Description of Radiative Dense Plasma Focus Computation Package
RADPFV5.011Abs&n and Downloads - S Lee
Model
(incorporating Time Match
Guard)
Features
·
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".
File6: EXCEL file containing
the ACTIVE SHEET AND THE EXECUTABLE (MODIFIABLE) MACRO PROGRAMME
CODE.
"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:
http://www.kirkbyites.net/DPF (containing the latest revisions) or
http://eprints.ictp.it/85/ (containing an earlier version RADPFV5.008)
Files 4 &
5 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
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 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..
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) |
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 |
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.
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.
Notes:
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.
leesing@optusnet.com.au
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.