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By: Rachael M. McDermott Thanks to Bruce Lipschultz, Bill Rowan, and Ian Hutchinson

MIT Plasma Science and Fusion Center. Analysis of Statistical Uncertainties in CXS Measurements of Ion Temperature and Rotational Velocity. By: Rachael M. McDermott Thanks to Bruce Lipschultz, Bill Rowan, and Ian Hutchinson for numerous consultations.

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By: Rachael M. McDermott Thanks to Bruce Lipschultz, Bill Rowan, and Ian Hutchinson

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  1. MIT Plasma Science and Fusion Center Analysis of Statistical Uncertainties in CXS Measurements of Ion Temperature and Rotational Velocity By: Rachael M. McDermott Thanks to Bruce Lipschultz, Bill Rowan, and Ian Hutchinson for numerous consultations

  2. Temperature and Rotational Velocity Measurements The temperature and rotational velocity from line shift and width are given by: wS is the thermal width at 1/e  is the line shift 0 is the rest wavelength = 4944.67A for Boron +4 line c is the speed of light m is the mass of the emitting ion The error propagated into the temperature and rotational velocity from the line width and shift are given by R. Seraydarian, K.H. Burrell, N.H. Brooks, R.J. Groebner, C. Kahn, MULTICHORDAL CHARGE EXCHANE RECOMBINATION SPECTROSCOPY ON THE DOUBLET II TOKAMAK, May 1985

  3. Uncertainty Calculations The statistical uncertainties associated with the width and shift of a spectral line due to the presence of a distribution of background photons centered on the same line are given by Here, wsig and wbck represent the width of the signal and the width of the background and Nsig and Nbck are the number of photons that contribute to each. The width of the spectral line is found from deconvolving the instrumental function from the measured width. The uncertainty in the instrumental function is given by The total uncertainty in line width is then given by I.H. Hutchinson, (2004) Statistical Uncertainty in Line Shift and Width Interpretation

  4. Typical CXS Spectrum Representative values for analysis parameters approximated from this spectrum: The line on the left is the Boron +1 line The line on the right is the Boron +4 line. The width of the Boron +1 line is 2A. The width of the background Boron +4 line is 3A. The width of the pedestal from the visible edges of the two lines is 8A. The intensity of the Boron +4 line is approximately 60 percent of the Boron +1 line The height of the pedestal is 500 (counts/pixel) Varied quantities : Intensity of the measured Boron +4 line Width of the measured Boron +4 line Ratio of signal to background (20 to 40 percent) Width of the background (3A to 8A)

  5. Ion Temperature = 50eV

  6. Ion Temperature = 200eV

  7. Ion Temperature = 500eV

  8. Results Summary Old Beam Background Width = 3A New Beam Background Width = 3A Old Beam Background Width = 8A New Beam Background Width = 8A

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