Ion acceleration by beating electrostatic waves

Edgar Choueiri

Electric Propulsion and Plasma Dynamics LabPrinceton University

Seminar at the Michigan Institute for Plasma Science and EngineeringThe University of Michigan

November 17, 2010

Acknowledgements

Ben Jorns (GS)Slava Spektor (GS)

Avi Ziskind (UG, Physics)Julia Ling (UG, Physics)

Buddy Gardineer (UG, MAE)

Bob Sorenson (Tech Staff)

Supported by AFOSR, DOE, NSF and NASA

Can nature inspire us a new plasma propulsion concept?

Why is it promising?

Under what conditions can it occur?

How does it work?

Can it be replicated in the lab?

Can nature inspire us a new plasma propulsion concept?

B

0.3 eVOxygen ions

10 eVOxygen ions

ES Waves

Bz = const

y

z

x

E,v

€

˙ ̇ x +ωci2 x =

qm

Ei cos(kix −ω it)i∑

θ

Bz = const

y

z

x

q, m

rL

Ion Acceleration by ES Waves

Bz = const

y

z

x

E,v

Ion Acceleration by ES Waves

Bz = const

y

z

x

E,v

Ion Acceleration by ES Waves

Bz = const

y

z

x

E,v

Ion Acceleration by ES Waves

Bz = const

y

z

x

E,v

Ion Acceleration by ES Waves

Two Beating waves: ω1-ω2=nωc

y

z

x

Why is it promising?

y

z

x

Two Beating waves: ω1-ω2=nωc

vv

f(v)

ω/k

Δv

vv

f(v)

ω/kv

Δv

BEW

SEW

Under what conditions can it occur?

200

150

100

50

0

Ion

Vel

ocity

500040003000200010000Time

ε = 49

ε = 50

No

Does it always occur?

Are there Necessary and Sufficient Criteria for Acceleration?

yesSpektor & Choueiri, Physical Review E, March 2004

aaa

PPDyL

Approach

Hamiltonian

Numerical Solution:Symplectic IntegrationAlgorithm

J. Comp. Phys. 92 230 (1991) Analytical Solution:

2nd order perturbation theory + Lie transformations

Phys. Plasmas 3(5), May 1996, 1545

Poincare surface of section (Reduced phase space diagram)

∑ −+=i

iii

iH )sincos(2

2

τνθρκκερ

time

ρ,θ

ρ0,θ0

200

150

100

50

0

Ion V

elocit

y

500040003000200010000Time

ε = 49

ε = 50

60

50

40

30

20

10

0

ρ

6543210θ

ε = 50

Poincare Cross Section

Numerical Simulation 2nd-order Perturbation Theory

Spektor & Choueiri, Physical Review, E, 69(4):Article No. 046402, 2004.

Can it be replicated/verified in the lab?

Transverse Helmholtz Antenna

Transverse Helmholtz antennaAntenna carriage

Configuration Transverse Helmholtz*

Power Supply 100W ENI

Matching circuit None

Frequency 1.92fci

Max RMS Field 15 G

€

ω 2 =ω ci2 + k 2 Te

m

ParametersParameters

RF Power 250 W (13.56 MHz)

Mag. Field (B) 500 G

fci 19 kHz

PB ~1 mT Argon

Ti 0.09 eV

PA 30 W

ne 1011 cm-3

Plasma Characterization

Dispersion Relation

!

"zTeTe

ri <<1

!

"zTeTe

# <<1!

"rTeTe

ri <<1

!

"rTeTe

# <<1

Plasma is uniform

Laser Induced Fluorescence System

Ar II transition

668.6130nm

4p4D05/2

4s4P3/23d4F7/2

442.72nm

Ion Heating in BWX II

MAXIMUM HEATINGMAXIMUM HEATING

SEW 55 ± 12%

BEW 90 ± 17%

BEW is unambiguously superior

Possibility of improving result

9/2010

Karney

1976

S3-3

1978 1998

Benisti et. al

2004

2006 2009 2010

BEW Heating

2010

Directed ion acceleration

Spektor and Choueiri.

Geometry: magnetic slope

Field magnitude

Geometry of system 2δ

BEW in a magnetic slope

BEW in a magnetic slope

1. Guiding centers move toward magnetic null

BEW in a magnetic slope

1. Guiding centers move toward magnetic null

2. Larmor radius increases

BEW in a magnetic slope

1. Guiding centers move toward magnetic null

2. Larmor radius increases

3. Trajectories pushed into magnetic slope

Thruster Proof of Concept

*Kline, Scime. Physics of Plasma, Dec. 1999

Antenna

Electrodes

Exhaust

BEW

€

j

Front View

Karney

1976

S3-3

1978 1998

Benisti et. al

2004

2006 2009 2010

BEW Heating

2010

Directed ion acceleration

Spektor and Choueiri.

Conclusions