Correlation Analysis of Electrostatic Fluctuation between Central and End

Cells in GAMMA 10

Y. Miyata, M. Yoshikawa, F. Yaguchi, M. Ichimura, T. Murakami and T. Imai

Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577, JAPAN

CONTENTS1. Abstract (Background and Research Purpose)

2. Experimental Setup in GAMMA 103. Gold Neutral Beam Probe (GNBP) and End Plate (EP) measurement

4. Experimental Results (GNBP,EPs and their Correlation)5. Summary

AbstractAbstract

[Background]

The fluctuations are observed in some magnetic confinement devices. The fluctuations due to the instabilities cause the anomalous transports. In the GAMMA 10 tandem mirror, the electrostatic and magneto hydrodynamic fluctuations are observed by some measurement systems and they are related to the radial transport. The decreasing of the plasma stored energy due to the radial transport was also observed.

[Research Purpose]

We show the effect of radial particle transport related value induced by the fluctuations measured by a Heavy Ion Beam Probe (HIBP). We show the result of the potential fluctuation of the end plates measurement. The correlation between the potential fluctuation measured by HIBP and that of end plates was assessed.

Study of Potential Formation in GAMMA 10Study of Potential Formation in GAMMA 10

Heavy Ion Beam Probe(HIBP) End Plate(EP)

End Plate(EP)

Beam Intensity 　⇒　Density

Beam Energy 　⇒　Potential

ee nnII //

E

Gold Neutral Beam Probe System at Central CellGold Neutral Beam Probe System at Central Cell

A beam probe is a useful tool on the basis of the energy conservation of a heavy ion beam for the potential and fluctuation measurements. The beam probe system consists of two parts. One is a beam source which produces a high energy ion beam. The other is a beam detector by using an electrostatic energy analyzer. The incident beam and the ionized ion beam in plasma are called the primary and secondary beams, respectively.

45 degree

1ch32ch

Deflection Electric Field

Ground Plate

●End Plate Measurement

E n d C ell

O u ter M irro rT h roa tE n d P late

#1#2# 3# 4# 5

Z A x isX A xis

M a gn etic F ield L in e

X AxisZ Axis

The end plates (EP) made of stainless steel is settled at both end sides of GAMMA 10 for receiving the end loss plasma. The EPs consist of some divided plates made of stainless steel. The EPs are divided into five sections in radial direction and connected to ground though the 1 Mof cement resistor. The EP #1, #2, #3 and #4 cover the region of radius compared at central cell ~5.5, 5.5~7.8, 7.8~11 and 11~16 cm, respectively. The #1, #2 and #3 EPs are divided into four. The #4 EPs are divided into eight sections in circumferential direction and normally connected.

End Plate measurement at West End CellEnd Plate measurement at West End Cell

Location of EPs (Compared at central cell )

05

101520

~#1~#2~#3~#4

Cen

tral

Rad

ius(

cm)

Rcc(cm)

Plate No. ~#1 ~#2 ~#3 ~#4

5.5 7.8 11 16Plug/Barrier Region

Experimental Result: Diamagnetism and Electron DensityExperimental Result: Diamagnetism and Electron Density

　 　 In order to study the feature of electrostatic fluctuation, it is necessary to produce the plasma in which the electrostatic fluctuation occurs with adjusting the heating and gas puffing sequences. After starting up the plasma with the both sides of plasma gun, ICRF heating systems are used in the central cell. We focused attention on ICRF heating time at 120 - 130 and 145 - 155 ms because we assess the effect of the radial particle transport. The plasma stored energy decreased with time in spite of ICRF heating at a constant power.

Radial Profile of Electron DensityTime Evolution of Diamagnetism

0

5 1011

1 1012

1.5 1012

2 1012

-20 -10 0 10 20

122.5 ms147.5 msE

lec

tro

n D

ensi

ty[c

m-3

]Radius[cm]

0

0.2

0.4

0.6

0.8

1

60 80 100 120 140 160

Diamagnetism

Dia

mag

net

ism

[10-5

Wb

]

Time[ms]

3% Down

　 　 The fluctuation near 9 kHz was identified by electrostatic probe established in circumferential direction. The observed fluctuation was estimated as the drift-type fluctuation with the azimuthally mode number of 2.

Experimental Result: GNBP measurement at Central Cell [1]Experimental Result: GNBP measurement at Central Cell [1]

Spectrum of Potential Fluctuation Level near Center

Time Evolution of Potential Fluctuation near Center

0.001

0.01

0.1

0 1 104 2 104 3 104 4 104

121.1 ms146.8 ms

Po

ten

tial

Flu

ctu

atio

n L

evel

[rel

.un

it]

Frequency[Hz]

Radial Profile of Potential Fluctuation Level

Drift-type fluctuation

10 ms averaged

0.01

0.1

0 2 4 6 8 10 12

120-130 ms145-155 ms

Po

ten

tial

Flu

ctu

atio

n L

evel

[rel

.un

it]

Radius[cm]

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12

120-130 ms145-155 ms

Co

her

ence

Radius[cm]

Small fluctuations give rise to the local transport. If the average value of the local transport is not zero, the net transport so-called the radial particle flux. In the case of GAMMA 10, the radial particle flux due to the electrostatic fluctuations is defined:

Radial Profile of Particle Flux Related Value

Radial Profile of Coherence between Potential and Density Fluctuations

Radial Profile of Density Fluctuation Level

Experimental Result: GNBP measurement at Central Cell [2]Experimental Result: GNBP measurement at Central Cell [2]

10 ms averaged

almost 0.8

two or three times more

nnr II sin~

)/~

(

DifferencePhase

LevelnFLuctuatioPotential

LevelnFluctuatioDensityI

Coherence

n

n

_:sin

__:~

__:~

:

0.001

0.01

0.1

0 2 4 6 8 10 12

120-130 ms145-155 ms

Den

sit

y F

luct

uat

ion

Le

vel[

rel.

un

it]

Radius[cm]0

0.05

0.1

0.15

0.2

0.25

0.3

0 2 4 6 8 10 12

120-130 ms145-155 ms

Rad

ial

Par

ticl

e F

lux[

rel.

un

it]

Radius[cm]

The EP potential fluctuation also had the peak near 9 kHz same as the potential fluctuation measured by GNBP. However, the drift-type fluctuation may not occur in a low plasma pressure case such as end cell plasma. The correlation between central and end cells was assessed for identifying the fluctuation measured by EPs.

Spectrum of #1 EP potential Fluctuation Level

Radial Profile of Potential fluctuation Level by using #1, #2 and #3 EPs

0.001

0.01

0.1

0 1 104 2 104 3 104 4 104

121.1 ms146.8 ms

Po

ten

tial

Flu

ctu

atio

n L

evel

[re

l.un

it]

Frequency[Hz]

Experimental Result: EP measurement at West End Cell [1]Experimental Result: EP measurement at West End Cell [1]

0.01

0.1

0 2 4 6 8 10 12

120-130 ms145-155 ms

Po

ten

tial

Flu

ctu

atio

n L

evel

[rel

.un

it]

Radius[cm]

~#1 #2 #3 #4~

We assessed the correlation between the potential fluctuations measured by GNBP and EP in same magnetic field line. The drift-type fluctuation measured at central cell correlated strongly with the fluctuation measured at end cell. This fluctuation at end cell appears identical to the drift-type fluctuation at central cell.

GNBPZ=1.18[m]

#1 EndPlateZ=13.4[m]

L=12.22[m]

Coherence

Radial Profile of Coherence between Central and End Cells

Experimental Result: EP measurement at West End Cell [2]Experimental Result: EP measurement at West End Cell [2]

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12

120-130 ms145-155 ms

Co

her

ence

Radius[cm]

~#1 #2 #3 #4~

almost 0.95

SummarySummary

The density and potential fluctuations were observed at central cell by using GNBP. The potential fluctuation of the end plates settled at both side of GAMMA 10 was observed.

The drift-type fluctuation with azimuthally mode number of 2 near 9 kHz increased, and the plasma stored energy decreased with time. The diamagnetism decreased at rate of 3 % and the radial profile of the particle flux induced by fluctuations was two or three times more.

The EP potential fluctuation also had the peak near 9 kHz and increased with time. The correlation between central and end cells was assessed for identifying the fluctuation measured by EPs. The drift-type fluctuation measured at central cell correlated strongly with the fluctuation measured at end cell.

The drift-type fluctuation which produces the radial particle transport was observed at central cell.

And, the drift-type fluctuation propagated from the central cell to the end cell.

Gold Neutral Beam Probe System at Central Cell [3]Gold Neutral Beam Probe System at Central Cell [3]

][m][exp

[eV])(

1003)( 1-

1 2

112

N

i

T

Uie

i

b

e

b

e

b

ee

e

ix

x

UT

Z

v

n.

v

vn

v

TSnQ

●Principle of Potential Fluctuation Measurement

)108224.800013329.0015633.0(

)014945.0084311.0717.21(26

2

RR

RRPE ch

b

●Principle of Density Fluctuation Measurement

　 The potential calculating formula that the arguments of the function are the ionization point and the peak channel of the beam intensity is obtained. The potential fluctuation is obtained from the small perturbation of the plasma potential.

Analyzer 　　 Plasma 　 Ion Source

Potential EnergyAcceleration Energy

cE

Z: Equivalent electron numberU: Ionization potentialN: Atomic shell number

R: Radial position (cm)Pch: Flying distance of secondary beam in the analyzer

　 A gold neutral particle is ionized due to the reactivity with electrons, and ionized particle deflected by the magnetic field. The ionization efficiency is obtained by the experimental rule of Lotz as indicated in the expression below. We obtain the density fluctuation because the detected signal is dependent on the density near electron temperature 100 eV.

<The feature of GNBP>・ Using the neutral primary beam and the negative gold ion by Cs sputtering・ High neutralization efficiency using the negative ion・ Reduce the effect of the leakage magnetic fields using the neutral beam・ High detection efficiency using Micro Channel Plate (MCP)

-0.2

0

0.2

-0.200.2

11.783kV9.783kV

13.783kV

37 ° 38 °39 °

40 °

41 °

36 °

Y-Axis (m)

X-A

xis

(m)

High Voltage Amp

Function Generator

Triangle Wave

Feature of GNBPFeature of GNBP

1.182

1.184

1.186

1.188

11.11.21.31.4

Current:2.2(mm)Current:11.3(mm)Current:20.0(mm)Current:28.3(mm)Newly:12.2(mm)Newly:21.3(mm)Newly:30.0(mm)Newly:38.3(mm)

Z-A

xis

(m)

Y-Axis(m)

Current Slit

Novel Slit

Multipoint Measurement using Novel Analyzer IIMultipoint Measurement using Novel Analyzer II

Figure shows the component of the energy analyzer and the trajectories of the secondary beam which pass the current and novel entrance slits in y-z plane. The secondary beams pass the current and novel slits within the slit width of 12 mm in y-z plane.

SummarySummary

There is radial particle transport as the loss induced by the fluctuations. It is possible to measure the potential and density fluctuations at the arbitrary point simultaneously in GNBP, the phase difference can be observed. The radial particle transport induces the decreasing of the plasma stored energy. This phenomenon is estimated the theoretically-predicted loss process induced by the radial transport due to the phase difference between the potential and density fluctuations.

●Spec of GNBP The energy and the incident angle of the primary beam passing the plasma center are about 12 keV and 40 degrees, respectively. Typical primary beam current is obtained 2 mA using the Faraday Cup. The GNBP system has two incident angle electrostatic deflectors of the vertical and the horizontal directions. A parallel plate type electrostatic energy analyzer with the incident angle of 45 degrees is installed on the x-y plane. In the analyzer, the micro-channel plate (MCP) detector of 32 anodes which is mounted along y direction is utilized for the beam detector. The width of an each anode is 2.4 mm. The current entrance slit is established on the ground plate in the energy analyzer. The current entrance slit size is 12 x 0.5 mm. ●Fluctuation Measurements The detected positive secondary beam is derived from the neutral primary beam ionized at the ionization point. The electron-impact ionization process is dominant in a case of the ionization of the primary beam. The secondary beam current depends on the electron distribution function at the ionization point. The density fluctuation is obtained from the perturbation of the detected beam intensity, and the potential fluctuation is obtained from the perturbation of the plasma potential.

Gold Neutral Beam Probe (GNBP)Gold Neutral Beam Probe (GNBP)

If the average value of drifts induced by azimuthally propagation density and electric field fluctuations is not zero, the radial particle flux rexists.

If the density, potential and azimuthal electric field fluctuations components are expressed as

The radial flux can be written as

where n=n- is the phase difference, is the coherence between and .Then we can estimate the radial particle flux using this expression.

EN~

,~

,~

,/~~~~

zrr BENVN

dtrkiikE

dtrki

dtrkinN n

))(exp(~~~

))(exp(~~

))(exp(~~

,)exp(~~Re

2 dinikB n

zr

.sin~~2 dnk

B nz

r

zBE ~

n~ ~

　　 The phase difference decides the The phase difference decides the direction of the flux and the growth of the direction of the flux and the growth of the fluctuation.fluctuation.

Radial Particle Flux induced by Potential and Density FluctuationsRadial Particle Flux induced by Potential and Density Fluctuations

The EP #1, #2, #3 and #4 cover the region of radius compared at central cell ~5.5, 5.5~7.8, 7.8~11 and 11~16 cm, respectively. The #1, #2 and #3 EPs are divided into four. The #4 EPs are divided into eight sections in circumferential direction and normally connected.

05

101520

~#1~#2~#3~#4

Cen

tral

Rad

ius(

cm)

Rcc(cm)

Plate No. ~#1 ~#2 ~#3 ~#4

5.5 7.8 11 16

Location of EPs (Compared at central cell )

End Plate measurement at West End Cell [2]End Plate measurement at West End Cell [2]

●Calibration of the flying distance due to the virtual potential in the energy analyzer

Virtual 400(V)

Virtual 0(V)

1ch32ch

Deflection Electric Field

Analyzer 　　 Plasma 　 Ion Source

Potential EnergyAcceleration Energy

Analyzer 　　 Plasma 　 Ion Source

Acceleration Energy

Virtual PotentialcEE

0

0.2

0.4

0.6

0.8

1

1.2

1012141618202224

Virtual Potential:0(V)Virtual Potential:400(V)

No

rma

liza

tio

n C

ou

nt(

rel.

un

it)

ChannelHigh Energy Low Energy

Gold Neutral Beam Probe System at Central Cell [2]Gold Neutral Beam Probe System at Central Cell [2]