by Leonid Dorf

Presented at Plasma Physics Summer School Presented at Plasma Physics Summer School August 2, 2006, PAugust 2, 2006, P--24 Plasma Physics Group, LANL 24 Plasma Physics Group, LANL

kB E

e– i+

P-24Plasma Physics

Special thanks to: Hall Thruster eXperiment at PPPL (go to URL: htx.pppl.gov), and Jahn, R. G. and Choueiri, E. Y. (2002). Electric Propulsion. In Encyclopedia of Physical Science and Technology, 3rd Edition (Academic Press, San Diego), Vol. 5, p. 125.

Electric propulsion (EP) devices utilize a constantly renewable on-orbit resource (electric power from solar arrays or a nuclear source) to minimize the consumption of non-renewable on-board propellant. The EP techniques group broadly into three categories: electrothermal propulsion, wherein the propellant is electrically heated, then expanded thermodynamically through a nozzle; electrostatic propulsion, wherein ionized propellant particles are accelerated through an electric field; and electromagnetic propulsion, wherein current driven through a propellant plasma interacts with an internal or external magnetic field to provide thrust. Such systems can produce a range of exhaust velocities and payload mass fractions an order of magnitude higher than that of the most advanced chemical rockets, which can thereby enable or substantially enhance many attractive space missions. The attainable thrust densities (thrust per unit exhaust area) of these systems are much lower, however, which predicates longer flight times. This talk will focus mainly on the electrostatic and electromagnetic propulsion techniques, also called plasma propulsion, due to the nature of the propellant. Principles of operation, key issues, and commonly used diagnostics are discussed in detail for such complex devices as magnetoplasmadynamic thruster (MPDT), pulsed plasma thruster (PPT), ion thruster (IT), Hall thruster (HT), cylindrical Hall thruster (CHT), VASIMR, and others. Key physical questions specific to Hall thrusters are also elucidated.

Abstract

Outline

Basic Concepts and Equations of Propulsion

Types of Plasma Propulsion

Electrothermal propulsion

Electrostatic Propulsion: Ion Thrusters

Electromagnetic Propulsion: MPD, PPT, TAL, VASIMR, HT, CHT

Hall Thruster Diagnostics: plume divergence, electron temperature, etc

Anode Sheath in Hall Thrusters

Rocket Equation

Vjet - V ∆m M - ∆m

Time = t Time = t + ∆t

M(t)V(t) V + ∆V

Momentum Conservation: P (t) = Const

Px(t) = M V

Px(t + ∆t) = (M – ∆m) (V + ∆V) – ∆m (Vjet – V) = M V + M ∆V – ∆m Vjet

∆m = µ ∆t

X

M dV/dt = µ Vjet – Rocket (Mescherskii’s) Equation

V(t) = Vjet ln[M0 / M(t)] – Tziolkovskii’s Formula

Electric Propulsion = Large Exhaust Velocity

32 /fuel sat jetM M P S Vη≈

2 /flight jet satt V M S Pη≈

Earth

Jupiter

Vjet (plasma) ~ 10 – 100 km/s >> Vjet (chemical) ~ 3 km/s

Interplanetary Missions:

Higher Vjet LESS FUEL (but longer time)

S

Limit on Exhaust Velocity

Vorbit 1

V + ∆V||

Earth

Vorbit 2 = V + ∆V

On-Orbit Station KeepingmN-level plasma thrusters are perfect for orbit correction tasks (precise, short-duration kicks)

/ satV T t M∆ = ∆

Limit on Vjet is set by mission time requirements

2 / jetT P Vη=

Types of Electric Propulsion

1. Electrothermal propulsion, wherein the propellant is heated by some electrical process, then expanded through a suitable nozzle

a. Resistojetsb. Arcjetsc. Inductively and radiatively heated devices

2. Electrostatic propulsion, wherein the propellant is accelerated by direct application of electrostatic forces to ionized particles

a. Ion Thrusters (IT)b. Field Emission Electric Propulsion (FEEP)c. Colloidal Thrusters

3. Electromagnetic propulsion, wherein the propellant is accelerated under the combined action of electric and magnetic fields

a. MagnetoPlasmaDynamic (MPD) Thrustersb. Hall Thrusters (HT)c. Pulsed Plasma Thrusters (PPT)d. Inductive Thrusters

1960 1970 1980 1990 1994 1998

Electric Propulsion in US and USSREr

nst S

tuhl

inge

r’s b

ook

“Ion

Prop

ulsi

on fo

r Spa

ce F

light

”

Resi

stoj

ets

beca

me

com

mon

opt

ions

for s

tatio

n ke

epin

g an

d at

titud

e co

ntro

l

Hall t

hrus

ters

hav

e be

en u

sed

on S

ovie

t and

Russ

ian

spac

ecra

ft si

nce

the

mid

-197

0s

Elec

troth

erm

al a

rcje

ts w

ere

adop

ted

for N

SSK

of m

any

com

mun

icat

ion

sate

llite

s in

GEO

1st us

e of

ion

thru

ster

s fo

r NSS

K

DEEP

SPA

CE 1

< 10 >10 > 10010s

Electrothermal ResistojetHeat is transferred to propellant (hydrazine) from some solid surface, such as chamber wall or heater coil

Power level: 750 WattsThrust level: 300 mNExhaust velocity: 3.5 km/sEfficiency: 80 %

Cathode (emitter) Anode (nozzle )Tangentialgas flow

Propellant (hydrazine) is heated by an electric arc driven through it

Power level: 1.5 kWThrust level: 200 mNExhaust velocity: 5 – 6 km/sEfficiency: 40 %

Electrothermal Arcjet

Glossary of Plasma Propulsion

[ ] cos ii i ioniz jet

MT mN V I Ve

µ η= ⋅ Θ ⋅ ⋅ =THRUST

SPECIFIC IMPULSE [ ] jetsp

VI s

g=

212i W c

in

T

m Pη η η η •= ⋅ ⋅ ≈ ⋅

⋅

IONIZATION EFFICIENCY

cos

( , ) ( , ) cos

( , ) ( , )( )

( )

ndef

ioutwards

n

ioutwards

d j

d jΘ

Ω Θ Θ Θ

Ω Θ Θ=

⋅ ⋅

⋅

∫

∫

ϕ ϕ

ϕ ϕπ

π

2

2

ηii

m

II

=

ηWi i i

in

M V IP

=⋅ ⋅ ⋅ < >1 2 2 2/ cos Θ

PLUME DIVERGENCE

ENERGY EFFICIENCY

THRUST EFFICIENCY

Ion Thrusters (Xe, Ar, Kr)

launched from Cape Canaveral on October 24, 1998. Deep Space-1 Ion Engine Images

Isp = 1500 – 4000 s Diam = 2.5 – 150 cm P = 50 W – 200 kW

In the US, ion engines were developed at NASA’s Lewis Research Center in the late 50-s under the guidance of Dr. Harold Kaufman. Flight experiments started from 1965.

Electrostatic Acceleration of Ions by Applied DC Voltage

1/ 2 3/ 20

24 29

q VjM d

ε ⎛ ⎞= ⎜ ⎟⎝ ⎠

Child-Langmuir law limits maximum ion current densitythat can be extracted from ionization stage (ion source)

PLASMA PLASMA

IONS ONLY

208

9jet ion jetmV jM VT V

A A q dε ⎛ ⎞= = = ⎜ ⎟

⎝ ⎠

1/ 22

jetion

qVVM

⎛ ⎞= ⎜ ⎟

⎝ ⎠

Maximum thrust density does notdepend on the mass flow rate

Key Issue of Ion Thrusters

Accelerator gridUpstream side

normal

normal

damaged

damaged

Accelerator gridDownstream side

normal

damaged

Screen gridDownstream side

Soulas, G. C., “Improving the Total Impulse Capability of the NSTAR Ion Thruster with Thick-Accelerator Grid Ion Optics,” IEPC-01-081

Y. Hayakawa, S. Kitamura, and K. Miyazaki. Endurance Test of C/C Grids for 14-cm Xenon Ion Thrusters. AIAA 2002-3958

Grid erosion due to ion bombardment limits thruster lifetime

Ion Thruster Diagnostics

(Non-Intrusive )

Laser-Induced Fluorescence –for measurements of ion velocity and energy

Laser Interferometry –for measurements of electron, ion, and neutral densities

Spectrographic analysisof quartz crystal microbalances and fused silica samples placed in the plume –for determining the content and origin of the non-propellant flux coming out (erosion assesment)

Schematic of the cw diode laser system(NASA GRC)

Ion Thruster Diagnostics (Intrusive )

High Speed Axial Reciprocating Probe (HARP) positioning table (probes can’t spend much time inside thruster)

Double and single Langmuir probes wereemployed at PDEPL (Michigan) to measure2-D electron temperature and density profilesinside the IT, which can give an insight to the issue of Discharge Cathode Assembly (DCA)erosion – another lifetime limiting process in IT.

E&M Propulsion: MPD ThrustersI sp = 1500 -8000 sec Power: 200 kW – 1 MW

Efficiency > 40% Thrust Density: 105 N/m2

Princeton 100 kW-class Lithium Lorentz-Force Accelerator (MPD-T)

Simple Thrust Formula for MPD Thrusters

I (z)

r

z

θ

1. ( , ) ( , )z rdF j z r B z r dVθ= − 0 ( )2. ( , )2I zB z r

rθµ

π≅

3. 2c cdI j rdz

π=( )4. ( , ) c c

rj z rj z r

r≅

( ) 20 0

0 0

5. 2 ln2 4

a a

c c

r rL Lc

r totar r

dI dr rT dz rdr j B dz I Idz r rθ

µ µππ π

= = =∫ ∫ ∫ ∫

20 ln4

ctot

a

rT I Ar

µπ

⎛ ⎞= +⎜ ⎟

⎝ ⎠

A ≤ 1 – geometrical factor

Pulsed Plasma Thrusters

In Ablative Pulsed Plasma Thruster (APPT), the surface of a Teflon©

block is successively eroded by intermittent arc pulses driven across its exposed face, and the ablated material is accelerated by a combination of thermal expansion and self-field electromagnetic forces.

Efficiency ~ 15 – 20%Isp ~ 5000 sec

Small power systems to drive plasma thrusters in short (10-usec) bursts of high instantaneous power (10 MW).

Flight-ready Teflon APPT module with 2 thrusters

APPT #1APPT #2

Variable Specific Impulse Magnetoplasma Rocket (VASIMR)

Vjet = 0 – 300 km/s

1. Neutral gas (hydrogen) is injected into the forward cell, where it is ionized. 2. The resulting plasma is then heated in the central cell, to the desired temperature

and density, by use of radio-frequency excitation and ion cyclotron resonance.3. Once heated, the plasma is magnetically and gas-dynamically exhausted by the

aft cell (asymmetric magnetic mirror = magnetic nozzle) to provide modulated thrust.

ELECTRODELESS !

Hall ThrustersPPPL

Buzek ClusterP5 Cluster

Michigan PDEPL:

12.3 cm HT

PPPL

12.3 cm HT

Power = 0.2 – 3 kW

Voltage = 0.1 – 1 kV

Current = 2 – 5 A

µ (Xe) = 2 – 5 mg/s

Vjet = 15 – 25 km/s

Thrust = 40 – 80 mN

Efficiency ~ 50%

Hall Thruster is an ExB Discharge Device

IH

CATHODE (neutralizer)

Magnetic coils

ANODE(gas distributor)

Magnetic core

Plasma jet

Ceramic walls

rLi >> Lchannel >> rLe

Hall Thruster Experiment at PPPL

2 kW Hall Thruster

Planar ProbeFor Plume

Measurements

Two-Plate EnergyAnalyzer

Probe ApparatusFor Near-AnodeMeasurements

Fast-ReciprocatingProbe Apparatus

Hall Thrusters Diagnostics (LIF and HF)Laser-Induced Fluorescenceapparatus was developed and used at Stanford Hall Thruster Facility (Plasma Dynamic Laboratory) for neutral velocity measurements in the near plumeto gain a better understanding of the charge exchange process in Hall Thrusters.

123

4

1 – well with the capsule inside,

2 – thruster, 3, 4 – probe connectors

probe connector design

High-Frequency (HF) probe diagnostics weredeveloped and employed at HTX (PPPL)to characterize 1 – 100 MHz plasma densityoscillations through measuring ion saturationcurrent near the thruster exit.

PPPL 9cm-Diameter Cylindrical Hall Thruster

Cathode

9 cm

BN channel

Anode/gasdistributor

Magnetic core

Power range: 200 – 1000 W

Discharge voltage: 200 – 300 V

Xenon mass flow rate: 1 – 3 mg/s

Thrust: 13 – 40 mN

Efficiency: 30 – 45 %

Channel OD = 9 cm

Cylindrical Hall Thruster has larger volume to surface ratio than conventional thrusters

N

N

E

B

AnodeCathode-neutralizer

Electromagnets

B

Ceramic channel

Ve

S

N

S

Annular part

• Electron drift is azimuthal ⇒closed drift

• Ion axial acceleration ∼ Ieθ x Br

• In a short annular part the density of neutrals is higher ⇒better for ionization

• Length of the annular region ∼ λion

• Compared to a conventional (annular)Hall thruster, the CHT has lowersurface-to-volume ratio ⇒potentially smaller wall losses in thechannel

Key Problem of Hall Thrusters

PPPL 1 kW HT PPPL 1 kW HT with S.E. PDEPL P5 HT (Michigan)

Large plume divergence (~90 deg) decreases thrust and efficiency. Most importantly, it limits lifetime of the satellite – ion bombardment

damages solar panel dramatically. Outgoing plasma jet may also interfere with radio-communication between the ground control and the satellite.

Controlling Plume with Segmented Electrodes Anode Cathode

B E

Segmented electrodes(localize potential drop -reduce beam divergence

30

35

40

45

50

55

150 200 250 300 350

Discharge Voltage, V

Hal

f Plu

me

angl

e, d

eg

WS

NS1 floating

NS1 cathodebiasNS2 floating

NS2 cathodebiasNS3 floating

NS3 cathodebias

Single electrode configuration

Anode mass flow rate = 1.7 mg/sProbe

1 kW HT

Segmented Electrode

Grooves (anti-sputtering)

Temperature Profile in Hall Thrusters

Te = β φplβ = 0.08 – 0.14

1. In acceleration region:

Discharge Voltage, VMax

imum

Ele

ctro

n Te

mpe

ratu

re, e

V measured

µ = 5 mg/s

RESULTS:

2. Maximum electron temperaturesaturates with discharge voltage

Anode Sheath = Adjoint Space-Charge Layer

Positive Anode Fall = Electron-attracting Anode Sheath

z

V e

V i

Ano

de p

lane

Neg

ative

fallPo

sitive

fall

Cat

hode

pla

ne

( )zϕ

Cha

nnel

exi

t pla

ne

Sheath

Negative Anode Fall = Electron-repelling Anode Sheath

-7-5-3-113579

11

0 2 4 6 8 10 12 14

Distance from Anode, mm

Plas

ma

Pote

ntia

l, V

At channel median = 5 mg/s = 0, biased probe

CLEAN ANODE = NEGATIVE ANODE FALL

COATED ANODE = POSITIVE ANODE FALL

m anϕ

Decreasing Anode Area Reverses Anode Fall

400 V

300 V200 V

400 V

300 V

200 V

CLEAN ANODECOATED ANODE

Decreasing Anode Collecting Surface Area Manifests Itself

Positive anode fallNegative anode fall

Hall thruster operation appears to be MORE STABLE WITH COATED ANODE

(i. e. with Electron-Attracting Anode Sheath or Positive Anode Fall)

0

0.2

0.4

0.6

0.8

1

150 200 250 300 350 400 450

Rel

ativ

e O

scill

Am

pl

Discharge Voltage, V

Coated Clean

3 mg/s

3 mg/s

5 mg/s

5 mg/s

Discharge Current Oscillations Measurements

Formation of an electron-repelling anode sheath (negative anode fall)is required to repel an excessive electron thermal flux from the anode.

Negative Anode Fall Formation Mechanism

Electron-neutral collisions are very weak near the anode, so is the magnetic field in the conventional configuration.

cm12~ ≈ΛΛ nnen

AN

OD

E thermal

thermal

thermal

e

eeSH

EATH Id

Additional electron flux gets drawn into the anode by the electron-attracting sheath that appears at the inner, metal anode surfaces.

conductivesurface

stainlesssteel anode,

Φan = 0

Φplasma ~ – 6 V

ANODE

CAVITY

e–

e–

Id

only 40%of discharge

current

dielectriccoating

ΛD ~ 0.075 mm ∆B = 0.6 mm

Thermal electroncurrent constitutes

Positive Anode Fall Formation Mechanism

Axis of symmetry

Φ pl

, V Z, mm

-6

-4

-2

0

2

4

0 2 4 6 8 10 12

OW

IW

MC

B negΦ

pl,

V

Z, mm4

6

8

10

12

0 2 4 6 8 10 12

OW

IW

MC

B 0

Φ pl

, V

Z, mm

-202468

101214

0 2 4 6 8 10 12

OW

IW

MC

B pos

B0 Bpos

Zero-B-Field Configuration = Reversed Fall

ANODE FALL IS POSITIVEANODE FALL IS POSITIVE

Vd = 300 V; m = 3 mg/s; Z = 0 = Anode; Φ = 0 = Anode

Bneg

ANODE FALL IS NEGATIVEANODE FALL IS NEGATIVE

0

5

10

15

20

25

30

0 1 2 3 4 5 6 7 8 9Distance from Anode, cm

Elec

tron

Tem

pera

ture

, eV

B0

Bpos

Bneg

Quasi-1D Model

300VdV = 3mg/sm =

1. Input parameters:

2. System of fluid equations for 3-species (e, i, n) quasineutral plasma. Includes ion wall losses terms “quasi-1D”

03 profiles ( ), , , = = Experimental values

r dB z I n sheath

3. Fitting parameter, α, for electron cross-field mobility, µe: ( )16erB z

αµ =

Boundary Conditions

There is only one value of α, which allows a

solution to be regular at the sonic transition point: Vi = Vs .

Reduced system: ( , , , )i i d edJ dz F J n I µ=

2 2( , , , ) (1 )i d e i sdn dz G J n I V Vµ= −

0, ,dI n Experimental=0

0

, and

0,s pos

ineg

V B BV

B

−⎧⎪= ⎨⎪⎩

( )16erB z

αµ =

( )0

( )cathL

d cathode dE z dz V L V= ⇒∫