1OS2010 1OS2010 1

Radial transport of high-energy ions due to

low-frequency fluctuations in the GAMMA 10 tandem mirrorM. Ichimura, Y. Yamaguchi, R. Ikezoe, Y. Imai, T.

Murakami, T. Iwai, T. Yokoyama, Y. Ugajin, T. Sato and T.

ImaiBudker Institute of Nuclear Physics, OS2010, July 5-9, 2010, Novosibirsk, RussiaContents

1. Motivation of the research 2. Diffusion near the cyclotron resonance

layer 3. Pitch angle scattering due to AIC-

modes 4. Radial transport due to low-frequency

fluctuations 5. Summary

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2OS2010 2

Motivation of the researchSaturation and/or reduction of the density and temperature (pressure) have been observed in high-power ICRF heating experiments on GAMMA 10

Transport induced by waves are possible candidates

Interactions * with ICRF waves Turning point diffusion near the cyclotron resonance layer * with high-frequency fluctuations in the ion cyclotron frequency range Alfvén Ion Cyclotron modes (AIC-mode) are spontaneously excited due to strong temperature anisotropy Pitch angle scattering due to AIC-modes * with Low-frequency fluctuations in kHz range Drift-type fluctuations and Flute-type fluctuations have been identified Radial transport of high-energy ions due to low-frequency waves

OS2010 2 /26

3OS2010 3

Diffusion due to existence of the resonance layerin GAMMA 10 (Nuclear Fusion 1988)

OS2010 3

GAMMA 10 plasmas are sustained by formation of high plasmas in the anchor cell. (Formation of plasmas does not depend on the magnetic field strength in the central cell and depends on that in the anchor cell.) Operation window is indicated that the cyclotron resonance layer exists within closed mod-B surface region

OperationWindow(a) – (b)

When the resonance layer exists on mod-Bsurface with open configuration, ions can diffuse along mod-B surface

/26

4OS2010 4OS2010 4

Diffusion is enhanced when the cyclotron layer exists in thermal barrier cell

without resonance layer

with resonance layer

/26

Diffusion due to existence of the resonance layerin Phaedrus-B (Phys. Fluids B 1992)

5OS2010 5

Phaedrus-B

Radial profile of the density and potential indicate the enhanced radial diffusion when the resonance layer exist in the thermal barrier cell

Enhanced end loss current with the resonance layer

/26

6

GAMMA 10 device and ICRF systems

/26OS2010

7OS2010 7OS2010 7

GAMMA 10 is an axisymmetrized tandem mirror with minimum-B anchors

GAMMA 10 Device

Z

Central cellEast anchor cell

West plug/barrier cell

East plug/barrier cell

West anchor cell

ICRF

B (T)

3

2

1

0

ECHECH

Potential

ICRF:Plasma ProductionIon HeatingMHD Stabilization

ECH:Potential FormationElectron Heating

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8OS2010 8OS2010 8

Magnetic Field Line and Antenna Configuration

RF1RF2RF3

300kW2300kW2200kW

Max. power Max. duration Frequency range

500ms500ms500ms

7.5 - 154.4 - 9.636 -76

MHzMHzMHz

RF1 System9.9, 10.3 MHz

RF2 System 6.36 MHz

Nagoya Type IIIantenna

Double Half Turn antenna

ICRF powers are injected only into the central cell

/26

Single layerFaraday shield

9OS2010 9OS2010 9

プラズマ

Plasma

Schematic Drawing and Photograph of RF Antenna System

DHT Antenna

TypeIII Antenna

Gas BoxDiamag. Loop

/26

10OS2010 10OS2010 10

Typical Plasma ParametersPeak ion temperature reached more than 10 keV with the slow Alfvén wave heating.Plasmas with a strong temperature anisotropy more than 10 have been formed

/26

Location of cyclotron resonance layers of RF1 and RF2

Temporal evolution of plasma parameters

n ~ 2 x 1012 cm-3, Ti > 5 keV

0

1

2

3Central Cell West Anchor Cell

TypeIII DHT

anchor midplane

cental cell midplane

0

1

2

0 2 4 6Z-axis [ m ]

RF2resonance

RF1 resonance

0

50

100 #215447

RF1 RF2

5

010

0

z = -0.33 m

5 z= 1.5 m

z = 1.9 m

0

10

20

50 100 150 200 250Time [ ms ]

11OS2010 11OS2010 11

0

1

2

3

4

Wa

ve

Nu

mb

er

0 10.80.4 1.20.60.2

(Wave Frequency)/(Cyclotron Frequency)

imaginary part > 0

0.6 0.8 1 1.2

Wa

ve

Am

plit

ud

e [

a.u

.]

(Wave Frequency)/(Cyclotron Frequency)

Applied RFExcitedAIC-wave

RealPart

Imaginary Part

Alfvén ion cyclotron (AIC) modes are excited due to a strong temperature anisotropy. The modes excited in the central cell of GAMMA 10 have several discrete peaks. The frequency of the AIC mode is just below the ion cyclotron frequency. The spatial mode structures of each discrete peak in radial and azimuthal directions are confirmed to be the same structure. The AIC modes are excited as eigenmodes in the axial direction.

Excitation AIC-modes due to strong anisotropy

-20

0

20

40

60# 208457

Am

plitu

de

[d

B]

Frequency [MHz]5.5 6 6.5

Tim

e

[ms]

0

100

50

AIC-modes RF2(6.36 MHz)

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Temporal evolution of the AIC modes

12 /26OS2010 12

Diagnostics

13OS2010 13OS2010 13

Photograph of Central Limiter and Probes

Segment limiter D = 0,36 m(Floated and divided into 8 sections in azimuthal direction)

(Floating potential and azimuthal structure of fluctuations)

Electrostatic probe array : ESP

(Ion saturation current and density fluctuation) Electrostatic probes are also set in the axial direction

Magnetic probe array :MP(RF wave measurement )

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14OS2010 14

central cell High Energy-ion Detector : ccHED

ccHED : at the central cellmidplane (to measure theradial transport)

eeHED:at the east end (to measure the axial transport)

Locations of ccHED and eeHED Schematic drawing of ccHED

The ccHED has a co-axial geometry. The ccHED is inserted perpendicularly to the magnetic field line and is positioned just outside of the limiter radius. By rotating the inner and the outer pipes together, a pitch angle distribution of hot ions can be measured. When a pin-hole aperture of which diameter is 0.2mm on the outer pipe is used, the resolution of the pitch angle becomes ±3 degrees. When apertures are arranged in the electron diamagnetic direction, no signals are detected and when the aperture covered with an aluminum foil, no signals are detected. These imply the discrimination of protons from electrons, neutrals and UV is possible.

B-field

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15OS2010 15

Measurement of pitch angle scattering of high-energy ions due to AIC-modes

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16OS2010 16

In GAMMA 10, Alfvén Ion Cyclotron (AIC) modes are spontaneously excited due to a strong temperature anisotropy. When the amplitude of the AIC modes becomes strong, high-energy ions trapped in the central cell (ccHED) are scattered to the end (eeHED).

Behavior of high-energy ions with small pitch angles (60 and 75 degrees) is the same as the behavior of un-trapped ions.The enhancement of the pitch angle scattering from perpendicular to parallel directions is suggested.

Pitch angle scattering due to AIC-mode

ccHED signals on the different pitch angles.

0

30

60

Time [msec]50

Sig

nal

of

HE

D

[a.u

.]

ccHED

eeHED

75250

AIC-mode

Pitch Angle 60

25Time [msec]

50 750

Pitch Angle 75

Pitch Angle 90

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17OS2010 17

Observation of low-frequency fluctuations related to AIC-modes

50 100 150 200 250

Time [ms]

Fre

que

ncy

[M

Hz]

6.5

6

5.5

#215447MP

RF2 6.36 MHz

AIC-modes

AIC-mode has several discrete peaks

Fluctuations with beat frequencies between each peak of AIC-modes are observed in the central cell

Low frequency waves

50 100 150 200 250Time [ms]

Fre

que

ncy

[kH

z]

100

50

0

#215447ESPch4

Floating potential of cc-limiter

Drift-type fluctuations

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In the central cell, two types of fluctuations are observed in lower-frequency region (drift-type and flute-type)

Temporal evolution of the frequency spectrum of the magnetic probe signal

18OS2010 18

50 100 150 200 250Time [ms]

Fre

que

ncy

[kH

z]

100

50

0

#215447ESPch5

50 100 150 200 250Time [ms]

Fre

que

ncy

[kH

z]

100

50

0

#215447eeHED

Pitch angle scattering due to low frequencyfluctuations

Electrostatic Probe

Drift-type fluctuations

No end-loss ions due to drift-type fluctuations

eeHED: high energy ion to the end

Pitch angle scattering due to low-frequency waves related to AIC-modes is clearly observed at the east end

50 100 150 200 250Time [ms]

Fre

que

ncy

[kH

z]

100

50

0

#215447 Limiter Potential

Limiter Floating Potential

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19OS2010 19

Measurement of radial transport of high-energy ions due to low-frequency

fluctuations

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20OS2010 20

central cell High Energy-ion Detector : ccHED

Signal of 5.5MeV -particle from 241Am

1v/d1sec/d

OS2010 20

0

6

12#198679 (82ms-83ms)

Time [ms]82 8382.5

Sig

nal I

nte

nsi

ty

[a.u

.]

Interpretation of ccHED signalWhen an aperture of the minimum size is used, pile-up signals are still obtainednear the plasma edge.

When ccHED is set at the location of r = 25 cm, discrete signals are obtained. (Limiter radius is 18 cm and Larmor radius of 10 keV hydrogen is about 1.4 cm.)

0

4000

8000

50 100 150 200 250

#198679 HED-raw

Time [ms]

0

6

12#198679 (82.1ms-82.3ms)

Time [ms]82.1 82.382.2S

igna

l Am

plitu

de

[a.

u.]

These discrete peaks are burst-like escaping High-energy ions (several hundreds particles).This burst frequency corresponds to that of the drift-type fluctuation.

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21OS2010 21

Raw signals of ESP and ccHED

OS2010 21

0

500

1000

1500

50 100 150 200 250

#215675

Time [ms]

ccH

ED

Sig

na

l

A

mpl

itud

e [

a.u

.]

50 100 150 200 250Time [ms]

Fre

que

ncy

[kH

z]

80

40

0

#215675ESP

50 100 150 200 250Time [ms]

Fre

que

ncy

[kH

z]

80

40

0

#215675HED

0

2000

4000

50 100 150 200 250

#215675

Time [ms]

ES

P S

ign

al

[a.u

.]As indicated in the power spectrum of ESP and ccHED signals, fluctuations with same frequency are clearly observed.

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22OS2010 22OS2010 22

Pitch angle dependence of the phase difference between signals of density and high-energy ions

-3 -2 -1 0 1 2 3

#211964

85 degree

Fre

que

ncy

[

kHz

]

Phase Difference [rad]

10

8

6

4

2

0-3 -2 -1 0 1 2 3

#212003

75 degree

EPhase Difference [rad]

Fre

que

ncy

[

kHz

]

10

8

6

4

2

0-3 -2 -1 0 1 2 3

#212000

65 degree

Phase Difference [rad]

Fre

que

ncy

[

kH

z ]

10

8

6

4

2

0

To determine the relation between fluctuations in density and high-energy ion signals, the pitch angle dependence of the phase differences between both signals is evaluated.

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23OS2010 23

B

B02sin

Pitch angles corresponds to the turning points of high-energy ions in the central cell

Turning points of ions which have pitch angles of 85, 75 and 65 degrees at the location of ccHED are indicated below.

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0

0.5

1

1.5

2

2.5central cell - B field

-3 -2.5 -2 -1.5 -1 -0.5 0

B

[ T

]

85 deg.75 deg.65 deg.

Z [ m ]

(pitch angle of 75 deg.)

24OS2010 24OS2010 24

Mode structure of the fluctuation

Azimuthal direction

Axial direction

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-3 -2 -1 0 1 2 3

#212003 ESP78

Phase Difference [rad]

Fre

que

ncy

[

kHz

]

40

30

20

10

0

m=1

m=2

Rotation in the direction of electron diamagnetic drift

-3 -2 -1 0 1 2 3

#212003ESP75

Phase Difference [rad]

Fre

que

ncy

[

kH

z ]

10

8

4

2

0

6

kz=1.38k

z=0.8

-3 -2 -1 0 1 2 3

#212003ESP85

Phase Difference [rad]

Fre

que

ncy

[

kHz

]

10

8

4

2

0

6

kz=1.38k

z=0.8

Axial wave number is estimated from phase differences between probes located at z = 0.33 m and 1.20 m.Two probes are set at the location of z = 0.33 m and have azimuthal angles of +22.5 and -22.5 degrees different from the probe at z = 1.2 m, respectively. Axial wave number is determined by values obtained from both probes.

25OS2010

0

0.5

1

1.5

2

2.5central cell - B field

B

[ T

]

85 deg.75 deg.65 deg.

B

B02sin

ccHED

0

1

2

3

-3 -2.5 -2 -1.5 -1 -0.5 0Z-axis [ m ]

Ph

ase

Diff

ere

nce

[

rad

]

kz=0.8

kz=1.38

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Radial transport near the turning points

Assume the phase differences at the midplane (pitch angle of 90 degree) is zero

High- energy ions interact with low-frequency fluctuations mainly near their turning points

26OS2010 26OS2010 26

Summary

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Three types of wave-particle interactions are observed in GAMMA 10.

1. Turning point diffusion near the cyclotron resonance layer is suggested in minimum-B configuration on the anchor cell.

2. Pitch angle scattering of high-energy ions due to AIC-modes and low-frequency waves which have differential frequencies between discrete peaks of AIC-modes.

3. Radial transport of high-energy ions due to drift-type fluctuations near their turning points in the confining mirror field.