electropropulsion of space vehicles

1

AE4451 PropulsionElectric Propulsion-1Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.

Electric Rocket Propulsion

A. Background


Electric Propulsion - Accelerators

Electrostatic,Static electric field alone accelerates charged particles

Lorentz,Magnetic and elec.

fields accelerate charged particles

Pressure,Electrically heat

propellant and use nozzle expansion

Accel. Force

<10-4−10-6<10-4<10-3

2,000-100,000+1,000-10,000300-1,500Isp(s)

ElectrostaticElectromagneticElectrothermal

eFr

mFr

p∇

WeightThrust

2


Electrical Heating

• Current passing throughconductor heats it byamount proportional toits resistance

• Wire

• Gas (Plasma)Discharge– resistance due

to collisions

RJQ 2=&

Current (A=C/s)

Resistance (Ohms)

J

Cathode Anode

e- i+J

VE ∇−=rr V E

r


Forces on a Charged Particle

• To examine how to use electrical energy to accelerate a propellant, consider acceleration of a particle with mass m and charge q

( ) pBuqEqdtudm rrrrr

+×+=Electrostatic

ForceLorentzForce

Collisional Force (Momentum Transfer)

Er

qeFr

+

Brq mFr

+ur

`

ur

Br

mFr

Elec. Field Mag. Field

(1)

3


Motion of Charged Particle in E&B Fields• How does charged particle move in electric

and magnetic fields• Electric field only

– electron lighter, higher accel.• Magnetic field only

– particle gyrates(centripedal accel.)

– radius of gyration– frequency of gyration

– No work; B and F perpendicular

Emq

dtud rr

=

( )Bumq

dtud rrr

×=

Er

+-

urBr

rg2qBBum

rg

rr×=

mqB

g =ω


Jr

Br

Induced Magnetic Fields

• In general, current flow induces a B field– B field induced by

linear current

– B field inducedby coil

Br

From Space Propulsion Analysis and Design, Humble, Henry and Larson, 1995

4


Motion of Charged Particle in E&B Fields

• Crossed E and B fields– E field accelerates

particle upward– B field causes

accelerationperpendicular to u

– overall result is driftvelocity normal to E and B

Er

Br

durheavy

light

2BBEud

rrr ×=


Plasmas• Gas composed of equal “amount” of negatively

and positively charged particles– electrically neutral– negative particles usually e-

– positive particles are positive ions– typically most of gas molecules remain

neutral• Momentum equation for plasma

Bjpuutu rrrrr

×+−∇=

∇⋅+

∂∂ρ

Current Density (A/m2)

5


Induced E Fields – Hall Effect• Electron acceleration

– lighter e- accelerate more quicklyand accommodate to flow field (most of j)

– collisional coupling (momentum) of electrons and heavies (ions and neutrals) is weak

plasma resistivity (Ωm)

enp

enBjBujE

e

e

e

∇−×+×−=⇒r

rrrrrη

Hall Effectaccelerates heavyparticles in charge

neutral plasma

2envm ecee=η

(2)

InducedE field dueto plasmamotion

electronpressure

termcollision freq.

electrons with heavies


Electric Rocket Propulsion

B. Examples

6


Electrothermal Rockets• Resistojet (1W-10kW)

– walls hotter than gas,lower Tmax

– can combine withchemical heating, e.g.,hydrazine monopropellant

• Arcjet (1 kW- 10 MW)– high Tarc>Twall

(1-4×104 K)– must mix with

rest of gas– very high To,

frozen flow losses in nozzleSpace Propulsion Analysis and Design,

Humble, Henry and Larson, 1995

Insulation

arc unstable


Resistojets• Heating methods

– flow over coils of wire– flow through hollow tubes– flow over heated cylinder or plate

• Material limits temperature/performance– conducting materials < 2700 K

rhenium, refractory metals/alloys (tungsten, tantalum, molybdenum), platinum, cermets

– max Isp ~ 300 sec• Power supply

– AC or DC– Power TcmRVQ p∆=== && 2

7


Arcjets• Gas heated by electrical discharge (arc)

– electrically conducting gas: plasma• Joule heating

• Nozzle and electrode erosion– high temperature, current arc

• Isp for H2 ~1200-1500 sec

TcmEjQ p∆=⋅= &rr

&

( ) enpjBujj ee∇⋅−×⋅−=rrrr

2ηenp

enBjBujE

e

e

e

∇−×+×−=r

rrrrrη

Hall Effectnormal to j

Resistive Heating

Work fromEM force

( ) enpjBjuj ee∇⋅−×⋅+=rrrr2ηWork from

pressure grad.

from (2)

no work


1.8 kW Hydrazine Arcjet

Space Propulsion Analysis and Design, Humble, Henry and Larson, 1995

• Telstar IV application– stationkeeping

• Hot gas from catalytically decomposed liquidN2H4

• Heated valveprevents N2H4from freezing

• Isp~570 sec• τ~230 mN

(~40mg/s)

8


Arcjet with Applied Magnetic Field• High current density in arc

tends to destroy electrodes• Add soleniod B Field

– adds azimuthal driftvelocity to arc

– improves azimuthalsymmetry of gas temperature

– reduces local electrodeheating, reduces erosion

– needed for high powers(≥100 kW)

• Microwave discharge– alternate to arc heating Space Propulsion Analysis and Design,



Electromagnetic Propulsion Systems • Use applied or induced magnetic fields to

produce acceleration of propellant– high currents/

powers requiredto produce significant induced fields

– high power availableonly (normally) inpulsed operation


9


Pulsed Plasma Thruster

• Propellant produced by vaporizing solid material with discharge

• B field induced by discharge also acts to accelerate vaporized propellant

• Advantage of simplicity• Acceleration

force~ j2

(discharge current)



Magnetoplasmadynamic (MPD) Thrusters• Resemble arcjets• Lower flow densities to

attain higher exhaust velocity

• Diffuse discharge,low erosion

• Self field requires high J• Applied B field

– allows higher Vat lower discharge currents

– increase accel.– larger Hall effect

Self-Field MPD Thruster

Applied-Field MPD ThrusterSpace Propulsion Analysis and Design,


10


MPD Thrusters (con’t)

• Most efforts focused on applications with exhaust velocities (Isp) greater than arc jets

• Typically require higher powers than currently available on in-space vehicles

• Exhaust speed– limited by erosion

and oscillations at high j

mjue &2∝


Hall Thruster

• Hall effect most noticeable at low particle densities

• Stationary Plasma Thruster (SPT)– developed in Russia– 10’s kW– axial current flow

across radial Bgenerates azimuthal electron flow

– induced (axial) Hall Eaccelerates ions

– also called “gridless” (neutral) ion thruster

– 1500-2000 s Isp with >50% efficiency using Xe and no oscillations like MPD Space Propulsion Analysis and Design,


11


Electrostatic Thrusters• Ion engine example• Near vacuum required• Ion source

– usually electronbombardmentplasma

– also ion contact: propellant flowingthrough hot poroustungsten

– field emission: chargedspray droplets/particles

• Electrons added toneutralize exhaust– thermionic emitters


L

A

Accelerator


Electrostatic Thruster Performance• Maximum exhaust velocity (Isp)

theoretically limited by voltagedifference across accelerator

• High thrust requires high mass flowrates and therefore current(and number, n) densities

• Ion current limitedby space-charge– field from lots of ions

overcomes appliedE field

( )inletexite VVmqu −= 2

enquj =

2

23

max

29

4LV

mqj o ∆= ε

sm

MWV )volts(800,13 ∆=

for singly ionized

meterFarad

o1210854.8 −×=εpermittivity

of free space

Child-LangmuirLaw

accelerator electrodespacing

( ) 22

238

max m)volts(1044.5

mAmps

LMWVj ∆×= −

for singly ionized

12


Electrostatic Thruster Thrust

• Maximum thrust

• High τ requires high ∆V and aspect ratio– space charge⇒D/L ~1– use many small ion beams to

get more thrust

( ) ee uqmjAum == &τ

euqmAjmaxmax =τ V

mq

qmA

LV

mqo ∆∆= 22

94

2

23ε

( ) 22max 98 LVAo ∆= ετ

A=cross-sectional area flow

for circular cross-sectionof diameter, D ( ) ( ) 22

max 92 VLDo ∆= επτ( ) NewtonsVLD in1018.6 2212 ∆×= −

DL


Electrostatic Thruster Thrust• For fixed specific impulse

– best propellant for high thrust• heavy molecules (particles)• xenon (Xe) good choice (MW=131.3)

esp uI =

qmA

∝maxτ

spaccelo

IqmA

LV

mq

2

23

max

294 ∆=ε

τ

13


Electrostatic Thruster Power

• Electrical energy converted to kinetic energy with some efficiency

• Must also account for energy used to create ions – ionization losses– given by ionization potential for atom

times current

VjAVIPower ∆=∆=

2

21

econv umVI &=∆η

qmmIP IIlossion

&εε ==


Electron Bombardment Xe+ Engine Example

• Operating conditions– ∆V=700 V, L=2.5 mm, 2200 holes (grids)

each with D=2.0 mm– MW(Xe)=131.3, εI(Xe)=12.08 eV

• Determine– τ, – ue, Isp– m– power required including ionization loss

.

14


Solution( ) 2212

max 1018.6 VLD ∆×= −τ( ) gridN /1094.17005.2/21018.6 62212 −− ×=×=

( ) mNgridNgridstotal 3.4/1094.12200 6,max =×= −τ

smsmMWVue 3.131700800,13800,13 =∆=

smue 860,31= sIsp 3248=⇒

sgum e41034.1 −×==τ&

mmqumPPP Ielossionexhaust && ε+=+= 22kg

kgMWm25

27

1019.21067.1

−

−

×=×=

Cq 1910602.1 −×=for singly ionized molec.

WW 18.19.67 +=WP 1.69= maximum effic. =67.9/69.1

= 98.3%

electropropulsion of space vehicles

Documents