Lifetime and Mission reliability assessment of multi-mode ion thruster

An approach to quantify the lifetime and mission reliability of multi-mode ion thruster is presented. The reliability of LIPS-300S thruster completing the Asteroid Exploration Mission is assessed. The procedure of this approach is (i) assess the life margin factor (LMF) against each failure mode according to the wear test results, then identify the engineering failure modes whose LMFs are less than 1.5; (ii) quantify the uncertainty in the lifetime based on each engineering failure mode and identify the key failure mode with the minimum LMF; (iii) sample the lifetime based on the key failure mode and obtain its 3-parameter Weibull distribution; (iv) simplify the throttle profile as operations at several representative throttle levels, then obtain the conditional lifetime distribution for each operation based on previous operations; (v) considering all possible failure modes, integrate the probability of completing each operation as the total reliability index. The results show that LIPS-300S can complete the Asteroid Exploration Mission with a reliability of 100%.


Introduction
"Multimodalization" is becoming a trend for ion thrusters. The external cause of this trend, on one hand, is a demand for all-electric satellites and deep space exploration. All-electric GEO satellite needs to complete orbit transfer at high powers and station keeping at low powers [1], while a thruster in deep space mission needs to adapt its throttle level for the output power of the solar panels [2,3]. On the other hand, the performance of ion thruster itself is adjustable within a wide range since the processes of ionization, ion acceleration and neutralization are mutual independent [4,5]. Multimode ion thruster supports the development of product spectrum which requires a specification reduction and an extension of application range [5,6]. A ring-cusp multimode ion thruster called LIPS-300S is being developed by LIP for Asteroid Exploration Mission (AEM) [7], which requires the thruster to operate for over 36,000 h with a total impulse of over 9.0MNs. The overall performance of LIPS-300S with 23 throttle levels includes an input power of 328~3050 W, a thrust of 10~116mN, and a specific impulse of 1269~3468 s.
While benefits are brought in by multi-mode ion thrusters, their lifetime and reliability assessments become tricky [8,9]. Especially when a mission requires the thruster to operate to its maximum lifetime, as AEM does, the lifetime and reliability quantification is necessary to reduce the mission risk. Based on the assessment of single-mode and dual-mode ion thrusters [10,11], the challenges in multi-mode cases are analyzed. Practical approaches to resolve these problems are discussed with examples from AEM, as to support the application of LIPS-300S.

Challenges in multi-mode cases
Besides the coupling of thruster failure modes, throttle levels, life models, input uncertainties and throttle profiles, which has been discussed in single-mode and dual-mode cases [10,11], new challenges in multi-mode case are as follows.
where P i,j (t) is the distribution function of time t based on FMi and TLj; α, β and τ are distribution parameters.
(2) More complicated throttle profile Assuming a throttle profile is marked with {MPk, TLj| MPk , t k }, where k = 1,2, …,q is the segment index, TLj| MPk the throttle level and t k the operating time during segment MPk. Then the reliability index based on FMi is (

3) Less representative life test results
The life test design of LIPS-300S is complicated due to 23 throttle levels under consideration. Different selections of throttle level, segment duration and test procedure will lead to different test results. A more reasonable test procedure would be based on representative throttle levels, mission-preferred or equally allocated segment durations, adaptation to extra or extended test processes, and end conditions including failure occurrence and truncation. Examples include the 30,352-h test on 16-throttle-level NSTA R and the 51,184-h test on 40-throttle-level NEXT [2,12].
It is generally required that a thruster be applicable for multiple missions. Even if a ground life test is completed at a high cost, it is still difficult to ensure new mission requirements with this result. This problem challenges the engineering application of multi-mode ion thrusters. The lifetime and reliability of a multi-mode ion thruster can only be quantified based on its throttle profile and missionrequired lifetime.
Life margin assessment based on thruster wear test Throttle profile and required lifetime for AEM It is planned to use LIPS-300S as the main propulsion system in AEM to complete a 2phase mission. Phase 1 is an orbit transfer from Earth to Mars, and phase 2 is the departure from Mars and cruise to the asteroid. The throttle profile {MPk', TLj| MPk' , t k' }, k' = 1,2, …,18 and delta-V are listed in Table 1.
In this 18-segment profile, 16 throttle levels are involved and the input power is generally decreasing throughout the throttle table. The required lifetime is 35,654 h (rounded up as 36,000 h), and the total delta-V is 8077 m/s.

Development and life-extending design of LIPS-300S
LIPS-300S is a "multimodalized" version of LIPS-300, which has completed the flight test on SJ-20 and a 10kh life test. These test results and validated models, along with the experience in LIPS-200 lifetime and reliability assessment [10,11], can be used for reference here. The characteristics of LIPS-300S compared with other products are shown in Table 2.
Compared with LIPS-300, three significant changes have been made to LIPS-300S: (i) a much higher required lifetime, (ii) much more throttle levels and a wider range of power and thrust, and (iii) a lower wear rate corresponding to the decreased maximum power, which is beneficial to its life extending. The characteristics of LIPS-300S contributing to its long life are considered as (i) three-grid ion optics, (ii) a lower discharge voltage, and (iii) lower maximum power or beam density. The design of LIPS-300S is based on the 10kh LIPS-300 test results and the previous life models of LIPS− 200 and LIPS-300. These life models are semi-empirical models based on erosion rates estimated by 2-D or 3-D PIC-MCC algorithm [13][14][15]. Life margin factor (LMF) is defined as the thruster lifetime based on a certain failure mode, divided by its required lifetime. Although the post-test analysis of LIPS-300 shows a sufficient lifetime for its preassigned mission, the lifetimes based on FM1, FM2, FM3, FM5, FM6 and FM12 are below 36kh, which means these LMFs are less than 1.0 for AEM. Thus modifications were made to prolong its lifetime based on these failure modes, including (i) FM1: fit the cathode flow rate to the magnetic field, which reduced the discharge voltage by over 5 V and mitigated the sputter erosion of the screen grid; (ii) FM2 and FM5: uniform the grid gap and improve grid aperture varying design, thus increased the beam flatness and reduced the accel grid erosion; (iii) FM6: increase the insert thickness; (iv) FM3 and FM12: attach sputtered material retention device to the discharge chamber and modify the harness.

Life margin analysis based on wear test of LIPS-300S
A 1200 h wear test consisting of 4 segments was conducted on LIPS-300S [16]. The  throttle profile for this test is {MP1, TL23, 1260 h; MP2, TL14, 840 h; MP3, TL09, 840 h; MP4, TL01, 420 h}. During the test, the operating pressure is lower than 3 × 10 − 3 Pa, which is considered in the erosion rate assessment. The vacuum chamber is 5 m in diameter and 8 m in length, which is considered large enough to neglect the influence of the back sputtering. The results [16] indicated that the performance of LIPS-300S met the requirements and showed no degration during the test. There was no sputtering contamination in the discharge chamber and the grid apertures showed no obvious enlargement within the measurement accuracy. The top orifice diameters of the neutralizer and the cathode increased during the first 300-h operation and then kept constant. Based on the test results and life models, the LMF against each failure mode is listed in Table 3. The failure modes specific to the cathode also apply to the neutralizer. The worst-case erosion, which occurs at the center of the grid, is considered in the lifetime assessment.
The failure mode with a LMF less than 1.5 is defined as an engineering failure mode (EFM), while the one with a LMF greater than or equal to 1.5 is a general failure mode. As we can see, the EFMs who need further assessment in AEM are FM1, FM2 and FM5.

Life models based on EFMs
Although the LMFs in Table 3 are all greater than 1.0, an uncertainty analysis is still necessary for the EFMs. Since there are uncertainties in both the test results and the life model, which eventually brings uncertainty to the lifetime and LMF result. Quantification of margins and uncertainties (QMU) [17,18] is applied here (see Ref. [10,11,18] for its conceptual and computational basis). The characteristic parameters of FM1, FM2 and FM5 are screen grid eroded mass, accel grid eroded mass, and electron backstreaming limit, respectively. Their corresponding thresholds are half of the screen grid mass, half of the accel grid mass, and accel grid potential, respectively. The lifetime based on each EFM at TLj is as follows (see Ref. [10,[19][20][21] for a detailed discussion).
where t mi,j , F i,j , and X j are the lifetime, life model, and correlated parameters based on FMi and TLj; the subscripts s and a represent screen and accel grid, respectively; the superscripts + and ++ represent singly-charged and doubly-charged ion, respectively; ρ and m are the density and atomic mass of grid material, respectively; l cc is the aperture spacing; d, V, φ, and t (with subscript a or s) are the thickness, aperture diameter, potential, and ion transparency of the grid, respectively; I b is the beam current; f the beam flatness; R the double to single ion current ratio; D the beam diameter; Y the sputter yield, which is a function of the ion impact energy, as shown in Table 4 [22]; dN d /dt and dN b /dt are the charge exchange (CEX) ion flux toward the accel-grid downstream and barrel surface, respectively; d ac is the critical accel-grid aperture diameter as electron backstreaming occurs, which is determined by Eq. (6) [23]. (Where) where V spc is the critical saddle point potential; ΔV c the potential correction term of the space-charge effect in the accel grid aperture; l g the screen-to-accel grid gap; V dp the discharge plasma sheath potential; V bp the downstream beam plasma potential; d 0 the beamlet diameter; T e , m e, and e are the temperature, mass, and charge of electron; N the number of apertures; ε 0 the permittivity of free space; m i the ion mass.

Throttle profile simplification for AEM
The throttle profile for AEM consists of 18 segments, as shown in Table 1. To quantify the life margin based on each segment would be very computationally expensive, and also unnecessary if the throttle profile can be properly simplified. Three aspects should be considered in this simplification: (i) the segments with similar throttle levels should be merged into one segment with a representative throttle level, (ii) the number of segments after merging should be in the range of 3 to 5, (iii) the segment duration after merging should be equivalent to the sum of its corresponding durations before merging.
With these considerations given, the above-mentioned throttle profile is simplified as shown in Table 5. The representative throttle level in each segment can cover a certain percentage of the original throttling range, which are 100% for TL21 in MP1, 86% for TL13 in MP2, 95% for TL08 in MP3, and 80% for TL05 in MP4.
The life model inputs of LIPS-300S based on this simplified throttle profile are listed in Table 6, where the sputter yields Y + and Y ++ at V d = 26 V are interpolated from Table 4.

Uncertainty quantification of lifetime based on EFMs
The maximum lifetime at each representative throttle level based on FM1 and FM2, as shown in Table 7, can be obtained by Eqs. (3) and (4). The lifetime based on FM5 is obtained in the following procedure: (i) substitute the data in Table 6 into Eq. (6) and derive the curve of d ac with V a , (ii) read the value of d ac at V a = − 200 V, and (iii) substitute d ac (V a = − 200 V) into Eq. (5) to obtain the FM5 lifetime at each representative throttle level. As shown in Table 7, if the thruster operates at TL21 throughout the mission, the LMFs against FM1, FM2 and FM5 are 1.15, 1.41 and 1.33, respectively, which is consistent with the extrapolated results (1.1, 1.4 and 1.2) in Table 3. For the other throttle levels, the LMFs against FM1, FM2 and FM5 are in the range of 1.46~2.52, 1.712 .05, and 1.61~1.99, respectively. As the throttle level becomes lower, the LMF against FM1 increases faster than FM2 and FM5 because the plasma density in the discharge chamber decreases faster than the CEX ion density.
To confirm the life margin with the input uncertainties considered, the lifetime uncertainty is quantified for the worst-case throttle level TL21 with Eq. (7) (see Ref. [21] for a detailed discussion).
U (t m ) is the lifetime uncertainty, U(X) the input uncertainty. The results are listed in Table 8.
The lifetime uncertainty varies within [5000, 7000] h, and this uncertainty makes the lifetime distributed. The lower bound of this distribution is compared with the required lifetime, which gives the conclusion whether the thruster meets the lifetime requirement. As the minimum LMFs show, the thruster lifetimes based on FM2 and FM5 are qualified, while the one for FM1 is not enough yet.
The results in Table 8 are conservative because only the worst-case throttle level is considered. However, this QMU shows that the LMF against FM1 is the smallest, which makes FM1 the key failure mode (KFM) in this mission. Besides, this LMF is less than 1.0, exposing a risk that FM1 could occur during AEM.

Quantification of the lifetime and mission reliability of LIPS-300S
Lifetime and reliability based on KFM and worst-case throttle level Through the analyses in Life margin assessment based on thruster wear test and QMU for lifetime based on EFMs, the risk of LIPS-300S completing AEM depends on the LMF and reliability based on FM1. Therefore, only the lifetime and reliability based on FM1 are assessed, which can give a conservative result and avoid the complexity of multi-mode operation.
A sensitivity analysis of FM1 lifetime according to Eq. (3) shows, the correlated parameters ranked by t m1,j sensitivity are: Y ++ , φ, t s , R, Y + , f, D, I b , d s , and l cc . These parameters are assumed to follow a uniform distribution within the interval determined by their uncertainties shown in Table 6. Extract a sample from each of these intervals randomly and substitute this sample set into Eq. (3) to obtain a lifetime sample. Repeat this process for 500 times and obtain 500 lifetime samples, which follow a distribution as shown in Fig. 1.
A cumulative distribution curve (CDC) of lifetime is obtained based on Fig. 1, and a corresponding Weibull distribution function is derived by fitting the curve, as shown in Fig. 2.

Lifetime assessment based on KFM and simplified throttle profile
The result in Lifetime and reliability based on KFM and worst-case throttle level is conservative, while a more accurate assessment should be based on the simplified throttle profile. Eq. (8) is still valid for the first segment MP1, whose completion is the initial condition of MP2. Thus, the maximum lifetime for MP2 is Generate 500 lifetime samples from Eq. (9) and derive their CDC and distribution function, as shown in Fig. 3 and Eq. (10).
The life models for MP3 and MP4 are Note that l is the segment index, while j is the throttle level index. The CDCs and distribution functions for MP3 and MP4 are shown in Fig. 4 -Fig. 5, and Eqs. (13)- (14), respectively.
Lifetime and reliability assessment of LIPS-300S for AEM Each type of failure could happen during the AEM operation. Assuming the wear mechanisms of these failure modes are mutually independent, the reliability index of completing AEM is the product of the indices based on all the failure modes, as shown below.
Where T t is the cumulative operating time throughout AEM. Since only the P (T i ) for i = 1 is not equal to 1, a reduced relationship based on the simplified throttle profile is Substitute Eqs. (8), (10), (13) and (14) into Eq. (16), the reliability index of LIPS-300S completing AEM is P 35654h ð Þ¼1 Therefore, LIPS-300S can complete AEM with a reliability of 100%.

Conclusion
A practical method to assess the lifetime and reliability of multi-mode ion thruster completing a certain mission is presented with an example of LIPS-300S for AEM. Due to the coupling between failure modes and the throttle profile, this assessment must be done segment by segment. The general steps are as follows.
1) Obtain the life margin against each failure mode according to test and life model results, which gives the EFMs with LMFs less than 1.5. 2) Based on test-verified life models, apply QMU approach to quantify the lifetime uncertainty based on each EFM. Further assessments are necessary for the key failure mode with the minimum LMF. 3) According to the life model and input uncertainties for the key failure mode, generate lifetime samples and obtain their Weibull distribution. 4) Simplify the throttle profile, then derive the conditional probability for each segment based on preceding operation. 5) Assuming each type of failure and the conditional operation in each segment are mutual independent, the reliability index can be obtained by probability calculation.
The results show that LIPS-300S can complete AEM with a reliability of 100%.
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