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Electromagnetic particle in cell modelling of plasma dynamics in breakdown and lift-off phases of plasma focus
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Type
Thesis
Author
Seng, Yeow Sing
Supervisor
Rawat, Rajdeep Singh
Lee, Paul Choon Keat
Abstract
The breakdown phase plays a critical role in determining plasma focus (PF) performance. To date, however, very little physical understanding about this initial phase is available. Experimental diagnostics to measure the plasma condition in this phase is also difficult, while the equations governing the plasma could not be solved analytically.
The primary purpose of this PhD work is to build and develop, right from the scratch, sufficiently complete and yet versatile simulation codes using the electromagnetic particle in cell (EMPIC) framework. These codes allow one to get a clear physical picture of what is going on, with essentially no approximations needed. The major aim of this PhD project is to model the breakdown phase and couple it into the initial axial run-down phase of the PF, a time period covering plasma densities ranging from the initial seed electron density of a few electron per cm-3 at the start to about 1015 electrons per cm-3 at the end of the simulation, spanning 15 orders of magnitude in total. The codes were run on a modest PC.
The EMPIC codes were tested for the PF1000 PF device like configuration, covering the first 105 ns of the operation, and stopping when voltage breakdown is imminent. A clear physical understanding of how the current sheath (CS) is built up emerged clearly from the simulation, beginning with the local growth of the electron avalanche that initiated a sliding discharge (of quasi-homogeneous density) which propagated down the insulator till it reached the anode. As the sliding discharge reaches the anode, the magnetic field begins to rise significantly, together with a sudden rise in the radial electric field which causes the lifting of the electron CS layer near the insulator. The magnetic field is therefore an important consideration in the voltage breakdown of the PF, followed by a significant growth in the current. Our result illustrates clearly the limitation of electrostatic PIC in simulating the PF beyond the stage of sliding discharge.
Simulation of the UNU-ICTP PF configuration was performed next, with a linearly rising voltage pulse as the applied voltage source. It was found that the essential stages leading to the formation of the CS are similar to the PF1000 configuration despite the difference in anode insulator configuration, namely, a local electron avalanche followed by a sliding discharge that bridges the anode cathode gap. The sliding discharge was analyzed in detail. The lifting off of the electron layer near the insulator surface near voltage breakdown was also present in the UNU-ICTP case, and the reason behind this was firmly established from the radial electric field result near the insulator surface. The simulations were also extended to insulators of different lengths, with results reported on the various ionization wave velocities pertaining to the sliding discharge. A clear signature of voltage breakdown was found from the generic looking current waveform, being clear that the current increases suddenly in a nearly linear fashion (within a short time domain) at the point of breakdown. This criterion allows us to compare the breakdown voltage and times for the different insulator lengths.
Our simulation culminates with the successful application of our circuit integrated codes to model the UNU-ICTP from the beginning all the way up to the early stage of the axial phase. The generated voltage waveform agreed very well with experimental measurements, with an initially oscillatory current superimposed on a linearly rising profile. By using a simple load consisting of a resistor and inductor to model the post-breakdown phase, it was concluded that the oscillations arise from the plasma inductance. Measuring the oscillation period therefore allowed the estimation of the inductance of the CS. The value obtained from simulation agreed well with that deduced from the experimental waveform. Our simulations also revealed clearly the lifting off of the CS, with the CS speed estimated from simulation data. At the kinetic level, the time evolution of the electron temperature and the electron neutral collision frequency were also estimated. The simulation results indicate the trend of the electron energy distribution function (EEDF) towards Maxwellization, albeit at a slower pace. Even after the occurrence of CS lift-off, the EEDF has yet to equilibrate to a Maxwellian distribution.
We concluded our work with a short chapter on future work and extensions to our present codes.
The primary purpose of this PhD work is to build and develop, right from the scratch, sufficiently complete and yet versatile simulation codes using the electromagnetic particle in cell (EMPIC) framework. These codes allow one to get a clear physical picture of what is going on, with essentially no approximations needed. The major aim of this PhD project is to model the breakdown phase and couple it into the initial axial run-down phase of the PF, a time period covering plasma densities ranging from the initial seed electron density of a few electron per cm-3 at the start to about 1015 electrons per cm-3 at the end of the simulation, spanning 15 orders of magnitude in total. The codes were run on a modest PC.
The EMPIC codes were tested for the PF1000 PF device like configuration, covering the first 105 ns of the operation, and stopping when voltage breakdown is imminent. A clear physical understanding of how the current sheath (CS) is built up emerged clearly from the simulation, beginning with the local growth of the electron avalanche that initiated a sliding discharge (of quasi-homogeneous density) which propagated down the insulator till it reached the anode. As the sliding discharge reaches the anode, the magnetic field begins to rise significantly, together with a sudden rise in the radial electric field which causes the lifting of the electron CS layer near the insulator. The magnetic field is therefore an important consideration in the voltage breakdown of the PF, followed by a significant growth in the current. Our result illustrates clearly the limitation of electrostatic PIC in simulating the PF beyond the stage of sliding discharge.
Simulation of the UNU-ICTP PF configuration was performed next, with a linearly rising voltage pulse as the applied voltage source. It was found that the essential stages leading to the formation of the CS are similar to the PF1000 configuration despite the difference in anode insulator configuration, namely, a local electron avalanche followed by a sliding discharge that bridges the anode cathode gap. The sliding discharge was analyzed in detail. The lifting off of the electron layer near the insulator surface near voltage breakdown was also present in the UNU-ICTP case, and the reason behind this was firmly established from the radial electric field result near the insulator surface. The simulations were also extended to insulators of different lengths, with results reported on the various ionization wave velocities pertaining to the sliding discharge. A clear signature of voltage breakdown was found from the generic looking current waveform, being clear that the current increases suddenly in a nearly linear fashion (within a short time domain) at the point of breakdown. This criterion allows us to compare the breakdown voltage and times for the different insulator lengths.
Our simulation culminates with the successful application of our circuit integrated codes to model the UNU-ICTP from the beginning all the way up to the early stage of the axial phase. The generated voltage waveform agreed very well with experimental measurements, with an initially oscillatory current superimposed on a linearly rising profile. By using a simple load consisting of a resistor and inductor to model the post-breakdown phase, it was concluded that the oscillations arise from the plasma inductance. Measuring the oscillation period therefore allowed the estimation of the inductance of the CS. The value obtained from simulation agreed well with that deduced from the experimental waveform. Our simulations also revealed clearly the lifting off of the CS, with the CS speed estimated from simulation data. At the kinetic level, the time evolution of the electron temperature and the electron neutral collision frequency were also estimated. The simulation results indicate the trend of the electron energy distribution function (EEDF) towards Maxwellization, albeit at a slower pace. Even after the occurrence of CS lift-off, the EEDF has yet to equilibrate to a Maxwellian distribution.
We concluded our work with a short chapter on future work and extensions to our present codes.
Date Issued
2016
Call Number
QC715.5.D38 Sen
Date Submitted
2016