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Electron transport coefficients in copper vapor plasma are calculated both by two-term expansion of electron Boltzmann equation Bolsig+ and tracking the random motion of electrons using Monte Carlo collision code METHES based upon recently evaluated cross section sets. The copper atoms are evaporated from hot electrode during the post-arc phase of vacuum circuit breakers, in which Townsend breakdown between electrode gaps is probable. The electron energy probability function, electron mean energy, flux/transport mobility and diffusion coefficients, as well as Townsend ionization coefficients are shown in reduced fields 10∼1000 Td at a typical vapor temperature 2000 K. The validity of two-term approximation is checked by comparison to well benchmarked METHES code. If the electrode temperature varies between 1500∼2500 K, the influence of vapor temperature on ionization coefficients is about 5% at 200.4 Td, and drops to 0.5% at 493 Td according to Bolsig+ results. Similar to classic gas discharge theory, the Paschen curve is proposed for Townsend breakdown of metal vapor. Using the calculated ionization coefficient and a constant secondary electron yield, the Paschen minimum is determined to be 106∼122 V at a critical value of the product of vapor density and gap length (4.7∼5.7)×1019 m-2. A satisfactory agreement was found with the previously measured ignition voltage between vacuum interrupter contacts after the arcing.

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The consistency of magnetic flux density of damping gap (CMDG) represents the balancing magnetic flux density in each damping gap of magnetorheological (MR) dampers. It can make influences on the performances of MR dampers and the accuracy of relevant objective functions. In order to improve the mechanical performances of the MR damper with a two-stage coil, the function for calculating CMDG needs to be found. By establishing an equivalent magnetic circuit model of the MR damper, the CMDG function is derived. Then, the multiobjective optimization function and the working flow of optimal design are presented by combining the parallel-plate model of the MR damper with the function posed before. Taking the damping force, the dynamic range, the response time, and the CMDG as the optimization objective, and the external geometric dimensions of the SG-MRD60 damper as the bound variable, this paper optimizes the internal geometric dimensions of MR damper by using a NSGA-III algorithm on the PlatEMO platform. The results show that the obtained scheme in Pareto-optimal solutions has existed with better performance than that of SG-MRD60 scheme. According to the results of the finite element analysis, the multiobjective optimization design including the CMDG function can improve the uniformity of magnetic flux density of the MR damper in damping gap, which meets the requirements of manufacture and application.

In this paper, an electromagnetic-field FDTD method coupled with plasma fluid model is put forward to investigate the different physical phenomena of high power microwave (HPM) flashover and breakdown on inner and outer surface of output-window. Based on the above theoretical models, a one-dimensional (1D) electromagnetic field and plasma interaction code is programmed by authors. By using the code, the HPM flashover and breakdown on inner and outer surface of output-window are simulated. The numerical results could be concluded as follows. For flashover and breakdown on outer surface, output microwave pulse is shortened without cut-off; there is a standing-wave distribution of electric field RMS (Root-Mean-Square) value before the window with fixed-positions of wave nodes and antinodes; there is a ultra-high-density (～1021 m-3) and ultra-thin (～mm) plasma shell with slow diffusion, microwave could penetrate the plasma-shell partly; the shortening of output microwave is caused by plasma absorption mostly. The output pulse of microwave could be lengthened by reducing the initial density or depth of plasmas; the other way is to shorten incident microwave pulse or reduce the value of incident microwave power. For flashover and breakdown on inner surface, there is also a standing-wave distribution of electric field RMS value before the window but the positions of wave nodes and antinodes vary with time; the plasma region moves toward the microwave source; with strong-outgassing, output microwave pulse is shortened without cut-off, there are “thread-like” ultra-high-density (～ 1021 m-3) and ultra-thin (～mm) plasma regions with slow diffusion, the distance between two “thread-like” regions is about a quarter of microwave wavelength, the shortening of output microwave is caused by plasma absorption mostly; with weak-outgassing and low electric field value, the output pulse of microwave is lengthened but cut-off finally, there are “belt-like” high-density (～ 1018 m-3) and thin (mm-cm) plasma regions with fast diffusion, the distance between two “belt-like” region is about a quarter of microwave wavelength, the shortening of output microwave is caused by plasma absorption mostly; with weak-outgassing and high electric field value, output pulse of microwave is cut-off quickly, “block-like” diffuse ultra-high-density (～1021 m-3) and deep (～ cm) plasma regions are formed with very fast diffusion, and the shortening of output microwave is caused by plasma reflection mostly.