Magnetohydrodynamic simulation for plasma focus devices

Data from the 2002 Imperial College plasma focus (ICpf) are used to study the dynamics of axial and radial phase as functions of pressure. The speeds are found to deviate from the ideal constant current electromagnetic rule of v $\sim ~P_{0}^{-n} $ , (where $n = 0.5$ ) with the modulus going below 0.5, due to the back-electromotive force varying the peak drive current even at fixed voltage operation. The amount of deviation depends on machine parameters and varies from a modulus of 0.3 for the NX1 axial phase to 0.47 in the INTI Plasma Focus (INTI PF) axial phase. The radial phase of the ICpf is characterized by a modulus of 0.48. The computed results are experimentally verified in the case of the NX1 and INTI PF axial phase. The effect on neutron yield is briefly discussed.

Experiments show that the performance of the plasma focus (PF) depends on several macroscopic parameters like the energy of the capacitor bank, current, voltage, electrodes dimension, and curvature of current sheath in the axial phase. Recent work (IEEE Trans. Plasma Sci., vol. 24, no. 3, pp. 1101-1105, 1996) shows that overriding the dependence of performance on the individual parameters listed above is the dependence on a combined parameter called the drive or speed parameter S=(I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> /a)/radicrho. This parameter S appears as most fundamental in the process of nondimensionalization of the magnetohydrodynamic equations coupling the highly supersonic motion of the plasma layer with the electromagnetic circuit equation. The drive parameter S is found to directly control the speed of the plasma layer in both axial and radial phases of the PF. A literature survey (IEEE Trans. Plasma Sci., vol. 24, no. 3, pp. 1101-1105, 1996) first pointed out that neutron-optimized Mather-type PF devices with a range of energies from a few kilojoules to hundreds of kilojoules all operate with a remarkably constant drive parameter. This constancy of S has been extended more recently (Plasma Phys. Control. Fusion, vol. 47, pp. A361-A381, 2005) to PF devices over eight orders of magnitude of storage energies, from a fractional of a joule to megajoules. In this paper, experiments on 2-3-kJ dense PF with modified anodes have been conducted to show that this drive parameter remains fairly constant for the different ratios of the anode length to anode radius. It is also suggested that there may be significant differences in the values of drive parameters for Filippov-type focus devices, Mather-type focus devices, and also hybrid-type devices

We describe the axial phase of the Mather plasma focus by two coupled equations of motion and circuit. We non-dimensionalised these equations resulting in two coupled equations which are characterised by only three scaling parameters α, β and δ which are ratios of electrical to transit times, inductances and impedances respectively. The normalised current waveform, trajectory and speed profile are unique for each combination of α, β, δ which are the ratios of characteristic times (electrical discharge vs. axial transit), inductances (tube inductance vs. static inductance) and impedances (stray resistance vs. electrical surge impedance). This leads to important information and insight into various aspects of the axial phase. In the present work we show that in a time-matched plasma focus shot we deduce the value of axial phase current fraction fc simply by measuring the calibrated voltage waveform and the uncalibrated current waveform. The scaling parameters β and δ are fixed; and by form-fitting the measured current waveform to the normalised current waveform using the value of α of the shot is determined uniquely; from which the peak current and the ratio of peak to average speed [the speed form factor (SFF)] are obtained. The average transit speed is measured by time-of-flight using the voltage upturn as indicator of end of axial phase. Then the SFF yields the peak speed. The measured voltage (back EMF), peak current and peak axial speed (all at the end of axial phase) allows the unambiguous measurement of fc. The value of the mass swept-up fraction fm is deduced from α which is the ratio of the characteristic discharge and the characteristic transit times, both deduced during the non-dimensionalisation of the equations. Analysis of a time-matched shot in the INTI PF at 15 kV, 3 Torr D2 gave fc = 0.68 and fm = 0.05.

The study of plasma sheath structure and its dynamics in the presence of external axial magnetic field (B/sub z/) in dense plasma focus has been made with the help of N/sub 2/-laser shadowgraphic technique. The shadowgraphs of axial phase show that in the presence of external B/sub z/ the current sheath gets diffused near the end attached to the central electrode when it reaches to the top of the central electrode. The shadowgraphs of radial collapse phase show clearly distinct hump formation above central electrode under the influence of B/sub z/. Moreover, during the radial collapse phase a part of the current sheath lying close to central electrode gets highly diffused in comparison to the rest of the current sheath. Diffused bubble formation on the ionization wave front and dominantly visible remnant of plasma sheath above central electrode have also been observed during the quiescent phase (the expansion phase after the peak compression).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The pinch performance of a plasma focus (PF) device is sensitive to the physical conditions of the breakdown phase. It is therefore essential to model and study the initial phase in order to optimize device performance. An external circuit is self consistently coupled to the electromagnetic particle in cell code to model the breakdown and initial lift phase of the United Nations University/International Centre for Theoretical Physics (UNU-ICTP) plasma focus device. Gas breakdown during the breakdown phase is simulated successfully, following a drop in the applied voltage across the device and a concurrent substantial rise in the circuit current. As a result, the plasma becomes magnetized, with the growing value of the magnetic field over time leading to the gradual lift off of the well formed current sheath into the axial acceleration phase. This lifting off, with simultaneous outward sheath motion along the anode and vertical cathode, and the strong magnetic fields in the current sheath region, was demonstrated in this work, and hence validates our method of coupling the external circuit to PF devices. Our method produces voltage waveforms that are qualitatively similar to the observed experimental voltage profiles of the UNU-ICTP device. Values of the mean electron energy before and after voltage breakdown turned out to be different, with the values after breakdown being much lower. In both cases, the electron energy density function turned out to be non-Maxwellian.

A magneto-hydrodynamic simulation of a plasma focus device with hemisphere electrodes is constructed. The snowplow model is used with help of the momentum conservation equation to describe the motion of the plasma sheath between the two concentric hemispheres. The model simulates various plasma parameters like plasma temperature and plasma sheath velocity. The circuit equation is used to calculate the discharge current and electrodes voltage across the two hemisphere terminals. A comparison between the cylindrical and spherical devices is built. The results show that the current dip and the spike voltage is expected to be much pronounced in the spherical devices. It is found also that the plasma sheath velocity and temperature in the case of the cylindrical system are higher than that in the spherical one.

The results are presented from the probe measurements of plasma parameters in the tubular plasma source used in research on plasma relativistic microwave electronics. Tubular plasma is produced as a result of background gas ionization by the electron beam emitted by the annular heated tungsten cathode in the axial magnetic field. The current–voltage characteristics of the probe were obtained for three discharge currents of 5, 9, and 20 A at three plasma column lengths of 10, 20, and 30 cm. It was shown that for all discharge currents and for all plasma column lengths, the electron temperature is equal to 20 eV at the time of performing measurements. It is also shown that in this source, the plasma density does not depend on the plasma column length in the lengths range from 10 to 30 cm. It was demonstrated that the discharge current is a linear function of the probe current, which makes it possible to control the relative changes in the plasma density during the experiment. For different discharge currents, the absolute value of plasma density was estimated to be in the range of 1012–1013 cm–3.

Results on coordinated experiments and MHD simulations on the axial phase sheath dynamics of dense plasma focus are presented. The aim of this effort is to use a repetitively fired dense plasma focus (DPF) to gather data from 100's to 1000's of shots per gas load, so as to better refine numerical codes. The experimental results will feed fully 3D simulations of DPF devices, adding new capabilities to the GORGON code.

The Hemisphere Plasma Focus Device, a new construction of plasma focus devices is constructed and operated with total energy of 7.7 kJ. The discharge takes place between two concentric hemispherical electrodes. The plasma sheath is accelerated and confined by electromagnetic force. Rogowiski coil and potential divider are used to characterize the discharge current, the discharge voltage and obtain the pinch effect in shape of sharp crevice. The deposited energy is about 31.5% of the input energy for 6kV charging voltage. The total system inductance is about 285 nH with low resistance of about 23 mΩ. The plasma inductance has maximum value at the pinch time. The pinch time decreases by increasing input energy and also by decreasing the helium gas pressure. The average sheath velocity varies in range between 1.5 and 2.7 cm/µs which indicates that the charge state is about 2 and plasma temperature should mostly be over 11.2eV.

Dense Plasma Focus (DPF) devices are pulse plasma devices which are capable to generate few keV to MeV ions. The burst of energetic ions presents in plasma shots generated by DPF devices, can be used for impanation in the desired materials for various application from electronics to spintronics. Here, we present an advance way of gradient implantation using DPF in the heavy metal without much effecting the surface properties of the thin film. In order to implant desired ions such as oxygen, carbon, nitrogen, argon etc. new electrodes were designed, providing gentler plasma pinch phase, with increased plasma volume. To study the effect of the new electrode design electrical characteristics were performed in detail and with the help Lee code the plasma parameter like plasma temperature, plasma duration etc. was estimated. Optical imaging diagnostic (using gated ICCD camera), faraday cup measurements and x-ray pin-diode spectroscopy, was used to investigate the plasma dynamics, plasma density and plasma temperature. The designed electrode assembly can be used to generate defects and modify the material properties required for electronics, photonics and spintronics applications.

We consider the snowplow model to describe the axial phase of a plasma focus device. We show that, within this framework, the dynamics of a given system can be recovered at different energetic and geometric scales. Then, we consider two different criteria that would plausibly optimize the plasma focus performance. By solving the dynamics equations for the axial phase, we estimate the values of the parameters that do indeed satisfy the aforementioned criteria and compare those values with the corresponding ones attached to few practical devices.

Deposition of tungsten nitride thin films by plasma focus device at different axial and angular positions

An algorithm for diagnosing the electron density and temperature of helium plasma at atmospheric pressure has been developed based on a revised helium collisional-radiative (CR) model. Atomic collision processes are included, and part of the atomic data of electron collision processes in the conventional CR model has been updated to expand its valid pressure. The algorithm uses eight emission lines in the visible-wavelength range as inputs to determine the electron density, electron temperature, and number density of the two metastable states by fitting the number density of the states corresponding to the emission lines. The algorithm has a considerably small theoretical error. In the microwave-discharged low-pressure helium plasma experiment, the results obtained with the algorithm agreed well with the results obtained with the probe method. The electron density and temperature of the atmospheric-pressure helium plasma obtained with the algorithm agreed well with the results of the continuum spectrum analysis.

The temporal and spatial characteristics of the neon ion beam emissions from a low energy plasma focus device have been studied by employing a multiple Faraday cup assembly and the CR-39 track detectors at different angular and axial positions. In addition, the operating gas pressures were also varied to study the temporal and spatial characteristics of the neon ion beam emissions. The Faraday cup analyses show that the ion flux strongly depends on the operating gas pressure as well as the angular positions. The estimated ion energy measurements at the aperture of the Faraday cup indicate that the plasma focus device is a source of polyenergetic ions ranging from approximately a few keV to a few hundreds of keV, irrespective of the angular positions. The exposed CR-39 detectors have shown the formation of multiple ion tracks with diameter ranging from 2 to 13 μm. The populations of lower diameter tracks (2–6 μm) are observed to be more at 0° and 10° angles. It is also noticed that the most populated track counts have shifted toward the higher diameter as the angular positions change from 0° to 70°. The present study enables us to predict a clear picture of ion flux and energy distribution inside the plasma focus chamber that will help to use the device for material irradiation application in a more controlled manner.

To study the effect of higher axial sheath velocities on neutron production, the geometry of the inner electrode (anode) of a 3-kJ Mather-type plasma focus device was modified. Double-stage stepped-anode configurations were tested with a speed-enhanced region long enough for a significant increase in speed but not long enough to allow the development of force-field flow-field separation at the end of the axial phase. Peak axial speeds up to 15 cm/μs were achieved without modifying the deuterium filling pressure and charging voltage. The neutron and soft X-ray productions were found to be dependent on sheath velocity. A new scaling law for the nonbeam component of the neutron yield was proposed.