X Ray Detection and Analysis for the PFRC Alexandra Bosh 7/28/2016 1
Objectives • Background – Purpose of Detecting X Rays • Detect X Rays • Calibrate X Ray Detectors • Analysis 2
Background – Purpose of Detecting X Rays • X ray distribution indicates the temperature of the plasma and can even give more detail, the full distribution function • Do the electrons follow a Maxwellian distribution or not? • Plotting count rate versus time determines if x ray production is constant or varying with time • Energy spectrum of x rays is determined from raw data collected from detectors. This information is crucial for determination of various properties of the plasma 3
Detecting X Rays • Amptek XR – 100SDD Silicon Drift Detector (SDD) • Allows for a higher count rate • Amptek XR – 100CR Si-PIN Detector - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 4
Detecting X Rays (cont.) 5
Calibration of X Ray Detector • In order to calibrate detector, the scale (x-axis), sensitivity (y-axis) and resolution for each detector must to be determined over all energy levels. 6
Calibration of X Ray Detector (cont.) Thanks Sam! 7
Calibration of X Ray Detector – Sensitivity • The sensitivity of the detectors, up to this point, has been trusted to be that of the written values from manufacturer. Charles is currently working on solving an issue that has been found. Work completed by Charles! 8
Calibration of X Ray Detector - Resolution • Resolution of detectors can be determined by taking into account the background noise Work completed by Charles Swanson and Alex Glasser! 9
Calibration of X Ray Detector – Scale Work completed by Charles Swanson, 5.9 keV Alex Glasser and 6.5 keV Peter Jandovitz! 10
Count Rate vs. Time 11
Analysis • Analysis of data collected would allow for determination of FRC bulk properties • Raw Data X Ray Temperature & Count Rate • Count Rate Electron Density • Electron Density & Temperature Plasma Pressure • Plasma Pressure 𝛾 • Plasma Pressure & Total Volume Stored Energy • Stored Energy & Power Confinement Time 12
Analysis – X Ray Temperature • Plot corrected counts vs. spectrum energy on a logarithmic-linear plot • Linear regression: 𝑧 = 𝑛𝑦 + 𝑐. • Temperature is the negative inverse of log slope 1 • 𝑈 = − 𝑛 13
Analysis – X Ray Temperature (cont.) • Comparison of analysis of ‘smooth’ data with data containing many zeros Both during RMF 14
Analysis – X Ray Temperature (cont.) ‘Smooth’ data Temp. = 150 Data with plenty of zeros Temp. = 185 Temp. = 73 15
Analysis – X Ray Temperature (cont.) • Comparison of the temperatures during Helicon only run and RMF run with same parameters of machine during each run Helicon only run: green RMF run: blue 16
Analysis – X Ray Temperature (cont.) RMF run Temp. = 201 eV Helicon only run Temp. = 145 eV 17
Analysis – Count Rate corrected counts • Count Rate = time collected Count Rate ≈ 2 counts sec Count Rate ≈ 58 counts sec 18
Analysis – Electron Density • Two ways: • Complicated-ish math or simplistic math • Interferometer measurements 19
Analysis – Electron Density • Two ways: • Complicated-ish math or simplistic math • Interferometer measurements 20
Analysis – Electron Density • Bremsstrahlung Reaction Rate • From Principles of Plasma Diagnostics by I. H. Hutchinson, Eq’ns 5.3.6 & 5.3.11 𝐻 𝐹 𝑦𝑠𝑏𝑧 , 𝐹 𝑓 = 16𝛽𝑑 2 𝜌𝑎 2 𝑠 2 1 𝑓 𝜖 𝐹 𝑦𝑠𝑏𝑧 𝜏𝜉 ∙ න 𝑒𝐹 𝑓 ∙ ∙ 𝑔 𝑈 𝐹 𝑓 = 3𝑡𝑟𝑠𝑢 3 𝐹 𝑦𝑠𝑏𝑧 𝜉 𝑓 𝑈 5.0 × 10 −6 cm 4 1 න 𝑒𝐹 𝑓 ∙ 𝐻 𝐹 𝑦𝑠𝑏𝑧 , 𝐹 𝑓 s 2 ∙ ∙ 𝑔 𝑈 𝐹 𝑓 𝐹 𝑦𝑠𝑏𝑧 𝜉 𝑓 • Assuming constant Gaunt factor (~2x error) 𝐹𝑦𝑠𝑏𝑧 1 𝑓 − = 9.6 × 10 −14 cm 3 ∙eV 2 𝑈 Thanks Charles! • 𝜖 𝐹 𝑦𝑠𝑏𝑧 𝜏𝜉 ∙ s 𝑈𝐹 𝑦𝑠𝑏𝑧 𝑈 21
Analysis – Electron Density • CC Detector Effective Emission Volume • Actual volume, as if seen from a point sourch through the slit mask: 2 𝑠 2 • 𝑊 𝑢𝑝𝑢 = 𝐵 3 𝑀 = 𝐵 2 2 ∙ 𝑀 𝑠 1 • Solid angle reduction factor Ω 𝐵 1 • 4𝜌 = 2 4𝜌𝑠 2 • Total effective volume 𝑓𝑔𝑔 = 𝑊 𝑢𝑝𝑢 Ω 4𝜌 = 𝐵 1 𝐵 2 𝑀 • 𝑊 2 = 5.8 × 10 −4 cm 3 4𝜌𝑠 1 Thanks Charles! 22
Analysis – Electron Density • Bremsstrahlung Rate Density • Rate density 𝜃 from reaction rate • 𝜖 𝐹 𝑦𝑠𝑏𝑧 𝜃 = 𝑜 𝑓 𝑜 𝜏 𝜖 𝐹 𝑦𝑠𝑏𝑧 𝜏𝜉 • Rate density from measure count rate • 𝜖 𝐹 𝑦𝑠𝑏𝑧 𝐷𝑆 = 𝜖 𝐹 𝑦𝑠𝑏𝑧 𝜃𝑊 𝑓𝑔𝑔 Thanks Charles! 23
Analysis – Electron Density (cont.) • Example: July 19, 2016 at 12:45pm (filename indicates 12:46am…), spectrum measured 1 • Rate density measured: 𝜖 𝐹 𝑦𝑠𝑏𝑧 𝜃 800eV = 1.6 × 10 3 cm 3 ∙eV∙s 800eV = 4.7 × 10 −20 cm 3 • Reaction rate calculated: 𝜖 𝐹 𝑦𝑠𝑏𝑧 𝜏𝜉 eV∙s 𝑈=150𝑓𝑊 1 1 • Scattering density measured: 𝑜 𝜏 = 𝑄 𝑑𝑑 ∙ 3 × 10 13 cm 3 ∙mTorr = 1.5 × 10 13 cm 3 1 • Electron density inferred: 𝑜 𝑓 = 3.4 × 10 9 cm 3 24
Analysis – Electron Density (Interferometer) Voltage is proportional to the line average electron density! ≈ 2 div 10 9 𝑑𝑑 ∙ mV = 𝟑. 𝟗 × 𝟐𝟏 𝟐𝟐 /𝒅𝒅 Τ 40 mV ∙ 7.9 × 25
Analysis – Electron Density (cont.) • From interferometer: 𝑜 𝑓 = 2.8 × 10 11 ≈ 1 × 10 11 • From analysis: 𝑜 𝑓 = 3.4 × 10 9 ≈ 1 × 10 9 too low! 26
Analysis – 𝛾 • For FRC: 𝛾 ≅ 0.5 − 1 (tokomak: 𝛾 ≅ 0.05) 𝑞𝑚𝑏𝑡𝑛𝑏 𝑞𝑠𝑓𝑡𝑡𝑣𝑠𝑓 = 𝑜 𝑓 ∙𝑙 𝑐 ∙𝑈 • 𝛾 = = 1 𝑛𝑏𝑜𝑓𝑢𝑗𝑑 𝑔𝑗𝑓𝑚𝑒 𝑞𝑠𝑓𝑡𝑡𝑣𝑠𝑓 = 𝐶2 8𝜌 𝐶 2 𝐶 2 • 𝑜 𝑓 ∙ 𝑙 𝑐 ∙ 𝑈 8𝜌 𝑜𝑈 = 𝑦𝑠𝑏𝑧 = 4𝜈 0 • B – field is measured during experiments. Analysis leads to determining the values of 𝑜 𝑓 and 𝑈 𝑦𝑠𝑏𝑧 , values that are required in order to classify an FRC. • If ions were more energetic their temperature would have to be taken into account 27
Analysis - 𝛾 (cont.) 𝐶 2 • 𝑜𝑈 = 4𝜈 0 • In general 𝐶: 50 − 100𝐻 , 𝑈 ≈ 150 − 300 𝑓𝑊 𝐶 2 = 4 × 10 −11 ∙ 10 9 𝑑𝑑 ∙ 2 × 10 2 𝑓𝑊 1 = 4 × 10 −11 𝑜𝑈 = 𝟗 × 𝟐𝟏 −𝟓 10 4 𝐻 28
Maxwellian Distribution? • Maybe? • Previous machine (PFRC-1) • Single particle simulation • Electron collision rate − 3 2 sec −1 • 𝜉 𝑓 = 2.91 × 10 −6 𝑜 𝑓 ln Λ 𝑈 𝑓 • At 200𝑓𝑊 , 𝜐 𝑓𝑓 ≈ 2 𝑡𝑓𝑑 • Other ways to reach Maxwellian • RMF only runs for 5 ms with water coolant or 250 ms with LN 2 ! S.A.Cohen; Berlinger, B.; Brunkhorst, Christopher; Glasser, A.H., (2007), Formation of Collisionless High- 𝛾 Plasmas by Odd-Parity 29 Rotating Magnetic Fields , Physical Review Letters
What do we expect? <E> ~ 300 eV RMF code Possible causes: a) Pulse pile-up b) Scattering off (mirror) field c) Plasma instabilities E vs t r vs z DATA!
Peter Jandovitz’s Poster Presentation, 0.8-5.0 keV X-ray Emission from the PFRC-2 Plasma 31
What Have We Determined Thus Far? • We are not looking at the bulk distribution • Questions • Maybe Heating minority population? • Not producing an FRC? 32
Not Producing an FRC? 33
Future Work • Why does the RMF amplify the count rate? • What is the effective temp of the bulk? • Put on the new detector 400 eV 34
Acknowledgements • CHARLES SWANSON!! • Peter Jandovitz • Sam Cohen • Alex Glasser • All other SULI interns • SULI, PPPL, DOE 35
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