SCIENCE CHINA Information Sciences, Volume 61, Issue 2: 022201(2018) https://doi.org/10.1007/s11432-017-9219-1

## Parameter influence on electron collectionefficiency of a bare electrodynamic tether

• AcceptedJul 5, 2017
• PublishedDec 22, 2017
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### Abstract

This study develops a coupled multiphysics finite element method forthe dynamic analysis of a bare flexible electrodynamic tether. Contrary tothe existing methods, the new method discretizes and solves the orbitalmotion limited equation and the dynamic equation of an elastic flexibletether simultaneously. First, the new method is verified via comparison withthe existing methods in a straight tether situation. Second, the number oftether elements, tether bending deformation, and two design parameters atthe cathodic end affecting the electrical current are investigated. It isdetermined that the tether bending deformation and the two parameters i.e.,the impedance $Z_{T}$ and $\varPhi_{\rm~PW}$ have asignificant impact on the electron collection efficiency of anelectrodynamic tether system. The results indicate that the proposed methodshould be applied in the refined mission analysis.

### Acknowledgment

This work was supported by Discovery Grant and Discovery Accelerate Supplement Grant of Natural Sciences and Engineering Research Council of Canada.

### References

[1] Zhu Z H. Mission design for a cubesat deorbit experiment using an electrodynamic tether. In: Proceedings of AIAA/AAS Astrodynamics Specialist Conference, Long Beach, 2016. 5573--5579. Google Scholar

• Figure 1

(Color online) Profiles of electrical current and potential bias along a bent tether.

• Figure 2

(Color online) Design schematic of electrical circuit at the cathodic end.

• Figure 3

(Color online) Comparisons of current profiles along a straight tether in different orbits with different calculation methods. (a) Equatorial orbit; (b) 53$^{\circ}$ inclined orbit; (c) Polar orbit.

• Figure 4

(Color online) Analysis of the number of tether elements. (a) Electrical current profile along tether; (b) EMF profile along tether.

• Figure 5

(Color online) Analysis of the tether bending effect. (a) Tether profile; (b) EMF profile along tether; protectłinebreak (c) electrical current profile along tether; (d) potential bias profile along tether.

• Figure 6

(Color online) Analysis of the impedance $Z_{T}$. (a) Electrical current profile along tether; (b) potential bias profile along tether.

• Figure 7

(Color online) The analysis of the potential bias of battery $\varPhi_{\rm~PW}$. (a) Electrical current profile along tether; protectłinebreak (b) potential bias profile along tether.

• Table 1   Physical parameters of EDT system
 Parameter Value Tether material Aluminum Elastic modulus of tether (${\rm~N}\cdot~{\rm~m}^{~-~2})$ 7.2 $\times~$ 10$^{10}$ Density of tether material (kg/m$^{3})$ 2700 Tether length (m) 500 Tether width (m) 0.004 Tether thickness ($\mu$m) 35 Mass of main satellite (kg) 2 Mass of sub-satellite (kg) 2 Dimensions of main satellite (m) 0.1 $\times~$ 0.1 $\times~$ 0.1 Dimensions of sub-satellite (m) 0.1 $\times~$ 0.1 $\times~$ 0.1
• Table 2   Maximum current at the anodic end (A)
 Name The first reference method The second reference method The proposed method Equatorial orbit 0.1070854 0.1070634 0.1070633 53$^{\circ}$ inclined orbit 0.0301559 0.0301567 0.0301569 Polar orbit 0.0074935 0.0074924 0.0074921
• Table 3   Length of positively biased segment in different cases (m)
 Name The first reference method The second reference method The proposed method Equatorial orbit 497.5217 497.5222 497.5222 53$^{\circ}$ inclined orbit 498.5358 498.5365 498.5365 Polar orbit 482.3310 482.3293 482.3293
• Table 4   Maximum current and potential bias
 Name 5 elements 10 elements 15 elements 20 elements 25 elements Current $I_{B~}$ (A) 0.116 0.110 0.108 0.107 0.106 Potential bias $\varPhi_{A}$ (V) 109.991 109.818 109.777 109.753 109.744
• Table 5   The length $L_{B}$ in different cases
 Name $\delta~$ = 0.04 $\delta~$ = 0.09 $\delta~$ = 0.13 $\delta~$ = 0.17 $\delta~$ = 0.20 $\delta~$ = 0.24 $\delta~$ = 0.27 $\delta~$ = 0.30 $\delta~$ = 0.32 Length $L_{B}$ (m) 497.53 497.44 497.28 497.01 496.58 495.85 494.44 490.74 471.55
• Table 6   Length $L_{B}$ and maximum current $I_{A}$ in differentcases
 $Z_{T}$=5 $\Omega~$ $Z_{T}$=50 $\Omega$ $Z_{T}$=100 $\Omega$ $Z_{T}$=150 $\Omega$ $Z_{T}$=200 $\Omega$ Length $L_{B~}$ (m) 497.52 476.77 456.56 438.71 422.68 Current $I_{A~}$ (A) 0.1071 0.1006 0.0943 0.0890 0.0844 Potential bias $\varPhi_{C}$ (V) $-0.5353$ $-5.0297$ $-9.4338$ $-13.3458$ $-16.8703$
• Table 7   The length $L_{B}$ in different cases
 $\varPhi_{\rm~PW}$ (V) 0 10 20 30 40 50 Length $L_{B}$ (m) 273.96 317.84 362.07 406.72 451.85 497.52
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