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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

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  • ReceivedApr 28, 2017
  • AcceptedJul 5, 2017
  • PublishedDec 22, 2017

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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