Accuracy of TEXTOR He-beam diagnostics

Similar documents
Hydrogen (atoms, molecules) in external fields. Static electric and magnetic fields Oscyllating electromagnetic fields

1 Adiabatic and diabatic representations

Statistical Analysis on Uncertainty for Autocorrelated Measurements and its Applications to Key Comparisons

Exercises and Problems

PHYS-3301 Lecture 7. CHAPTER 4 Structure of the Atom. Rutherford Scattering. Sep. 18, 2018

Measurement uncertainty of the sound absorption

Provläsningsexemplar / Preview TECHNICAL REPORT INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE

Kinetics of Complex Reactions

The improvement of the volume ratio measurement method in static expansion vacuum system

The target reliability and design working life

Miscellaneous Notes. Lecture 19, p 1

Diffusivity and Mobility Quantization. in Quantum Electrical Semi-Ballistic. Quasi-One-Dimensional Conductors

Exam II Covers. STA 291 Lecture 19. Exam II Next Tuesday 5-7pm Memorial Hall (Same place as exam I) Makeup Exam 7:15pm 9:15pm Location CB 234

SOLUTIONS: ECE 606 Homework Week 7 Mark Lundstrom Purdue University (revised 3/27/13) e E i E T

True Nature of Potential Energy of a Hydrogen Atom

Discrete Mathematics for CS Spring 2008 David Wagner Note 22

Worksheet 23 ( ) Introduction to Simple Linear Regression (continued)

Quantum Annealing for Heisenberg Spin Chains

DETERMINATION OF MECHANICAL PROPERTIES OF A NON- UNIFORM BEAM USING THE MEASUREMENT OF THE EXCITED LONGITUDINAL ELASTIC VIBRATIONS.

Ray Optics Theory and Mode Theory. Dr. Mohammad Faisal Dept. of EEE, BUET

Linear Regression Demystified

MATH/STAT 352: Lecture 15

Modeling of Plasmas and Neutrals Including Plasma-Wall Interaction for Long Term Tokamak Operation

Chapter 8: Estimating with Confidence

THE NUMERICAL SOLUTION OF THE NEWTONIAN FLUIDS FLOW DUE TO A STRETCHING CYLINDER BY SOR ITERATIVE PROCEDURE ABSTRACT

Because it tests for differences between multiple pairs of means in one test, it is called an omnibus test.

Physics Oct Reading

BIOS 4110: Introduction to Biostatistics. Breheny. Lab #9

( θ. sup θ Θ f X (x θ) = L. sup Pr (Λ (X) < c) = α. x : Λ (x) = sup θ H 0. sup θ Θ f X (x θ) = ) < c. NH : θ 1 = θ 2 against AH : θ 1 θ 2

All Excuses must be taken to 233 Loomis before 4:15, Monday, April 30.

Unit 5. Gases (Answers)

Estimation of the Mean and the ACVF

Investigating a new estimator of the serial correlation coefficient

Hypothesis Testing. Evaluation of Performance of Learned h. Issues. Trade-off Between Bias and Variance

Mark Lundstrom Spring SOLUTIONS: ECE 305 Homework: Week 5. Mark Lundstrom Purdue University

TR/46 OCTOBER THE ZEROS OF PARTIAL SUMS OF A MACLAURIN EXPANSION A. TALBOT

Chapter 10: Power Series

6.3 Testing Series With Positive Terms

EECS564 Estimation, Filtering, and Detection Hwk 2 Solns. Winter p θ (z) = (2θz + 1 θ), 0 z 1

Example: Find the SD of the set {x j } = {2, 4, 5, 8, 5, 11, 7}.

Nonequilibrium Excess Carriers in Semiconductors

a b c d e f g h Supplementary Information

Lecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting

1. Hydrogen Atom: 3p State

ANALYSIS OF EXPERIMENTAL ERRORS

Development of QM. What do we know from classical physics? 1. Energy can take any continuous value.

THE KALMAN FILTER RAUL ROJAS

10.6 ALTERNATING SERIES

Session 5. (1) Principal component analysis and Karhunen-Loève transformation

THE SYSTEMATIC AND THE RANDOM. ERRORS - DUE TO ELEMENT TOLERANCES OF ELECTRICAL NETWORKS

The Poisson Distribution

FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING. Lectures

CSE 527, Additional notes on MLE & EM

11 Correlation and Regression

NUMERICAL METHODS FOR SOLVING EQUATIONS

Holistic Approach to the Periodic System of Elements

Lecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting

Modified Decomposition Method by Adomian and. Rach for Solving Nonlinear Volterra Integro- Differential Equations

Statistical Inference (Chapter 10) Statistical inference = learn about a population based on the information provided by a sample.

ANALYSIS OF DAMPING EFFECT ON BEAM VIBRATION

On a Smarandache problem concerning the prime gaps

Analysis of Experimental Data

Series III. Chapter Alternating Series

Hot electrons and curves of constant gain in long wavelength quantum well lasers

Recent Experimental Results in ADITYA Tokamak

Section 11.8: Power Series

Response Variable denoted by y it is the variable that is to be predicted measure of the outcome of an experiment also called the dependent variable

OPTIMAL ALGORITHMS -- SUPPLEMENTAL NOTES

Paired Data and Linear Correlation

Chapter 4. Fourier Series

Number of fatalities X Sunday 4 Monday 6 Tuesday 2 Wednesday 0 Thursday 3 Friday 5 Saturday 8 Total 28. Day

The Born-Oppenheimer approximation

Definitions and Theorems. where x are the decision variables. c, b, and a are constant coefficients.

A statistical method to determine sample size to estimate characteristic value of soil parameters

TRACEABILITY SYSTEM OF ROCKWELL HARDNESS C SCALE IN JAPAN

The Riemann Zeta Function

Chapter 5 Vibrational Motion

Stochastic Matrices in a Finite Field

Activity 3: Length Measurements with the Four-Sided Meter Stick

(all terms are scalars).the minimization is clearer in sum notation:

Polynomials with Rational Roots that Differ by a Non-zero Constant. Generalities

ENGI Series Page 6-01

Last time: Moments of the Poisson distribution from its generating function. Example: Using telescope to measure intensity of an object

ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER / Statistics

Jaynes-Cummings Model

Chimica Inorganica 3

HE ATOM & APPROXIMATION METHODS MORE GENERAL VARIATIONAL TREATMENT. Examples:

Overview. p 2. Chapter 9. Pooled Estimate of. q = 1 p. Notation for Two Proportions. Inferences about Two Proportions. Assumptions

P1 Chapter 8 :: Binomial Expansion

Comparing Two Populations. Topic 15 - Two Sample Inference I. Comparing Two Means. Comparing Two Pop Means. Background Reading

Comparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series

Andrei Tokmakoff, MIT Department of Chemistry, 5/19/

Formation of A Supergain Array and Its Application in Radar

Probability, Expectation Value and Uncertainty

ENGI 4421 Confidence Intervals (Two Samples) Page 12-01

Orthogonal Gaussian Filters for Signal Processing

Confidence Intervals for the Population Proportion p

Nernst Equation. Nernst Equation. Electric Work and Gibb's Free Energy. Skills to develop. Electric Work. Gibb's Free Energy

RAINFALL PREDICTION BY WAVELET DECOMPOSITION

Chapter 6 Sampling Distributions

Transcription:

Accuracy of TEXTOR He-beam diagostics O. Schmitz, I.L.Beigma *, L.A. Vaishtei *, A. Pospieszczyk, B. Schweer, M. Krychoviak, U. Samm ad the TEXTOR team Forschugszetrum Jülich,, Jülich, Germay *Lebedev Physical Istitut, Moscow, RF Itroductio stadard He-beam diagostics o TEXTOR Atomic processes ivolved Evaluatio procedures Atomic data Results - stadard, ew - compariso of itesity profile fits compariso for differet atomic data compariso for differet discharge coditios compariso of differet diagostics Summary & coclusios

Stadard TEXTOR He-beam diagostics imagig fibre guide image itesifier Li chael He chaels iterferece filters photo objectives f=25mm ijectio system lier ALTlimiter lie emissio collisios ijected He & Li atoms 20 20 vacuum vessel i / 1 costat relaxatio time τ r sufficietly small temporal resolutio: t=τ r (max) spatial resolutio: x = t v Strahl o p & d collisios 18-3 /10 m e 15 10 5 0 0.5 0.5 6 8 1 4 4 T/eV e 1 1.5 8 6 15 10 5 0 liie itesity ratios: siglet : siglet I(668m) / I(728m) e depedet siglet : triplet I(728m) / I(706m) T e depedet M.Brix (2000)

bdx d i = Trilateral Euregio Cluster pop. processes + σ e,jiv j,j i Atomic processes e + σ p,jiv ioj j,j i + A j depop.processes σ e,ij v i,j i σ p,ijv i,j i ji j j, j> i j, j< i e A ij i iois, i io i σ v σ v σ p cx, i iois, i v io e i e io i i i electro collisio excitatio io collisio excitatio spotaeous emissio electro collisio ioisatio io collisio ioisatio charge exchage

Evaluatio procedures For kow T e (r) ad e (r) -> lie itesity profiles I ( r) = λ k A ki I ( r) = k A ki However, we eed for kow -> T e (r) ad e (r) λ M. Brosda ad M.Brix have already show that it is possible to restore T e ad e profiles from lie profiles I 1 (r); I 2 (r); I 3 (r) Possible approaches: o-statioary (NS): direct solutio of the geeral (time / space) depedet equatio ad fit I (r) = A to the measured oe. quasi-statioary (QS): approx. solutio of the NS equatios: o the right the St-solutio of the balace equatios for rel. populatios k / 1 of the excited states is iserted. λ k ki statioary (St): the derivatives are eglected assumig that the time costat of the measured processes are larger tha the relaxatio times τ for the trasitios used.

Atomic data - levels The followig atomic levels of He I have bee icluded i the model: (1): 1s 2 1 S; 1sl 1 L; 1sl 3 L; = 2; 3; 4, l = 0; 1; 2 (1i):1s4f 1 F; 3 F (2): 1s_1 (siglets), 1s_3 (triplets), = 5; 6; 7 summed over all l (3): 1s; = 8; 9 summed over all l ad S (c): c = 1s groud state of He II "effective" levels have bee itroduced, which describe group of levels summed over some quatum umbers (decreases drastically the dimesios of the statistical matrix). group (1): SL couplig is a good approximatio. group (1i) ad ay levels with l > 2: deviatio from the SL couplig is sigificat. The matrix of the eige-vectors i itermediate couplig was obtaied for the states (1i) usig the GRASP92-code (Drake). For the levels 1s; = 8; 9 summed over all l ad S the type of couplig is ot importat. For the levels 1s_1 (siglets), 1s_3 (triplets), = 5; 6; 7 a effective mixig due to deviatio from the SL couplig was itroduced.

Atomic data eergies, radiatio, collisio with e The followig atomic levels of He I have bee icluded i the model: (1): 1s 2 1 S; 1sl 1 L; 1sl 3 L; = 2; 3; 4, l = 0; 1; 2 (1i):1s4f 1 F; 3 F (2): 1s_1 (siglets), 1s_3 (triplets), = 5; 6; 7 summed over all l (3): 1s; = 8; 9 summed over all l ad S (c): c = 1s groud state of He II Eergy levels: from NIST A for 1s2p 1,3 P 1s 2 1 S from Wiese (NSRDS-N.B.S.) A for groups (1), (1i) from ATOM, itermediate couplig for 1s4f 1s3d, SL for others A for trasitios iside ad betwee groups (2), (3): Kramers formula <σv> ex for group (1): CCC-89 cross sectios (Bray) <σv> ex from group (1) to groups (1i),(2),(3),c: ATOM code (Norm.BA) <σv> ex iside groups (1),(2),(3): semiclassical method (Beigma) trasitios to group (1i): itermediate couplig

Atomic data collisios with p,d, CEX The followig atomic levels of He I have bee icluded i the model: (1): 1s 2 1 S; 1sl 1 L; 1sl 3 L; = 2; 3; 4, l = 0; 1; 2 (1i):1s4f 1 F; 3 F (2): 1s_1 (siglets), 1s_3 (triplets), = 5; 6; 7 summed over all l (3): 1s; = 8; 9 summed over all l ad S (c): c = 1s groud state of He II Collisios with heavy particles at thermal eergies may oly cotribute for trasitios with = 0 <σv> p, d for the most importat 3l 3l : from CC-method (code ATCC (Borodi)) for all other trasitios: Norm. Bor approximatio (Borodi) <σv> CEX from the metastable state 1s2s from code CAPT (Shevelko) with cross sectios for 4 from (Jaev) Normalized Bor Approximatio Close couplig method

Results Compariso of differet models ST w/o p ST w p Ti =T e STs ST w/o p ST w p T i =T e ST w p T i =2T e ST w p T i =2T e STs proto collisios do ot seem to play a strog role some effect is of course expected at high desities T i effects are still weak

Results T e & e diagram (ew) ST w/o p ST w p T i =T e ST w p T i =2T e 20 20 8 18-3 /10 m e 15 10 5 0.5 0.5 6 8 1 4 4 1 1.5 6 15 10 5 evaluatio rages could be exteded proto collisios reduce the electro desities icrease the electro temperatures 0 0 T/eV e

Results Compariso for itesity profile fits (Ohmic discharge) (# 96705) 667m 706m 728m NS for large radii: τ r is too large ST STs for small radii: stroger impact of higher l-mixig (ot yet cosidered)

Results Compariso for Ohmic discharges (# 98026) NS ST STs for large radii: τ r is too large for small radii: stroger impact of higher l-mixig (ot yet cosidered) For Ohmic discharges: The deviatio betwee Brix's CRM ad the ew oe accouts to 10% for T e ad is egligible for e. The impact of proto collisios as well as of the ew atomic processes (CXRS ad a ew ioisatio rate coefficiet) seems to have a mior effect.

esults Compariso for itesity profile fits (small NBI-heatig) (# 95907, 300kW) 667m 706m 728m T e & e strog deviatios (especially for T e ) ST STs NS for all models at small radii Ifluece from higher levels!?

Results discharges with small NB-heatig (# 95896, 300kW) ST NS STs T e & e much better coicidece ow

Results discharges with strog NB-heatig (# 96710, 1200kW) NS ST STs T e & e agai much better coicidece ow, NS allows extesio ito the cofied plasma

Results compariso with differet diagostics e He- & Li-beam data extrapolate well ito the HCN data TS seems too small (calibratio error?) Zoom T e He-data extrapolate well ito the HCN & TS data

Summary & Coclusio A exteded model (to Brix 2000) with proto collisios ad CEX processes has bee tested o TEXTOR discharges. Oly margial deviatios => impact of the proto collisios is weak uder the target plasma coditios ivestigated. Evaluatio with the o-statioary approach (NS) ehaces the radial extesio of the profile ad cacels relaxatio pheomea. A method to apply the NS method as stadard evaluatio is uder developmet. For the measuremet errors the rage of T e = 30% ad e = 10% give by Brix 2000 is still valid. Proto collisios (witht i =T e ) do ot exceed these margis. Compariso of the e (r) ad T e (r) profiles obtaied with other edge are i reasoable agreemet with those from He. BES o thermal He should be a reliable method for measuremets withi 2.0 10 18 m -3 < e < 3.0 10 19 m -3 ad 20 ev < T e < 300eV.