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Lorentz Force Characteristics of a Bare Electrodynamic Tether System with a Hollow Cathode

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Abstract

The electrodynamic tether (EDT) is a type of propulsion system that uses the geomagnetic field and ionospheric plasma and has the potential to conduct a space-debris removal mission without consuming a large amount of propellant. To understand the dynamic properties of the bare EDT system, an orbital dynamic model based on a detailed environmental space model and the real discharge characteristics of a hollow cathode plasma contactor (HCPC) was built. By numerical simulation, the differences in the bare tether performance caused by various orbital conditions and HCPC voltage models (at constant or various voltages) were compared and discussed. The results suggest that dynamic distinctions generated by the two bias voltage models increased as the latitude increased from 0° to 60°.

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Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Abbreviations

A:

Cross-sectional area, mm-2

\( \hat{A} \) :

Pre-exponential factor of Maxwellian distribution

a :

Semi-major axis, km

\( \hat{a} \) :

Factor in the fitting equation, the same as \( \hat{b} \), \( \hat{c} \), \( \hat{d} \),\( \hat{e} \), and \( \hat{f} \)

B :

Magnetic field strength, nT

C D :

Atmospheric drag coefficient

E :

Electric field strength, V/m

e :

Orbital eccentricity

F :

Force, mN

f :

Specific force, m/s2

G:

Gravitational constant, 6.67 × 10-11 N∙m2/kg2

g :

Gravitational acceleration, m/s2

\( {g}_n^m \) :

Gaussian coefficient, which is also shown as \( {h}_n^m \)

H:

Scale height of the atmosphere, km

h :

Altitude, km

h ∗ :

Reference height, km

I :

Current, A

i :

Orbital inclination, degrees

i :

Unit vector

L :

Bare tether length, km

l :

Length coordinate along the tether, km

M P :

Magnetic potential, V∙m/s

M :

Mass, kg

n :

Numerical density, m-3

\( {P}_n^m \) :

Regularised Legendre function

p :

Latus rectum, km

q:

Elementary charge, 1.602×10-19C

r :

Radius, km

T :

Temperature, eV

v :

Velocity, m/s

V :

Potential, V

A:

Spacecraft end of the bare tether

a :

Ambient

B:

Current transition point of the tether

C:

HCPC end of the bare tether

CGe :

From the bare EDT center of gravity to the earth core

e :

Electron

emission :

Emissions of electrons

ex :

External force

g :

Gravitation

k :

Keeper

ion :

Ion

lorentz :

Lorentz force

n :

Normal direction

neutral :

Neutral particle

o :

Original

p :

Plasma in ambient

pe :

From any point to the center of Earth

relative :

Bare EDT velocity relative to the geomagnetic field

tether :

On the bare tether

θ :

True anomaly

μ :

Gmearth, m3/s

Π :

Perimeter

ρ :

Density, kg/m3

ρ ∗ :

Density at the reference point, kg/m3

\( \hat{\rho} \) :

Radius of curvature, km

σ :

Collision cross-sectional area, m2

Ω :

Longitude ascending node, degrees

ω :

Argument of periapsis, degrees

ω r :

Angular velocity, rad/s

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Authors and Affiliations

  1. Beijing Institute of Technology, Beijing, China

    Kan Xie, Haoxiang Yuan, Fuwen Liang, Wei Wang & Qimeng Xia

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Xie, K., Yuan, H., Liang, F. et al. Lorentz Force Characteristics of a Bare Electrodynamic Tether System with a Hollow Cathode. J Astronaut Sci 68, 327–348 (2021). https://doi.org/10.1007/s40295-021-00256-1

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