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Measurement of Plasma Density Produced by Pulsed Voltage using 94-GHz Microwave

Interferometry*

2004년도한국물리학회가을학술논문발표회Oct. 22, 2004제주대학교

(제주도제주시)* Supported by KSTAR Project at KBSI.

정진현정진현, , 배영순배영순, , 조무현조무현, , 남궁남궁원원

PohangPohang University of Science and TechnologyUniversity of Science and Technology

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The microwave interferometer system is a well-

established technique for the measurements of

line-integrated plasma densities without

perturbing plasmas. A 94-GHz microwave

interferometer system was used to investigate the

transient behavior of the pulsed plasma produced

by a sudden step voltage in the order of -500 V

applied to an electrode. The microwave

interferometry data in Argon plasma density is in

the order of 1010 ~ 1011 cm-3 with the pressure in

the range of 100 mTorr. It is observed that the

time dependence of the plasma density depends

on the gas pressure and the flat-top voltage of the

pulse. It is also observed that the time constants of

plasma density build up and decay have different

characteristics.

• * Work supported by KSTAR Project at KBSI.

Abstract

The wavelength in the plasma is always longer than in vacuum

.

The phase difference between when there is a plasma and when not is then

.

Schematics of Microwave Interferometers

1 12 ( )po p

Lφ πλ λ

∆ = −

21/ 2

2(1 )pp o

ωλ λ

ω−= −

pL

Plasma

Source( )

gλ

pλ

gL 2 ( )g p

g p

L Lφ π

λ λ= −

oλSplitter

detector

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Microwave Interferometers (Heterodyne type)

WR10 waveguide

ϕ

Quadraturephase detector

To oscilloscope

Gunn Oscillator

94.2 GHz

Gunn Oscillator94.0 GHz

Attenuator

Attenuator

Mixer

Mixer

Phase Shifter

DC break

Isolator

Isolator

Plasma

RF

LOIF

RFLOIF

G GMicrowave SourceGunn Oscillator

94.2 GHz

94.0GHz

Phase Shifter

Quadraturephase detector

Mixer

DirectionalCoupler (10dB)

RF Amplifier

Mixer

Passed plasma

o0Power Splitter

o90Power Splitter

) sin( φω +tRF

t)(ωLOsin

)90 sin( oLO t +ω

RF

LO

IF

RF

LO

IF

Low Pass

Filter

Low Pass

Filter

In Phase Port

QuadraturePort

φsin

φcos t)(ωLOsin

Reference signal

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• Phase shift due to plasma

GHz is where, 2.94fωω for ),dr(m t)(r,n(GHz)f

1108.42

dr ]ωω

[1cωφ(t)

o22

p3

eo

16

2/1a

a 2

2p

⟨⟨×≅

−=

−−

+

−

∫

∫

OQoLORFQ

OILORFI

V]t)f(fπcos[2KQ Vt])f(fπsin[2KI

+ϕ+−=+−=

balance. phase is and

offset,-dc are and

,amplitudesoutput are t is (2 where,

VV

K,K ),()ff

o

OQOI

QI

LORF

ϕ

ϕ−π

))sin(M

)cos((tan)t( o

o1

ϕ+ϕ

=ϕ −

Q

I

OI

OQ

KK

VIVQ

M−

−=where,

Plasma density calculation

• Because of the non-linearity of the phase quadraturephase detector, the digitized value (I and Q) should be corrected before the phase shift calculation.

(t))(10.1811)mn( 153 ϕ×××>=< − GHzf L

• Therefore, the line-averaged electron density is

Cathode

d

Horn Antenna

FET switch module2 kV max

1kV max(negative)

Gas Inlet

Pumping port

1μF, 2kV max. 1kΩ

Rsh1 Csh1

Rsh2 Csh2

Rp

Rsh Csh

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Vinput

Current

Q=KQcosφ

I=Kisinφ

0 5 10 15-10

-5

0

5

10

Plasma Density

Vinput(Negative Pulse)

Line

Inte

grat

ed P

lasm

a D

ensit

y [1

010cm

-3]

Current [A

]Time [µsec]

Current

-4

-2

0

2

4

6

-20 0 20 40 60 80

-2

0

2

4

6

8

10

12

Time [µsec]

Line

Inte

grat

ed P

lasm

a D

ensi

ty [1

010cm

-3]

750 V 700 V 600 V 500 V

Vinput (Negative Pulse)

-20 0 20 40 60 80 100

-4

-2

0

2

4

6

8

10

12

14

Time [µsec]

Line

Inte

grat

ed P

lasm

a D

ensit

y [1

010cm

-3]

700 mTorr 600 mTorr 500 mTorr

Vinput(Negative Pulse)

Time resolved plasma density from various input voltage & pressure.

Increasing pressure leads to longer time constants for densitiesIncreasing pressure leads to longer time constants for densities, caused by higher number of collisions., caused by higher number of collisions.

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10 15 20 25 30 35-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

Vin

put [k

V]

Time [µsec]

1000 mTorr 900 mTorr 800 mTorr 700 mTorr 600 mTorr

-20 0 20 40 60 80 100

-4

-2

0

2

4

6

8

10

12

14

Time [µsec]

Line

Inte

grat

ed P

lasm

a D

ensit

y [1

010cm

-3]

700 mTorr 600 mTorr 500 mTorr

Vinput(Negative Pulse)

10 15 20-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Current

Line

Inte

grat

ed P

lasm

a D

ensit

y [1

011cm

-3]

Time [µsec]

800 mTorr 700 mTorr 600 mTorr

0.0

0.5

1.0

1.5

2.0

2.5C

urrent [A]

τ−

≈RC

oVV exp10 15 20 25 30 35

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time[µsec]

Model: y=yo+Aexp(-x/t) Chi2:0.00017 R2:0.99005

Parameter Value--------------------------------------t1 1.1993E-6--------------------------------------

Vin

put [k

V]

Time resolved plasma density from various Ar gas pressure.

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400 450 500 550 600 650

0

1

2

3

4

5

Capacitance: ~5nF

Capacitance: ~1nF

Vinput [V]

Dec

ay ti

mec

onst

ant [µs

ec]

Decay timeconstant

0

1

2

3

4

5

Resistance [kΩ

]

Resistance [Ohm]

600 700 800 900 1000

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Pressure [mTorr]

Line Integrated Plasma D

ensity [1010cm

-3]

Falli

ng ti

me

[µse

c] Plasma Density

falling time of Vinput

0

5

10

15

20

25

30

Results II.

Before ignitionBefore ignition

After ignitionAfter ignition

350 400 450 500 550 600 650 700 750 800

0.5

1.0

1.5

2.0

2.5

3.0

Breakdown voltage

Vinput [V]

Dec

ay ti

mec

onst

ant [µs

ec]

Pressure: 900mTorr d=1cm d=3cm

350 400 450 500 550 600 650 700 750 8000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Breakdown voltage

Vinput [V]

Dec

ay ti

mec

onst

ant [µs

ec]

900 mTorr 2500 mTorr

Tow different values of decay time constants are visible in mostTow different values of decay time constants are visible in most experimentsexperiments.

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We have studied the fundamental properties of the pulsed plasma generated from negative voltage.

• At the beginning of the pulse, the plasma density rises slower than the pulse rise time and reaches the peak value and after that, the density settles down at steady state.

• The time that plasma density reaches a maximum point is determined by pressure & input voltage.

• We measured the decay time constants in the after glow for Ar gas at various plasma conditions. As a results, increasing pressure leads to longer time constants for densities and shorter time constants for voltages caused by higher number of collisions and ionizations.

•Tow different values of decay time constants are visible in most experiments. It means that, after ignition, resistance of plasma increase while capacitance of plasma decrease exponentially.

Summary & Conclusions