Description of Radiative Dense Plasma Focus Computation
Package RADPFV5.15b
and Downloads - Lee model code
Features
· Numerical
Experimental Facility
· Simulate
any Mathers-type plasma focus, computes dynamics
· Design
new plasma focus machines
· Thermodynamics
included; H2, D2, Ne, Ar, Xe, He, N2, Kr and
D-T
· Model
parameters to fit experimental axial, radial phase times
· Radiative
phase computes line radiation, recombination and total yield. Computes neutron
yield for deuterium operation; based on an improved beam-target model and
calibrated at an experimental point of 0.5MA Yn=5.6x10^9 (extended
to D-T). Termination of computation of slow phase: transit time for slow
disturbance speed. Plasma Self-absorption
based on revised equations presented in File 3; appendix by N A D Khattak.
Also includes:
Time guard feature
Choice of Tapered electrode [note:
if this feature is not wanted ensure taper? y=1, n=0 cell is filled with a ‘0’]
Quick choice of specified machines; one
click loading of chosen machine; at present 3 machines may be click-loaded: the
UNU/ICTP PFF, the NX2 and the PF1000 [note: if
this feature is not wanted ensure the relevant cell in top RH corner of sheet
is filled with a ‘0’]
Acknowledgement: Scroll down to see acknowledgement.
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".
File7:
EXCEL file containing the ACTIVE SHEET AND THE EXECUTABLE (MODIFIABLE) MACRO
PROGRAMME CODE.
"Radiative Dense Plasma Focus Computation
Code" RADPFV5.15b
In
addition, there are files for the computation of thermodynamic data
needed for this 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 about 1M.
(see last page for more hints on saving/copying )
These
files may also be downloaded from the following URL:
http://www.kirkbyites.net/DPF (only a sketch) or
http://eprints.ictp.it/85/ (containing an earlier version
RADPFV5.008)
Files 4 & 5 & 6 contain earlier versions of the
code.
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
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 configured to any conventional Mather-type
plasma focus by inputting machine parameters: inductance, capacitance,
electrode radii and length. And
operating parameters: charging voltage and fill gas pressure. The
thermodynamics (specific heat ratio and charge number as functions of
temperature) are included for 6 gases namely hydrogen, deuterium, neon, argon
and helium. The gases may be selected by
simply inputting atomic number, molecular weight and dissociation number (2 for
deuterium and hydrogen, 1 for the others).
The results are the following: waveforms for the total
discharge current and tube voltage, axial phase trajectory and speed, radial
trajectories for the shock front, current sheath and column length and the
corresponding speeds, plasma temperature and radiation yields (Bremsstrahlung,
line and recombination) and power; and thermodynamic quantities such as
specific heat ratios and charge numbers. These are output in graphical as well
as tabular forms. Also computed are plasma pinch current and neutron yield, and
any distributions, if required.
Are the results any good?
But are there any indications that our computed results are
anywhere near the actual results that may be measured on the device in actual
operation?
NOT if we just guess the model parameters fm, fc,
fmr, fcr; as suggested above. Then the results are just hypothetical;
although with experience we may assign some reasonable values of the model
parameters for the particular machine in its particular operating conditions.
And the results may be valid for planning or designing purposes.
How do we make the results realistic?
The standard practice is to fit the computed total current
waveform to an experimentally measured total current waveform.
From
experience it is known that the current trace of the focus is one of the best
indicators of gross performance. The axial and radial phase dynamics and the
crucial energy transfer into the focus pinch are among the important
information that is quickly apparent from the current trace.
The exact time profile of the total current trace is
governed by the bank parameters namely capacitance Co, external, or
static inductance Lo and circuit resistance ro,
by the focus tube geometry namely electrode radii, outer ‘b’ and inner anode
‘a’, and the anode length ‘zo’; and on the operational parameters which
are the charging voltage Vo and the fill pressure Po and
the fill gas. It also depends on the fraction of mass swept-
up and the fraction of sheath current and the variation of
these fractions through the axial and radial phases. These parameters determine
the axial and radial dynamics, specifically the axial and radial speeds which
in turn affect the profile and magnitudes of the discharge current. The detailed profile of the discharge current
during the pinch phase will also reflect the joule heating and radiative
yields. At the end of the pinch phase the total current profile will also
reflect the sudden transition of the current flow from a constricted pinch to a
large column flow. Thus the discharge current powers all the dynamic,
electrodynamic, thermodynamic and radiation processes in the various phases of
the plasma focus. Conversely all the dynamic, electrodynamic, thermodynamic and
radiation processes in the various phases of the plasma focus affect the
discharge current.
It is then no exaggeration to say that the discharge current
waveform contains information on all the dynamic, electrodynamic, thermodynamic
and radiation processes that occurs in the various phases of the plasma focus.
The discharge current of a plasma focus is one of the simplest
measurement that is routinely carried out. Yet this easily measured waveform
carries all the information of the physical processes in the plasma focus.
Our standard practice for any existing plasma focus is to
obtain a measured current trace. Then we fit the computed current trace to the
measured current trace. The fitting process involves adjusting the model
parameters fm, fc, fmr, fcr one by
one, or in combination until the computed current waveform fits the measured
current waveform.
Once this fitting is done our experience is that the other
computed properties including dynamics, energy distributions and radiation are
all realistic
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 should be compared. Our experience with a number
of machines shows that the fit is usually very good, occasionally almost
exact..
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.
Besides the model parameters, sometimes (when all else fails
in the fitting process) the inductance (as published or given by the
experimenters) needs to be adjusted. The reason is that the inductance Lo may
be given as the short circuit bank inductance whereas it should be the ‘static’
inductance of the plasma focus; ie the inductance of the PF before the current
sheet moves. Usually also the value of stray resistance ro needs to be guessed
at as few experimenters determine this carefully. We usually start with the
value of ro as 0.1 of (Lo/Co)0.5; and make small adjustment as
necessary. Sometimes, especially for PF’s using very low values of Co, it may
also be necessary (when all else fails) to adjust the value of Co (for sub-uF
capacitor banks, the closely spaced connecting parallel plates and parallel
connecting cables may actually significantly change the value of Co. In one or
two cases where there is very good fit in current profiles but the absolute
values of currents don’t match, it has been reasonable to suspect that the
calibration constant for the current profile has been given wrongly by the
experimenter.
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. (This gives a length which will provide an average axial speed of
5 cm/us which usually gives a peak speed at end of axial phase of 8cm/us. For
operation in H2 or D2 20% longer may be better; for neon operation
to get suitable line radiation (12-13.5 A) for SXR microlithography purposes,
20% shorter may be better as we require a lower speed to get to the correct
level ionization stages. The focus is normally operated so that the start of
current dip (signifying the end of the axial phase) occurs at or just after
peak current. For argon to generate SXR a high speed is required so use the
same length as for H2. For xenon, if the aim is for EUV (around 13
nm) for experiments for NGL the model has predicted a requirement for very low
speeds, around 1.3cm/us! So it appears one needs very short anodes, at least 5
times shorter than that needed for D2. However there is not much
experimental experience accumulated so far.
For pressure values assign as follows: D2:
4 torr; neon: 1.5 torr; Ar: 0.7 torr.
For
xenon, runs on the code suggest several torr to go with the very short anode
length.
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 and recombination 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 emission in specific
lines. Plasma self-absorption effects (adapted from equations discussed by
Khattak in File 3) have been implemented in the code.
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.
Most recently a reasonable beam-target mechanism has been
incorporated into the code.
Acknowledgement
This model and code is the result of almost 40 years of
experimental work on shock waves and the Plasma Focus. It incorporates the best
experience (as understood by me) shared with each and every one of the students
and Fellows I have trained and each and every one of the colleagues I have
worked with. Some of them are named here: Dr Chow Sai Pew, (the late) Dr Chen You Hor, Yong Yeow Chin,
Prof (Dr) Tou Teck Yong, Dr Liu Mahe, Dr Bing Shan, Assoc Prof (Dr) Paul C K
Lee, Assoc Prof (Dr) Rajdeep Singh Rawat, Dr Moo Siew Pheng, Assoc Prof (Dr)
Kwek Kuan Hiang, Prof (Dr) Wong Chiow San, Dr Chew Ah Chuan, Dr Adrian Serban,
Dr Susetyo Mulyodrono, Assoc Prof Zhang Guixin, Prof (Dr) Jalil Ali, Assoc Prof
(Dr) Saw Sor Heoh, Dr Alin Patran, Tan Thian Hoo, Dr Suresh Kumar, Chin You
Hon, Dr. C.K.Chakrabarty, Ashutosh Srivastava, Assoc Prof (Dr) N A D Khattak.
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; and xenon) are also preloaded. The
pre-selected operational conditions and gas are shown.
The programme may be
operated directly from the sheet. Place the cursor in any empty cell; then
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
recombination emission power in watts
U line emission power in watts
V sum of S,T & U
W sum of power ie of R & V
X time-integrated
Joule heating in Joules
Y time-integrated Bremsstrahlung in
Joules
Z time-integrated
recombination emission in Joules
AA time-integrated
line emission in Joules
AB Total
radiation in Joules
AC
Total energy gain/loss in J, ie X+AB
AD
plasma self-absorption corrected coefficient
AE plasma
radiation power (if black body) in W
AF specific
heat ratio
AG effective
plasma charge number
AH Thermal
neutron yield
AI Beam-target
produced neutron yield
AJ Total
neutron yield
AK plasma
ion density per m^3
AM Surface
radiation power in W
AN plasma
self-absorption corrected coefficient
AO radial
phase piston work in J
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) |
Circuit Current |
Voltage |
|
|
|
Fig 2 (top
right) |
axial position |
axial speed |
|
|
|
Fig 3 |
Radial shock
position |
radial piston
position |
axial focus
length |
|
|
Fig 4 |
Current |
voltage |
|
|
|
Fig 5 |
Radial shock
speed |
radial piston
speed |
Elongation
speed |
line radiation
energy |
|
Fig 6 |
Plasma
temperature |
|
|
|
|
Fig 7 |
Joule heat
energy |
Bremsstrahlung
energy |
recombination
energy |
Line radiation |
|
Fig 8 |
Joule power |
Bremstrahlung
power |
recombination
Power |
Line 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) select '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.
The complete computer package (active sheet and macro code)
is provided as an EXCEL File RADPFV5.13.2 (latest)
Open the file.
When the EXCEL Sheet appears, press ‘Ctrl + A”. The programme
will run and present data in the 8 Figures and inset.
Notes:
It is recommended that you keep a reference copy of
RadPFV5.13.2 (or the current version), which you can refer to. Modified programmes should be kept under
another title such as RadPFTrialVersion. (so that you can get back to the
original latest version should your trial code not work)
The model has been tested for the UNU/ICTP PFF 3kJ plasma
focus, in the following ranges, operating at 14kV.
Deuterium 0.5 to 19 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.
leesing@optusnet.com.au
See the following for a further hint on efficient saving of
RADPFV5.08 (applies also to later versions.)
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.
If you know why, please let me know; would really appreciate the reasons
behind this.
1. The original copy as downloaded (using 'save target as')
is around 1M
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 1M.
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, 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 1M.
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 16M.
If you click on the Red Cross and then Yes to the message
you save a file (with same content) of perhaps couple of M. Of course you would
no longer have the original file, having replaced it with the file containing
the computed results. One more reason to always keep a reserve copy.