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Current rev: $Id: topics.html,v 1.18 1998/06/30 21:12:53 emk Exp $

Contents

1. SSD QE at SX700
2. Paper on BESSY calibration of FPC
3. Derivation of synchrotron formula
4. Synchrotron radiation algorithm
5. (Preliminary) XSPEC fit to BESSY-PTB white beam spectrum on ssd_x
6. Mathematica prediction of BESSY flux through 5 mm aperture
7. Finite element analysis of FPC window bowing,
8. BESSY Monochromator SSD results from JMKMOD fitting within XSPEC
9. Deadtime and Pileup Correction in the HXDS FPCs and SSDs

SSD QE at SX700

1. A mathcad calculation using the estimates of QE provided by Jutta Auerhammer, compared by Ed Kellogg with calculated QE from Henke 96 with a manual chisq search. This shows that the fit is not very good. It is to be expected, since Auerhammer's estimates did not account for pileup and pulser deadtime. Also, the Henke tables do not account for the EXAFS structure near the O and AL edges.

Preliminary report on FPC absolute calibration at BESSY

Paper entitled `` High Accuracy Calibration of the HXDS Flow Proportional Counter for AXAF at the PTB Laboratory at BESSY'' by J. M.  Auerhammer, G. Brandt, F. Scholze, R. Thornagel, and G. Ulm, Physikalisch-Technische Bundesanstalt, and B. J. Wargelin, W. C. McDermott, T. J. Norton, I. N. Evans and E. M. Kellogg, Smithsonian Astrophysical Observatory   presented at the SPIE 1998 San Diego meeting. SPIE 1998 manuscript, SPIE_98.PS . This paper describes two independent measurements of the detector absolute quantum efficiency. First, the response to  monochomatic radiation is measured with absolute efficiency calibrated by photodiode transfer to the PTB standard cryogenic electrical substitution radiometer. This measurement also gives the pulse height redistribution function. Second, measurements of the FPC response to undispersed synchrotron radiation are presented, wherein the incident flux is calculated without recourse to any photometric measurements; rather, one measures the storage ring parameters - magnetic field, electron beam energy, beam current, beam divergence, distance from the source to the detector aperture, and aperture radius. The absolute x-ray flux is then calculated from relativistic electrodynamics. The typical uncertainty of these preliminary measurements is < 2% in the 0.2-4 keV range.
 

1. Derivation of synchrotron formula

by E. Kellogg
• Derivation, landscape Postscript from Mathcad, apbig.ps
We begin with the treatment by J. D. Jackson in "Classical Electrodynamics", 1962, J. Wiley & Sons.  Using Mathcad, we express the photon spectrum of x-rays emerging from the storage ring tangent point as a function of the ring parameters - electron energy, circulating storage ring current, magnetic field, distance from tangent point to detector, diameter of the circular detector aperture, and the angular displacement of the detector from the orbit plane. We discuss evaluation of the required Bessel functions.  In order to calculate the spectrum, we derive expressions for the electron gyroradius, and perform the 2D integration of the flux distribution over the circular detector aperture.  We calculate the flux at a set of energies, and we do an integration over all x-ray energies from the detector LLD at 308 eV to a high enough energy to include essentially all the flux.
• Units, landscape Postscipt from Mathcad, units.ps
A description of the units used in the Mathcad documents.
2. Synchrotron radiation algorithm.

by E. Kellogg
Algorithm, landscape Postscript from Mathcad, algorithm.ps
The document used as a specification for Mike McDermott to write the FORTRAN program used in XSPEC and other programs for synchrotron radiation fits to HXDS detector data.  This algorithm uses the formulae given in the derivation above.
 
3. XSPEC fit to BESSY-PTB white beam spectrum on ssd_x.

by S. Serej, E. Kellogg & M. McDermott.
• White Beam ssd_x graph, XSPEC, xbes3lgenew.ps

A postscript graph showing predicted and observed counting rates from the BESSY-PTB white beam on ssd_x, from Oct. 1997. The residuals, plotted as chi, are also shown. They appear essentially random and consistent with statistics above ~1.6 keV (20eV/channel). This indicates that the energy scale for ssd_x in the response matrix is very good, as well as the overall model fidelity. At lower energies, we included three lines and three filters. Note that the main Ge L lines are expected at 1219 and 1188 eV, so we may be seeing Ge fluorescence.
• XSPEC parameter files for xbes3lgenew
• Model parameter 9 is the synchrotron fit normalization, expected to be 1 if all is well. The value obtained here is ~16% away from ideal normalization, similar to 13% seen in the earlier overall integration discussed below(without a spectral fit). We believe that the pilup corrections will account for about 10% of that difference.
• Model parameters 10, 13 and 16 are the line energies. Line 10 is 31 +/- 20 eV from Ge L_beta, and the combination of 13 and 16 have a weighted mean energy difference from the tabulated line energy of 18 +/- ~50 eV, so they agree within errors for Ge L_alpha fluorescence, although line 13 wants to be broad. This could be because the response matrix does not yet handle the line shape with pileup properly. If we take the sum of norms for lines 13+16 to correspond to Ge L_alpha, and divide by the norm of line 10, taken to be Ge L_beta, we get a ratio of 4.4, close to the nominal ratio of 4.
• Model parameter 19 is set to 2, aluminum, for the known Al windows on ssd_x. The fitted value of parameter 20, the Al thickness, is close to the nominal value of 2000 Å = ~2 x 10^-5 cm that we expected.
• Model parameter 22 is set to 6, for carbon, with a fitted value given by parameter 23, comparable to the nominal value of 1.25 x 10^-4 cm that we expected.
• Model parameter 23, is set to 32 for Ge, because we thought that if we see Ge fluorescence, it might be from a dead layer of Ge on the surface of ssd_x. The fitted value is an upper limit of ~7 x 10^-6 cm, or ~70 Å. The fitted line rate, the sum of gaussian norm for all three lines(parameters 12+15+18), ~150 Hz, would have to be caused by an incident flux of 15,000 Hz, because the L fluorescence yield is only about 1% for Ge (Zombeck). Therefore, the line emission is not caused by fluorescence of the synchrotron x-rays transmitted through the detector aperture, and aluminum and carbon windows, which number only 1050 Hz.

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4. Mathematica prediction of BESSY flux through 5 mm aperture. by E. Kellogg.

Gives some numerical predictions and a graph for the flux passing through a 5 mm diameter aperture with parameters correct for the SSD5 in the Oct 26, 1997 run.  This does not include any detector effects, such as filters or fluorescence lines. The numerical values were compared with the output of  the FORTRAN program written by Mike McDermott for the XSPEC trials.
• Mathematica notebook excerpt, syncheval.nb.ps >

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5. Finite element analysis of FPC window bowing, by E. Kellogg & L. Cohen.

The deflection of the polyimide window is calculated using a finite element calculation, normalized to the total deflection measured by Dick Goddard on an actual window assembly under pressure.   The  figure is taken from the HXDS Critical Design Review. It shows a plot of window deflection. The even numbers on the abscissa are the locations of the gold-plated tungsten wires. The filled squares in between are the measured bulge deflections of the windowlets. The local deflections are typically 0.25 mm. The total deflection is 1.5 mm at the center of the window assembly.

Using the above data and the known geometry of the window assembly and support wires, we made a model of the deflection of the sindow and wires under the differential pas pressure. The maximum deflections of the wondowlets and the overall structure were normalized to the observed values. The model gives the deflection over many grid points within a cell. From these, we calculated the slope of the window surface. The window slopes from the model are used to derive effective window thicknesses and then calculate x-ray transmission as a function of position, both in a single unit cell windowlet and over the entire assembly.  The global deflection adds to the nominal 50 mm gas depth. The slope of the window makes its effective thickness greater by as much as 15% near the edge of a windowlet unit cell, which decreases x-ray transmission at low energies.
 

• Mathcad report on deflections and x-ray transmission maps, memdisp.ps

This document shows graphs of the calculated deflections, and implicitly shows the format of the data files referred to just following this. It also shows maps of x-ray transmission at 277 eV (C-K).
• data file of calculated windowlet deflections from the finite element model

See  memdisp.ps for information on the format of this file. The first two columns are the coordinates along the plane of the window surface (say x and y) and the third column is the deflection (say z). If C is a 2D array of deflections, and D is the data file, C_i,j = D_j+41i.
• data file of calculated window assembly large-scale deflections from the finite element model.

See  memdisp.ps for information on the format of this file. It's a column that represents a 2D array. If D is the file and E is a 2D array of deflections, E_i,j = D_j+39i.

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6. BESSY MONOCHROMATOR SSD results from JMKMOD fitting within XSPEC

The various JMKMOD parameters, from Peter Barnes' analysis, as a function of energy, obtained from fits to SSD monochromatic spectra obtained at the BESSY synchrotron source. Also provided is an easy-to-use SM script for plotting these data.
Download:
• 1st release memo explaining the last 2 files
• 2nd release update
• 4th release update (there was no official 3rd update, it got buried)
• data file of JMKMOD parameters
• SuperMongo script for plotting the parameters
You may want to read Peter Barnes' tips and tricks document while looking at some of the fitted spectra and/or the parameter plots described therein. This document not only tells you just about everything I learned, but also suggests where future improvements to the modelling (and the model) can be made. 

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7. Deadtime and Pileup Correction in the HXDS FPCs and SSDs

A memo and some programs by Brad Wargelin that explain data reduction techniques for making proper deadtime adjustments in these detectors.
Download:
• the main memo
• analysis files described in the memo:
• test.data
• do98_12.f
• do98_12.out
• correct.in
• correct4.f
• correct4.out
• the raw data files:
• acq80208d1i0.pha
• acq80212d1i0.pha
• acq80213d1i0.pha
• acq80217d1i0.pha
• acq80223d1i0.pha
• acq80224d1i0.pha
• acq80229d1i0.pha
• acq80230d1i0.pha
• acq80231d1i0.pha
• acq80235d1i0.pha
• acq80236d1i0.pha
• acq80237d1i0.pha
• acq80238d1i0.pha
• acq80239d1i0.pha
• acq80240d1i0.pha
• acq80243d1i0.pha
• acq80244d1i0.pha

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