Estimation of T e from ECE data Estimation of n e from reflectometry data

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Max-Planck-Institut für Plasmaphysik, EURATOM Association Estimation of n e and T e with microwave diagnostics and investigations on profile changes with RMP Estimation of T e from ECE data Estimation of n e from reflectometry data Behaviour of profiles with RMP Working title: Working topics: Sylvia K. Rathgeber

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Working title:. Estimation of n e and T e with microwave diagnostics and investigations on profile changes with RMP. Estimation of T e from ECE data Estimation of n e from reflectometry data Behaviour of profiles with RMP. Working topics:. Sylvia K. Rathgeber. Motivation. - PowerPoint PPT Presentation

Transcript of Estimation of T e from ECE data Estimation of n e from reflectometry data

Page 1: Estimation of T e  from ECE data   Estimation of n e  from reflectometry data

Max-Planck-Institut für Plasmaphysik,EURATOM Association

Estimation of ne and Te with microwave diagnostics and

investigations on profile changes with RMP

Estimation of Te from ECE data

Estimation of ne from reflectometry data

Behaviour of profiles with RMP

Working title:

Working topics:

Sylvia K. Rathgeber

Page 2: Estimation of T e  from ECE data   Estimation of n e  from reflectometry data

Motivation

ECE diagnostic: long-standing workhorse for Te analysis

Why another ECE analysis? What is different?

9/28/2010 Sylvia K. Rathgeber 2

Shine-through Current ECE analysis:

Trad = Te, ν → R

Te = 250 eV in SOL ↔Power flux density > 600 MW/m2

Page 3: Estimation of T e  from ECE data   Estimation of n e  from reflectometry data

Max-Planck-Institut für Plasmaphysik,EURATOM Association

Estimation of Te profiles in the framework of Bayesian

Probability Theory via forward modelling of ECE radiation

Sylvia K. Rathgeber

W. Suttrop, R. Fischer

9/28/2010

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Outline

Current ECE analysis(Principle, insufficiency of assumptions, correction, validity range)

Future ECE analysis (Integrated Data Analysis, Bayesian Probability Theory, Forward modelling of ECE data)

Results

9/28/2010 Sylvia K. Rathgeber 4

Page 5: Estimation of T e  from ECE data   Estimation of n e  from reflectometry data

Principle of ECE analysis

Electrons gyrate around magnetic field lines

→ emit radiation with cyclotron frequency and its harmonics:

Tokamak:

→ each cyclotron frequency can be assigned to the position of its resonance in the plasma

ECE intensity is identifiedwith black-body intensity:

Assume Maxwell-distributed gyrotron velocity :

9/28/2010 Sylvia K. Rathgeber 5

em m

eBm

Rm

ReBmR

emm

00)(

)( 8

)()(23

2

TkhTkc

II BradBBB

)()( RTI eeerad TTT ,

R

RBRBBB tttot

00)(

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Local thermal equilibrium

Assumption of Maxwell-distributed only valid in LTE

Non-thermal contributions might play a role

Future work

9/28/2010 Sylvia K. Rathgeber 6

erad TT ?LTE

!

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Non-local measurement

Cold resonance:

non-local measurement→ emission profile broadened:• Doppler broadening: observation

not perpendicular to field line

• Relativistic effects: relativistic massincrease results in frequency shift

9/28/2010 Sylvia K. Rathgeber 7

Rm

ReBR

eX

002

2)(

?R

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Shape of emissivity profile

Consider emission profile:

• Doppler broadening• Relativistic effects

9/28/2010 Sylvia K. Rathgeber 8

X

RR2

||5||

22

2||

2/322

0

22

22

2

)2

)(exp(

))cos1((

)2

()1(cossin16

)(

ddTk

cm

Tk

mn

cej

eB

e

X

eB

ee

XX

R

Page 9: Estimation of T e  from ECE data   Estimation of n e  from reflectometry data

Interaction of radition and plasma

Absorption and reemission of radiation on ray path

9/28/2010 Sylvia K. Rathgeber 9

)()( BBII ?

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Radition transport

Consider radiation transport:

9/28/2010 Sylvia K. Rathgeber 10

)()( BBII

)()(

)()(

I

I

jj

BB

)(

)()(

BBI

j Kirchhoff’s law

(valid in LTE)

)()()()(

Ijds

dI

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The saving: Optical depth

Plasma optically thick:

Reabsorption narrows the observed layer

9/28/2010 Sylvia K. Rathgeber 11

)()( 0)()(

)()(

)(

BB

BB

IIII

jj

ds

dI

1)( dss 318103)( keVmTn critee

Page 12: Estimation of T e  from ECE data   Estimation of n e  from reflectometry data

Outline

Current ECE analysis(Principle, insufficiency of assumptions, correction, validity range)

Future ECE analysis(Integrated Data Analysis, Bayesian Probability Theory, Forward modelling of ECE data)

Results

9/28/2010 Sylvia K. Rathgeber 12

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Integrated Data Analysis

Combination of measured data from

different diagnostics for one joint analysis

Challenges:

Complemetary data → synergistic effects

Combined error analysis → error reduction

Resolve data inconsitensies → revelation of systematic errors

9/28/2010 Sylvia K. Rathgeber 13

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Bayesian recipe

9/28/2010 Sylvia K. Rathgeber 14

)(p

Dd

)(fD )|( dp

)( )|( )|( pdpdp )|( dp )|( dp )(p

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Forward modelling of ECE data

9/28/2010 Sylvia K. Rathgeber 15

if maximized

if n

ot m

axim

ized

Calculation: jν(s), αν(s)Integration → I(ν)

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IDA at ASDEX Upgrade

9/28/2010 Sylvia K. Rathgeber 16

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Outline

Current ECE analysis(Principle, insufficiency of assumptions, correction, validity range)

Future ECE analysis(Integrated Data Analysis, Bayesian Probability Theory, Forward modelling of ECE data)

Results

9/28/2010 Sylvia K. Rathgeber 17

Page 18: Estimation of T e  from ECE data   Estimation of n e  from reflectometry data

Testing: Artficial profiles

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Core:high ne & Te

→ plasma optically thick

Edge:steep Te gradient & low ne

→ shine-through conditions

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Modelling of Trad

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High optical depth & constant Te :Trad = Te

Low optical depth & constant Te:Trad < Te

Low optical depth & Te gradient:Trad > Te

→ rise too small to explain shine-through

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Emissivity profiles

9/28/2010 Sylvia K. Rathgeber 20

Inward-shift of emissivity maximum

Intensity reaches black-body level

Absorption < Emission → no black-body

Higher Te in observed layer than at resonance

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Conventional IDA of L-mode

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Plasma optically thick:Te = Trad, ECE

Plasma optically thin:spline fit with edge condition

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Forward modelling of L-mode

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Data consistent within separatrix

Plasma optically thick:Te slightly reduced

Around separatrix: Te > Trad, ECE

SOL: no data fit possible

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Conclusion & Outlook

Conclusion

Forward modelling of ECE radiation transport included in IDA

Slight corrections in Te profile due to finite optical depth and relativisticly broadened emssivity profile

Shine-through still unresolved

Outlook

Include Doppler broadening (consider finite acceptance angle of antenna, increase precision for general emissivity profile)

Consider non-Maxwellian velocity distribution

9/28/2010 Sylvia K. Rathgeber 23

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Literature

W. Suttrop. Practical Limitations to Plasma Edge Electron Temperature Measurements by Radiometry of Electron Cyclotron Emission. Technical Report 1/306, Max-Planck-Institut für Plasmaphysik, 1997.

I.H. Hutchinson. Principles of Plasma Diagnostics. Cambridge University Press, 1987.

H.J. Hartfuss, T. Geist, and M. Hirsch. Heterodyne methods in millimetre wave plasma diagnostics with applications to ECE, interferometry and reectometry. Plasma Physics and Controlled Fusion, 39: 1693-1769, 1997.

A. Gelman, J.B. Carlin, H.S. Stern, and D.B. Rubin. Bayesian Data Analysis. Chapman & Hall, 1980.

R. Fischer, et. al. Probalistic lithium beam data analysis. Plasma Physics and Controlled Fusion, 50(8): 085009 (26pp), 2008.

R. Fischer, et. al. Integrated density profile analysis in ASDEX Upgrade H-modes. In 35th EPS Conference on Plasma Physics. Contributed Papers, 32D, pages P–4.010, 2008.

R. Fischer, et. al. Multiple diagnostic data analysis of density and temperature profiles in ASDEX Upgrade. In 36th EPS Conference on Plasma Physics. Contributed Papers, 33E, P–1.159, 2009.

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Heat conduction

Parallel heat conduction strongly depends on T:

Small changes in T cause large changes in power flow

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2/5|| TK

2/70 )(7

2T

LA

PSOL

tyconductivi:2000

platedivertor to

difference erature temp:200

platedivertor todistance :100

densityflux power :][

1,0

2

Sm

eVT

mL

WmA

P

e

SOL

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Diagnostic implementation

ASDEX Upgrade:

Frequency range accessible to radio frequency (RF) receiver techniques as well as 'quasi'-optical techniques

Currently installed at ASDEX Upgrade:• Michelson interferometer:

• 8-channel polychromator:

• 60-channel heterodyne radiometer:

→ input RF signal interferes with similar signal from local oscillator

→ down-conversion to intermediate frequency

→ facilitated amplifying and filtering

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GHzTB X 1002

cmRmst 10,30 cmRmst 5,1

mmRst 5,32

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Diagnostic implementation Heterodyne

radiometer:• 4 antennas on

low field side

• 5 mixer

• 3 IF chains (36/12/12 channels) IF amplifier Band pass filter Data acquisition

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GHz

GHz

LO

RF

167,133,128,101,95

18789

kHzS 25.31MHz600/600/300

• Absolute calibrated by measurements of black-body radiation from laboratory hot (773 K) and cold (77 K) sources

GHzLORFIF 182||

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Radial resolution

Radial resolution dependson frequency resolution:

Frequency resolution is limited by:• Doppler broadening

(ASDEX Upgrade: 86° ≤ θ ≤ 94°)

• Relativistic effects: relativistic mass increase results in frequency shift

9/28/2010 Sylvia K. Rathgeber 28

Plasma core: RF bandwidth (ΔνRF=600MHz) matches resolution limit due to line broadening (relativistic effects dominant)

Plasma edge: resolution determined by receiver (ΔνRF=300MHz)

RR

Rm

ReBmR

em

00)(

Page 29: Estimation of T e  from ECE data   Estimation of n e  from reflectometry data

Temperature resolution

Temperature resolution is limited by noise in black-body radiation emitted from the plasma (much higher than noise of receiver)

Black-body fluctuations given by radiometer formula:

High signal-to-noise ratio/ good temperature resolution needs low video bandwidth (→ long integration time) or high RF bandwidth (→ low radial resolution)

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RF

Vradrad TT

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Harmonic overlap

Resonance frequencies:

160-200 GHz: depending on optical thickness, radiation consists of 2nd and 3rd harmonic

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mRTB

Rm

ReBmR

em

65.1,5.2

)(

00

00

Only 1st and 2nd harmonics are feasible for measurements of and from the low field side

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Low density limit: optical depth

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Te = Trad only in case of optically thick plasma (τ >> 1)

τ strongly decreases with increasing harmonic number

→ 1st harmonic O-mode and 1st and 2nd X-mode are mostly optical thick in the bulk plasma

typical ASDEX Upgrade parameters:

measurements

][109.3 192 keVTn eeX

318103)( keVmTn critee

Page 32: Estimation of T e  from ECE data   Estimation of n e  from reflectometry data

High density limit: Cut-off

Below eigenfrequency of plasma electromagnetic waves are completley shielded by electrons → cut-off

O-mode waves (E || B0):

X-mode waves (E ┴ B0):

Cut-off density:

9/28/2010 Sylvia K. Rathgeber 32

e

epCO m

en

0

2

)4(2

1 22pccCO

202 Bm

mne

mOCO

2,)1( 20 mBm

mmne

mXCO

23192 ][102 TBmn XCO

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Consequence of limitations

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2nd harmonic X-mode is the best candidate

for ECE measurements

according to limitations due to harmonic overlap,

cut-off and optical depth

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Doppler broadening

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Trad = Te in case of high optical depth

Trad < Te in case of low optical depth

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Doppler & Relativistic effects

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Trad = Te in case of high optical depth

Trad < Te in case of low optical depth and constant Te

Trad > Te in case of low optical depth and Te gradient