameters are inappropriately chosen the Time Match Safeguard will stop the programme execution and give appropriate instructions to remedy. 


Another safeguard for inappropriately low operating pressures is also incorporated into the code which stops the execution and gives you appropriate warning.


You may also need to adjust the source data of the figures. Source data has been set for a maximum of 7000 points for Figs 1 & 2, and 6000 points for the other Figures.


The Active sheet comes pre-loaded with parameters of the UNU/ICTP PFF

 Operating parameters set as 13kV in neon at 3 torr



If you have difficulties you cannot solve, please e-mail me parameters of your machine.



See the following for a further hint on efficient saving of RADPFV5.08


Further hints for efficient saving of RADPFV5.08


3 methods of saving copies: Copy then Paste - small storage required for a copy

                                          Open RADPFV5.008 then Save As- large storage required for a copy

                                          Open RADPFV5.008 then click top Red Cross to exit, click Yes to message 'Save changes…'-small storage required for a copy


1.. The original copy as downloaded (using 'save target as') is around 150K, say 150K.

2 Without opening the file, Use Copy, then Paste to make a copy in a folder separate from your working area.  Keep this copy as a reference copy, which you can always return to to make another copy, using Copy then Paste

3. Copy then Paste (without opening the file) will make a copy of 150K.

4. Open the file, then click File, click Save As, will save a copy of several M; with the same content!!

5. If you have opened the file, and made any changes, to save as a small file do not use Save As.

Instead click on red cross at top left hand corner as though to exit. Message 'want to save changes' appears click yes and the changed file will replace the old file keeping storage space to a minimum.


e.g. if you open the file, add a comma to one of the 'unused' cells; click File, click Save As, you will end up with a copy (with an extra inconsequential comma) of several M.

Instead of clicking File, if you click top right hand corner Red Cross, message 'Do you want to save changes…" appears, click yes, the file with the extra comma is saved in place of the old file, without the extra comma and the storage space is still 150K.


Another example: If you open the file, run computation by using CTRL+a, the active sheet now has 8 filled graphs and one filled inset (unlike the original active sheet with all empty graphs). If you save with Save As method you will save a file of perhaps 6M.

If you click on the Red Cross and then Yes to the message you save a file (with same content) of perhaps 700K. Of course you would no longer have the original file, having replaced it with the file containing the computed results. One more reason why always keep a reserve copy of the original.