Figure
1.
The schematic diagram of primary discharge and plasma expansion.
| Citation: |
Dejie WEI, Jianwen WU, Liying ZHU. Study on plasma expansion model of primary discharge on spacecraft solar array[J]. Plasma Science and Technology, 2024, 26(11): 115301. DOI: 10.1088/2058-6272/ad718b
|
In the space plasma environment, primary discharge may occur on the solar array and evolve into a destructive sustained arc, which threatens the safe operation of the spacecraft. Based on the plasma expansion fluid theory, a new multicomponent plasma expansion model is proposed in this study, which takes into account the effects of ion species, ion number, initial discharge current, and Low Earth Orbit (LEO) plasma environment. The expansion simulation of single-component and multicomponent ions is carried out respectively, and the variations of plasma number density, expansion distance, and speed during the expansion process are obtained. Compared with the experimental results, the evolution of propagation distance and speed is closed and the error is within a reasonable range, which verifies the validity and rationality of the model. The propagation characteristics of the primary discharge on the solar array surface and the influence of the initial value on the maximum propagation distance and the propagation current peaks are investigated. This study can provide important theoretical support for the propagation and evolution of the primary discharge and the key behavior of the transition to secondary discharge on spacecraft solar array.
With the development of space stations and satellite technology, the demand for power supply system is increasing. As the core energy source, solar array plays a decisive role in the reliable operation and safe life of spacecraft. In the space plasma environment, surface charging occurs on the solar array, which forms a reverse potential gradient between the coverglass surface, interconnect and the substrate (also called triple-junction). When the potential difference exceeds the discharge threshold, the primary discharge occurs and generates a high-concentration plasma cluster. Under the combined action of the inter-string potential difference and the space environment, a coupling path is formed, causing a temporary sustained arc discharge, also called secondary discharge [1–3]. The discharge energy and time are much higher than that of primary discharge, which seriously damages the insulation layer of the solar array, and even causes the room temperature vulcanized silicone rubber (RTV) and polyimide between the solar array and substrate to be pyrolyzed and carbonized, forming a low-resistance path and causing the short circuit phenomenon, which resulting in partial burning or overall failure of the solar array [4–6]. Therefore, it is very important to explore the key behavior such as expansion, evolution and propagation of high-concentration plasma bubbles generated by primary discharge to prevent destructive sustained arc.
Plasma expansion can explain the evolution of primary discharge and the key behavior of transition to sustained arc from the microscopic perspective. Vaughn et al [7] used this method in their early research on potential arcs of large spacecraft in LEO. Due to the assumption of discharge around plasma bubbles expanding outward from the arc, this model is called the “Perimeter Theory”. Aiming at the phenomenon that the low-energy electrostatic discharge induces a higher-energy sustained discharge in Geostationary Orbit (GEO), Katz et al [8] assumed that the plasma expands at a constant speed and neutralizes immediately when the plasma reaches the solar array coverglass, the discharge current peaks are estimated and compared with experimental results. Amorim et al [9] proposed an improved “Perimeter Theory” model to explain the discharge current observed on a 0.6×1.3 m2 solar array. The assumptions of the model include three points: (1) the plasma bubble expands at a constant speed; (2) the front edge of the plasma bubble neutralizes the potential charge of the coverglass surface immediately; (3) the total arc current is completely determined by the surface capacitance swept out. Based on the experimental results of the EMAGS3 project, the ONERA laboratory developed a plasma bubble expansion model using the Child-Langmuir law and two-dimensional Cartesian grid in spacecraft plasma interaction system (SPIS). It is also assumed that the expansion speed is constant, and the surface potential evolution and current are calculated [10–12]. In addition, the cathode spot model is established, the coupling of the two models is realized, and the influence of plasma emission on its expansion is explained [13]. However, the movement of ions and the change of number density distribution in the plasma expansion process cannot be obtained, and the key behavior of primary discharge evolution is ignored. Ferguson et al [14, 15] discussed and analyzed the shortcomings of the perimeter theory hypothesis, and established an improved perimeter theory model to explain the physical laws of the current initiation, multiple wave peaks and propagation speed of primary discharge. Although the view that expanding plasma causes surface discharge is widely recognized, the assumption of perimeter theory is highly controversial, especially in the absence of any physical meaning, the constant expansion speed is assumed, and the various ion components generated by the material diversity of the primary discharge position are not considered.
Experimental test is the most direct method to explore the primary discharge propagation characteristics of space solar array, and can provide effective data support for theoretical model research. However, due to the limitation of space simulation environment test technology, it is difficult to carry out large-area solar array discharge tests and obtain plasma expansion distribution. At present, the key tests focus on the expansion speed and propagation distance of primary discharge. Masui et al [16] measured the propagation speed of the plasma generated by primary discharge through experiments, and used high-speed and image enhancement cameras to capture discharge images. The square root reciprocal relationship between the plasma propagation speed and time was obtained. Inguimbert et al [17] carried out discharge expasion experiments in electron environment and plasma environment with a large solar panel of 4×2 m2. It was found that the primary can neutralize the total charge of the panel and the maximum duration of discharge is correspond to a propagation of the plasma bubble until it reached the edges of the panel. Gong et al [18, 19] conducted an experimental investigation on plasma generation through hypervelocity impact (HVI) and proposed the space-time expansion model of HVI-generated plasma. It was found that the electron density of plasma exhibits vibrational decay with increasing time and distance, decaying from 1019–1020 m−3 to 1014–1015 m−3 magnitudes. The duration of transient plasma is approximately 60–120 μs and electron density is in the range of 1014–1015 m−3. Okumura et al [20] measured the propagation length and speed of primary discharge in LEO and GEO (geostationary orbit) simulation environments, respectively. It was found that the propagation distance under different working conditions was limited, and the propagation speed decreased with time. Young and Crofton [21] studied the influence of conductor material at the arcing point on the propagation behavior of primary discharge. By measuring a series of concentric electrode currents flowing into the surface of Kapton, the change of surface neutralization behavior with time and radial distance of the arcing point was detected. The above experimental results can provide important guidance and data support for analyzing simulation results.
In this paper, aiming at the shortcomings of the “Perimeter Theory” model, based on the plasma expansion fluid theory, a new multicomponent plasma expansion model is proposed. Firstly, the improved advantages and theories of the model are introduced in section 2.1, and the calculation method of the model is described and the expansion calculation of single-component particles is carried out in section 2.2. Secondly, in section 3, considering the species and proportion of ions, the calculation of multicomponent ions is carried out, and the validity and rationality of the model are verified by comparing with the experimental results. Then, the propagation characteristics of primary discharge in the space solar array are analyzed, and the effect of the initial value of primary discharge is discussed in section 4. Finally, in section 5, the primary discharge propagation is tested in the ground simulation experiment system.
As shown in figure 1, primary discharge occurs at the triple junction of solar array, and the generated plasma expands on the surface under its electric field. The positively charged coverglass collects electrons from the plasma to neutralize charges. Compared with previous models, the plasma expansion model proposed in this paper mainly has the following three improvements. (1) Optimization of initial conditions: in the previous discussion of arc plasma problems, it is assumed that the arc generates the sustain constant ion current and expands at a constant speed, this model not only considers the effect of the space background plasma environment, but also keeps the number of ions fixed in the expansion process, neither added nor reduced, and the ion expansion speed is determined by its self-consistent electric field, which is closer to the real working condition of plasma bubble expansion. (2) Consideration of multicomponent ions: there are various materials at the junction of solar cells, such as RTV, silver, silicon, gallium arsenide, and so on, the generated plasma should contain multicomponent ions. (3) Isotropic plasma expansion: plasma expansion adopts hemispherical.
The dense plasma has a significant shielding effect on the external electric field. The Debye length can be expressed as:
| λD=√ε0kTe(ne+nj)e2, | (1) |
where, ε0 is the vacuum dielectric constant, k is the Boltzmann constant, Te is the electron temperature, ne and nj are the number densities of electrons and ions, respectively. For the plasma bubble expansion area in this study, as the expansion radius changes from 0.1 mm to 3 m, the plasma number density changes about 1020–1012 m−3, and the Debye length is about 1.6 μm–1.6 cm. The ratio of Debye length to plasma bubble expansion radius is always less than 0.5%. Therefore, the Debye shielding makes the external electric field unable to affect the expansion of the plasma bubble.
In the process of plasma bubble expansion, The electron satisfies the Boltzmann equation, and the ionic fluid satisfies the mass and momentum conservation equations, which are expressed as:
| ne=n0exp(eϕ/kTe), | (2) |
| ∂nj∂t+1r2∂∂r(r2njuj)=0, | (3) |
| mj(∂uj∂t+uj∂uj∂r)=qjE, | (4) |
where, r is expansion radius, uj is motion speed, qj is ion charge, E is electric field intensity, and j represents different ion species.
The self-consistent electric field can be calculated by the Boltzmann equation:
| E=kTee∂ln(ne/nen0)n0)∂x. | (5) |
The plasma is electrically neutral:
| ne=∑nj=n. | (6) |
Assuming that the plasma collides within a very small radius r0, the electron and ion temperatures are approximately equal. At the same time, it is assumed that the arc provides a constant current for each ion, and the initial average ion radial speed at r0 is half of the ion thermal speed.
| I≡I(r0)=∑Ij, | (7) |
| uj(r0)=√2Teπmj, | (8) |
| nj(r0)=Ij2πr20uj(r0)qj, | (9) |
| n0=∑nj(r0). | (10) |
As the plasma expands, the ionic fluid moves in the self-consistent electric field in the range of r > r0. By numerically solving the time evolution of ion continuity, momentum, and plasma potential equations, the distribution changes during plasma expansion can be obtained.
Taking the LEO plasma environment as the background, the plasma number density is 1×1011 m−3. The electron temperature of the arc ions measured by the previous arc spectrum is 3–6 eV [15], so Te = 4.5 eV. To compare with the previous experimental research, the average primary discharge current I0 = 0.84 A, and the ion mass m0 = 100 AMU. The initial values of ion speed and number density can be calculated by equations (8) and (9):
| u0=1661.4m/mss,n0=5.03×1020m−3. | (11) |
The first-order upwind difference method is used to discretize and iteratively solve equations (3)–(5). The Euler grid is used as the discrete grid, which is divided into non-uniform grids with density first and sparsity later in the 1 mm–3 m region so that the initial region of plasma expansion has better resolution. Grid division calculation can be expressed as:
| Δri=r0(1+αi2), | (12) |
| α=6(N−1)N(2N−1)(rNr0−N), | (13) |
where, N is the total number of grids, i is the grid number; N = 100, r0 = 1 mm, rN = 3 m, Δt = 5×10−7 s. The ion number density distribution is calculated, and normalized by the initial value, as shown in figure 2.
In figure 2, it is evident that at the same time, as the radius r increases, the ion number density in the expansion region gradually decreases, which is approximately exponential decay. At the expansion radius of 1 m, the ion number density decays to about 1013–1014 m−3, which is very close to the estimated value in [22] and the optical measurement value in [23]. There are fluctuations at the plasma expansion front, because there is a large difference between the expansion plasma density and the background plasma density at the front, and there is discontinuity, which leads to serious electric field distortion and large fluctuation in the ion number density distribution. Meanwhile, the change in the average expansion speed over time can be calculated according to the change in the expansion front, as shown in figure 3. It can be seen that the average expansion speed gradually decreases over time, eventually stabilizing. The reason is that the plasma expands in the electric field formed by itself, as indicated by equation (5), which is closely related to its number density distribution. The ion number density decays exponentially along the radial direction, and the gradient becomes smaller. Therefore, the formed electric field decreases, and the expansion speed gradually decreases and tends to be gentle.
As primary discharge occurs at the spacecraft solar array, the plasma expands and neutralizes with the charged coverglass, resulting in discharge propagation, and causing longer and worse discharges. According to the calculation results of single-component ions, as the plasma expands radially, the neutralization radius rneu increases, while the plasma density at the expansion front decreases and the increase in neutralization radius slows down. Assuming that the glass covers the entire solar array, and the potential of coverglass surface relative to the spacecraft ground is V0, the initial charge per unit area Q0 can be expressed as:
| Q0=V0⋅Cs, | (14) |
where, Cs is the average capacitance per unit area of the coverglass, 2×10−7 F/m2.
When the plasma expands and neutralizes the surface charge of the coverglass, the neutralization current density is equal to the current density je of the electron fluid in the plasma, which can be expressed as [14]:
| je=en(r)√eTe2πme, | (15) |
| jneu(r)=je(r),V(r)>0. | (16) |
According to the relationship between the surface potential of the coverglass and the amount of charge, it can be obtained that
| dV(r)dt=−jneu(r)Cs. | (17) |
The total electron current of the arc can be obtained by the surface integral of the neutralization current on the array region.
| Ie=∫jneuds. | (18) |
In the LEO plasma environment, it is assumed that the coverglass surface is uniformly charged to 300 V relative to the spacecraft ground. Since the spacecraft solar array is composed of various materials, the plasma generated by primary discharge should contain multicomponent ions. It is assumed that the arc current generated by the plasma expansion is composed of five single-charged ions. The initial values of primary discharge current and ion temperature are consistent with those of the above single-component ions. Utilizing equations (7)–(9), the number density and initial speed of each ion can be calculated, as shown in table 1.
| Particle | Mass (AMU) | Percent (%) | Number density (m−3) | Speed (m/s) |
| H | 1 | 60 | 3.02×1019 | 16614.5 |
| C | 12 | 15 | 2.62×1019 | 4796.2 |
| O | 16 | 15 | 3.02×1019 | 4153.6 |
| Si | 28 | 9 | 2.40×1019 | 3139.8 |
| Ag | 108 | 1 | 5.23×1018 | 1598.7 |
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Different from the calculation of single-component ions, the coupling effect between multi-component ion fluids needs to be considered in the expansion process. Therefore, the coupling electric field strength is required in each iteration calculation.
| E=kTee∂ln((5∑i=1ni)/(5∑i=1ni)n0)n0)∂x. | (19) |
The unified discrete iterative calculation of five ions is carried out, and the normalized results of plasma number density are obtained, as shown in figure 4. It can be seen that there are multiple wave peaks in the radial distribution of ion number density at the same time because the expansion speeds of different mass ions are different. Taking the distribution of 50 μs as an example, there are five wave peaks in the radial distribution of ions, which are H, C, O, Si, and Ag from right to left. The mass of H is the smallest and the expansion speed is the fastest, while the mass of Ag is the largest and the expansion speed is the slowest, so there are expansion wave peaks within 600 μs. Due to the similar mass of C and O, the expansion speed difference is small, the distance between their expansion wave peaks is relatively close and only appears in the first few spectra. Different with the single-component ions, the number density of multi-component ions decreases significantly only at the earlier time, and not after 50 μs. The reason is that H expands the fastest, reducing the number density difference between the subsequent expanding ions and the background plasma, so there is a significant decrease only at the point where H has not expanded to 3 m.
By equations (15)–(17), the current density distribution per 50 μs can be calculated, as shown in figure 5. Near the arc discharge point, the plasma density is high, which can quickly neutralize the surface potential of the coverglass, and the neutralized coverglass surface no longer collects electrons. The vertical line depicted in figure 5 represents the boundary between the neutralized and unneutralized coverglass. Over time, the neutralization boundary and current density wave peaks move backward along the radial direction, which is similar to the result of ion number density distribution.
In [20], according to the experimental measurement, the propagation length of primary discharge is defined as the distance between the position of the solar cell string with the observed minimum neutralization current and the initial discharge point, and the propagation speed is calculated by the reciprocal of the propagation length to time. The relationship between propagation distance and time is obtained by fitting the experimental measurement data in LEO, which is expressed as:
| Lp=A×t0.5, | (20) |
where, the range of A is 47–110, with an average value of 74.
Since the plasma expansion model incorporates multicomponent ions, the expansion front of a specific ion cannot be used as the expansion boundary. The different characteristics of various ion propagation are the change in ion number density, that is, the change of the current density. Therefore, the current density weighting method is used to calculate the expansion distance.
| Lp=∫rNr0Jneurdr∫rNr0Jneudr. | (21) |
The expansion distances at different moments of the experimental fitting and the simulation in this paper can be calculated by equations (19) and (20), respectively, as shown in table 2. It is observed that compared with the experimental fitting value, the error of the simulated calculation value is less than 7%, which is within a reasonable error range.
| Time (μs) |
Simulated calculation (m) |
Experimental fitting (m) |
Relative error |
| 50 | 0.49 | 0.52 | 5.65% |
| 100 | 0.69 | 0.74 | 6.13% |
| 150 | 0.87 | 0.91 | 4.32% |
| 200 | 0.99 | 1.05 | 5.27% |
| 250 | 1.09 | 1.17 | 6.44% |
| 300 | 1.22 | 1.28 | 5.02% |
| 350 | 1.32 | 1.38 | 4.83% |
| 400 | 1.43 | 1.48 | 3.61% |
| 450 | 1.51 | 1.57 | 3.97% |
| 500 | 1.58 | 1.65 | 4.22% |
| 550 | 1.65 | 1.74 | 5.17% |
| 600 | 1.69 | 1.81 | 6.95% |
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The relationship between the expansion distance and time is shown in figure 6, which is approximately a power function, fitted and expressed as:
| Lp=81.2316t0.519. | (22) |
The simulation results are very close to the experimental fitting mean value of [20].
The propagation speed can be obtained by time differentiation of propagation distance, which is expressed by:
| vp=dLpdt=42.156t−0.481. | (23) |
The simulated expansion speeds of 20 μs and 100 μs calculated by equation (22) are 7675.5 m/s and 3539.2 m/s, which measured in the experiment are 8000 m/s and 4000 m/s, the relative errors are 4.1% and 11.5%, respectively. Combined with the calculation of expansion distance error, the correctness and effectiveness of the multicomponent plasma expansion model are fully proved. Compared with single-component ions simulation, the propagation speed of multicomponent ions is smaller. The main reason is that the propagation speed of single-component ions is determined by the expansion front, which is consistently in a high ion density gradient, resulting in a faster expansion speed. However, the lightest ion in the multicomponent ions expands faster, reducing the number density gradient of the expansion front of the remaining ions, making its electric field smaller, resulting in slower ion expansion. Compared with the assumption of constant speed expansion of all ions in previous research models, this model is closer to the real working conditions, which further demonstrates the rationality of multicomponent ions simulation.
Assuming that the primary discharge occurs at a corner of a 1.8×2 m2 solar array, the discharge propagation is simulated and predicted by using the above multicomponent plasma expansion model. The initial conditions of the model are consistent with the above, and the distribution of current density with time and position is obtained by the discrete calculation method. By equations (17), (18) and (20), the propagation current over time at different distances that primary discharge may propagate can be calculated.
It is assumed that the primary discharge propagates to the distance of 0.6 m from the arc point, inducing the temporary sustained neutralization reaction, and the propagation current changes with time as shown in figure 7. Compared with the typical plasma expansion current waveforms tested in [7] and [15], it can be seen that the two have the same characteristics. As mentioned above, multiple current wave peaks appear due to different ion speeds, and the trend of current changes over time remains consistent. But there are some time lags, which are mainly caused by three reasions. (1) The difference in ion species, charge number and proportion leads to the different expansion speeds from the experiment, resulting in the time lags of the current. (2) It is assumed that the surface neutralization reaction occurs immediately in this simulation, the simulated discharge current rises sharply, and the discharge current rise takes a certain time in experiment. (3) The randomness of the primary discharge position in the experiment may cause the difference of plasma expansion and propagation.
Additionally, according to the propagation distance of table 2, the current peaks at different positions that may be propagated by a discharge are counted, as illustrated in figure 8. Notably, if a continuous neutralization reaction occurs when the primary discharge propagates within 0.5 m from the arcing position, the maximum discharge current reaches 4.64 A, which makes it very easy to produce higher concentration plasma clusters to induce a temporary sustained discharge arc, thus causing serious damage to the insulation layer and working performance of the solar array.
By changing the initial current and the plasma electron temperature of the primary discharge, the maximum propagation distance and the current peaks of the primary discharge in 600 μs under six different conditions are obtained, as shown in table 3.
| Condition | Te (eV) | I0 (A) | Lpmax (m) | Imax (A) |
| 1 | 4.5 | 0.50 | 1.68 | 2.44 |
| 2 | 4.5 | 0.84 | 1.69 | 4.64 |
| 3 | 4.5 | 1.20 | 1.69 | 7.07 |
| 4 | 4.5 | 1.60 | 1.70 | 9.98 |
| 5 | 3.0 | 0.84 | 1.62 | 6.64 |
| 6 | 6.0 | 0.84 | 1.75 | 3.53 |
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From conditions 1–4, it is observed that when the plasma electron temperature generated by primary discharge remains constant, the maximum propagation distance remains almost unchanged with the increase of the initial current, while the propagation current peak increases significantly. The reason is that the plasma electron temperature remains unchanged, that is, the initial expansion speed remains unchanged, so that the plasma number density gradient changes slightly during the expansion process of conditions 1–4, and the expansion speed changes slightly, the maximum expansion distance is almost unchanged. The increase of the initial current makes the plasma number density increase, and the maximum propagation current increases obviously when the expansion speed is close.
By comparing and analyzing conditions 2, 5, and 6, it can be concluded that when the initial current remains unchanged, the maximum propagation distance increases obviously with the increase of plasma electron temperature, while the propagation current peak decreases. The reason is that when the plasma number density is constant, the increase of the initial expansion speed makes the plasma number density gradient change greatly. Similarly, the expansion speed increases and the maximum expansion distance increases. At the same time, the increase of expansion speed makes the plasma number density decrease rapidly, and the propagation current peak decreases. In summary, as the primary discharge initial current increases, the propagation current peak increases, and with the increase of the plasma electron temperature generated by the primary discharge, the maximum propagation distance of primary discharge increases, the propagation current peak decreases, and its effect is higher than that of the primary discharge initial current.
Based on the ground simulation experiment system, a small solar array is used to carry out the discharge propagation experiment in the LEO plasma environment, as shown in the figure 9. The plasma source is an electron cyclotron resonance source, and the plasma density is 1×1011 m−3, which is consistent with the simulation. The distance between the two strings of the GaAs solar array is 2 mm, and the thickness of the coverglass is 0.09 mm. The cells are connected by silver interconnects and fixed on the aluminum substrate using RTV.
The discharge propagation process is captured, as shown in the figure 10. Applying a bias voltage, paimary discharge (marked by yellow circle) occurs at the “triple-junction” in figure 10(a). During the expansion of high-concentration plasma, a discharge phenomenon (marked by red circle) is induced at the edge of the adjacent string, as shown in figures 10(b) and (c). The discharge propagation current is measured, as shown in the figure 11. Compared with the simulation results under the same conditions, as analyzed in section 4.1, there are similar multiple current peaks, consistent trends, and time lags. In addition, there are also some differences in current peak, mainly because the solar array used in the experiment is smaller, compared with the large solar cell array, the distributed capacitance is smaller. Even if the compensation capacitance is added, there are still some differences, resulting in different current peaks.
Based on the plasma expansion fluid theory, a new multicomponent plasma expansion model is proposed in this study. The simulation and analysis of multicomponent ions are carried out. The propagation characteristics of primary discharge on the solar array surface are analyzed from the perspective of microscopic ions. The conclusions are as follows:
(1) During the plasma expansion process, the ion number density decays exponentially, and its gradient becomes smaller, the expansion speed gradually decreases and tends to be gentle. The different mass of multicomponent ions makes the expansion speed different, so there are multiple expansion fronts, and the ions with faster expansion speed reduce the number density gradient at the expansion front of the other ions, so that the expansion speed becomes slower, which is more in line with the real situation and reflects the rationality of multicomponent plasma expansion model.
(2) According to the characteristics of multicomponent ions expansion, the propagation distance is calculated by the current density weighted average method. The fitting results are close to the experimental results, and the errors are less than 7%. Meanwhile, the propagation speeds at 20 μs and 100 μs are 7675.5 m/s and 3539.2 m/s, respectively. Compared with the average propagation speeds measured by experiments, the errors are 4.1% and 11.5%, which are within a reasonable error range, and the correctness and effectiveness of the model are fully proved.
(3) The propagation current waveform of the primary discharge in simulation exhibits the similar multiple current peaks and trend characteristics as experiment results. Notably, the propagation current peak is higher within 0.5 m from the arc starting point, up to 4.64 A, which extremely causes worse discharge. The effect of the initial values of the model is explored, revealing that the propagation current peak increases with the increase of the primary discharge initial current, and as the increase of the plasma electron temperature generated by the primary discharge, the maximum distance of primary discharge propagation increases, the propagation current peak decreases, and its effect is higher than that of the primary discharge initial current.
For future research, the persistence of plasma clusters generated by primary discharge should be considered, the cathode spot model will be used to predict the termination behavior of discharge, and the multi-stages model of cathode spot-plasma expansion will be established, which can accurately simulate the whole process of generation-propagation-termination of primary discharge. Meanwhile, the possible formation of shock during plasma expansion will be discussed.
This work was supported by National Natural Science Foundation of China (Nos. 51937004 and 51977002) and sponsored by Beijing Nova Program (No. 20220484153).
| [1] |
Zhu L Y et al 2017 Plasma Sci. Technol. 19 055304 doi: 10.1088/2058-6272/aa607a
|
| [2] |
Vayner B and Ferguson D 2023 J. Spacecr. Rockets 60 1566 doi: 10.2514/1.A35678
|
| [3] |
Hess S L G, Payan D and Sarrailh P 2023 IEEE Trans. Plasma Sci. 51 2556 doi: 10.1109/TPS.2023.3250712
|
| [4] |
Li K et al 2007 Sci. China Ser. E: Technol. Sci. 50 213 doi: 10.1007/s11431-007-0007-3
|
| [5] |
Zhu L Y et al 2019 Plasma Sci. Technol. 21 025302 doi: 10.1088/2058-6272/aaf18a
|
| [6] |
Sokolovskiy A N et al 2022 IEEE Trans. Plasma Sci. 50 4865 doi: 10.1109/TPS.2022.3222967
|
| [7] |
Vaughn J A et al 1994 J. Spacecr. Rockets 31 54 doi: 10.2514/3.26402
|
| [8] |
Katz I et al 2000 ESD triggered solar array failure mechanism In: 6th Spacecraft Charging Conference Hanscom AFB: AFRL Science Center 2000: 39
|
| [9] |
Amorim E 2005 Electrostatic discharges on a 1M2 solar array coupon-influence of the energy stored on coverglass on flashover current In: 9th Spacecraft Charging Technology Conference Tsukuba 2005: 331
|
| [10] |
Roussel J F et al 2012 IEEE Trans. Plasma Sci. 40 183 doi: 10.1109/TPS.2011.2177672
|
| [11] |
Sarrailh P et al 2013 IEEE Trans. Plasma Sci. 41 3429 doi: 10.1109/TPS.2013.2276454
|
| [12] |
Inguimbert V et al 2017 IEEE Trans. Plasma Sci. 45 1864 doi: 10.1109/TPS.2017.2686653
|
| [13] |
Monnin L et al 2021 J. Appl. Phys. 130 223302 doi: 10.1063/5.0061320
|
| [14] |
Ferguson D C and Vayner B V 2013 IEEE Trans. Plasma Sci. 41 3393 doi: 10.1109/TPS.2013.2279760
|
| [15] |
Ferguson D C et al 2018 J. Spacecr. Rockets 55 116 doi: 10.2514/1.A33812
|
| [16] |
Masui H, Toyoda K and Cho M 2008 IEEE Trans. Plasma Sci. 36 2387 doi: 10.1109/TPS.2008.2003191
|
| [17] |
Inguimbert V et al 2013 IEEE Trans. Plasma Sci. 41 3370 doi: 10.1109/TPS.2013.2259150
|
| [18] |
Gong L F et al 2021 Int. J. Impact Eng. 158 104022 doi: 10.1016/j.ijimpeng.2021.104022
|
| [19] |
Wang J et al 2024 Int. J. Impact Eng. 186 104896 doi: 10.1016/j.ijimpeng.2024.104896
|
| [20] |
Okumura T et al 2011 J. Spacecr. Rockets 48 326 doi: 10.2514/1.50907
|
| [21] |
Young J A and Crofton M W 2017 IEEE Trans. Plasma Sci. 45 3349 doi: 10.1109/TPS.2017.2765244
|
| [22] |
Vayner B, Ferguson D and Galofaro J 2009 Effect of solar array size on sustained arc inception In: 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition Orlando: AIAA 2009 doi: 10.2514/6.2009-115
|
| [23] |
Hu M and Kusse B R 2004 Phys. Plasmas 11 1145 doi: 10.1063/1.1644582
|
Figures(11) / Tables(3)
Supported by: Beijing Renhe Information Technology Co., Ltd. 
| Particle | Mass (AMU) | Percent (%) | Number density (m−3) | Speed (m/s) |
| H | 1 | 60 | 3.02×1019 | 16614.5 |
| C | 12 | 15 | 2.62×1019 | 4796.2 |
| O | 16 | 15 | 3.02×1019 | 4153.6 |
| Si | 28 | 9 | 2.40×1019 | 3139.8 |
| Ag | 108 | 1 | 5.23×1018 | 1598.7 |
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| Time (μs) |
Simulated calculation (m) |
Experimental fitting (m) |
Relative error |
| 50 | 0.49 | 0.52 | 5.65% |
| 100 | 0.69 | 0.74 | 6.13% |
| 150 | 0.87 | 0.91 | 4.32% |
| 200 | 0.99 | 1.05 | 5.27% |
| 250 | 1.09 | 1.17 | 6.44% |
| 300 | 1.22 | 1.28 | 5.02% |
| 350 | 1.32 | 1.38 | 4.83% |
| 400 | 1.43 | 1.48 | 3.61% |
| 450 | 1.51 | 1.57 | 3.97% |
| 500 | 1.58 | 1.65 | 4.22% |
| 550 | 1.65 | 1.74 | 5.17% |
| 600 | 1.69 | 1.81 | 6.95% |
DownLoad:
CSV
| Condition | Te (eV) | I0 (A) | Lpmax (m) | Imax (A) |
| 1 | 4.5 | 0.50 | 1.68 | 2.44 |
| 2 | 4.5 | 0.84 | 1.69 | 4.64 |
| 3 | 4.5 | 1.20 | 1.69 | 7.07 |
| 4 | 4.5 | 1.60 | 1.70 | 9.98 |
| 5 | 3.0 | 0.84 | 1.62 | 6.64 |
| 6 | 6.0 | 0.84 | 1.75 | 3.53 |
DownLoad:
CSV
