Fluctuation Measurements in DIII-D Edge Electron...

QTYUIOPEdge Electron Temperature Fluctuations in DIII-D - R. D. Lehmer APS97 - 1

Edge Electron Temperature Fluctuation Measurements in DIII-D

R. D. Lehmer, J. A. Boedo, R. A. Moyer - UC-San Diego

J. G. Watkins - Sandia National Laboratories

K. H. Burrell - General Atomics


AbstractMeasurements of the electron temperature fluctuations in the edgeof tokamaks have shown that Te fluctuations can not be neglectedwhen determining the cross field heat and particle transport (Liewer,McChesney, Zweben, and Gould, Phys. Fluids 29 (1986) 309). Amodified phase compensated triple probe (Tsui, Bengtson, Li, et al.,Rev. Sci. Instrum. 63 (1992) 4608) is utilized on the existingmidplane reciprocating probe hardware on DIII-D to add phasecorrelated Te fluctuations to the existing measurement of ionsaturation current and floating potential fluctuations. With thistechnique, we are able to infer the cross field conductive heattransport and make better estimates of the particle and convectiveheat transport. The design and implementation of a high-bandwidthtriple probe measurement in a high heat flux, beam-heated tokamakdischarge will be discussed. Preliminary measurements from thediagnostic upgrade will be presented, along with comparisons of theconvective and conductive heat flux estimates up to the separatrixin L- and H- mode plasmas.


Goal of Measurement

• To Improve the Understanding of the Cross Field Heat Transport Mechanisms in the Shear Layer and SOL.

Need to Compare Convective vs. Conductive Heat Transport.• Reciprocating Scanning Probe Measurements at DIII-D Have So Far

Neglected Te Fluctuations. - Unable to Infer Conductive Heat Transport.

• Correlated ne, Eθ and Te Fluctuation Measurements are Necessary to Determine Conductive Heat Flux.

• With Correlated Te Fluctuation Measurement, Improved Estimates for Local Particle Transport and Convective Heat Flux can be made.

To Measure the Turbulently Driven Heat Flux in the Edge of DIII-D


Turbulently Driven Heat Fluxes are Determined from the Correlation of ne, Te, and Eθ

Ref: Liewer, McChesney, Zweben, and Gould, Phys. Fluids 29 (1986) 309

˜ Q tot = ˜ Q conv + ˜ Q cond

Q Tconv e r= 52

Γ

Γr nE B= ˜ ˜ /θ φ˜ ˜E pθ θφ= −∇

˜ φ p = ˜ φ f + α ˜ T e

˜ Q cond =5

2n ˜ T e

˜ E θ / Bφ

˜ n

n=

˜ I sat

Isat

+˜ T eTe

ConvectiveHeat Flux

ConductiveHeat Flux

Measured and First Order Inferred Quantities

Te Fluctuations Measurement Allows for Red Terms to be Estimated.


Probe Methods Considered for Determining the Heat Flux in the Edge of DIII-D

• Fast Swept Probes (TJ-I, TEXT):For DIII-D: Requires ~1-3kW RF amplifier (@1-2MHz)Fit Probe Characteristics with very few points (5-10)

• Triple Probe Method (TEXT, TEXT-U, Phaedrus-T, and TBR):Passive - Requires No Sweeping or Voltage Tracking; Ease of Analysis.Capacitance Problems in DIII-D Preclude Its Use at High Frequencies (>10kHz).

• Second Harmonic Detection (TEXTOR):Uses 1kW Power Amplifier; Transmission Line Eliminates Capacitance Effects.Non-Linear Behavior about Vf Determines Amplitude of Te Fluctuations.


Triple Probe Technique Will Not Work at DIII-D Because of the Construction of the Probe

• Triple Probe Technique Compares the Fluctuating Floating Potential to the Potential Fluctuations on One Tip on a Biased Double Probe.

• Triple Probe Techniques Work in Smaller Tokamaks (TEXT, TBR, etc), but Large Parasitic Capacitance in UCSD/SNLA Scanning Probe Causes Rolloff (30kHz).

• Probe Head and Drive Tube not Designed to Measure Fluctuating Potential and Current Simultaneously on the Same Pin.

• This Technique Would Require Major Vacuum Hardware Redesign.

I+

I-

Ip

Rp

Ip

V’1

Isat

V2

50Ω100kΩ

50Ω

300pF

Probe


Second Harmonic Detection System for UCSD/SNLA Scanning Probe at DIII-D

• Floating Single Probe.• Driven at 400kHz to Approximately 0.5Te About Vf.• Non-Linear Response to Sweeps About Vf Generates Harmonics

in Collected Current. • Current is Analog Filtered at 1st and 2nd Harmonics (800kHz).

Bandwidth for Te Fluctuations will be About 200kHz.• Expansion of Idealized Probe Characteristic about Vf Relates Ratio

of Current in Harmonics to the Electron Temperature (for U0 < Te). First Order Solution is Te = U0(Iω/4I2ω).


Schematic Diagram of Second Harmonic Detection System Power Components

50Ω

Transmission Line

MachineGround

Dummy Transmission Linefor Balanced Circuit Operationwith No Plasma.

SignalTransformer

Power Amplifier1kW Max@ 400kHz

Currentto Filters

ProbeTip

Improvement of Design Previously Used by UCSD at TEXTOR Tokamak(J. Boedo, et al., to be Submitted to RSI)


Current Status: Interim Check-Out Phase

• If Balanced Circuit Design Works with Plasma, We Can Determine Average <Te> from Harmonic Detection and Compare to Equilibrium Te from Double Probe.

• Temporary Installation of Existing Power Amplifier and Electronics in Existing Isolated Rack for Scanning Probe for Up Coming Operations Period.

• In this Arrangement, Excessive Cable Lengths Will Make Correlated Fluctuation Measurements and Heat Flux Estimates Difficult - not Part of the Interim Check-Out Goals.

Goal: Test Power Supply Capacity and Balanced Circuit Design.


Upgrade Scheduled to be Complete in March, ‘98


Harmonic Detection System at DIII-D Will Incorporate Several Improvements

• Improvements:– Power Supply Feedback System– New 1kW Power Supply– New Electronics (Adjustable Gains, Increased Filter Bandwidth)

• Other Upgrades:– Vacuum System Upgrade (New Pump and Controls)– Piggyback Electronics Box


Significant Modifications to Reciprocating Probe Support Equipment Required to Install Upgrade

• Additional Space Requires Adjacent to Probe for Electronics and Power Systems Requires Redesign and Relocation of Some Vacuum Support Systems.

210• NBI

RCP

6’ 8” Level

Racks(LowerLevel)

ProposedNew P/SLocation

Probe PumpStand Relocated

Adjacent to 210 NBILower Level

DIII-DPiggybackElectronics

Box

V1.2A


I2ω

Iω

UoMPY100

SRS235400kHz

Funct. Gen.(-14dBm)

ENI2100LPowerAmp.

(50dBm)

200HzLowpass

Z2

X1

OUT

AMMod.

-1.25VY1

REF10

80k10k

-+

-+

Fire Probe - Resets Integrator

-+

Use Active Power Supply Feedback Control to Maintain Constant U0/Te Ratio

VI

IVOUT = −10 1 252ω

ω

.

• Feedback Circuit Maintains (Uo/Te = 4I2ω/Iω = constant = 0.5)• Inverting Integrator with Reset at Time of Shot

If I2ω/Iω < .125 then Uo increased and if I2ω/Iω > .125 then Uo decreased.

• 200Hz Low Pass Filtering Reduces Effect of ELM’s and Disruptions, but Maintains Response to Te Gradients.


Harmonic Detection System is not a Permanent Replacement for Base Electronics Package

• Swept Double Probe Measurement is Still the Primary Method of Determining Equilibrium Te and ne Profiles.

• Plug Compatible Systems - Allows Switch of Diagnostic Capabilities During a Pit Run.

DetachableElectronics Box

StandardElectronics Box

MezzanineLevel


Comparison Studies of RMS Level of Te from Harmonic Detection and Te from Double Probe

• Conduct Preliminary Tests in Piggyback Mode on Non-Critical Run Days.• Interim Test Configuration: Replace Turbulent Isat Measurement with Te

Measurement and Retain Double Probe Capability.

B

Isat~ Vf

~

Swept Tipfor Te

Spare

B

~ Vf~Swept Tip

for Te

DoubleProbe Tips

Arrangement for Comparison Studies Normal Operating Arrangement with Te


Expansion of Single Probe I-V Characteristic in Series of Bessel Functions

In the region of the floating potential, the response of a probe can bewritten as (J. Boedo, et al., to be submitted to RSI):

I Ie V

kTp sate

= −

( exp )1∆

.

If ∆V V V U tp f= − = 0 cos( )ω ,

expcos( )

cos( )eU t

kTI

eU

kTI

eU

kTnwt

e en

en

00

0 0

1

2ω

=

+

=

∞

∑where In are the Modified Bessel functions of integer order.The Modified Bessel functions can be expanded as:

I xx

n n kk

n k

n kn

( )!( )!

=+

+

+=

∞

∑2

20 2

I xx x

0

2 4

14 64

( ) ...= + + + I xx x

1

3

2 16( ) ...= + +

I xx x

2

2 4

8 96( ) ...= + + I x

x x3

3 5

48 768( ) ...= + +


For Sweep Amplitudes Smaller than Te, Ratio of Bessel Functions can be Reduced to Simple Form

Given that

I xx x

0

2 4

14 64

( ) ...= + + + I xx x

1

3

2 16( ) ...= + +

I xx x

2

2 4

8 96( ) ...= + + I x

x x3

3 5

48 768( ) ...= + +

if x<<1, then (J. Boedo, et al., to be submitted to RSI):I x

I x

x2

1 4

( )

( )=

and

I x

I x

x3

1

2

24( )( )

=

Therefore, if x = eU0/kTe = 0.5, then Second Harmonic in CurrentResponse to Sweep will be about 10% of the Fundamental Harmonicand the Third Harmonic will be about 1% of the Fundamental.


Probe Potential Offset Due to Rectification is Small Compared to Potential Fluctuations

• For Typical Sweep Amplitude (U0/Te = 0.5), Rectification can Generate Small Displacement in Probe Potential Away from the Floating Potential.

• Largest Displacements would be where Te is Large (3-4 Volts max).

• Displacement is Small Compared to Vf Fluctuation Level (10-30 Volts RMS). Plasma is Likely to Absorb Excess Charge on Probe Due to these Fluctuations.

• Floating Potential of Tip Also Varies in Time Due to Motion of Scanning Probe.

V/Te

I/Isa

t

U0/Te= 0.5

Offset = 0.04Te

Plasma

Resistive Load


• Bulk of Turbulent Particle Flux is Observed to Occur Below 200kHz.

• Electron-Electron Collision Rate Places an Upper Limit on the Rate that the Electron Energy Distribution can Respond.

• For Typical DIII-D Edge/SOL Parameters:

Electrostatic Fluctuations Responsible for Turbulent Particle Flux are much Slower than νee.

νee

e

xn

T= 2 9 106

32

.ln Λ

νee x x s=( )( )

( )= −2 9 10

10 10

301 5 106

136 1

32

. .


FILTER

BANDPASS

400KHZ

50Ω20Ω

1KΩ 1KΩ

50Ω 250Ω

50Ω50Ω

FILTER

BANDPASS

800KHZ

50Ω20Ω

1KΩ 1KΩ

50Ω 105Ω

50Ω50Ω

ENI250WAMP50db

50Ω Out

Probe

31mA500K

100K

1K

160pf

3.3V FastHigh VoltageClamp CKT.

1K

31mA500K

100K

1K

160pf

3.3V FastHigh VoltageClamp CKT.

1K

1K

1K

20Ω

PeakDetector

PeriodicSample &Hold Timing Circuit

PeakDetector


PeakDetector


20Ω

20Ω

20Ω

Z

To A/D

Z

To A/D

Z

To A/D

50Ω

50Ω

50Ω

4

15

78

4

15

78In

626

2

Out 35

6

4

15

78

4

15

78In

626

2

Out 38

3

4

15

78

4

5

7

26

3

11

26

4

5

78

WCCW

6

CW

WW

3CCWCW

CCW

WCW

2

CCW

CWW

CW

8

CCW1

3

3

3

9

2

* Not e : Inpu t A/ D is 1MΩ to avoid signal l eve l att enuated.

4

1V per Amp

OverAl l

Ove rAl l

OverAl l

9 Td=1.25us

7

1 0Khz -> 1 2Mhz

Pr obe T ip

Tokamak GND

1. Td=0

2. Td=0Av=0.10 7

Vd iv ide r

3. Td=2.5us

Td=2.5usAv=0.1 05

6. Td=2.5us

4. Td=-0.40 4us

5. Td=5.0 95us

8. Td=5.08us7. Td=-0 .276us

(4 00KHz)Td=7.1 91usAv=2 1.6

(80 0KHz)Td=6.05 4usAv=50.4

Schematic Diagram of Harmonic Detection Circuits

Ref: J. Boedo, et al., EPS ‘95


Ratio of Filter Responses is Linear Over Required Bandwidth, but SNR is High

• Individual Output Amplitudes for Each Filter Begin to Roll-Off above 50kHz, however, Ratio of Amplitudes Remains Approximately Constant.

• We will Test System with this Bandwidth and Proceed to Specify Filters with Higher Bandwidth.

0

0.2

0.4

0.6

0.8

1

1.2

Ratio

: Am

p(1)

/Am

p(2)

0 50 100 150 200 250

Frequency (kHz)

0

0.25

0.5

0.75

1

1.25

Out

put A

mp/

Ref S

igna

l (re

lativ

e)

0 50 100 150 200 250

Frequency (kHz)

1st Harmonic (400kHz)2nd Harmonic (800kHz)


Phase Delays in Each Harmonic are less than Characteristic Time of Sample and Hold Circuit

• Phase Delay through Circuits is Constant Up Through Maximum Frequency (200kHz):

8.5µs for 1st Harmonic6.9µs for 2nd Harmonic


Harmonic Detection System at TEXTOR Characterized Turbulent and Equilibrium Edge Te

• Good Agreement with Equilibrium Te Profile from Double Probe at Edge; Divergence in SOL Due to Over Drive of Harmonic Circuit (U0/Te >1).

• Normalized RMS Fluctuation Levels (Including Te Fluctuations) Similar to Observations from TEXT and TJ-I.

MachineTEXT [1,3] 0.3-0.5 0.15-0.2 0.2-0.5 0.2 0.1 0.3-0.5TJ-1 [5] 0.3-0.5 0.4-0.5TEXTOR 0.2-0.3 0.2-0.7 0.3-0.7 0.15-0.25 0.2 0.2-0.4

n~

n

SOL

Te~

Te

SOL

V f~

kTe

SOL

n~

n

edge

Te~

Te

edge

V f~

kTe

edge

0

20

40

60

80

Te

(eV

)

45 46 47 48 49 50

Radius (cm)

Te Harmonics

Te Double Probe

Ref: J. Boedo, EPS 1995

Fluctuation Measurements in DIII-D Edge Electron...

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