Use of propulsion systems that couple electyrodynamic tethers to ion thrusters, as suggested in the literature, is

discussed. The system establishes electrical contact with the ionospheric plasma, at the anodic end of the tether, by

ejecting ions instead of collecting electrons; also, the ion thruster adds its thrust to the Lorentz force on the tether. In this paper, we analyze the performance of this coupled system, as measured by the ratio of mission impulse (thrust times mission duration) to the overall system mass, which includes the power subsystem mass, the tether subsystem mass, and the propellant mass consumed in the ion thruster. It is shown that a tether acting by itself, collecting electrons at its anodic end, substantially outperforms the coupled system for times longer than a characteristic time of the ion thruster, for which propellant mass equals the power subsystem mass; for shorter times performances are shown to be similar

Charro, Mario

Sanmartín Losada, Juan Ramón

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

 1
PERFORMANCE OF COUPLED  ED-TETHER / ION THRUSTER SYSTEM 
 
Juan R. Sanmartin1 and Mario Charro 
E.T.S.I. Aeronauticos, Universidad Politecnica de Madrid 
Plaza Cardenal Cisneros, 3,   28040 Madrid, Spain 
Phone: +34913366302     Fax: +34913366303 
e-mail:  1 jrs@faia.upm.es 
 
Abstract 
Use of propulsion systems that couple electyrodynamic tethers to ion thrusters, as suggested in the literature, is 
discussed. The system establishes electrical contact with the ionospheric plasma, at the anodic end of the tether, by 
ejecting ions instead of collecting electrons; also, the ion thruster adds its thrust to the Lorentz force on the tether. In 
this paper, we analyze the performance of this coupled system, as measured by the ratio of mission impulse (thrust  
times  mission duration) to the overall system mass, which includes the power subsystem mass, the tether subsystem 
mass, and the propellant mass consumed in the ion thruster. It is shown that a tether acting by itself, collecting electrons 
at its anodic end, substantially outperforms the coupled system for times longer than a characteristic time of the ion 
thruster, for which propellant mass equals the power subsystem mass; for shorter times performances are shown to be 
similar. 
 
I. Introduction 
         Ion Thrusters, and in general electrical propulsors, are more efficient than chemical rockets for missions that allow 
long times, requiring low thrust. In turn, electrodynamic (ED) tethers are much more efficient than ion thrusters for 
much longer times. This can more than balance the facts that tether-thrust might be ambient-plasma dependent, and that 
it exhibits low pointing accuracy. Further, those facts in the end would not hinder the slow average action of ED tethers. 
         The standard ED tether ejects electrons at a (cathodic) end, typically through a hollow cathode (HC), and collects 
electrons passively, either at the anodic end, as in the TTS1R mission,1 or over a segment of tether left bare of insulation 
and coming out positively biased;2  anodic use of a HC was tested in the PMG mission.3 It has now been suggested that, 
instead of collecting electrons, ions could be ejected at the anodic tether end by an Ion Thruster, which, furthermore, 
would add to the propulsive capability of the system.4 
         In ion thrusters, electrons from a HC are also emitted immediately downstream in the ion beam, to limit space- 
charge effects that would affect thruster performance (and would charge the attached spacecraft). In the suggested ED 
Tether / Ion Thruster hybrid scheme, the thruster would operate, without its neutralizing HC, at one end of the tether, 
and the HC  would operate at the other end, the neutralization current that would flow through the tether allowing the 
standard Lorentz thrust by the geomagnetic field. In order for the system to work, the ion thruster needs be able to 
function without having its neutralizer operating in the vecinity, but, rather, kilometers away, i.e. effectively without 
neutralizer. Space charge spreading of the ion beam makes thrusters operate less efficiently; the higher the beam 
divergence the less delivered thrust and specific impulse, for the same input power. Hopefully, the reduction in 
propulsive efficiency might be low in new-generation ion thrusters for space exploration, which will have lower beam 
densities and higher exhaust  velocities (higher specific impulses). 
     The suggested ED Tether / Ion Thruster hybrid system, combining ED-tether propulsion and a modified electrostatic 
propulsion, was said to merge the propellant-less propulsion capability of electrodynamic tethers and the efficient 
propulsion capability of electric propulsion, with any increase in mass with respect to the ion thruster, or the ED tether, 
working alone, to be assessed on a case-by-case basis depending on the application.4  It is here shown, however, that 
full account of all masses and due consideration of mission duration show the suggested hybrid system substantially 
outperformed by ED-tethers for their long-mission niche, and performing similarly to ED-tethers and ion thrusters 
otherwise.       
 
II. Mass-to-impulse ratio in space propulsion 
        The simpler figure of merit for space thrusters is the ratio between mass of the system dedicated to thrusting and 
total impulse required by the mission;  that ratio should be minimum.  Reboost of the International Space Station and 
'space-tug' operations are examples of missions well characterized by a total impulse  Fτ.  For a chemical rocket, mass 
is basically propellant mass, which is  mass-flow-rate  m&  times mission duration  τ,  whereas mission impulse is 
duration  τ  times thrust  (F = m& vexh);  here  vexh  is the velocity of gases at exhaust. We are ignoring for simplicity a 
correction from tankage and plumbing.  One then has 
 
                                        
impulsespecificgexhvF
m
impulsemissionTotal
systemthrustingofMass
×≡== 0
11
τ
τ&
.                              (1) 
ε 
 2
The greater the specific impulse the better, but there are clear limitations to how large the specific impulse (or how large 
the exhaust velocity) can be in case of chemical combustion. 
     One way to move to greater exhaust velocities is through electrical propulsion, which makes use, however, of a 
power plant that adds to the mass of the system. If  Ws  is the supply power, 
                                                                     Ws  = F vexh /2η  = η2/2exhvm&                                                           (2) 
 
with  η  the propulsive efficiency, and  β  is the inverse specific power of the supply plant, one arrives at5 
                     τη
β
τ
βτ
2
1 exhv
exhvF
sWm
impulseMission
massSystem +=+= &                                                                       (3) 
                                                                                                         ⎟⎠
⎞⎜⎝
⎛ +⇒ τ
τ exh
exhv
1
1
,                                    (3') 
         weeks
skm
exhv
kw
kgexhv
exh ηβη
βτ 65.0
2
/30
)(14.1
2
2
×××≈≡ ⎟⎠
⎞⎜⎝
⎛
.                                                              (4) 
 
Typical values of state-of-the-art Ion Thrusters are  η ∼ 0.65,   vexh ∼ 30 km/s  (over 10 times greater than chemical 
rocket values);  corresponding values for Hall thrusters are   η ∼ 0.50,    vexh ∼ 15 km/s. 6 
      Only for   τ >> τexh,   however, does the mass-to-impulse ratio in Eq. (3') reaches down to the value of inverse 
exhaust velocity,  1/ vexh.  In fact, for   τ << τexh,   that ratio diverges, any gain in using electrical propulsion being fully 
lost. It is clear that one cannot discuss the advantages of electrical versus chemical propulsion without reference to 
mission duration. This is already manifest in the Tsiolkovsky equation for the standard mission requiring a thruster to 
impart some velocity increment  Δv  to a payload, which, in the case of electrical propulsion, reads7 
       
                                                                ττ
ττ
/
/1
ln
exhratiomasspayload
exh
exhvv +
+×=Δ .                                            (5) 
Again, we have  Δv  vanishing for   τ << τexh,    
       An ED bare-tether uses no propellant, though expellant is consumed at the hollow cathode. The expellant mass-
flow-rate, however,  is 2-3 orders of magnitude smaller than at an electrical propulsor and can be fully ignored.5  One 
then has 
                                        System mass  ≈  βWs  +  αt × ρAtLt,                                                                                         (6) 
                                                                                                  F = Iav Lt B⊥,                                                                  (7) 
 
where  αt ∼ 2-3  accounts for tether-related hardware (deployer / ballast mass), and  Iav   and  B⊥  are current averaged 
over tether length and geomagnetic component perpendicular to the orbital plane. Finally, one finds7 
 
avimEc
orbUt
mW
sWorbU
BtLavI
tLtAtsW
impulseMission
massSystem
2στ
ρα
τ
β
τ
ραβ +=
⊥
+=                                                                      (8) 
                                                                                                      ⎥⎥⎦
⎤
⎢⎢⎣
⎡
+⇒
avimEt
orbU
2~
11
ητ
β
,                                 (8') 
 
where    Wm =  Iav Em Lt   is the magnetic (thrust) power,  Em = UorbB⊥  the motional field,   ηt  = Wm/Ws   the tether 
propulsive efficiency,   iav  =  Iav / σcEmAt   the average current normalized with the short-circuit current (in absence of 
power supply), ctmEmE βσρα //~ =  a normalized motional field that can be checked to be typically around unity, 
and  ρ,  σc,  At ,  and   Lt  tether density, conductivity, cross-section area and length.  
          Both  ηt   and  iav   take values of order unity that come out from detailed bare-tether analysis.5  Comparing now  
Eqs.(3, 3') with  Eq. (8')  clearly shows a much lower mass-to-impulse ratio for the ED-tether  (i.e., equivalent "specific 
impulse" of  ED-tether  much greater than   vexh/g0)  in case   τ  >> τexh ;  they are comparable in case   τ  ∼ τexh. 
 
 
 3
III. Performance of coupled ED-Tether / Ion Thruster 
          There are basically two possible arrangements, either having the power supply at the bottom (Fig.1) or at the top 
(Fig.2), though only the second one would allow the tether be positive relative to the plasma, and thus to operate as a 
bare tether. In either case, neglecting the small bias at the HC, one has voltage and power supply given as  
 
                                      VItZtLmEs ++=ε ,                  2ItZItLmEIVIssW ++== ε .                 (9a, b) 
where  Zt  = Lt/σcAt  is the tether resistance and   η × VI   is the ion-thruster output power,  ½ 2exhvm& . We then have 
 
                        System mass  ≈  τm&  +  βWs  +  αt ρAtLt,                                                                               (10)                                
                                                                                          ⊥+= BtLIexhvmF & ,                                       (11) 
 
yielding a mass-to-impulse ratio 
                                       ( )τ
ρασηβτ
⊥+
++++
=
⎟⎟
⎟
⎠
⎞
⎜⎜
⎜
⎝
⎛
BtLIexhvm
tLtAt
tAc
ItLItLmE
exhvmm
impulseMission
massSystem
&
&
&
2
2
2
                    (12) 
 
                                                     
                                                        
i
mEctorbUiorbUexhv
exhv )1(
2/
1
1
2
1
1 μ
σρα
τμτ
β
τη
β
μ
μ
+
×+
+
+×++
+
⇒ ⎥⎦
⎤⎢⎣
⎡
,           (12') 
 
where we defined  μ  ≡ ⊥BtLIexhvm /& . 
            We rewrite  Eq. (12')  as 
 
                                
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ ×××
+
++
+
=×
effexh
v
orbUexhexh
exhv
impulseMission
massSystem
η
η
τ
τ
μτ
τ
μ
μ 2
1
1
1
1
                    (13) 
where 
                                                                                          
imE
i
eff 2~
1
1
1 ++=η .                                                      (14)   
 
We note that for well designed bare tethers, the square bracket in Eq. (8')  reads as the right-hand-side of  (14) with  iav  
replacing  i. 5 
          Cases  μ → ∞   (μ = 0)  correspond to ion thruster (ED-tether) working alone, the right-hand-side of Eq. (13) 
taking the respective forms 
                                                   τ
τ exh+1 ,                                          
⎥⎥⎦
⎤
⎢⎢⎣
⎡
×
effexhv
orbUexh
η
η
τ
τ 2
,                             (15a, b) 
whereas it takes the form 
                                                            
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ ×++
effexhv
orbUexhexh
η
η
τ
τ
τ
τ 2
2
1
1
2
1
                                                     (15c) 
 
for a middle hybrid system,   μ = 1.   The limits of  the expressions in  (15a, b, c)  for long times,   τ  >>  τexh,   are  1,  0,  
and  ½  respectively. The ED-tether is the clear winner. Note that taking into account the small HC-expellant mass 
consumed would just turn the zero limit from (15b), corresponding to an  "infinite specific impulse",  into a  0.01 - 
0.001  value.  
      For   τ  = τexh,   the expressions in  (15a, b, c)  become 
 
 4
                              2,                       [2 Uorbη / vexh ηeff] ,                       1 +  ½ × [2 Uorbη / vexh ηeff],                     (15'a, b, c) 
 
respectively, which are comparable (the square bracket being around unity for present-day ion-thrusters in LEO), 
though the plain ED-tether is still the winner.  Note that the expected reduction in the efficiency  η  of an ion-thruster 
working in the hybrid scheme, and the higher exhaust velocity of future ion-thrusters, will both enhance the advantage 
of the plain ED-tether, though they will increase  τexh  too. 
 
IV. An ED-Tether / Ion Thruster system 
         Consider now the system discussed as example in Ref. 4.  Its ion thruster had 
              specific impulse = 4,000 s,                        thrust   Nexhvm 2.0=& ,   
                                        power    m& vexh2/2η  = 5.7 kw,                  inverse specific power   β  = 1/48 w/kg   ≈ 20.8 kg/kw, 
corresponding to 
                                                 vexh ≈ 40 km/s,          η = 0.7,                 τexh ≈ 39 weeks            ( m&   = 5 × 10-6 kg/s).   
 
The tether was a round aluminum wire with 
                                                                           radius  = 1mm,         Lt = 7 km,             (tether mass ≈ 59.4 kg), 
the current and Lorentz force being 
                                                                        I = 3.2 A,                             ILtB⊥  = 0.44 N,      
corresponding to 
                            μ = 0.45,                                        1/σcAt  ≈ 0.009 Ω/m              ( Zt = 63 Ω) 
and yielding 
                              B⊥ ≈ 0.2  gauss,                   Em  ≈ 0.15 V/m                            (IEmLt  ≈ 3.36 kw,    Zt I2= 0.65 kw) 
  
and finally 
                                  i ≈ 0.194,                                   mE~ ≈ 1.774           ⇒    ηeff   ≈  0.35. 
(With a heavy ion-thruster system at the anodic end,  we set   αt = 2,  making ct βσρα /  ≈ 0.086 V/m.) 
           The right-hand-side of  (13)  here reads 
                                   ⎟⎠
⎞⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛ ××++×
35.0
7.0
40
15
45.1
/
1
45.1
45.0 ττ
τ
τ exhexh , 
 
with a   mass-to-impulse ratio  ≈  40 km/s × 3.2   for   τ  >> τexh.  This was the value given in Ref. 4 as (equivalent)  
specific impulse. Note, however, that it is only valid for  τ  >> τexh;  for such times the (μ = 0) ED-tether's equivalent 
specific impulse,   40 km/s × 4τ /3τexh,   is much greater. Corresponding values for τ  = τexh   would be  40 km/s × 
1.45/1.65  for the hybrid system of Ref. 4,  as against   40 km/s × 4/3  for the plain ED tether.  
       We emphasize here that the  ED-tether would indeed work. A well designed bare tether, to make the bracket in (8') 
read as the right-hand-side of (14), would be a thin tape  (0.1 mm thin,  π/10 mm wide to keep mass and resistance), 
with an upper segment insulated; the greater perimeter would result in increased current collection and ohmic effects. 
Also, the value  i ≈ 0.19  above is far from optimal; the supply power  Ws  should be made to give a current  i  = 1/ mE~  
≈ 0.56,  which yields a maximum  ηeff   in Eq. (14).5 
  
V. Conclusions 
          We have shown that taking fully into account all system masses, and giving due consideration to mission duration, 
the suggested hybrid system is substantially outperformed by ED-tethers for their long-mission niche, and performs 
similarly to ED-tethers and ion thrusters otherwise. The point is that coupling an ion thruster to an ED-tether system 
increases the mass-to-impulse ratio of the ion thruster but decreases the ratio of the ED-tether (enormously so in case of 
very long missions). Independently, the hybrid system appears as much more complex than either ion thruster or ED-
tether working alone. 
 
References 
1  N.H. Stone and C. Bonifazi, Geophys. Res. Lett 25, 409-412 (1998). 
2 J.E. McCoy et al., "Plasma Motor-Generator (PMG) flight experiment results", Proceedings of 4th International 
Conference on Tethers in Space (Washington, 10-14 April 1995) pp. 57-82. 
3  J.R. Sanmartin, M. Martinez-Sanchez and E. Ahedo, J. Prop. Power 9, 353-360 (1993). 
4  D. Nicolini and W.J. Ockels,  "Coupled Electrodynamic Tether/Electrostatic Propulsion System", 28th International 
 5
          Electric Propulsion Conference, Toulouse-France, 17-21 March (2003). 
5  J.R. Sanmartin, R.D.Estes, E.C. Lorenzini and S.A. Elaskar,  "The Efficiency of Electrodynamic Tether Systems", 
          submitted to  J. Space. Rockets. 
6  M. Martinez-Sanchez and J.E. Pollard, J. Prop. Rockets 14, 688-699 (1998). 
7  P. Fortescue and J. Stark, Spacecraft Systems Engineering, J. Wiley (1995), Ch.6. 
 
 
 
 
 
 
 
 
 
Fig. 1 Potentials of tether and ambient-plasma versus distance 
h  from tether bottom 
φ 
φpl 
e− 
I Ions 
φt 
V 
e− 
HC 
I 
IT 
h 
Fig. 2  Same as Fig.1 for power supply at top 
φ 
φpl 
e− I 
Ions 
φt 
V 
e− 
ε 
h 


Performance of coupled ED-tether/ion thrsuter system

Use of propulsion systems that couple electyrodynamic tethers to ion thrusters, as suggested in the literature, is discussed. The system establishes electrical contact with the ionospheric plasma, at the anodic end of the tether, by ejecting ions instead of collecting electrons; also, the ion thruster adds its thrust to the Lorentz force on the tether. In this paper, we analyze the performance of this coupled system, as measured by the ratio of mission impulse (thrust times mission duration) to the overall system mass, which includes the power subsystem mass, the tether subsystem mass, and the propellant mass consumed in the ion thruster. It is shown that a tether acting by itself, collecting electrons at its anodic end, substantially outperforms the coupled system for times longer than a characteristic time of the ion thruster, for which propellant mass equals the power subsystem mass; for shorter times performances are shown to be similar

Performance of coupled ED-tether/ion thrsuter system

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