Studies of Fast Ionization Wave Discharge PlasmasStudies

The Ohio State University Nonequilibrium Thermodynamics Laboratory

Studies of Fast Ionization Wave Discharge PlasmasStudies of Fast Ionization Wave Discharge PlasmasUsing Optical Diagnostics

with Sub-Nanosecond Time Resolution

K. Takashima, A. Montello, W.R. Lempert, and I.V. AdamovichK. Takashima, A. Montello, W.R. Lempert, and I.V. Adamovich

Objectives

• Generating controlled, reproducible nsec pulse duration dischargesi l t l d i l (F t I i ti W ) t i iin plane-to-plane and axial (Fast Ionization Wave) geometries, in adischarge section with access for optical diagnostics

• Measurements of FIW speed in a wide range of pressures (P~1-100torr), and voltage waveforms (peak voltage, rise time, pulse repetitionrate)

• Development and testing of a new, portable psec CARS diagnosticDevelopment and testing of a new, portable psec CARS diagnosticsystem

• Time- and spatially resolved measurements of rapidly varyingelectric field in nsec pulse discharges (plane to plane and FIW) by IRelectric field in nsec pulse discharges (plane-to-plane and FIW) by IR(E-field) psec CARS

• Measurements of electron density in nsec pulse discharges byTh tt i *Thomson scattering*

*with luck

“Single pulse” nanosecond discharge in plane-to-plane geometry: spatially uniform?


20

Voltage, kV

p p g y p y

0

10

20Air, P=60 torr, ν=40 kHz

30

-20

-10

0 50 100 150 200-30

Time, nsec

Single pulse 100 pulse average

Broadband ICCD camera images, gate 2 μsecAir, P=60 torr, pulse repetition rate 10 Hz

Single pulse 100 pulse average

Repetitive nanosecond pulse discharge: effect of residual ionization on spatial uniformityp y

20Voltage, kV

10

20Camera gate: 1 µsec

-10

0

cathode

0 10 20 30 40 50 60 70Time, μsec

-20

anode

Single pulse ICCD camera images in air from 40 msec “burst” (P=60 torr, ν=40 kHz, 1000 pulses in a burst, 1 μsec camera gate)

Air plasma remains uniform during entire pulse burst at P=40-100 torr(after first 1-2 pulses): effect of residual ionization

Same result for short camera gates (down to 4 nsec): justifies the use of a quasi-1-D approach

Effect of residual ionization: uniform plasma on nanosecond time scale


Air, P=60 torr, ν=40 kHz, pulse #100 in the burst

Same result for shorter camera gates (down to 4 nsec): justifies the use of a quasi-1-D approach

Nanosecond pulse discharge plasma / sheath model(quasi-1-D drift-diffusion, time-dependent)

L

(q , p )

• Equations for electron and ion number density• Poisson equation for the electric field plasma

sheath

cathode anode

• Poisson equation for the electric field• Nitrogen, plane-to-plane discharge geometry• Both electrodes covered with quartz plates• Voltage pulse: Gaussian fit to experimental waveform

l ε

lsE

Voltage pulse: Gaussian fit to experimental waveform

T d i i ti ffi i t E/N fit t

sec15,20,exp2)(2

nkVVtt

lL

VtE peak

peakpeakapp ==

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

+= τ

τε

l,ε• Townsend ionization coefficient vs. E/N: fit to experimental data; local kinetics only• Dielectric plate charging / plasma shielding:

dd ⎞⎛ )()(

Numerical or analytic solution: time dependent

( ) ( )[ ]dxtxtxL

ledttdV

Ll

dttdV L

egapapp ∫ Γ−Γ+⎟

⎠⎞

⎜⎝⎛ += +0

0

,,12)(21)(

εεεCd CdCs(t) R(t)

Numerical or analytic solution: time-dependent electron density and electric field in the plasma and in the sheath, coupled pulse energy

Nanosecond pulse discharge plasma / sheath model:key processes and time scales

Eapp(t) - applied electric field (Gaussian fit to experimental pulse shape)2ttV ⎤⎡ ⎞⎛

ey p ocesses a d t e sca es

νi - electron impact ionization frequency

sec15,20,exp2)( nkVVtt

lL

VtE peak

peakpeakapp ==

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

+= τ

τε

22 00 nelnle ese μμ)( ⎥

⎤⎢⎡ BpAE

νc + νs - frequency of dielectric charging / sheath formationνRC - RC frequency of the load after breakdown (plasma / charged dielectrics / sheath)

a 11 0 −== νν,,

21 0

0

0

0

LLlL

ess

ec ε

μν

εεε

μν =⎟⎠⎞

⎜⎝⎛ +

=,exp)( ⎥⎦⎤

⎢⎣⎡−=EpApEiν

E0 =E(t0) - breakdown field

aaCR iloadplasma

RC ln== νν

( ) ( ) BpEtt

tEE ipeakapp

00

000 2/ln4

,γτν

τ=

−=

E*=E(t*) - field in the plasma at the moment when coupled power peaks

( )a

aEE

aaaa

EBpaE

EEEE

sc

iii 3

,ln

,23exp,,

0*

0* /

0

*

2

/

10

0

00 =

−=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

+== ξξ

νννγνν

Nanosecond pulse discharge plasma / sheath model:key results

)( *⎧ app tEE(t): electric field in the plasma

ey esu ts

( )0,)(1

,1exp1

)(

)( 2*

*

0

=⎪

⎪⎪⎪⎪

⎨

⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛+

≤′+′

= ∞p

app

i

app

p EtEEE

ttt

tEξξ

νγ

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

RC

appp

tEtEtE

ν)(

),(max)(&

[ ],

)()(exp

*

1

2*021

10

⎪⎪⎪⎪

⎩

>′+−′+

⎟⎠

⎜⎝

i

pp

tttt

E

ξξ

νξξ

ξ ⎥⎦⎢⎣ RC

[ ] )(2

2

,2

)()()()( tEll

lLE

ll

lLtEtEtEtE app

s

s

s

spappapps

ε

+

+=

+

−⋅−+=

∞

∞

∞

∞

Es(t): electric field in the sheath

⎟⎟⎠

⎞⎜⎜⎝

⎛= ∞

∞

∞∞

0

ln)( n

nEElsis

ss ν

μ

ls∞: steady state sheath thickness

ss εε

ne(t): electron density in the plasma

aaan

aaann

aaan

aaaantn

EtEEtE pp

ln1

ln11,

1ln1)( 00

/)(/)(

0

00 −≈⎟

⎠⎞

⎜⎝⎛ −+=

−−

≈⎟⎟⎠

⎞⎜⎜⎝

⎛ −+= ∞∞ γγγ

Analytic and numerical solutions: Electric field in the plasma and in the sheathp

• Rapid field drop in the plasma after breakdown

• Dominant effect: plasma shielding by charging dielectric100

E, kV/cmplasma

• Dominant effect: plasma shielding by charging dielectric plates, sheath formation

• Steady-state electron density after shielding ne~1012 cm-3

•Steady-state sheath thickness / plasma thickness << 11

10

90 nsec

89 nsec

88 nsec87 nsec

Steady-state sheath thickness / plasma thickness << 1• Uniform field in the plasma• Analytic and numerical solutions: excellent agreement0.1

1

x cm

92 nsec

0.0 0.2 0.4 0.6 0.8 1.0

sheath

x, cm

Plasma electric field, kV/cmnumerical model

analytic solution

161820 applied voltage

1E+12

1E+13

ne, cm-3

89 nsec

92 nsec

plasma

1 5E 12

2.0E+12

Electron density, cm-3

shielded plasma

Vapp/(L+2l/ε)

468

101214

breakdown

1E+8

1E+9

1E+10

1E+11

86 nsec

88 nsec

88.5 nsec

h th5.0E+11

1.0E+12

1.5E+12

numerical model

analytic solution

70 75 80 85 90 95 100Time, nsec

024

shielded plasma1E+7

1E+8

x, cm

80 nsec

0.0 0.2 0.4 0.6 0.8 1.0

sheath

86 88 90 92 940.0E+0

Time, nsec

breakdown

Analytic and numerical solutions: Electron density in the plasma and coupled powery p p p

Power density, kW/cm3

numerical model50 1.2

Coupled pulse energy, mJ

analytic solution

30

40

V /(L+2l/ε)

breakdown

0.6

0.8

1.0

P*=60 torr V k=20 kV

0

10

20 Vapp/(L+2l/ε)

shielded plasma

0.0

0.2

0.4P 60 torr, Vpeak 20 kV

Numerical, w/o sheath

Numerical, with sheath

Analytic solution

80 90 100 110 120Time, nsec

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡+⎟

⎟⎠

⎞⎜⎜⎝

⎛≈+= peakloadafterbreaktotal V

VVCQQQτνπ2

21

2

02

1E+7 1E+8 1E+9 1E+10 1E+11 1E+12 1E+13

Initial electron density, cm-3

• Most of the power coupled during breakdown pulse,

• Coupled pulse energy scales as the number density, can be increased by reducing τpulse

1.0~)(~/ 1−pulseRCbreakafter QQ τν

⎥⎦

⎢⎣

⎟⎠

⎜⎝ pulseRCpeakV τν2

• Pulse energies in N2 and air are almost the same: attachment insignificant at short pulse durations• Analytic and numerical solutions: excellent agreement• Good agreement with pulse energy inferred from O atom measurements by Two-Photon LIF

Fast Ionization Wave (FIW) discharge Test section schematic


Test section schematic

Air, P=10 torr, Upeak =16 kVν=10 kHz, L=20 cm

Wave propagation velocity ~ 4 cm/nsec (measured by capacitive probes)( y p p )

x=20 cmx=0

15

20

4cm

10

15

age

[kV]

4cm 10cm 18cm

0

5

Vol

ta

10 20 30 40 50 60-5

Time [ns]

Previous FIW discharge experimentsMoscow Institute of Physics and Technology (A. Starikovskii, S. Starikovskaya et al.)

Arrival time and amplitude of fast ionization wave in nitrogen P=24 torrArrival time and amplitude of fast ionization wave in nitrogen, P 24 torr

Kinetic modeling of FIW propagation(quasi-1-D, long wavelength approximation)


ne, cm-31

Space charge, nC

(q , g g pp )

1E+10

1E+11

1E+12

1E+13

31.6 nsec

10 nsec

1 nsec

3

4

5

10

1 nsec

1E+7

1E+8

1E+9

0 5 10 15 20 25 300

1

231.6 nsec

10 nsec

0 5 10 15 20 25 30x, cm

20

25E, kV/cm

x, cm

• Ey<<Ex

• Nitrogen, P=10 torr, Upeak=25 kV

5

10

15

31.6 nsec10 nsec

1 nsec • Channel height 1 cm, electrode gap 20 cm

• Both wave speed and peak electric field decrease along the length, u=1-4 cm/nsec

0

x, cm0 5 10 15 20 25 30

• Kinetic model needs to incorporate full Boltzmann equation, non-local kinetics effects. Collaboration with modeling experts welcome!

IR (E-Field) nsec CARS schematic and measurement region


InSb473nm Dichroic Mirrors

CaF2 Lens

IR LP Filter

PωPωSω ASω

vΔ

Spectrometer

476nm BP FilterFocusing Lens

500mm CaF2 Lens

IR Dichroic MirrorBeam Dump

CARS Generated Along ~11 mm Line Segment (Determined using scanning

CARS Energy Level Diagram

vΔ

Delay Path

SpectrometerCamera

500mm LensField Measurement

Volume

2

Non-Resonant CARS Signal vs Axial Location Relative to Nominal Waist

2.5

Segment (Determined using scanning microscope slide and NR background)

YAGDelay Path

Broadband Dye Laser

Volume532 nm

607 nm Volta

ge

0 5

1.0

1.5

2.0

Tunable Dye Laser

Position (mm)

-20 -10 0 10

0.0

0.5

Preliminary raw IR nsec CARS data(electric field measured between two plane electrodes

in atmospheric air, no breakdown)


in atmospheric air, no breakdown)

averaged over 32 pulses

averaged over 128 pulses128 pulses

Overview of new psec CARS system


Delay Path

Ekspla Nd:YAG laser10 Hz, ~150 psec pulses

125 mJ per pulse max @ 532 nm

Modeless Psec Dye LaserBroadband centered @ 607 nmBroadband centered @ 607 nm

~ 6% conversion efficiencyFromSpectrometer

Schematic of psec dye laser


Thin Film Polarizer ( fl t 90%)(reflect ~90%)

λ/2“Pump”

λ/2

Beam splitter ~80:20 HR 2

Reflecting prism

Beam splitter ~50:50

λ/2 beam outλ/2

Beam dumps

400 mm spherical lens (AR)

HR 1

Cylindrical lens ~100 mm (AR)

HR 3

Beam dumps

RA prism

“Stokes” beam out

Cylindrical lens ~50 mm (AR)

iris 600 mm lensoscillator cell

pre-amp cell

amplifier cell

Portable, broadband psec CARS diagnostic system


diagnostic system

First sensitivity test of psec CARS:Detecting N2 and CO in an optical absorption cell


g 2 p p

N2(v=0)

N2(v=0)

N2

CO(v=0)N2

(outside)

M t f CARS i l f i id th ll (20 30 h t i l l ti )

CO(v=0)

Most of CARS signal comes from inside the cell (20-30 shot signal accumulation)Blue: 8 torr CO, 74 torr N2 Red: 9 torr CO, 120 torr Ar

Capable of detecting O2(a1Δ) generated in electric discharges (partial pressure ~1 torr)p g 2( ) g g (p p )

Next sensitivity test: taking CARS spectra of N2-CO mixture vibrationally pumped by a c.w. CO laser

Here is what we expect to see (and more): Spontaneous Raman Spectra in CO/N2=4/96, P=400 torr (2001)

1.0E+0Relative population

N21.0E-1

1.0E 0

CO, experiment (Tv=3500 K)

N2, experiment (Tv=2200 K)

CO, calculation (Tv=5300 K)

N2, calculation (Tv=2700 K)

CO

v=39

1.0E-3

1.0E-2

570 575 580 585 590 595 600 605 610 615

Wavelength, nm

CO

0 10 20 30 401.0E-4

Vibrational quantum number

Laser power: 15 W, T≅500 K

5 vibrational levels of N2, 40 vibrational levels of CO

(signal averaging over a few hundred pulses)

Work in Progress / Technical Issues


N FIW di h ti till i l h• New FIW discharge section still in glass shop

• Need an IR detector / 1-D detector array with short response time(~10 nsec)

• Need to determine sensitivity limit at low pressures and electric field

• Need to synchronize high voltage nsec pulses and CARS laser pulsesd t l l “jitt ”and control pulse “jitter”

• Effect of EMI noise from the pulser on CARS system electronics yetto be determined

Documents

Studies of Fast Ionization Wave Discharge PlasmasStudies