S K H Auluck

The Resistive Gratton-Vargas (RGV) model has been described in 3 publications [1-3]. Its computational development was carried out using Mathematica, which is very user friendly. But not many researchers working with the Dense Plasma Focus have access to it. To enable the DPF community to have access to the basic functionality of the RGV model, a stand-alone executable code has been created using FORTRAN. This document describes usage of this code, which may be downloaded from the following link

https://drive.google.com/drive/folders/0B7rzinCrV7tNRjZHZS1NSjRUb1E?usp=sharing

The code is contained in the file GV.exe. It reads data supplied by the user from a file with the name GVinp.inp. The data includes a name that identifies the facility and shot number if any. The output of the code is contained in a .txt file with name containing that identifier. The output file also contains the set of parameters that were used for the run.

The structure of the .inp file is as below:

----------------------------------------------------------------------------------------------------------------

&DPF

ANODE_R=60., ANODE_L=304., INSULATOR_R=60.1,

INSULATOR_L=75.,CATHODE_R=75., CAPACITNC=262.6, INDUCT=17.,

RESIST=5.2, VOLTAGE=31., PRESSURE=10.0, DPF_NAME='PF-360'

&END

========================================================

shot20140122_7. Data kindly provided by Prof. Marek Sadowski

========================================================

            ANODE_R=ANODE RADIUS IN MM

       ANODE_L=ANODE LENGTH IN MM

       INSULATOR_R=INSULATOR RADIUS IN MM

       INSULATOR_L=INSULATOR LENGTH IN MM

       CATHODE_R=CATHODE RADIUS IN MM

       CAPACITNC=CAPACITANCE IN MICROFARAD

       INDUCT=INDUCTANCE IN nH

       RESIST=RESISTANCE IN MILLIOHM

       VOLTAGE=VOLTAGE IN kV

       PRESSURE=DEUTERIUM PRESSURE IN TORR

       DPF_NAME='THE NAME YOU WANT ON OUTPUT FILE'

       ==================================================

         IN THE OUTPUT FILE

         1ST COLUMN :: TIME NORMALIZED TO QUARTERCYCLE TIME

         2ND COLUMN :: CURRENT NORMALIZED TO I0 (SEE PAPER)

         3RD COLUMN :: FRACTION OF ENERGY REMAINING IN C

         4TH COLUMN :: FRACTION OF ENERGY CONVERTED TO MAGNETIC ENERGY

         5TH COLUMN :: FRACTION OF ENERGY DISSIPATED IN RESISTANCE

         6TH COLUMN :: REMAINING ENERGY IS WORK DONE

         7TH COLUMN :: TAU (SEE PAPER)

         8TH COLUMN :: DYNAMIC DIMENSIONLESS INDUCTANCE

         9TH COLUMN :: TIME IN MICROSECONDS

         10TH COLUMN:: CURRENT IN KILOAMPERES

           11TH COLUMN:: TOTAL INDUCTANCE IN nH

-----------------------------------------------------------------------------------------------------------

Eight examples have been provided along with the code. Each example has an input file with .inp extension. To run a particular example, the user copies the contents of the corresponding .inp file, pastes it in the directory and renames the copy as GVinp.inp. Then double click the executable file GV.exe. This generates the output file.

Each example is accompanied with a Excel file, that graphically compares the calculated current waveform with the experimental waveform data. The calculated data is imported into the spreadsheet from the .txt output file. The user may experiment by changing the pressure, inductance or resistance values, running the code and refreshing the text import, which should be reflected in the graph.

Also included in the Excel file is a graph that shows the energy flow as a function of time normalized to quarter-cycle time. One can see the effect of change in any parameter on the energy flow. Total inductance variation as a function of time is also included.

The Resistive Gratton-Vargas model is still a 'work-in-progress'. It does not claim to be anything other than an oversimplified model that happens to reproduce experimental current waveforms of some DPF facilities. Its use is to be taken in the spirit of an adventurous exploration.

That disclaimer apart, the very fact that it has the ability to reproduce DPF current waveforms is an interesting scientific fact. Even more interesting is the fact that the fitted values of inductance and pressure differ significantly from experimental values. Both the agreement and the discrepancy probably arise from as-yet-undiscovered aspects of DPF physics.

I gratefully acknowledge Prof. Marek Sadowski, Dr. E.C Hagen, Dr. Eric Lerner and Dr. Marek Scholz for making available current waveform data from their facilities.

References:

1. S K H Auluck, PHYSICS OF PLASMAS 20, 112501 (2013)

arXiv version: https://arxiv.org/abs/1310.4570

2. S K H Auluck, PHYSICS OF PLASMAS 22, 112509 (2015)

arXiv version: https://arxiv.org/abs/1608.01439

3. S K H Auluck, PHYSICS OF PLASMAS 23, 122508 (2016)

arXiv version: https://arxiv.org/abs/1611.08567