Improvement of surface flashover in vacuum

Surface flashover of insulation systems is a basic issue in the field of high voltage and electrical insulation. To improve the surface flashover performance is of great significance for the development of advanced power transmission equipment and insulation materials. This study reviews the research progress of surface flashover in vacuum regarding to effective methods to improve the surface flashover performance in vacuum, including insulation system optimisation and material modification. The former one is beneficial to reduce the electric field distortion, and the later one is able to adjust the surface trap parameters of the material through physical and chemical methods. In addition, the ‘U-shaped’ curve is proposed to reveal the relationship between surface flashover voltage and surface trap level, discovering the synthetic effects of surface traps on surface flashover. It is expected that the ‘U-shaped’ curve will become a guidance to improve surface flashover performance through adjusting trap parameters. Moreover, several suggestions are made to build unified surface flashover model which is suitable to the range from high vacuum to high pressure.


Introduction
The surface flashover of the insulation system is a basic problem in the field of high voltage and electrical insulation. The surface flashover voltage is much lower than the vacuum (or gas) breakdown voltage or the solid breakdown voltage at the same electrode distance, reducing the withstand voltage capability and damaging the safe and stable operation of electrical systems. Eventually, not only the power energy storage and transmission but also the economy will be affected negatively [1][2][3][4]. It is an important factor making components prone to failure in lowvoltage systems [5]. Moreover, it is also the weak point in highvoltage systems. Therefore, to improve the surface flashover performance is the important guarantee for the reliability and the safe operation of power equipment, and has great significance for the advanced power transmission and transformation equipment to develop towards the higher voltage level.
The researches about surface flashover have been carried out for nearly half a century, and many significant research results have been already achieved. Especially from the 1980s to the early 1990s, most scholars focused on surface flashover in vacuum and atmosphere environment, and a large number of experimental researches on the surface flashover behaviour were conducted, thereby many mechanisms and models for explaining the occurrence and development of surface flashover were proposed successively. There are two surface flashover models in vacuum generally recognised currently, namely the Secondary Electron Emission Avalanche (SEEA) model proposed by Anderson et al. in the early 1980s [6], and the Electron Triggered Polarity Relaxation (ETPR) model proposed by Blaise et al. in the early 1990s [7,8]. From the mid to late 90s to now, the researches on surface flashover started to concentrate more on the electric field calculation of insulation systems, experimental and simulation analyses of surface charges on solid surface, and methods to increase surface flashover voltage.
This study reviews the research progress of surface flashover in vacuum from the perspective of effective methods to improve the surface flashover performance. These methods can be divided into insulation system optimisation methods and material modification methods, including constructing the functionally graded insulation system or 45° insulation system, ozone oxidation and fluorination treatment, electron beam irradiation treatment, nanostructured fillers-doping treatment, phenolphthalein-adding treatment, heart treatment and so on. Besides, the controversial relationship between surface flashover voltage and surface trap level is discussed.

Insulation system optimisation
According to the classic surface flashover models [6][7][8], it is generally agreed that primary electrons are generated in the initial stage of surface flashover, also known as the stage of the primary electron generation. When a high voltage is applied to both ends of the insulator, the electric field strength at the electrode triple junction (electrode-vacuum-dielectric) is much higher than the average field strength between the two electrodes. Primary electrons will be emitted from the electrode triple junction as a result of the Schottky effect or the field emission effect, marking the beginning of surface flashover. Hence, the electric field distortion at the electrode triple junction has an important effect on the surface flashover performance. Reducing the electric field distortion at the electrode triple junction can suppress the occurrence of surface flashover form the initial stage. For this purpose, methods can be considered from two factors: the electric field distribution in the insulation material and the distortion degree in partial electric field on the insulation material surface.

Functionally graded insulator system
According to the electric field distribution in the insulation material, some methods to reduce the electric field distortion at the electrode triple junction can be carried out by changing the material characteristic. For example, the permittivity has a nonnegligible effect on the surface flashover performance in vacuum reported in some researches [9][10][11][12][13][14]. Regardless of whether in the organic material [10] or the inorganic material [11], the higher the relative permittivity of the insulation material is, the worse the insulation performance in vacuum is generally. It accounts for the facts that the permittivity can affect the electrical field strength at the electrode triple junction. Authors have done a lot of researches on the insulation system optimisation to reduce the electric field distortion at the triple junction by using the functionally graded insulation system. Functionally graded insulation system can suppress the electron emission, and succeed in improving surface flashover performance in vacuum [15][16][17][18][19][20]. A schematic diagram of the multilayer functionally graded insulation system is shown in Fig. 1 [16]. The matrix material is denoted as layer A, and the inserted layer between the electrode and the layer A is denoted as the layer B (C, D, …). 'CTJ' and 'DTJ' represent the cathode triple junction (cathode-dielectric-vacuum) and the dielectric triple junction (dielectric-dielectric-vacuum), respectively, and 'N' represents the number of inserted layers between the electrode and layer A.

2.1.1
Organic functionally graded insulation system: Polyethylene as the research object, authors designed three-layer, five-layer and seven-layer functionally graded insulator systems by adding different contents of carbon black semiconductive master batch to change the permittivity and conductivity of each layer [16,17]. The results in Table 1 show that, compared with neat polyethylene, the highest first flashover voltages of the three-layer, five-layer and seven-layer functionally graded insulation systems are increased by 25, 57 and 75%, respectively. Taking the five-layer functionally graded insulation system (electrode-C-B-A-B-C-electrode) as an example, the relationship between the flashover voltage in vacuum and the permittivity of each layer is shown in Fig. 2. The Sample-0 represents the neat polyethylene, whose relative permittivity is 2.2, as the standard sample.
In order to explore the mechanism of improving the surface flashover voltage, the electric field distributions of multi-layer functionally graded insulation system were simulated, as shown in Fig. 3 [16]. The simulation results prove that the electric field strength at CTJ are significantly suppressed, when the permittivity of the inserted layer is sequentially reduced from the electrode to the polyethylene matrix (namely the layer A). When the number of inserted layers is more, the permittivity difference is smaller between the layers, making the electric field strength at CTJ lower and the electric field distribution more uniform. The decrease in electric field strength enhances the barrier of electron emission from the electrode to the vacuum, preventing the thermal emission effect and the tunnelling effect of electrons at CTJ.
It is worth noting that the multi-layer functionally graded insulation system reduces the electric field distortion at CTJ, but increases the electric field distortion at DTJ meanwhile. When the electric field strength at DTJ increases to a certain extent strength, partial discharge and partial breakdown may be caused at DTJ, thereby bringing about surface flashover. Therefore, for the functionally graded insulation system, the permittivity and breakdown strength of the inserted layer have an important influence on the surface flashover performance, and it is necessary to select an inserted layer with suitable dielectric properties.

2.1.2
Inorganic functionally graded insulation system: Hereinbefore, I-V characteristic curve is linear for the carbon black semiconductive master batch/polyethylene. Namely, the electrical properties do not change with changes in the applied electric field. In this section, two kinds of inorganic functionally graded insulation systems, linear one and non-linear one, will be introduced [18,19].
For investigating inorganic linear functionally graded insulation system, Al 2 O 3 ceramics as the research object, authors designed the functionally graded insulation system with different Mo addition in Mo/Al 2 O 3 cermet to change the permittivity and conductivity of each layer [18]. Compared to the Al 2 O 3 ceramics, the highest first flashover voltages of functionally graded Fig. 1 Schematic diagram of a multilayer dielectric [16]  insulation systems are improved significantly, as shown in Table 2.
It is worth noting that the surface flashover voltage will become to decrease after Mo additions to certain content. When Mo particles is increasing further, the chain structures between Mo particles may form on the surface of inserted layer. Specifically, inorganic non-linear functionally graded insulation system was also studied. Based on the Mo/Al 2 O 3 cermet-Al 2 O 3 ceramic-Mo/Al 2 O 3 cermet, Mo/Al 2 O 3 cermet was replaced by the ZnO varistor and designed as ZnO varistor ceramic-Al 2 O 3 ceramic-ZnO varistor ceramic (Z-A-Z ceramic), three-layer functionally graded insulation systems with different voltage gradient [19]. With the decrease of varistor voltage gradient, the DC surface flashover increases of Z-A-Z ceramic. Compared to the Al 2 O 3 ceramics, the DC surface flashover voltage and the impulse surface flashover are improved by 81 and 136%, respectively. It should be noted that the relationship between surface flashover voltage and the potential gradient is not monotonic. With the increase of varistor voltage gradient, the E′ 1 (the electrical field at vacuum-ZnO varistor ceramic-cathode triple junctions) also increases, but the E′ 2 (the electrical field at vacuum-ZnO varistor ceramic-Al 2 O 3 ceramic triple junctions) decreases. Hence, the electric field E′ 1 at CTJ will clamp at varistor voltage gradient when ZnO varistor ceramic breaks down. Decreasing E′ 1 contributes to increasing the initial electron emission barrier to suppress the surface flashover at the CTJ. However, the corresponding E′ 2 may be so high that it will cause surface flashover at the DTJ. Therefore, it does need to balance the effects of both, and select an appropriate varistor voltage gradient to obtain the best surface flashover performance. In brief, the tremendous improvement in surface flashover performance in vacuum is attributed to not only the gradient distribution of permittivity or conductivity to smooth the electric field distribution in the CTJ, but also the clamping effect of non-linear I-V characteristic on the electric field at electrode triple junction after a whole breakdown of grain boundaries in the ZnO varistor.

45° insulation system
The electric field distortion in the partial region of the insulation material is closely related to the shape of the insulation material, the shape of the electrode and their contact status. Based on the above, the initial researches started with different shapes of insulation material [20][21][22][23], and developed to the researches of contact angles between insulation materials and electrodes [23][24][25][26]. Studies have shown that the contact angles for different materials to achieve optimal surface flashover performance in vacuum were not the same. In general, there is a consensus that 45° contact angle can make the surface flashover performance in vacuum of the insulation material in the best state. Regarding the effect of different contact angles on the electric field distortion at electrode triple junctions, Schachter and Jordan used Maxwell's equation to calculate the electric field strength at the interface between the electrode and the insulator, and found that the electric field strength was closely related to the contact angle between the electrode and the insulator [14,27]. It was also verified from the perspective of theoretical calculations. Controlling the contact angle can affect the electric field strength at the electrode triple junction, thereby affecting the emission and moving trajectory of the electrons. Ultimately, it will affect the occurrence and development of surface flashover in vacuum. Numerous studies indicate that 45° contact angle can improve surface flashover performance in vacuum. Some results are summed up to improve the surface flashover of 45°c ontact angle as shown in Fig. 4 [1,[21][22][23][24][28][29][30][31][32][33][34]. It can be seen that, compared with DC, the contact angle has a great effect on the surface flashover performance under short pulse power. Both the SEEA model and the ETPR model consider surface flashover to occur from the cathode [6,7]. However, it may also occur from the anode under certain conditions. In 1979, Anderson proposed the anode-initiated surface flashover model [35], and the development process of surface flashover was completely different from that of the cathode. The anode-initiated surface flashover model is adapted for the insulation system with a contact angle of 40°-70° between the electrode and the insulator. For these systems, the electric field strength at the anode triple junction (ATJ) is the strongest, and the electric field strength at CTJ is the weakest. Authors studied and verified that 45° insulator between the flat electrodes has the unique advantage of preventing electric field concentration at CTJ. However, it also relatively increased the electric field at ATJ meanwhile. The surface flashover can occur, only when the electric field strength at ATJ is sufficiently high to exceed the breakdown strength of the insulator. Hence, ATJ had to withstand higher electric field strength than CTJ correspondingly. Therefore, it is very significant to suppress the electric field strength at ATJ for preventing the surface flashover in vacuum. Based on the polyethylene functionally graded insulation systems, authors proposed the 45° three-layer system to reduce the electric field at ATJ by controlling the permittivity of the inserted layer [20]. For the three-layer 45° insulation system, the simulation calculation on the electric field distribution under ideal conditions is shown in Fig. 5. The 45° three-layer system sample has a smaller electric field distortion at ATJ than the polyethylene standard sample, which will promote surface flashover performance effectively. The surface flashover voltage in vacuum of 45° threelayer system can be improved greatly when the relative permittivity in the layer B (ε B ) is in the range from 2.7 to 12. The highest first flashover voltage can reach to 81.8 kV when the ε B is 5.4,  [1,[21][22][23][24][28][29][30][31][32][33][34] increased by 33 and 57%, compared with the polyethylene threelayer standard sample and column standard sample. Fig. 6 concludes the above experimental results by showing the relationship among the electric fields at ATJ and DTJ, the surface flashover voltage and breakdown strength. In Zone-1, the optimal surface flashover performance can be predicted to appear. In this zone, the decreasing electric field at ATJ (E ATJ ) has a positive effect on surface flashover performance, which plays a more important role than the bulk-breakdown strength (E b ) with a negative effect. In Zone-1, the surface flashover voltage is the function of E ATJ and E b . In Zone-2, however, the negative impact of E b on the flashover performance in vacuum will become more and more dominant, and gradually surpass the positive effect of the decreasing E ATJ , ultimately leading to the decrease of the surface flashover performance in vacuum. At the same time, as the ε B is further increasing, the electric field at DTJ1 (E DTJ1 ) will gradually increase to reach its high field strength, which may also cause surface flashover to occur at the E DTJ1 . Hence, in Zone-2, the flashover voltage is the function of E ATJ , E DTJ1 and E b .
Combining the optimisation of contact angle and electrode structure, a new insulation system for improving surface performance in vacuum has been proposed [21,[36][37][38][39]]. The insulators system was further optimised to embed the anode into the 45° insulation system, which can effectively reduce the electron emission from ATJ, thereby suppressing surface flashover. The surface flashover performance of this insulation system reached the best, when the embedded depth in the insulator was 1/4 of the total height of the insulator [36]. This functionally graded insulation system also has perfect surface flashover characteristic in the gas environment. Researchers from ABB Ltd. studied a double-layer insulator with the anode embedded into epoxy resin [40]. It was found that the average AC flashover voltage and the average lightning impulse flashover voltage in SF 6 of the double-layer insulators, whose permittivity combination was 6.2 and 9.1, were increased by 30.5 and 20.4%, respectively. In recent years, Zhang G. et al. try to use 3D printing technology to obtain functional materials with uniform gradient distribution of permittivity [41,42]. Compared with the matrix material, the flashover voltages in vacuum of PLA and ABS gradient materials prepared by 3D printing are increased by 19.1 and 21.1%, respectively, which has a good development prospect [42].
Insulation system optimisation methods reviewed above can suppress the occurrence of surface flashover from the initial stage of surface flashover, mainly through reducing the electric field distortion at the electrode triple junction. Besides, some insulation system optimisation methods can also suppress the development process of surface flashover through restraining the electron multipactor process. Since the high gradient insulator (HGI) was proposed, it has exhibited surface flashover characteristics [43][44][45][46][47]. Since HGI consists of many alternative layers of conductors and dielectrics, there are some problems in the poor bonding between conductors and dielectrics, difficult processing technology and high cost. Recently, a new system of HGI exhibits good mechanical and insulation characteristics, through substituting the conductor layers with metal rings embedded into the dielectric materials [48]. Compared with conventional HGI insulators with same materials, the flashover voltage can be improved by 40-50% [48]. Meanwhile, the surface grooves on the insulator surface, such as rectangular grooves [49][50][51][52][53][54] and triangular grooves [49,51,[55][56][57], can make electron multipactor suppressed and delay the occurrence of surface flashover, thereby improving the surface flashover characteristics [49][50][51][52][53][54][55][56][57]. A composite micro-textured surface structure proposed recently is fabricated in two stages with periodic triangular grooves in the first stage and micro-holes coated on the inner surface of grooves in the second [57]. Compared with the untreated insulators in the best state, the surface flashover strength in vacuum is improved by 150% [57]. Moreover, modulating electric field distribution in whole insulator more uniform can be regarded as a method to modify the electric field distortion. Recently, a new inverted T-type arrangement of insulator strings is proposed to greatly improve surface flashover voltage [58]. The electric field intensity of the horizontal tension string part is reduced, though the electric field distortion of the suspension string part is more serious. Therefore, it is not easy for the local arc to develop into full flashover due to the more uniform electric field distribution [58].

Material modification
In addition to the insulation system optimisation, the material modification also provides a productive approach to control the surface flashover performance in vacuum. Material modification can be mainly divided into insulator surface modification and insulator bulk modification. Whether surface modification or bulk modification, both will change the surface trap characteristics of the material and further affect the surface flashover in vacuum.

Surface modification
Generally, surface modification methods include sanding, coating, fluorination or oxidation, electron beam irradiation, plasma treatments and so on. For the effect of surface roughness on surface flashover in vacuum [59][60][61][62][63][64], studies show that the surface flashover voltage increases along with the increase of roughness. The charge density on the material surface decrease significantly as the roughness increase, but the surface flashover voltage is increased [61,62]. The principles of roughness affecting the surface flashover voltage also are studied, and the results show that different roughness characteristics can cause the incident angle of electrons to change, hence affecting the surface flashover voltage  [63]. The increase in roughness causes electrons to be directly emitted on the insulator surface rather than to collide with the surface to excite secondary electrons. This phenomenon results in a decrease in the secondary electron emission coefficient, finally, an increase in the surface flashover voltage [64]. Besides, using HF to coat the metal and its oxides on insulator can reduce surface resistance and the accumulation of surface charges, so that the surface flashover voltage in vacuum can be increased [65]. Coating insulation materials with metals and metal oxides can reduce surface resistance and surface charge accumulation, thereby increasing flashover voltage [60,[66][67][68][69][70][71][72][73][74][75]. Plasma treatment on the insulator surface is regarded as a way to improve the surface flashover performance effectively as well [76][77][78][79], because plasma treatment would lead active sites introduced on the surface, reacting with the atmosphere to generate new groups. Researchers generally used dielectric barrier discharge (DBD) with a plate-inparallel configuration to generate non-thermal plasma and then improve the insulation characteristics [80][81][82]. However, such plasma source can only be applied to flat and thin materials, and sometimes discharge filaments in the DBD may damage the material surface. In recent years, the atmospheric pressure plasma jet (APPJ) has been attracting great attention as a new plasma source, which provides uniform spatial distributions of high energy ions and electrons to treat complex surfaces of materials [76,83,84]. There are some experimental results of plasma treatment on insulator surfaces in Table 3, which indicates surface flashover in vacuum can be improved by DBD or APPJ method [76,[81][82][83][84].
Numerous studies have shown that surface fluorination is an effective way to improve the surface flashover performance in vacuum of insulator materials [85][86][87][88][89][90][91][92][93][94], including epoxy and its composite [85,93], high-density polyethylene (HDPE) [93], polystyrene (PS) [94] and other materials. Authors apply the fluorination treatment method in low-density polyethylene (LDPE) to improve the surface flashover voltages and the surface potential decay (SPD) to characterise properties of insulator surface [95]. As shown in Fig. 7, the surface flashover voltage in vacuum of the LDPE treated by fluorination is enhanced, and gradually increased with the increase of fluorination time. As the trap level decreases, the surface flashover voltage gradually increases. In other words, the trap level is inversely proportional to the surface flashover voltage. Authors further analyse the reasons for the reducing of the trap level. On the basis of the infrared spectroscopy, it is found that fluorination treatment change the chemical composition of the surface layer of LDPE, in Fig. 8. The C-H absorptions in 2800-3000 and 1430-1460 cm −1 largely decrease, but trap level increase as fluorination treatment time increase. A significant increase, however, happen in 900-1400 cm −1 , corresponding to C-F, C-F 2 and C-F 3 absorptions. Thereby, fluorination treatment can be applied to improve the surface flashover voltage by affecting trap level of the material surface layer [87,[96][97][98][99][100][101].
The trap become shallower, accelerating the transport and reducing the charge accumulation [97-100, 102, 103], including positive and negative charges [99]. Diminishing charge accumulation is contributed to weaken the electric field distortion on the surface, which improves the surface flashover voltage. Simulation researches also demonstrate the similar result [85,87]. Table 3 Results of insulation materials treated by DBD or APPT plasma [76,[81][82][83][84] Method Results [81] PMMA; the number of C-F n increasing; DBD; water contact angle increasing from 68° to 105°; Ar:CF 4 = 0:1 surface resistance increasing; roughness increasing; secondary electron emission coefficient decreasing; surface flashover voltage in vacuum improving. [82] EP; roughness increasing; DBD; shallow trap increasing; 20°C, conductivity increasing; 20% surface flashover voltage in vacuum improving. [76] PMMA; water contact angle decreasing from 68° to 16°; APPJ; flashover voltage in vacuum improving. Ar gas [83] EP; surface flashover voltages improved by 18  optimal gas ratio to improve surface flashover voltage: CF 4 in 0-5%, especially at 3%. He + CF 4 The secondary electron emission coefficient is also changing with the different fluorination time [93]. Shao T. et al. analyse the stability of fluorination treatment [94], and find that the surface flashover voltage remains stable with little difference, compared with that conducted immediately after fluorination treatment. In addition, increasing temperature during the fluorination treatment benefits to accelerate the charge dissipating further [104], and the surface flashover voltage in vacuum also can be gradually increased with higher temperature [86]. It is worth noting that fluorination treatment for too long may severely damage the structure of the material surface. Due to physical defects, some traps will be introduced again, leading to a negative effect on the percentage improvement in the surface flashover voltage in vacuum [93,96]. Furthermore, the fluorination treatment can be also applied to improve the resistance to electrical tracking [101], partial discharge [102] and breakdown performance [105]. Similar to the fluorination treatment, the oxidation treatment can also productively increase the surface flashover voltage in vacuum. Authors used ozone oxidation treatment in LDPE in order to improve the surface flashover voltages [106], which results are as shown in Fig. 9. Ozone oxidation treatment has a positive impact on improving the surface flashover voltage increased by 26% at the peak of flashover voltage curve. These results illustrate that ozone oxidation treatment introduces shallow traps on the material surface [106,107]. On account of the continual increase of shallow traps, the carrier mobility accelerates gradually, leading to surface charges dissipating faster. The faster dissipation of surface charges contributes to relieving the distortion of electric field at CTJ, ultimately enhancing the surface flashover characteristics. In addition, authors apply ozone oxidation treatment technology to epoxy resin composite materials, and find that the surface flashover voltages both in vacuum and SF 6 (0.2 MPa) can be increased by more than 10%, after micro-Al 2 O 3 /epoxy modified by ozone oxidation treatment [108,109].
In recent years, the electron beam irradiation has also attracted attention to enhance surface flashover performance. Initially, the study about the effect of electron beam irradiation on surface flashover originated from the phenomenon of surface discharge on spacecraft in the space environment. Fujii et al. study the surface flashover characteristics of printed circuit boards in aircraft and believe that the increase in electron beam energy would cause the surface flashover voltage to decrease [110,111]. Zheng X. et al. also study the impact of different energy electron beams on the surface flashover characteristics and think that the space negative charge of CTJ, radiation-induced conductivity and radiation degradation are the important factors to enhance surface flashover voltage under different radiation electron beam energies [112][113][114]. At the same time, electron beam irradiation treatment can also be used as a treatment method for insulator surface to improve surface flashover voltage, when irradiation conditions are appropriate in certain range.
Authors have made a series of studies on the improvement of surface flashover in vacuum of insulating material modified by electron beam irradiation [115][116][117][118]. Fig. 10 exhibits the surface flashover performance in vacuum of PI film after irradiated by different energies [116,117]. These results point surface flashover voltages and irradiation energy show a positive correlation. Surface flashover climbed and finally reached a stable step with the increase of irradiation energy, improved by 26%. The surface flashover has the similar variation trend with the trap level, as the increase in irradiation energy is higher. It means that the increase in trap level can inhibit the development of surface flashover. In other words, the electron beam irradiation can improve the surface flashover voltage through introducing the deep level. When the trap level increases, transport and multiplication processes of secondary electron are limited, thus improving surface flashover voltage. The relevant results illustrate that the trap level and density also became larger, after PET modified by electron beam irradiation [119]. Conducting electron beam irradiation treatment on several materials, including PTFE, PMMA and PA6, similar results are obtained. It is considered that the increasing surface flashover voltage is attributed to the increase in trap level and density [120]. In addition to the effective results in vacuum, the surface flashover in LN2 is also improved after AlN/epoxy nanocomposites modified by electron beam irradiation [121]. For micro-Al 2 O 3 /epoxy, there are similar results that surface flashover voltage in SF 6 is promoted due to electron beam irradiation [122].

Bulk modification
The surface properties of insulator are affected by bulk properties, and the surface properties also can be indirectly influenced by changing the bulk properties, thereby affecting the surface flashover performance in vacuum. There are lots of the bulk modification methods, such as doping the inorganic filler to change the microstructure, or physical or chemical methods to change the aggregation structure of polymer bulk.
Nanocomposite dielectrics have been attracting attention, since the concept of nanocomposite dielectrics was born [123]. Due to the unique three-layer structure [124][125][126][127], the nanocomposite has many excellent insulation properties, such as ageing resistance, partial discharge resistance, high breakdown field strength and the suppression effect on space charges [128], which brings new life and vitality to insulation composite materials. Numerous studies evidence that the surface flashover performance voltage can be improved by nanoparticles doped in the polymer matrix. As shown in Fig. 11, authors used different types of polymers and nanostructured fillers to research the effect of nanostructured fillers doped into the polymers to promote surface flashover [129][130][131][132][133][134][135], including PS [129], LDPE [120,133,134], epoxy (EP) [131,132,135]. In Fig. 11, it is similar that surface flashover voltage curves change with the increase of the loading of nanoparticles, although the voltage curve peaks are corresponding to different loading contents. The optimal loading contents corresponding to the max voltage and improvement percentage are shown in Table 4. These results show that proper contents of nanoparticle doping can increase the surface flashover voltage in vacuum [129][130][131][132][133][134][135]. The trap parameters of nanocomposite are extracted by using thermally stimulated depolarisation current (TSC) method [135,136]. The surface flashover voltage is normalised, and then the relationship between surface flashover voltage normalised and deep trap level is as shown in Fig. 12 [130,135,136]. It can be seen that nanoparticle doping increases the trap level and the surface flashover voltage, whether for LDPE or EP nanocomposites. The surface flashover voltage normalised and the trap level show a proportional relationship. After the nanoparticles are added in polymer, interaction zones are introduced in the polymer matrix, according to the multi-region structure around nanoparticles [137]. The multi-region structure model of the interaction zone is divided into the bonded region, transitional region and normal region, where the transitional region has largest thickness and is also the key region. The interaction region is regarded as a phase state different from the matrix. There will be a new potential barrier, which can interact with the potential barrier in matrix to change the trap parameter of nanocomposites. A small number of nanoparticles can form large independent interaction zones in the matrix, which overlap with the potential barrier in matrix to make the trap of nanoparticles deeper. Some related research results show that the addition of micro-fillers in nanocomposites can significantly increase the depth levels, while the shallow traps increase less or even decrease. Considering surface flashover voltage, it has been confirmed that deep traps will increase the surface flashover voltage [138]. For the PI matrix, the DC flashover voltage of ZnO/PI nanocomposites is significantly increased, compared with neat PI. The experimental results indicate that the doped ZnO nanoparticles introduce deeper traps, which reduces carrier mobility, secondary electron emission and space charge accumulation [139]. Recently, to explore an alternative method of nano-doping in insulator, radio frequency magnetron sputtering method is proposed to modify the cellulose paper, leading to ZnO fillers not only exist on the surface of cellulose paper but also enter into its interior [140]. After sputtered for 15 min, the surface flashover of oil-impregnated paper is improved by 23%.
Authors use heat treatment to change the aggregation structure of semi-crystalline polymers, mainly the crystallinity and grain size. In six samples, the first five samples, from Sample-A to Sample-E, are, respectively, conducted with heat treatment, but the Sample-F is not conducted with any treatment, as the standard sample [141,142]. Fig. 13 displays the effect of different heat treatment methods on the surface flashover voltage in vacuum. Compared to Sample-F, the surface flashover performance of Sample-E is the best, increased by up to 76% under DC power and up to 19% under pulse power. It can be seen that the surface flashover voltage increases along with the increase of the trap level, and reach a peak in Fig. 13. It should be pointed out that the surface flashover voltage decreases when the trap energy level further increases. As the trap level is too deep, the charge accumulation in traps is serious to form the partial polarisation. Once an external disturbance disturbs the state, it is easy for mass trap charges to release, which in turn makes the occur of surface flashover easier.
To research the effect of heart treatment on the trap level, the polarised microscope is used to obtain the crystalline morphologies of samples. In Fig. 14, the grain sizes of the six samples are quite different [141]. The grain size of samples after low temperature quenching, in Sample-A and Sample-B, is obviously smaller, and the crystallisation is not complete, only forming small crystal grains. The samples crystallising naturally at normal temperature are completely crystallised, forming larger crystal grains. As the grain size becomes larger, the trap level deepens gradually. It is found that the trap parameters can be adjusted by controlling the aggregation structure of the polymer, so as to improve the surface flashover voltage in vacuum.
In the above work, it was found that the aggregation structure of XLPE was controlled by the heat treatments. However, it is difficult to keep the aggregation structure stable during operation, because the insulating materials used in equipment must experience temperature change. Therefore, it is of great engineering significance to find a stable modification method for  [129][130][131][132][133][134][135]  practical application of insulation materials. LDPE is widely used in electrical insulation engineering. Due to its relatively strong crystallisation ability, it is difficult to control the crystal form of LDPE. Previous work has proved that phenolphthalein addition can change the morphology of LDPE [143]. Authors use phenolphthalein-adding treatment as another way to control the aggregation structure of LDPE in order to improve the surface flashover performance in vacuum [144]. LDPE samples modified by phenolphthalein were prepared by melt blending method. Fig. 15 shows the relationship between the surface flashover voltage in vacuum and the phenolphthalein concentration [144]. It can demonstrate that the surface flashover voltage of the LDPE modified by phenolphthalein is improved successfully. The surface flashover voltage increases as the trap level increases in Fig. 16 [144]. As the phenolphthalein concentration increases, the spherulite size decreases significantly and the trap level increases.
Controlling the aggregate structure of LDPE by phenolphthalein effectively makes the trap level gradually increase, and the surface flashover performance in vacuum be improved. Generally speaking, the aggregation structure of semicrystalline polymers has a significant effect on trap parameters. By adjusting the trap parameters, the deeper trap level can be obtained to suppress the secondary electron multiplication process, thereby increasing the surface flashover voltage in vacuum.

Relationship between bulk trap and surface trap distribution
Hereinbefore, SPD methods and TSC methods are used to extract trap parameters when it is needed to describe the relationship of trap parameters and the surface flashover voltage. Can the two methods be used as substitutes for each other or reflect the similar law of trap parameters in insulator? There are some differences between the test principle of SPD and TSC methods. The SPD data is derived from decaying surface potential caused by the trapped charge detrapping under the isothermal condition after insulation surface corona charged [145,146]. The TSC data is extracted from the corresponding current peak formed by the charge detrapping during the temperature rising after insulator fully polarised. It can be seen that SPD and TSC methods are both related to charge trapping and detrapping [147,148]. Therefore, the two methods have a certain similarity in characterising the trap parameters. Authors studied the trap parameters of LDPE modified by phenolphthalein. Fig. 17 showed the variation of trap level with phenolphthalein concentration measured by the two methods [106].
It can be seen that the TSC and SPD trap parameters both indicate that the trap level increases first and then decreases with the increase of the phenolphthalein concentration, and the maximum value appears at 1 wt% of the phenolphthalein concentration. This was due to the fact that the charge transport characteristics on insulator surface and in insulator bulk affect each other. When the incident electrons are captured by the insulator surface layer, the electrons will migrate from the cathode to the anode under the electric field. However, the charge will migrate along the perpendicular component of electrical field as well, when the electric field in the insulator has a perpendicular component to the cathode-anode connection line. It can lead electrons on surface layer to migrate to the insulator bulk, and then transport in the insulator bulk. In addition, it can also cause the electrons in the insulator bulk to migrate to the surface layer, accumulating more negative charges on the surface, or recombining with the positive charges on the surface, which will affect the charge and the electric field distribution. These reveal that the charge transport on insulator surface and in insulator bulk are closely related. Therefore, the surface traps affect the charge transport not only on surface but also in insulator, thereby having an impact on the surface flashover voltage in vacuum, which can reasonably explain the reason why insulator bulk modification can regulate the surface flashover.

'U-shaped' dependence of surface flashover performance on the surface trap level
In the above results of the modification method to improve surface flashover performance, it is found that adjusting trap parameters can effectively improve surface flashover performance in vacuum. Some of these results show that the trap levels became shallower after insulator modification, and have a negative correlation with the surface flashover voltage [82,87,[93][94][95][96]106]. In other results, however, the trap levels become deeper after insulator modification and have a positive correlation with the surface flashover voltage [117,119,120,122,130,135,136,138,139,141,144,149]. These studies suggest that there seems to be a controversy about the effect of trap parameters on surface flashover performance.
In order to further discuss the relationship between trap level and surface flashover voltage in vacuum, the authors chose epoxy resin composites as the research object, modified by ozone oxidation treatment, electron beam irradiation treatment and nanoparticle doping treatment. SPD method was used to extract surface trap parameters and the surface flashover in vacuum experiment was carried out under DC power. The 'U-shaped' curve was obtained eventually, for the relationship between surface flashover voltage and surface trap level, as shown in Fig. 18 [109]. It is not monotonous for surface flashover voltage to change with the increase of the deep trap level. The surface flashover voltage curve drops off first and then climb up, like the letter 'U'. The lowest point of the 'U-shaped' curve is ∼1 eV at the trap level, and dividing the 'U-shaped' curve into left and right parts. In the left part, where the epoxy insulator is modified by the ozone oxidation treatment, the surface flashover voltage decreases monotonically. On the contrary, in the right part, the surface flashover voltage increases monotonically where the epoxy insulator is modified by electron beam irradiation and nanoparticle-doping treatment.
Combined with simulation calculations, the comprehensive results show that the effects of surface traps on the surface flashover performance are different in both parts of the 'U-shaped' curve. The flashover mechanism corresponding to different parts in the 'U-shaped' curve is stated in Fig. 19 [109]. In Fig. 19a, namely in the left part, the surface charges near the cathode may dissipate to the insulator bulk or surface, since the surface conductivity and mobility are relatively high. Due to some positive charges accumulated on the surface, electrons in the vacuum (desorbed gas) will be accelerated by the electric field and attracted to impact the insulator surface. Hence, some electrons will excite secondary electrons and increase the positive charges on the insulator surface, which may dissipate along the surface or migrate to the insulator bulk. The electron avalanche will form resulting from a large number of secondary electrons colliding with the desorbed gas and ionising, thereby causing the surface flashover. In these physical processes above, the surface conductivity and carrier mobility will decrease as the deep trap level increases. It is difficult for the positive charges trapped on the insulator surface to dissipate along the insulator surface or into insulator bulk, which brings about the surface electric field severely distorted so that the surface flashover voltage will be reduced, corresponding to the left part of the relationship curve in Fig. 19b. In this case, the surface flashover performance is mainly determined by the shallow trap level, and the surface flashover voltage decreases as the trap level increases. In Fig. 19c, there is a physical process similar to that in the left part in Fig. 19a, but the surface conductivity and mobility are low. Hence, the charge dissipation along surface and to the insulator bulk will be no longer the key factors affecting surface flashover. With the increase of the surface deep trap level, the initial and secondary electron emission processes will be suppressed, making positive charges decrease on insulator surface. The electric field on the insulator surface is more uniform, so it is more difficult for the surface flashover to occur, corresponding to the right part of relationship curve in Fig. 19b. In this case, the surface flashover performance is mainly determined by the deep trap level, and the surface flashover voltage increases as the trap level increases.
The 'U-shaped' curve not only reveals the synthetic effects of surface traps on the surface flashover performance, but also provides a broad view on methods adjusting surface trap parameters to improve surface flashover performance. Based on the effective methods to improve surface flashover performance, this study reviewed the research progress of surface flashover in vacuum. These effective methods can be divided into insulation system optimisation methods and material modification methods. The former methods mainly use the functionally graded insulation system and 45° insulation system to improve surface flashover performance, which are attributed to not only the smooth effect on the electric field distribution in electrode triple junctions, but also the clamping effect of non-linear I-V characteristics. In addition, the material modification methods include the insulator surface modification methods and insulator bulk modification methods by adjusting the trap parameters of the material. The surface modification methods can improve surface flashover voltage in vacuum by directly adjusting surface trap parameters to effect charge transport on surface. However, bulk modification methods can also achieve the aim to improve flashover voltage by affecting charge transport on surface according to the coupling effect between charge transport on insulator surface and in bulk. Moreover, the 'U-shaped' curve is proposed to reveal the relationship between surface flashover voltage and surface trap level. The 'U-shaped' curve discovers the synthetic effects of surface traps on surface flashover, which to a certain extent ends the debate what trap is beneficial to surface flashover performance, the deep one or shallow one. Therefore, the research idea of adjusting trap parameters to improve surface flashover is broadened.
Finally, there are some ideas about the surface flashover model to be expressed. When it comes to the surface flashover in vacuum, what does the 'vacuum' stand for? In fact, the 'vacuum' is an ideal state in the theoretical model, which is barely to be obtained in actual experimental operations. Consequently, the experimental results of surface flashover in vacuum we obtain so far are actually the results in the experimental environment at a high vacuum degree, in other words, in a very low pressure. It cannot be denied that, in the experiment of surface flashover in vacuum, there are some tenuous extraneous gases or desorbed gases, which is also mentioned in some classic surface flashover models. Therefore, the surface flashover in vacuum and in some pressure are not completely independent. Besides, most of the methods to improve the surface flashover performance in vacuum are also applicable in some pressure, which also supports the above view. Unfortunately, there is no widely accepted surface flashover model adapting to surface flashover in vacuum and some pressure currently. Combining some classic models and the gas-solid coupling surface flashover model [150], in authors' opinions, the effects of desorbed gas and adsorbed gas on surface flashover can be considered together, regarded as a breakthrough point to further explore surface flashover model. In this way, the wide pressure-range surface flashover model will be obtained. Furthermore, it is expected that the surface flashover mechanisms are unified preliminarily, successfully applied in the range from high vacuum to high pressure. Although it is very difficult to go beyond the traditional theory, it is worth to overcome the difficulties and advance the research on surface flashover model.