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This work investigates the transient anode temperature and plasma parameters considering the electrode movement and the arc expansion. A transient self-consistent model is established using the dynamic mesh approach. Two cases with different maximum arc currents, representing various anode activity, have been studied. The simulations predict significant changes in spatial distribution of species densities, electron temperature and anode surface temperature in case with the anode spot formation. Furthermore, the influence of opening velocity on the plasma parameters has been studied numerically. The model was validated by comparison with experimental data for anode surface temperature as well as spectrally filtered arc images. Results of this comparison are presented and discussed.

Supersonic plasma has been widely used. A vacuum arc ion source provides one possible method for generating supersonic plasma. An external magnetic field can effectively avoid the wall loss of the plasma in the ion source and improve the ion yield. In this work, a two-dimensional magnetohydrodynamic model is established, considering different components including ions and electrons. With the help of simulation, we explore the physical characteristics of the supersonic vacuum arc plasma formed from a copper disk cathode. The characteristics that we focus on include plasma composition, current density distribution, plasma velocity, and plasma temperature. These characteristics as well as the ion yield are compared when different magnetic fields generated by solenoids near the cathode are applied, as well as when the arc current is different. The results show that, in the absence of an external magnetic field, ions expand freely with the approximate axial velocity and average ion charge state. With the increase of external magnetic flux density, the wall loss of the plasma will decrease, and the axial velocity and average ion charge state will increase, but the magnetic saturation phenomenon exists. The simulation results are consistent with the experimental results.

A two-dimensional self-consistent model has been established in order to investigate the distribution of F-containing species in He/CF4 atmospheric pressure plasma jet and the effect of CF4 concentration on the reactive F-containing species. A portion of electron energy is consumed whenever an F is ionized from the CF4, resulting that the average densities of CF 4 + , CF 2 + and CF+ decrease sequentially. The density of CF 3 + is greater than CF 4 + density due to Penning ionization of He* with CF4 and He+ + CF4 → CF 3 + + F + He. In the case of He + 0.5% CF4 at 200 ns, the electron impact reactions mainly concentrate on the streamer head on the dielectric surface. The Penning ionization of He* with CF4 dominates in the region of 0 < r < 2.2 mm benefits from long-lived He* of high density and the high concentration CF4 in this region. As gas flow gradually mixes with ambient air (r > 2.2 mm), the Penning ionization of metastable He with N2 and O2 dominates in this area. As the CF4 concentration increases from 0.1% to 1%, the densities of F-containing positive ions all increase significantly. CF3, F and F2 also show the upward trend while there is little change in the spatial densities of CF2 and CF. The F-containing neutral species flux benefits from two factors: the diffusion and the conversion of positive ions. In the case of 0.1% CF4, due to the low density of CF 2 + , CF+ and F+ and the diffusion of F, the F flux for is consistent with CF2 and is greater than CF. However, when CF4 concentration exceeds 0.5%, the concentration of CF 3 + , CF 2 + and CF+ are much higher than F+. The quenching of positive ions dominates on the dielectric surface in the case of 0.5% and 1% CF4, resulting that the flux of F is lower than that of CF2 and CF.

The mechanical DC vacuum circuit breaker based on forced-over-zero technology will inevitably generate vacuum arc during the actual interrupting process. Since the current drop frequency is usually very high, the vacuum arc usually exhibits obvious transient characteristics, and the excessive transient characteristics may even become a key factor limiting the interruption capacity. In order to improve the mechanical DC vacuum circuit breaker arc interrupting capability, this paper establishes a vacuum arc transient magneto-hydrodynamic simulation model in the DC interrupting process and studies the plasma transport characteristics of the vacuum arc under different DC interrupting conditions. The results show that the ion pressure, ion density and ion temperature decrease with decreasing arc current, while the ion velocity gradually increases during the DC interrupting process. The increase in breaking current and current drop frequency will increase the ion density in the arc column at the moment of current crossing zero, resulting in more difficult vacuum arc interrupting. The results of the study can provide an important theoretical basis for a deeper understanding of the vacuum arc transient process in the DC interrupting process and improve the DC vacuum circuit breaker arc interruption capability.

A two-dimensional (2D) axisymmetric fluid model is built to investigate the effect of different O2 and H2O admixture on the plasma dynamics and the distribution of reactive species in He atmospheric pressure plasma jet (APPJ). The increase of O2:H2O ratio slows down both the intensity and the propagation speed of the ionization wave. Due to the decrease of both H2O ionization rate and H2O Penning ionization as well as the stronger electronegativity of O2, the increase of O2:H2O ratio results in a significant reduction of electron density in the APPJ, which restricts the occurrence of electron collision ionization reactions and inhibits the propagation of plasma. The excitation energy loss of O2 is not the reason for the weakening of the plasma ionization wave. The densities of O2 +, O− and O2 − increase with the rise of O2 admixture while H2O+ decreases due to the decrease of electron density and H2O concentration. OH− density is affected by both the increase of O− and the decrease of H2O so it shows a peak in the case of O2:H2O = 7:3. O is mainly produced by the excitation reactions and the electron recombination reaction (e + O2 + → 2O), which is directly related to the O2 concentration. OH is mainly produced by e + H2O → e + H + OH so the OH density decreases due to the decrease of electron density and H2O concentration with the increase of O2:H2O ratio. On the dielectric surface, when the propagation of the streamer extinguishes, O flux shows an upward trend while the OH flux decreases, and the propagation distance of O and OH decreases with the increase of O2:H2O ratio.

In this paper, the spatial-temporal evolution of the anode temperature in the vacuum arc during the formation of an anode spot is investigated by numerical simulation and experiments. A transient self-consistent model is established to calculate the arc parameters and the anode temperature. The simulations predict that the maximum anode temperature always occurs after the current peak. Ion density and atom density at the anode side increase significantly during the formation of the anode spot. In the anode spot mode, more evaporated anode material comes into the arc column, leading to higher plasma temperature around the spot. The anode vapor can reduce the energy flux from the plasma to the anode center, providing more uniform anode temperature distribution and correspondingly smoother plasma parameter distributions in the vicinity of the anode center. In addition, a higher Cr fraction in the electrodes can result in a higher anode temperature. Near-infrared spectroscopy and high-speed camera thermography are used to study the anode temperature experimentally in order to verify the simulation results. A reasonable agreement was found.

In the arc-burning process of high-current vacuum arc(HCVA), the metal particles（MPs） splashed from the active anode will have a significant influence on the plasma characteristics of the arc column. In this paper, the influence of MPs with different characteristics on the characteristics of HCVA is studied by establishing a HCVA model containing single or multiple MPs. The simulation results show that when the MPs vaporized metal vapor (MV) enters the interelectrode region, once the arc column plasma cannot ionize all atoms immediately, the ionization layer and the neutral atom vapor area (NAVA) will be formed in the adjacent region of the MPs. When the metal particle (MP) diameter and temperature increase, the number of vaporized mental atoms increases, so that the influence range of metal vapor increases, and the area of ionization layer and the neutral atom vapor area increases. In addition, when the arc current increases or the MPs are closer to the cathode surface, the greater the ion number density and ion pressure around the MPs are, the stronger the compression on the metal vapor will be, resulting in the decrease of the area of nization layer and the neutral atom vapor, and the increase of the net ionization rate of the ion number density. When multiple MPs exist in the interelectrode region at the same time, the metal vapor vaporized by the MPs will affect each other. In the central region of multiple MPs, the density of metal vapor becomes the largest, while the net ionization rate of ion number density is distributed in the periphery region of the metal particle group.

Color-tunable white organic light-emitting diodes (CT-WOLEDs) having daylight chromaticity and a wide correlated color temperature (CCT) span can mimic our circadian cycle and realize application for lighting or decoration. The effects of the recombination zone and energy distribution on the electro-optical properties and color span are investigated in this paper. We find that it is beneficial to expand the CCT span by increasing the distance between the red ultrathin phosphorescent emissive layer and the center of the recombination zone. By increasing the concentration (y) of mCP in mixed host material in the emitting layer and the thickness (z nm) of the red ultrathin phosphorescent emissive layer, the CCT spans can be expanded towards high CCT and low CCT, respectively. The widest CCT span reaches 4032 K (2391–6423 K) in a simple all-phosphorescent CT-WOLED with a maximum luminance and power efficiency of 9249 cd m−2 and 15.35 lm W−1, respectively.

A 3D transient model of a cathode-spot crater and droplet formation in a vacuum arc is developed. The model includes mass, momentum, heat transfer (energy), current continuity and potential equations. Using the energy flux density, current density and pressure as external parameters, the shape of the cathode-spot crater and the temperature, velocity, potential and current density distributions at each time step are determined via numerical simulation. Under symmetrical conditions, the 3D simulation results are highly consistent with those from the previous 2D model. The new cathode spot tends to appear in the direction in which the protrusion is largest because the liquid-metal velocity is lower and the liquid-metal ridge radius is larger in this direction. The effect of the external transverse magnetic field is considered by using a symmetric space function to represent the pressure and energy flux density of the plasma cloud. Simulation results show that even small changes in the plasma cloud distribution have a significant impact on the cathode-spot crater process and droplet formation. Since the pressure is asymmetric, the crater becomes asymmetric and the new cathode spot tends to appear opposite to the direction of the Ampere force. Based on this phenomenon, a possible explanation for the retrograde motion phenomenon of cathode spots is proposed.

In a switchgear, an external transverse magnetic field (ETMF) is generated by the U type loop consisting of the vacuum interrupter, external busbar and conductive rod connected to the vacuum interrupter. The ETMF will make the vacuum arc deflected and strengthen the contraction of the arc. This can increase the probability of breaking failure. To weaken the adverse effect of the ETMF, the real magnetic field data of the arc area with different structure parameters when the length of conductive rod, external busbar and phase distance is changed are obtained by establishing simulation model in this paper. Taking the real magnetic field data as the boundary condition, this paper obtains the typical parameters of the vacuum arc plasma with different structure parameters by using the established three-dimensional high-current vacuum arc magnetohydrodynamics model. The simulation results show that the ETMF makes the transverse magnetic field (TMF) of the arc area asymmetric, which leads to an arc deflection. Reducing the length of the conductive rod connected to the vacuum interrupter to 50 mm can effectively improve the asymmetry of the TMF caused by the EMTF, weaken the arc deflection phenomenon, make the distribution of the plasma parameters more uniform, and increases the utilization of the anode contact surface. Moreover, it can not only reduce the heat flux density into the anode as a whole, but also reduce the heat flux density in the high heat flux density area, so as to effectively reduce the degree of anode activity and improve the negative effects caused by the anode activity. The changes of other external structural parameters have less influence on the improvement of the vacuum arc deflection phenomenon. Increasing the phase spacing to 275 mm or reducing the length of the external bus bar to 100 mm can only slightly weaken the arc deflection.

An improved two-dimensional axisymmetric swirl model based on former work has been developed to describe the detailed physical process in the formation and development of vacuum arc cathode spot. In the current model, the influence of plasma cloud, evaporation, backing ion, thermo-field (T-F) emission, back-diffused electron, self-generated magnetic field and Lorentz force are all considered. External parameters include electron temperature, near cathode voltage drop, average charge number, ion number density, space function and time function. The compositions of current density, energy flux density and external pressure are discussed and the influence of external parameters are studied. Simulation results show that electron current density from T-F emission is the most important component for current density; as for energy flux density and pressure, ion flux from plasma cloud is dominant. Ablation on a refractory metal is much less than that on a fusible metal under the same external conditions. The simulation results are in good agreement with other researchers' results.

A two-dimensional (2D) rotary axisymmetric model has been developed to describe the formation and development of cathode spot in vacuum arc. The model includes hydrodynamic equations and heat transfer equation which considers surface evaporation and Joule heating. Parameters used in this model, such as the distributions of pressure, energy flux density, and current density, come from experiments and other researchers' work. In this model, cathode spot maintains 30 ns and during this time, all parameters are fixed. The simulation results show that when the energy flux density is 1.5–3 × 1012 W, discharge current is 1–6 A and the pressure is 1–3 × 108 Pa, the crater radius is 1.4–4.1 µm, the crater depth is 1.4–2.1 µm, the velocity of liquid metal is 154–428 m s−1 and the maximum temperature is 2145–5342 K which is located in the area with radius 0.5–1.5 µm. Besides, on the chromium cathode, the maximum temperature is higher mainly because of the lower thermal conductivity.

Based on the two-temperature magnetohydrodynamic model, a high-current vacuum arc (HCVA) in vacuum interrupters is simulated and analysed. The phenomenon of plasma backflow in arc column is found, which is ultimately ascribed to the strong magnetic pinch effect of HCVA. Due to plasma backflow, the maximal value of ion density at the cathode side is not located at the centre of the cathode side, but at the paraxial region of the cathode side, that is to say, ion density appears to sag at the centre of the cathode side (arc column seems to be divided into two parts). The sag of light intensity is also found by experiments.

Based on the improved two-dimensional axisymmetric magnetohydrodynamic model, the vacuum arc characteristics under different distributed axial magnetic fields (AMFs) were analysed in this paper. First, a uniform cathode spot distribution was assumed, and the influences of the azimuthal self-magnetic field and different radially distributed AMFs on the vacuum arc characteristics were analysed. Then, in order to simulate the real situation, according to the experimental results of other researchers, a non-uniform distribution of cathode spots was considered in the simulation. The simulation results showed that the effect of the current density of the cathode side on the vacuum arc characteristics (such as distribution of axial current density at the anode side and heat flux density to the anode) was significant.

In vacuum arc (VA), when the arc current is very high (usually in the tens of kilo-ampere), the heat flux density injecting into an anode is larger and leads to a higher anode temperature with the increasing of current. The strong anode evaporation drives the evaporated atoms from the anode surface to the arc column. Simultaneously, the anode evaporated atoms impact with the cathode plasma, and then the micro processes as ionization and recombination between anode atoms and plasma will happen. In this paper, the two fluid three-dimensional (3D) magneto-hydro-dynamic (MHD) model of VA considering ionization and recombination processes is built, and the influence of the anode vapor and its micro processes on the arc column is obtained by solving the two fluid MHD equations, which control anode neutral atoms and cathode plasma, respectively. In the model, the ionization of neutral atoms and the recombination of ions are both considered, the mass, momentum and energy exchange caused by the ionization and recombination processes are also considered. Moreover, the influence of ionization and recombination processes on the electromagnetic process of VA is also considered in the model. By numerical simulation, the anode vapor distribution, cathode plasma distribution and VA distribution, such as density, temperature, pressure, etc, are all obtained, and the parameters related to ionization and recombination processes are also obtained. When the anode temperature is high enough, the anode neutral vapor will enter into the arc column, and strong ionization happens at the interface between anode vapor and cathode plasma. Then, the anode vapor will be quickly ionized (usually smaller than a few microseconds) and generate a lot of ions (usually higher than 1021 m−3 orders of magnitude). The anode neutral vapor has the same temperature with the anode surface, which is much lower than the temperature of the arc column, so the anode neutral vapor obviously has a cooling effect on the arc column. Whether anode neutral vapor will enter into the arc column or not, is determined by the balance between anode neutral vapor and cathode plasma.

A series of triggering experiments was carried out to investigate the characteristics of vacuum arc controlled by TMF/RMF-AMF contacts. During all the experiments, the current ranged from 5–20 kA (rms) and both the arc appearance and behavior of cathode spots were captured by high-speed camera with corresponding arc current and arc voltage. A 3D steady magnetohydrodynamics (MHD) model was built to simulate and analyze the vacuum arc behavior under TMF/RMF-AMF contacts, and arc plasma parameters were calculated based on the above model. The experimental results showed that arc deflection was visible under both low and high current. Under high current, arc core formed, which meant the arc contracted significantly. In addition, the anode became much more active under high current. The behavior of the cathode spots showed that they split themselves into other new cathode spots. Under high current, the bulk of the spots rotated along a clockwise direction on a transverse magnetic field (TMF) plate, which caused much noise and oscillation in the arc voltage. The simulation results show that ions are likely to gather on the branches of the TMF plate on the anode plane, as a result of the effects between the electromagnetic force and pressure gradient of the arc plasma. The current contracts in the center of the TMF plate on the cathode which was due to the thin connecting rod there. The anode contraction of the current is caused by the Hall effect. Ions move along a clockwise direction on the TMF plate, which is driven by Ampere force. The current contraction resulted in significant melting in the center of the cathode surface while the other region suffered from uniform melting. The melting caused by the anode contraction is more significant than that of the cathode.

In this paper, the characteristics of the plasma jet of a low-current vacuum arc with a single cathode spot (CS) in an external axial magnetic field (AMF) up to 150 mT is investigated experimentally, at a constant arc current ranging from 20 A to 60 A. The experiments are conducted with Cu butt contacts in a demountable vacuum chamber. Images of the plasma jets are photographed with a high-speed digital camera with an exposure time of 2 μs. The uniform constant AMF (B n ) within the inter-contacts region is supplied by Nd–Fe–B permanent magnets. The influence of the external AMF on the shape of the jet near the anode surface as well as in the arc column is mainly investigated. A luminous 'spot' is observed on the anode surface facing the position of the CS under a relatively strong AMF. The mechanism of the appearance of the luminous 'spot' is proposed to be connected to the secondary plasma originating from the anode. Moreover, with the increase in the strength of the AMF, the spreading angle of the cone-shaped plasma jet in the arc–column region decreases gradually. The plasma jet, subjected to a relatively strong AMF (120 mT and 150 mT), becomes cylindrical in shape in the arc–column region and conical in shape in the near-electrode regions. The overall geometry of the plasma jet looks like a dumbbell.

A high-current vacuum arc subjected to an axial magnetic field is maintained in a diffuse status. With an increase in arc current, the energy carried by the arc column to the anode becomes larger and finally leads to the anode temperature exceeding the melting point of the anode material. When the anode melting pool is formed, and the rotational plasma of the arc column delivers its momentum to the melting pool, the anode melting pool starts to rotate and also flow outwards along the radial direction, which has been photographed by some researchers using high-speed cameras. In this paper, the anode temperature and melting status is calculated using the melting and solidification model. The swirl flow of the anode melting pool and deformation of the anode is calculated using the magneto-hydrodynamic (MHD) model with the volume of fraction (VOF) method. All the models are transient 2D axial-rotational symmetric models. The influence of the impaction force of the arc plasma, electromagnetic force, viscosity force, and surface tension of the liquid metal are all considered in the model. The heat flux density injected into the anode and the arc pressure are obtained from the 3D numerical simulation of the high-current vacuum arc using the MHD model, which gives more realistic parameters for the anode simulation. Simulation results show that the depth of the anode melting pool increases with an increase in the arc current. Some droplets sputter out from the anode surface, which is caused by the inertial centrifugal force of the rotational melting pool and strong plasma pressure. Compared with the previous anode melting model without consideration of anode deformation, when the deformation and swirl flow of the anode melting pool are considered, the anode temperature is relatively lower, and just a little more than the melting point of Cu. This is because of liquid droplets sputtering out of the anode surface taking much of the energy away from the anode surface. The azimuthal velocity of the anode melting pool for arc current 12.5 kA root-mean-square (rms) is larger than that for 17.5 kA (rms), which is likely to be caused by the thinner liquid layer, and also a smaller melting pool mass of 12.5 kA.

Axial magnetic field (AMF) technology is a most important control method of vacuum arc, particularly for high-current vacuum arcs in vacuum interrupters. In this paper, a review of the state of current research on vacuum arcs under AMF is presented. The major aspects of vacuum arc in an AMF such as arc voltage, the motion of cathode spots, and anode activities are discussed, and the most recent progress both of experimental and simulation research is presented.

The facet temperature distribution of a room temperature continuous-wave (CW) operating quantum cascade laser was experimentally measured based on the micro-Raman intensity ratio analysis of the Stokes and anti-Stokes phonon lines. A ‘W’-shaped temperature distribution was observed in the active region. We found that the traditional thermal simulation using the Fourier law is not sufficient in explaining our experimental results and other simulation models need to be explored. The active region temperatures at different CW operating currents were also measured. Our work is useful for device failure analysis and optimization of thermal management.

In order to reduce the thermal loss due to spectral mismatch of solar cell absorption, the quantum cutting with Tb3+–Er3+ couples as spectral converters is experimentally observed. One high-energy ultraviolet photon (Tb3+ 7F6 → 5L1) is quantumly cut into two lower energy photons: one in the near-infrared region (Er3+ 4I9/2 → 4I15) and the other in the blue region (Tb3+ 5D4 → 7F6), both of which can be efficiently absorbed by solar cells. A quantum efficiency, ηQE, of up to 188% is calculated, which is close to the theoretical limit of 200%. The energy mismatch in the energy transfer from Tb3+ (5L1 → 5D4) to Er3+ (4I9/2 → 4I15/2) is 237 cm−1, less than the phonon energy of 400 cm−1 in NaYF4, making the energy transfer nearly resonant. The energy migration among Tb3+ donors is treated approximately by the diffusion model and the initial process of energy transfer among the Tb3+–Er3+ couples is found to be dipole–dipole interactions.

On the basis of a numerical model analysis, the photovoltaic performance of a partially shadowed dye-sensitized solar cell (DSC) module is investigated. In this model, the electron continuity equation and the Butler–Vollmer equation are applied considering electron transfer via the interface of transparent conducting oxide/electrolyte in the shaded DSC. The simulation results based on this model are consistent with experimental results. The influence of shading ratio, connection types and the intensity of irradiance has been analysed according to experiments and numerical simulation. It is found that the performance of the DSC obviously declines with an increase in the shaded area due to electron recombination at the TCO/electrolyte interface and that the output power loss of the shadowed DSC modules in series is much larger than that in parallel due to the ‘breakdown’ occurring at the TCO/electrolyte interface. The impact of shadow on the DSC performance is stronger with increase in irradiation intensity.

Anode activity is critical for the success or failure of vacuum interrupters when the arc current attains a certain limiting value. Anode vapour from anode activity will influence high-current vacuum arc (HCVA) characteristics, and further influence interrupting successfully or not. In order to investigate the interaction between the arc column and anode vapour, a transient two-dimensional anode activity (subjected to HCVA column) model is established in this paper. Based on this model, the anode thermal process under ideal heat flux density and heat flux density from the arc column are simulated, respectively. The simulation results show that for sinusoid current, anode surface temperature first increases rapidly, then decreases slowly. With the increase in the heat flux density to the anode, the anode surface temperature will increase. The maximal value of the anode surface temperature appears near 7 ms (50 Hz current waveform), which is also in agreement with other simulation results. Anode evaporation cools the anode surface, which leads to a more uniform anode surface temperature at the contact centre than that near the contact edge. When the anode is melted, the radial distribution of the anode surface temperature appears as an inflection point. The simulation results are also compared with the experimental results and the results of other researchers. Reasonable agreement is observed. According to the anode activity model, the anode boundary condition of the HCVA model with anode vapour can be defined.

Based on a two-dimensional magnetohydrodynamic model, the dynamic process in a high-current vacuum arc (as in a high-power circuit breaker) was simulated and analysed. A half-wave of sinusoidal current was represented as a series of discrete steps, rather than as a continuous wave. The simulation was done at each step, i.e. at each of the discrete current values. In the simulation, the phase delay by which the axial magnetic field lags the current was taken into account. The curves which represent the variation of arc parameters (such as electron temperature) look sinusoidal, but the parameter values at a discrete moment in the second 1/4 cycle are smaller than those at the corresponding moment in the first 1/4 cycle (although the currents are equal at these two moments). This is perhaps mainly due to the magnetic field delay. In order to verify the correctness of the simulation, the simulation results were compared in part with the experimental results. It was seen from the experimental results that the arc column was darker but more uniform in the second 1/4 cycle than in the first 1/4 cycle, in agreement with the simulation results.

The motion of vacuum arc cathode spots has a very important influence on the efficiency of removing the oxide film on the metal surface. In this paper, the characteristics of cathode spot motion are investigated experimentally. Experiments were conducted in a detachable vacuum chamber with ac (50?Hz) arc current of 1?kA (rms). A stainless steel plate covered by an oxide layer was used as the cathode. The motion of cathode spots during the descaling process was photographed by a high-speed digital camera with an exposure time of 2??s. Experimental results indicate that the motion of cathode spots is influenced by the interaction among individual cathode jets and the position of the anode as well as the surface condition. The waveform of arc voltage is also influenced by the motion of cathode spots.