Working title: Estimation of ne and Te with microwave diagnostics and investigations on profile changes with RMP Working topics: Estimation of Te from ECE data Estimation of ne from reflectometry data Behaviour of profiles with RMP Sylvia K. Rathgeber

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 9/28/2010 Sylvia K. Rathgeber

Sylvia K. Rathgeber W. Suttrop, R. Fischer 9/28/2010 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

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

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 : 9/28/2010 Sylvia K. Rathgeber

Local thermal equilibrium ! Assumption of Maxwell-distributed only valid in LTE Non-thermal contributions might play a role Future work ? LTE 9/28/2010 Sylvia K. Rathgeber

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 9/28/2010 Sylvia K. Rathgeber

Shape of emissivity profile Consider emission profile: Doppler broadening Relativistic effects 9/28/2010 Sylvia K. Rathgeber

Interaction of radition and plasma ? Absorption and reemission of radiation on ray path 9/28/2010 Sylvia K. Rathgeber

Radition transport Consider radiation transport: Kirchhoff’s law (valid in LTE) 9/28/2010 Sylvia K. Rathgeber

The saving: Optical depth Plasma optically thick: Reabsorption narrows the observed layer 9/28/2010 Sylvia K. Rathgeber

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

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

Bayesian recipe Reasoning about parameter θ: prior (uncertain) prior information prior distribution + physical model likelihood distribution + (uncertain) measured data + Bayes Theorem posterior distribution 9/28/2010 Sylvia K. Rathgeber

Forward modelling of ECE data ne(ρ), Te(ρ) → ne(s), Te(s) Modelling: Trad(ν) Likelihood: TECE, rad(ν) ↔ Tmod, rad(ν) Posterior: p(ne(ρ), Te(ρ)|dECE) Estimates: ne(ρ)±Δne(ρ), Te(ρ)±ΔTe(ρ) Calculation: jν(s), αν(s) Integration → I(ν) Prior information if not maximized if maximized 9/28/2010 Sylvia K. Rathgeber

IDA at ASDEX Upgrade ne(ρ), Te(ρ) mapping ρ(x) → ne(x), Te(x) DLIB(ne(x), Te(x)) LIthium Beam emission profile dLIB DDCN(ne(x)) line integra-ted DCN data dDCN DECE(ne(x), Te(x)) ECE radiation temperature dECE results: p(ne(ρ), Te(ρ)|dLIB, dDCN, dECE, dTS) estimates: ne(ρ)±Δne(ρ), Te(ρ)±ΔTe(ρ) DTS(ne(x), Te(x)) Thomson Scattering data dTS addl. infor-mation, constraints, model parameters 9/28/2010 Sylvia K. Rathgeber

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

Testing: Artficial profiles Core: high ne & Te → plasma optically thick Edge: steep Te gradient & low ne → shine-through conditions 9/28/2010 Sylvia K. Rathgeber

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 9/28/2010 Sylvia K. Rathgeber

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 9/28/2010 Sylvia K. Rathgeber

Conventional IDA of L-mode Plasma optically thick: Te = Trad, ECE Plasma optically thin: spline fit with edge condition 9/28/2010 Sylvia K. Rathgeber

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 9/28/2010 Sylvia K. Rathgeber

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

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. 9/28/2010 Sylvia K. Rathgeber

Heat conduction Parallel heat conduction strongly depends on T: Small changes in T cause large changes in power flow 9/28/2010 Sylvia K. Rathgeber

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 9/28/2010 Sylvia K. Rathgeber

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 9/28/2010 Sylvia K. Rathgeber

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) 9/28/2010 Sylvia K. Rathgeber

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) 9/28/2010 Sylvia K. Rathgeber

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 9/28/2010 Sylvia K. Rathgeber

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 9/28/2010 Sylvia K. Rathgeber

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

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 9/28/2010 Sylvia K. Rathgeber

Doppler broadening Trad = Te in case of high optical depth Trad < Te in case of low optical depth 9/28/2010 Sylvia K. Rathgeber

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 9/28/2010 Sylvia K. Rathgeber