## 4 Conclusions  
This article discusses the differences in armature acceleration effects based on different inter-stage distances and energization methods. It is pointed out that the distance between stages is the key factor affecting the selection of coil energization direction. To verify this, the article performs field-circuit coupling simulations on a four-stage synchronous induction coil launching device model by ANSYS Maxwell software. The results are as follows:  
1. The armature exit velocity of the PP energization method is superior to that of the PN energization method in the device with an inter-stage distance of 5 mm. However, in the device with an inter-stage distance of 15 mm, the armature exit velocity of the PN energization method is superior to that of the PP energization method.
2. In the coil launch device with the PN energization method, the previous and next drive coils mainly provide a deceleration effect on the armature. Conversely, in the coil launch device with the PP energization method, the previous and next drive coils mainly provide an acceleration effect on the armature.
3. Different inter-stage distances affect the coupling relationship between each drive coil and the armature. Increasing the inter-stage distance weakens the effect of the induced current in the coil on the armature launch process.
4. There is a threshold value of 7.5 mm for the inter-stage distance of the drive coils, which accounts for 37.5% of the length of the drive coils. If the inter-stage distance does not exceed this threshold value, selecting the PP energization method for the launch device will result in a better armature exit velocity. However, if the inter-stage distance exceeds this threshold value, selecting the PN energization method for the launch device will result in a better armature exit velocity.  
The simulation results of this model are consistent with the theoretical analysis and align with the validation of consistency with other existing studies. That is, the different acceleration modes generated by the two coil energization methods result in a threshold distance between each driving coil, which is a key factor in determining the energization direction of the launcher coil. This conclusion provides a basis for the selection of coil energization methods and valuable references for determining the energization direction of multi-stage SICL coils.  
Conceptualization, Y.G.; methodology, Y.G.; software, Y.G.; validation, Y.G.; formal analysis, X.W.; investigation, Y.G.; resources, X.W.; data curation, Y.G.; writing--original draft preparation, Y.G.; writing--review and editing, Y.G., X.W. and J.K.; visualization, Y.G.; supervision, X.W.; project administration, X.W. and J.K.; funding acquisition, X.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded in part by the Natural Science Basic Research Program of Shaanxi Province Program under Grant 2024 JC-YBMS-346, in part by the Natural Science Pre-study Foundation of Shaanxi University of Science and Technology under Grant 2020 BJ-53, in part by the Open Fund for Nation-al Engineering Laboratory of Energy-Saving Motor and Control Technology, Anhui University under Project KFKT202205.  
Not applicable.  
Data availability Statement: Data is contained within the article.  
The authors declare no conflicts of interest.