EXTROVERT
Space Propulsion 13
Electric Propulsion Continued
EXTROVERT
The "jet" or exhaust power (Pjet) of any thruster is:
Space Propulsion 13
Pjet = 1/2 gc Isp F
Thus, for a situation where we wish to fix the thrust at a constant value, as specific
impulse increases, the jet power must also increase.
Jet power is in turn a function of the total "bus" electric power (Pe) and the overall
efficiency (h) of converting electric power into jet power:
Pjet = Pe h
..The mass of the electric power system (as well as power conditioning and
thrusters) is proportional to the total "bus" electric power:
Mpower = a Pe
where a is the overall system specific mass (typically in kg/kW electric). Finally, ..
M0 / Mb = exp (DV / gc Isp)
The propellant mass (Mp) is simply the difference between M0 and Mb:
Mp = M 0 - Mb
EXTROVERT
Space Propulsion 13
Designing Electric Propulsion
Path A: Power Source Based on Chosen Thruster and Mission
Specify Mission – Select Thruster – Select Power Source
Design Thermal Mgmt System – Design Power Conditioning System –
Assess Performance
Path B: Power Source Based on What is Available from Spacecraft
Specify Mission –Select Power Source - Select Thruster –
Design Power Conditioning - Design Thermal Mgmt System –System –
Assess Performance
EXTROVERT
Space Propulsion 13
Optimum Specific Impulse
Courtesy: Robert.H. Fris
http://www.islandone.org/APC/Electric/impulse.gif
EXTROVERT
Space Propulsion 13
System Analysis
Thrust or Jet Power:
mi
Pj 
.
mpUe 2
mdotp, mass flow rate
of propellant
2
: Initial mass
Required source power
System inert mass
Ps 
Pj
T
minert   Ps 
Ps

Specific mass of propulsion system (Kg/W)
:
 : Specific power of propulsion system (W/Kg)
EXTROVERT
Space Propulsion 13
If thrust duration (assuming constant thrust) is
.
mp 
,
mp

 Ue m p

2T 
2
minert
mpay  mf  minert

mpay
mi
e
DV
Ue
where
mf
is final mass achieving
DV 

2
Ue   Ue

 1 e

 2T 


DV
EXTROVERT
Space Propulsion 13
Design goal: maximize payload mass fraction. Define:
T 

U0
DV
DV 
U0
*
Ue

*
U

U0
DV *
mpay
Ue*
e
mi

DV * 
 *2
1
Ue*
 1  e
 Ue
2



EXTROVERT
Space Propulsion 13
Propulsion system mass per unit of jet power:
Jet-specific mass

1
j 

T T
Optimal exhaust speed:
Ue0
Where k ~ 1

k
j
EXTROVERT
If  j is too high, or the allowable thrust time is too low,
optimum speed may be less than that from chemical
rockets.
Space Propulsion 13
May still use electric propulsion for missions with electric
power supply;
Primary electric propulsion will not benefit from power system
sharing until it is a large scale mission with many MW of power
Possible uses -> station-keeping (no benefit to impulsive thrust)
-> lifting large structures (low g; continuous thrust)
 DV  2.3DVimpulsive 
-> Electric primary propulsion needs
with modern chemical system
1000s to compete
I>sp
Isp(450s)
EXTROVERT
Space Propulsion 13
Specific Impulse Ranges
Electrothermal:
500 – 1000 s
Electromagnetic: 1000 – 7000s
Electrostatic:
2000 – 100,000s
EXTROVERT
Space Propulsion 13
Electromagnetic Propulsion
Electromagnetic force per unit volume on a gas carrying
current in a magnetic field
Fm  j  B
B
magnetic induction field in gas (Tesla)
j
Electric current density In gas (A/m2)
Fm
N/m3
EXTROVERT
Space Propulsion 13
Electromagnetic Propulsion Systems
Unsteady vs. Steady
Self-field vs. Applied Field.
Self Field:
Discharge currents whose own magnetic fields are high enough
for efficient thruster performance without needing external applied
magnetic fields. High power (MW)
Available in short pulses from capacitor bank: unsteady operation.
EXTROVERT
Z-Pinch and q-Pinch Engines
Space Propulsion 13
z -Pinch Engine: Current has component parallel to axis of symmetry.
q-Pinch Engine: Current is in azimuthal direction
In both, current and self-fields combine to implode (pinch) plasma
Gives 10 – 40 km/s velocity.
(See Humble, Fig. 9.11)
EXTROVERT
Pulsed Inductive Thruster
Space Propulsion 13
Coil and plasma currents are azimuthal; magnetic field is radial.
Plasma accelerates parallel to axis of symmetry
Ablation-supplied propellant for pulsed operation. See Fig. 9.12, Humble.
www.islandone.org/ APC/Elec
http://www.airpower.maxwell.af.mil/airchronicles/aureview/1973/Nov-D
EXTROVERT
Pulsed-Plasma Microthruster
Space Propulsion 13
www.mae.cornell.edu/ campbell/mp
EXTROVERT
Magnetoplasmadynamic Thrusters
Space Propulsion 13
Discharge current interacts with its own magnetic field to accelerate
flow axially and radially.
At low particle density, electromagnetic force density greatly exceeds
pressure gradients in the gas.
“J × B Lorentz body force
compresses and
accelerates a quasineutral plasma along the
central axis.
Because self-induced
magnetic field is only
significant at very high
power, low power MPD
thrusters often resort to
an externally applied
magnetic field in order to
enhance the acceleration
process (applied field
MPD thrusters).”
http://fluid.ippt.gov.pl/sbarral/pics/mpd_thruster.jpg
EXTROVERT
Space Propulsion 13
Hall Effect
Applied magnetic fields increase electromagnetic forces in plasma. They also force current
to flow in spiral paths, increasing the total voltage.
Hall effect is evident in electromagnetic thrusters at low particle density.
Xenon with radial magnetic field and axial current flow from an upstream anode: Stationary
Plasma thruster.
5-20 KW; Isp 1500 – 2000 s; high efficiency.
Axial current across radial magnetic field generates azimuthal electron flow. Internal Hall
electric field in axial direction transmits axial e-mag force on electron flow, to plasma ions.
Charge-neutral device.