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

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.

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

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  1. Working title: 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 topics: Sylvia K. Rathgeber

  2. Motivation • ECE diagnostic: long-standing workhorse for Te analysis • Why another ECE analysis? What is different? • Shine-through • Current ECE analysis: • Trad = Te, ν → R • Te = 250 eV in SOL ↔ • Power flux density > 600 MW/m2 Sylvia K. Rathgeber

  3. 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

  4. 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 Sylvia K. Rathgeber

  5. 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 identified with black-body intensity: • Assume Maxwell-distributed gyrotron velocity : Sylvia K. Rathgeber

  6. Local thermal equilibrium ! • Assumption of Maxwell-distributed only valid in LTE • Non-thermal contributions might play a role Future work ? LTE Sylvia K. Rathgeber

  7. Non-local measurement ? • Cold resonance: • non-local measurement → emission profile broadened: • Doppler broadening: observation not perpendicular to field line • Relativistic effects: relativistic mass increase results in frequency shift Sylvia K. Rathgeber

  8. Shape of emissivity profile • Consider emission profile: • Doppler broadening • Relativistic effects Sylvia K. Rathgeber

  9. Interaction of radition and plasma ? • Absorption and reemission of radiation on ray path Sylvia K. Rathgeber

  10. Radition transport Consider radiation transport: Kirchhoff’s law (valid in LTE) Sylvia K. Rathgeber

  11. The saving: Optical depth Plasma optically thick: • Reabsorption narrows the observed layer Sylvia K. Rathgeber

  12. 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 Sylvia K. Rathgeber

  13. 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 Sylvia K. Rathgeber

  14. Bayesian recipe Sylvia K. Rathgeber

  15. Forward modelling of ECE data Calculation: jν(s), αν(s) Integration → I(ν) if not maximized if maximized Sylvia K. Rathgeber

  16. IDA at ASDEX Upgrade Sylvia K. Rathgeber

  17. 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 Sylvia K. Rathgeber

  18. Testing: Artficial profiles • Core: • high ne & Te • → plasma optically • thick • Edge: • steep Te gradient & low ne • → shine-through • conditions Sylvia K. Rathgeber

  19. Modelling of Trad • 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 Sylvia K. Rathgeber

  20. Emissivity profiles • Inward-shift of emissivity maximum • Intensity reaches black-body level • Absorption < Emission → no black-body • Higher Te in observed layer than at resonance Sylvia K. Rathgeber

  21. Conventional IDA of L-mode • Plasma optically thick: • Te = Trad, ECE • Plasma optically thin: • spline fit with edge condition Sylvia K. Rathgeber

  22. Forward modelling of L-mode • Data consistent within separatrix • Plasma optically thick: • Te slightly reduced • Around separatrix: • Te > Trad, ECE • SOL: no data fit possible Sylvia K. Rathgeber

  23. 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 Sylvia K. Rathgeber

  24. 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. ContributedPapers, 33E, P–1.159, 2009. Sylvia K. Rathgeber

  25. Heat conduction • Parallel heat conduction strongly depends on T: • Small changes in T cause large changes in power flow Sylvia K. Rathgeber

  26. 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 Sylvia K. Rathgeber

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

  28. Radial resolution • Radial resolution depends on frequency resolution: • Frequency resolution is limited by: • Doppler broadening (ASDEX Upgrade: 86° ≤ θ ≤ 94°) • Relativistic effects: relativistic mass increase results in frequency shift • Plasma core: RF bandwidth (ΔνRF=600MHz) matches resolution limit due to line broadening (relativistic effects dominant) • Plasma edge: resolution determined by receiver (ΔνRF=300MHz) Sylvia K. Rathgeber

  29. 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) Sylvia K. Rathgeber

  30. Harmonic overlap • Resonance frequencies: • 160-200 GHz: depending on optical thickness, radiation consists of 2nd and 3rd harmonic • Only 1st and 2nd harmonics are feasible for measurements of and from the low field side Sylvia K. Rathgeber

  31. Low density limit: optical depth • 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 Sylvia K. Rathgeber

  32. 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: Sylvia K. Rathgeber

  33. Consequence of limitations 2nd harmonic X-mode is the best candidate for ECE measurements according to limitations due to harmonic overlap, cut-off and optical depth Sylvia K. Rathgeber

  34. Doppler broadening • Trad = Te in case of high optical depth • Trad < Te in case of low optical depth Sylvia K. Rathgeber

  35. Doppler & Relativistic effects • 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 Sylvia K. Rathgeber

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