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Circuital characterisation of space-charge motion with a time-varying applied bias.

Kim C, Moon EY, Hwang J, Hong H - Sci Rep (2015)

Bottom Line: Here we show that the microscopic details of the space-charge in terms of resistance and capacitance evolve in a parallel topology to give the macroscopic behaviour via a charge-based circuit or electric-field-based circuit.We identify a significant capacitive current due to the rate of change of the capacitance.Our results and approach provide a facile platform for a comprehensive understanding of the behaviour of space-charge between electrodes.

View Article: PubMed Central - PubMed

Affiliation: 1] School of Mechanical Engineering, Yonsei University, Seoul 120-749, Republic of Korea [2] Department of Mechanical Engineering, Kyung Hee University, Yongin 446-701, Republic of Korea.

ABSTRACT
Understanding the behaviour of space-charge between two electrodes is important for a number of applications. The Shockley-Ramo theorem and equivalent circuit models are useful for this; however, fundamental questions of the microscopic nature of the space-charge remain, including the meaning of capacitance and its evolution into a bulk property. Here we show that the microscopic details of the space-charge in terms of resistance and capacitance evolve in a parallel topology to give the macroscopic behaviour via a charge-based circuit or electric-field-based circuit. We describe two approaches to this problem, both of which are based on energy conservation: the energy-to-current transformation rule, and an energy-equivalence-based definition of capacitance. We identify a significant capacitive current due to the rate of change of the capacitance. Further analysis shows that Shockley-Ramo theorem does not apply with a time-varying applied bias, and an additional electric-field-based current is identified to describe the resulting motion of the space-charge. Our results and approach provide a facile platform for a comprehensive understanding of the behaviour of space-charge between electrodes.

No MeSH data available.


Related in: MedlinePlus

Experimental validation of the parallel circuit topology.(a) Va-I loops for frequencies of 20 kHz (□), 10 kHz (◊) 5 kHz (△) and 1 kHz (○). The coincidences of Imean(•) were as follows: 0.206 mA for 0.2 kHz, 0.207 mA for 0.5 kHz, 0.206 mA for 1 kHz, 0.204 mA for 2 kHz, 0.207 mA for 5 kHz, 0.204 mA for 10 kHz and 0.204 mA for 20 kHz, average: 0.2054 mA, standard deviation: 0.0013 mA. The 2-kHz loop is plotted between 1- and 5-kHz loops (not shown). The 0.2-kHz and 0.5-kHz loops were almost identical to line A. (b) The experimental DC current-voltage curve reveals typical wire-to-cylinder corona discharge, and can be fitted with I = 0.00405 Va(Va − Vci), where Vci = 3.4 kV is the corona discharge initiation voltage28. Data for f = 20 kHz and Vo = 1.0 kV are shown by the ‘○’ symbols and data for f = 100 kHz and Vo = 0.1 kV by the ‘▲’ symbols. Difference between DC data and 8 symbols; average: 0.00042 mA, standard deviation: 0.0012 mA.
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f3: Experimental validation of the parallel circuit topology.(a) Va-I loops for frequencies of 20 kHz (□), 10 kHz (◊) 5 kHz (△) and 1 kHz (○). The coincidences of Imean(•) were as follows: 0.206 mA for 0.2 kHz, 0.207 mA for 0.5 kHz, 0.206 mA for 1 kHz, 0.204 mA for 2 kHz, 0.207 mA for 5 kHz, 0.204 mA for 10 kHz and 0.204 mA for 20 kHz, average: 0.2054 mA, standard deviation: 0.0013 mA. The 2-kHz loop is plotted between 1- and 5-kHz loops (not shown). The 0.2-kHz and 0.5-kHz loops were almost identical to line A. (b) The experimental DC current-voltage curve reveals typical wire-to-cylinder corona discharge, and can be fitted with I = 0.00405 Va(Va − Vci), where Vci = 3.4 kV is the corona discharge initiation voltage28. Data for f = 20 kHz and Vo = 1.0 kV are shown by the ‘○’ symbols and data for f = 100 kHz and Vo = 0.1 kV by the ‘▲’ symbols. Difference between DC data and 8 symbols; average: 0.00042 mA, standard deviation: 0.0012 mA.

Mentions: First, we attempt to reproduce the parallel topology discussed above. The terms CL and CQ (see Fig. 1c) result from KL (due to the electrodes) and KQ (due to the space-charge), whereas CEE and CS (see Fig. 1d) result from KEE (for the volume) and KS (for the surface). The summation of these geometrically separated energies corresponds to the parallel connection of two capacitors. However, concerning the space-charge, it is not clear whether the drift of the point charge ΔQ (see Fig. 1a) corresponds to a parallel or series connection of CΔQ and RΔQ. In this respect, it is helpful to experimentally confirm the parallel connection between RQ and the two capacitances. With periodic conditions, the mean circuit current of the proposed parallel circuit should always be equal to the mean resistor current for a given Vm because the mean of the capacitor current is zero regardless of frequency. For Vm = 9 kV, as shown in Fig. 3a, the experimental result reveals that the Va-I loop contracted to the line A as the frequency decreased from 20 kHz to 1 kHz. Consequently, Imean for each axisymmetric current loop exactly coincides with one centred point for all frequencies, which corresponds to a parallel circuit topology. Figure 3b provides further support of this when Vm and Vo are varied. The solid line in Fig. 3b shows the DC current-voltage curve, which is the same as the Vm-Imean curve for f = 0 kHz. For f = 20 kHz and Vo = 1.0 kV, the centred point coincides exactly with the Vm-Imean curve at the three points of Vm, and with f = 100 kHz and Vo = 0.1 kV, the centred point coincides exactly with the Vm-Imean curve at the five points of Vm.


Circuital characterisation of space-charge motion with a time-varying applied bias.

Kim C, Moon EY, Hwang J, Hong H - Sci Rep (2015)

Experimental validation of the parallel circuit topology.(a) Va-I loops for frequencies of 20 kHz (□), 10 kHz (◊) 5 kHz (△) and 1 kHz (○). The coincidences of Imean(•) were as follows: 0.206 mA for 0.2 kHz, 0.207 mA for 0.5 kHz, 0.206 mA for 1 kHz, 0.204 mA for 2 kHz, 0.207 mA for 5 kHz, 0.204 mA for 10 kHz and 0.204 mA for 20 kHz, average: 0.2054 mA, standard deviation: 0.0013 mA. The 2-kHz loop is plotted between 1- and 5-kHz loops (not shown). The 0.2-kHz and 0.5-kHz loops were almost identical to line A. (b) The experimental DC current-voltage curve reveals typical wire-to-cylinder corona discharge, and can be fitted with I = 0.00405 Va(Va − Vci), where Vci = 3.4 kV is the corona discharge initiation voltage28. Data for f = 20 kHz and Vo = 1.0 kV are shown by the ‘○’ symbols and data for f = 100 kHz and Vo = 0.1 kV by the ‘▲’ symbols. Difference between DC data and 8 symbols; average: 0.00042 mA, standard deviation: 0.0012 mA.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4488748&req=5

f3: Experimental validation of the parallel circuit topology.(a) Va-I loops for frequencies of 20 kHz (□), 10 kHz (◊) 5 kHz (△) and 1 kHz (○). The coincidences of Imean(•) were as follows: 0.206 mA for 0.2 kHz, 0.207 mA for 0.5 kHz, 0.206 mA for 1 kHz, 0.204 mA for 2 kHz, 0.207 mA for 5 kHz, 0.204 mA for 10 kHz and 0.204 mA for 20 kHz, average: 0.2054 mA, standard deviation: 0.0013 mA. The 2-kHz loop is plotted between 1- and 5-kHz loops (not shown). The 0.2-kHz and 0.5-kHz loops were almost identical to line A. (b) The experimental DC current-voltage curve reveals typical wire-to-cylinder corona discharge, and can be fitted with I = 0.00405 Va(Va − Vci), where Vci = 3.4 kV is the corona discharge initiation voltage28. Data for f = 20 kHz and Vo = 1.0 kV are shown by the ‘○’ symbols and data for f = 100 kHz and Vo = 0.1 kV by the ‘▲’ symbols. Difference between DC data and 8 symbols; average: 0.00042 mA, standard deviation: 0.0012 mA.
Mentions: First, we attempt to reproduce the parallel topology discussed above. The terms CL and CQ (see Fig. 1c) result from KL (due to the electrodes) and KQ (due to the space-charge), whereas CEE and CS (see Fig. 1d) result from KEE (for the volume) and KS (for the surface). The summation of these geometrically separated energies corresponds to the parallel connection of two capacitors. However, concerning the space-charge, it is not clear whether the drift of the point charge ΔQ (see Fig. 1a) corresponds to a parallel or series connection of CΔQ and RΔQ. In this respect, it is helpful to experimentally confirm the parallel connection between RQ and the two capacitances. With periodic conditions, the mean circuit current of the proposed parallel circuit should always be equal to the mean resistor current for a given Vm because the mean of the capacitor current is zero regardless of frequency. For Vm = 9 kV, as shown in Fig. 3a, the experimental result reveals that the Va-I loop contracted to the line A as the frequency decreased from 20 kHz to 1 kHz. Consequently, Imean for each axisymmetric current loop exactly coincides with one centred point for all frequencies, which corresponds to a parallel circuit topology. Figure 3b provides further support of this when Vm and Vo are varied. The solid line in Fig. 3b shows the DC current-voltage curve, which is the same as the Vm-Imean curve for f = 0 kHz. For f = 20 kHz and Vo = 1.0 kV, the centred point coincides exactly with the Vm-Imean curve at the three points of Vm, and with f = 100 kHz and Vo = 0.1 kV, the centred point coincides exactly with the Vm-Imean curve at the five points of Vm.

Bottom Line: Here we show that the microscopic details of the space-charge in terms of resistance and capacitance evolve in a parallel topology to give the macroscopic behaviour via a charge-based circuit or electric-field-based circuit.We identify a significant capacitive current due to the rate of change of the capacitance.Our results and approach provide a facile platform for a comprehensive understanding of the behaviour of space-charge between electrodes.

View Article: PubMed Central - PubMed

Affiliation: 1] School of Mechanical Engineering, Yonsei University, Seoul 120-749, Republic of Korea [2] Department of Mechanical Engineering, Kyung Hee University, Yongin 446-701, Republic of Korea.

ABSTRACT
Understanding the behaviour of space-charge between two electrodes is important for a number of applications. The Shockley-Ramo theorem and equivalent circuit models are useful for this; however, fundamental questions of the microscopic nature of the space-charge remain, including the meaning of capacitance and its evolution into a bulk property. Here we show that the microscopic details of the space-charge in terms of resistance and capacitance evolve in a parallel topology to give the macroscopic behaviour via a charge-based circuit or electric-field-based circuit. We describe two approaches to this problem, both of which are based on energy conservation: the energy-to-current transformation rule, and an energy-equivalence-based definition of capacitance. We identify a significant capacitive current due to the rate of change of the capacitance. Further analysis shows that Shockley-Ramo theorem does not apply with a time-varying applied bias, and an additional electric-field-based current is identified to describe the resulting motion of the space-charge. Our results and approach provide a facile platform for a comprehensive understanding of the behaviour of space-charge between electrodes.

No MeSH data available.


Related in: MedlinePlus