[PPT] - Voltage-dependent coherent drift modes and turbulent transition PowerPoint Presentation

SLIDE 1

M. Cappelli
T. Ito, N. Gascon, and A. Marcovati, C. Young

Stanford University

Voltage-dependent coherent drift modes and turbulent transition regimes in small magnetron devices

SLIDE 2

Very small (~ 5 mm diameter discharge, 2 mm gap)
Strong radially-inward B (~ 1 T Bpeak, 0.3 – 5 T Bplasma)
Low pressure (~100 mTorr)
Very strong axial gradients (mm) – expect gradient drifts
Indium-tin-oxide anode (transparent)

Magnetron Details

SLIDE 3

Coherent Rotating Modes

E x B is is Cou

unter Clo

lockwis ise

B

x

E

unambiguous direction confirmed by varying framing rate
the structures rotate in the - E x B direction (retrograde)
coherent (segmented anode confirms current-carrying)
the total discharge current shows no evidence of fluctuations

SLIDE 4

Instability Controlled by Gap Voltage

m = 3 m = 4 m = 5

discharge gap voltage controls structure fr

freq equency and mode

de
within mode: frequency de

decreases with increasing voltage (unexpected)!

wavelength of the modes increase (m decreases) with increasing voltage

6 11 16 21 26 31 36

E0Ln (V)

255 260 265 270 275 280 285 100 200 300 400 500 600 700 800

Gap Voltage (V) Frequency (kHz)

m = 3 m = 4 m = 5

Movie frames

SLIDE 5

1 2 3 4 5 6 −0.04 −0.03 −0.02 −0.01 0.01 0.02

AC Signal (a.u.) Time (ms)

Ch 1 Ch 2 Ch 3

“Turbulent” Regimes between Coherent States

temporal behavior of oscillations erratic/turbulent

between modes

broad range of frequencies
anode segments serve as “probes” for wavelet analysis
wavenumber Nyquist ~ 280 m-1

6 11 16 21 26 31 36

E0Ln (V)

255 260 265 270 275 280 285 100 200 300 400 500 600 700 800

Gap Voltage (V) Frequency (kHz)

m = 3 m = 4 m = 5

voltage between modes

SLIDE 6

Three-wave coupling

wavelet analysis reveals high frequency quasi-coherent

states (~ five) with strong interconnectivity

three-wave coupling satisfying momentum and energy

selection rules

3-wave mixing in azimuthal waves

k1 k2 k3

𝑙2 −130 + 𝑙3 100 = 𝑙5 −30 𝑛−1 𝑔

2 1.31 + 𝑔 3 2.16 = 𝑔 5 3.47 𝑁𝐼𝑨

SLIDE 7

Hypothesis for Retrograde Motion

J comparable to Hall thrusters

(~0.1A/cm2)

similar densities/smaller length

scale

field reversal necessary to restrict

diffusion-driven electrons

plasma rotation in local E x B direction
field drives ions towards anode

simulated potential showing field reversal

Scharfe, M.K., et al Physics of Plasmas, 13(8), p.083505.

field reversals predicted in anode region
f Hall thrusters
potential well ~ 5 V
causes ions to stream towards anode
region of strong ionization
can potentially lead to reversal in

ionization (S-H) spoke instabilities

SLIDE 8

Hypothesis for Retrograde Motion

Meezan, et al, 2001. Physical Review E, 63(2), p.026410.

J comparable to Hall thrusters

(~0.1A/cm2)

similar densities/smaller length

scale

field reversal necessary to restrict

diffusion-driven electrons

plasma rotation in local E x B direction
field drives ions towards anode
field reversals predicted in anode region
f Hall thrusters
potential well ~ 5 V
causes ions to stream towards anode
region of strong ionization
can potentially lead to reversal in

ionization (S-H) spoke instabilities

anode-streaming ions seen in early LIF

data (Meezan et al 2001)

SLIDE 9

Gradient Drift-wave Theory

Governing Equations

𝜖𝑜 𝜖𝑢 + 𝑾𝐹×𝐶 ∙ 𝛼𝑜 − 2𝑜 𝑾𝐹×𝐶 + 𝑾𝐸 ∙ 𝛼𝑚𝑜𝐶𝑝 = 𝜑𝐽𝑜 + 𝐸𝐵 𝜖𝑜 𝜖𝑨

electron mass and momentum

𝜖𝒘 𝜖𝑢 + 𝒘 ∙ 𝛼 𝒘 + 𝑟 𝑁 𝛼𝜚 = 0 𝜖𝑜 𝜖𝑢 + 𝛼 ∙ 𝑜𝒘 = 𝜑𝐽𝑜 + 𝐸𝐵 𝜖𝑜 𝜖𝑨

ion mass Ion momentum

source term : ionization and diffusive loss along B

Linear Perturbation – Fourier Analyzed ෤ 𝑜 𝑜𝑝 = 𝜕∗ − 𝜕𝐸 𝜕 − 𝜕𝑝 − 𝜕𝐸 + 𝑗𝜑∗ 𝑓 ෨ 𝜚 𝑙𝑈 ෤ 𝑜 𝑜𝑝 = 𝑙⊥

2

𝜕 − 𝑙𝑦𝑤𝑝𝑦 2 𝑓 ෨ 𝜚 𝑁 ෤ 𝑤𝑦 = 𝑙𝑦 𝜕 − 𝑙𝑦𝑤𝑝𝑦 𝑓 ෨ 𝜚 𝑁 ෤ 𝑤𝑧 = 𝑙𝑧 𝜕 − 𝑙𝑦𝑤𝑝𝑦 𝑓 ෨ 𝜚 𝑁

𝜕2 − 2𝑙𝑦𝑤𝑝𝑦 +

𝑑𝑡

2𝑙⊥ 2

𝜕∗−𝜕𝑝 𝜕 + 𝑙𝑦𝑤𝑝𝑦 2 + 𝑑𝑡

2𝑙⊥ 2 𝜕𝑝+𝜕𝐸

𝜕∗−𝜕𝐸

−

𝑗𝑑𝑡

2𝑙⊥ 2𝜑∗

𝜕∗−𝜕𝐸 = 0

anode-streaming ion velocity (depends on well depth EoLn) net loss (diffusion less ionization) 𝑾𝐹×𝐶 = − 𝑪𝑝 𝐶𝑝

2 × 𝑭

𝑾𝐸 = − 𝑪𝑝 𝐶𝑝

2 × 𝑙𝑈

𝑓𝑜 𝛼𝑜 𝜑∗ = 𝑙𝑨

2𝐸𝐵 − 𝑤𝐽

෨ 𝑊

𝑦 = − 𝑗𝑙𝑧

𝐶𝑝 ෨ 𝜚 = − 𝑗𝑙𝑧 𝐶𝑝 𝑙𝑈 𝑓𝑜𝑝 𝜕 − 𝜕𝑝 − 𝜕𝐸 + 𝑗𝜑∗ 𝜕∗ − 𝜕𝐸 ෤ 𝑜

Ions Elec

SLIDE 10

Gradient Drift-wave Theory

Governing Equations

𝜖𝑜 𝜖𝑢 + 𝑾𝐹×𝐶 ∙ 𝛼𝑜 − 2𝑜 𝑾𝐹×𝐶 + 𝑾𝐸 ∙ 𝛼𝑚𝑜𝐶𝑝 = 𝜑𝐽𝑜 + 𝐸𝐵 𝜖𝑜 𝜖𝑨

electron mass and momentum

𝜖𝒘 𝜖𝑢 + 𝒘 ∙ 𝛼 𝒘 + 𝑟 𝑁 𝛼𝜚 = 0 𝜖𝑜 𝜖𝑢 + 𝛼 ∙ 𝑜𝒘 = 𝜑𝐽𝑜 + 𝐸𝐵 𝜖𝑜 𝜖𝑨

ion mass Ion momentum

source term : ionization and diffusive loss along B

𝑾𝐹×𝐶 = − 𝑪𝑝 𝐶𝑝

2 × 𝑭

𝑾𝐸 = − 𝑪𝑝 𝐶𝑝

2 × 𝑙𝑈

𝑓𝑜 𝛼𝑜

Simon-Hoh (like) Instability but the B-field curvature (drift) term overtakes the density gradient term relieving the requirement of the usual S-H condition that 𝐹𝑝

𝑒𝑜 𝑒𝑦 > 0.

SLIDE 11

Comparison to Experiments

Growth Rate Frequency

peak growth rate depends on well depth (voltage)
increased field (voltage) favors lower mode number (as seen in experiments)
expect a hysteresis (also seen in experiments)
within a mode, increasing voltage decreases frequency

SLIDE 12

Coherent Fluctuations Drive Transport

Electron Current Density

Current falls to zero (so ) Τ ෥ 𝑜 𝑜𝑝 ≈ 1 𝐾𝑓 = 𝑆𝑓 𝑓෥ 𝑜 ෨ 𝑊

𝑦 =

𝑙𝑧𝑜𝑝𝑙𝑈 𝐶𝑝 ෤ 𝑜 𝑜𝑝

2

𝜉∗ 𝜕∗ − 𝜕𝐸

≈ 1

2 𝑓𝑜𝑝𝑀𝛼𝜉∗ ෤ 𝑜 𝑜𝑝

2

To match the experiment freqencies

𝜉∗ = 3 × 106 𝑡−1 𝑀𝛼 ≈ 10−3 𝑛 𝑜𝑝 = 1018 𝑛−3 ෤ 𝑜 𝑜𝑝

2

≈ 1 If we further assume:

𝜉∗ = 3 × 106 𝑡−1 𝑀𝛼𝐶 = 2 × 10−3 𝑛

Model 𝐾𝑓 ≈ 0.5 𝐵/𝑛2 Consistent with experimental estimates

f current density

SLIDE 13

Summary

small magnetron discharge can generate very coherent plasma
scillations
fluctuations propagate opposite external E x B direction
likely due to presence of field reversal (potential well) driven by

strong gradients in plasma density

drift-wave theory describes this behavior fairly well
“turbulence” between modes
evidence of three-wave coupling within this turbulence
transport during the coherent modes consistent with drift theory
S-H “like” with strong curvature drift term
cross-field current uniquely determined by gradient length scale

and ionization

Acknowledgements: AFOSR

SLIDE 14

Extra Slides

SLIDE 15

Linear Perturbation – Fourier Analyzed ෤ 𝑜 𝑜𝑝 = 𝜕∗ − 𝜕𝐸 𝜕 − 𝜕𝑝 − 𝜕𝐸 + 𝑗𝜑∗ 𝑓 ෨ 𝜚 𝑙𝑈 ෤ 𝑜 𝑜𝑝 = 𝑙⊥

2

𝜕 − 𝑙𝑦𝑤𝑝𝑦 2 𝑓 ෨ 𝜚 𝑁 ෤ 𝑤𝑦 = 𝑙𝑦 𝜕 − 𝑙𝑦𝑤𝑝𝑦 𝑓 ෨ 𝜚 𝑁 ෤ 𝑤𝑧 = 𝑙𝑧 𝜕 − 𝑙𝑦𝑤𝑝𝑦 𝑓 ෨ 𝜚 𝑁

𝜕2 − 2𝑙𝑦𝑤𝑝𝑦 +

𝑑𝑡

2𝑙⊥ 2

𝜕∗−𝜕𝐸 𝜕 + 𝑙𝑦𝑤𝑝𝑦 2 + 𝑑𝑡

2𝑙⊥ 2 𝜕𝑝+𝜕𝐸

𝜕∗−𝜕𝐸

−

𝑗𝑑𝑡

2𝑙⊥ 2𝜑∗

𝜕∗−𝜕𝐸 = 0

anode-streaming ion velocity (depends on well depth EoLn) net source (ionization and diffusion) Characteristics Frequencies 𝜕∗ = − 𝑑𝑡

2𝑙𝑧

𝜕𝑗𝑑𝑀𝛼𝑜 𝜕𝐸 = − 𝑑𝑡

2𝑙𝑧

𝜕𝑗𝑑𝑀𝛼𝐶 𝜕𝑝 = 𝑙𝑧𝑊

𝐹×𝐶

෨ 𝑊

𝑦 = − 𝑗𝑙𝑧

𝐶𝑝 ෨ 𝜚 = − 𝑗𝑙𝑧 𝐶𝑝

𝑙𝑈 𝑓𝑜𝑝 𝜕 − 𝜕𝑝 − 𝜕𝐸 + 𝑗𝜑∗

𝜕∗ − 𝜕𝐸

෩ 𝑜

𝑆𝑓 𝑓 ෥ 𝑜 ෨ 𝑊

𝑦 = 𝑙𝑧

𝐶𝑝 𝑙𝑈 𝑓𝑜𝑝 𝜑∗

𝜕∗ − 𝜕𝐸

෤ 𝑜 𝑜𝑝

2

SLIDE 16

First experiments with Ne, He

Frequency/mode increases with

decreasing M!

Ar (m = 3) =200 kHz,
Ne (m = 1) = 500 kHz
He (m = 0) = 10 MHz
Ar (linear), Ne (non-linear), He

(pulsating at ~0.5-1MHz)

Behavior shows strong dependence on ion mass

1 2 3 4 5 6 7 8 9 10

3
2
1

1 2 3 4 5

t [s] [a.u.] Ar Ne He

Primary scaling of frequency

frequency of oscillations scaling:
Primary scaling however does not

describe the inverse voltage dependence within modes

∅ 𝑁

1/2

< 𝑔 < ∅ 𝑁

1

SLIDE 17

Complex regimes between azimuthal modes

Gap Voltage (V) Frequency (kHz) Mode a coherent m = 3 Mode b coherent m = 4 Mode c Turbulent (between m = 3/4) Mode d Turbulent (between m = 4/5)

m=3 m=4

Arrows indicate direction of voltage change (hysteresis)

Argon 150 mTorr

Start

SLIDE 18

Transport and current flow: resistive behavior

hysteresis in I-V curve with increasing/decreasing current
“turbulent state” between m = 3, m = 4 modes (reproducible)
turbulent states do not greatly enhance the current
turbulent case near m = 4, m = 5 boundary exhibits non-linear wave-coupling

m=3 m=4 “turbulent states”

SLIDE 19

Breathing mode dynamic via time- resolved ion velocities in a BHT-600 Hall thruster

M.A. Cappelli C.V. Young and A. Lucca-Fabris

W. Hargus, N. McDonald, C. Charles

Princeton Workshop 2018

SLIDE 20

Time-Resolved LIF

BHT-600 D=100 mm fl = 200 mm D=100 mm fl = 200 mm Vacuum Chamber 125 mm Mono PMT Lock-In Amp (1) Lock-In Amp (n)

…

S-H (1) S-H (n)

…

Lock-In Amp (2) S-H (2) BNC Splitter Trigger (+ Delay) Discharge Current

+

1 2 3 4 −110 −100 −90 −80 −50 −40 −30 −40 −20 −110 −100 −90 −80

Time-Resolved LIF: process only part of PMT signal to obtain one velocity measurement at one time

SLIDE 21

Hardware for Time Resolution

Voltage Comparator Digital Pulse Delay Generators 10x SRS Lock-In Amplifiers 9x Sample Hold Circuits PMT (Voltage) Signal Splitter Circuit Power Supplies

SLIDE 22

BHT-600: Time-Resolved Axial + Radial LIF

Z Y X

W. A. Hargus Jr. and C. S. Charles, J. Propul. Power. 26, 135 (2010)
LIF measures velocity in direction of beam

so 2 beams = 2 velocity components (2D)

First study of 2-D ion dynamics with time-

resolved LIF and largest survey of a single

perating condition

▪ By the numbers:

Exit Plane! BaO Cathode! Acceleration Channel!

24! mm! 32! mm! 58! mm! 10 mm!

Outer Pole! Inner Pole!

ˆ z ˆ y ˆ x

#VDFs

SLIDE 23

BHT-600 Hall Thruster

Z Y X

W. A. Hargus Jr. and C. S. Charles, J. Propul. Power. 26, 135 (2010)
Time-resolved axial + radial ion LIF in the plume

Cathode Bisector

SLIDE 24

BHT-600 LIF Results: Channel Ion Velocities

Z Y

−50 −40 −30 −20 −10 −10 −5 5 10 15 20 25 30 Y (mm) Z (mm) Campaign 1: Y−Z Plane (Axial)

SLIDE 25

BHT-600 Results: Time-Resolved Channel

Moving potential hill captured with LIF

SLIDE 26

BHT-600 Results: Time-Resolved Channel

It seems that the

acceleration zone retreats towards the anode when the discharge current decreases

SLIDE 27

BHT-600 Results: Center Jet, Near Wall

Axial LIF traces show double

populations near the thruster

Suggests residual ionization is
ccurring in the central jet

with local potential tied to breathing mode dynamics of channel

SLIDE 28

BHT-600 Results: Center Jet, Downstream

Slightly off-centerline centerline

SLIDE 29

BHT-600 Results: Channel Outside

SLIDE 30

Thank You

SLIDE 31

BACKUP SLIDES

SLIDE 32

BHT-600 Results: 2-D Plume Ion Velocities

Z X

Time-resolved axial + radial ion LIF in the plume

20 40 60 80 100 120 −50 −40 −30 −20 −10 10 20 30 40 50

Z (mm) X (mm)

SLIDE 33

Hall Thrusters: Breathing Mode

Thruster works most efficiently when propellant

is ionized in cycles

Neutrals fill channel
Ionization wave moves from exit to anode
Ions leave all at once
Wait for more neutrals to refill

Boeuf and Garrigues. Journal of Applied Physics 84, 3541 (1998). Bareilles et al. Physics of Plasmas 11, 3035 (2004).

1 2 3 4 Current (A) −110 −100 −90 −80 295 300 305 Voltage (V) −50 −40 −30 Power Spectral Density (dB/Hz) 20 40 60 80 100 −40 −20 Time (ms) PMT Signal (mV) 60 120 180 −110 −100 −90 −80 Frequency (kHz)

SLIDE 34

BHT-600 Results: Center Jet

Luminous central jet is not well understood and usually appears in

efficient operating modes

20 40 60 80 100 120 −50 −40 −30 −20 −10 10 20 30 40 50

Z (mm) X (mm)

V. Hruby et al. AIAA-1999-3534 (1999).

SLIDE 35

BHT-600 Hall Thruster

Exit Plane! BaO Cathode! Acceleration Channel!

24! mm! 32! mm! 58! mm! 10 mm!

Outer Pole! Inner Pole!

ˆ z ˆ y ˆ x

Z Y X

W. A. Hargus Jr. and C. S. Charles, J. Propul. Power. 26, 135 (2010)

SLIDE 36

BHT-600 Results: Time-Averaged Channel

Axial Location (mm) Velocity (km/s)

−10 −5 5 10 −5 5 10 15 20 25 (mV) 5 10 15 20 25 30 35 40 45 50

−10 −5 5 10 20 40 60 80 100 E−Field (kV/m) Axial Position (mm) −10 −5 5 10 50 100 150 200 250 300 Potential (V)

As usual, time-averaged data only tells part of the story…

SLIDE 37

BHT-600 Results: Center Jet, Time-Resolved

Axial LIF traces show

asymmetry in time:

Ion beam from one

side of channel dominates for half cycle before switching

Could be related to helical

plasma wave seen previously in plume1

0.25 0.5 0.75 1 LIF Signal (a.u.) 0.25 0.5 0.75 1 LIF Signal (a.u.) 0.25 0.5 0.75 1 LIF Signal (a.u.) 5 10 15 20 25 0.25 0.5 0.75 1 Frequency (GHz) LIF Signal (a.u.) 5 10 15 20 25 Frequency (GHz) 5 10 15 20 25 Frequency (GHz)

8 ms 9 ms 10 ms 11 ms 12 ms 13 ms 14 ms 16 ms 17 ms 18 ms 19 ms 20 ms

1A. W. Smith, PhD Thesis, Stanford University (2009)

SLIDE 38

BHT-600 Hall Thruster

Current and voltage oscillations 180° out of phase in both thrusters
Issue of power supply dynamics influencing thruster operation deserves more attention1

−80 −60 −40 −20 −40 −20 50 100 150 200 250 Time (ms) −20 2 4 Current (A) −80 −60 −40 −20 220 240 260 Voltage (V) −40 −20 1 −20

1 2 3 4 Current (A) −110 −100 −90 −80 295 300 305 Voltage (V) −50 −40 −30 Power Spectral Density (dB/Hz) 20 40 60 80 100 −40 −20 Time (ms) PMT Signal (mV) 60 120 180 −110 −100 −90 −80 Frequency (kHz)

1W. Liqiu, et al. Physics of Plasmas, 18, 063508 (2011).

SLIDE 39

BHT-600 Results: Center Jet, Time-Avg

Double radial peaks = crossing beams
Time-averaged radial ion LIF traces are

asymmetric – small potential deviations

Multiple axial ion populations observed

closer to the thruster

x = −4 mm x = −2 mm −20 −10 −20 −10 −20 −10 10 20 −20 −10 −20 −10 x = −4 mm x = −2 mm −20 −10 25 34 45 54 74 100 Radial LIF Axial Location (mm) −20 −10 −20 −10 −20 −10 −20 −10 x = −4 mm x = −2 mm −20 −10 −20 −10 −20 −10 −20 −10 −20 −10 25 34 45 54 74 100 Axial LIF Axial Location (mm) x = −4 mm x = −2 mm −20 −10 −20 −10 −20 −10 −20 −10 −20 −10

Time−Avg Time−Sync Mean 10 20 10 20 10 20 10 20 −10 −5 5 10 15 20 10 20 z = z = z = z = z =

Time−Avg Time−Sync Mean −10 −5 20 z = 20 mm z = 15 mm z = 10 mm z = 5 mm z = 2 mm

SLIDE 40