Use of a Mylar filter to eliminate vacuum ultraviolet pulse pileup in low-energy x-ray measurements

The Princeton Field-Reversed Configuration-2 (PFRC-2) is an FRC heating and confinement experiment.¹ The FRC plasma is formed and heated by odd-parity rotating magnetic fields (RMF_o). The PFRC-2 plasma emits x rays via bremsstrahlung and line emission. Bremsstrahlung radiation is of interest in order to measure electron energy distribution functions (EEDFs),² from which electron number density n_e and temperature T_e can be extracted. Figure 1 shows schematics of the PFRC-2 experiment where an FRC is present (bottom) and without the FRC (top), which occurs in the absence of RMF_o. Two Silicon Drift Detector (SDD) x-ray pulse-height detectors in the center cell measure the x-ray emission above 150 eV from two viewing chords. A microwave interferometer is used for electron density measurements of the bulk plasma. The x-ray lines-of-sight (LOSs) are indicated in the figure.

The x-ray detectors in our experiments, Amptek FAST SDD X-123, perform x-ray pulse-height energy analysis.³ As the x-ray count rate increases, which frequently occurs during RMF_o plasma heating, there is increased probability of two or more x rays arriving at the detector within the pileup resolving time and thus being registered as one x ray with energy greater than that of a single incident x ray and less than or equal to the energy sum of the incident x rays. This phenomenon is referred to as pulse pileup (PPU). PPU presents an issue to x-ray measurements of high-count-rate sources since it corrupts the x-ray spectra, resulting in erroneous measurements of properties of interest. For PFRC-2 RMF plasma, various spectra were found to be distorted by PPU, inferred from changes in spectra shape with changes in x-ray flux. The light-tight C1 window by Amptek,⁴ composed of a mesh-supported aluminum-coated silicon-nitride (Si₃N₄) film installed with the SDD, has a region of higher transmissivity in the vacuum ultraviolet (VUV) region, and, hence, was unable to prevent this PPU. The potential for PPU to be generated by this photon energy range in the PFRC-2 was the impetus to investigate the Mylar filter.

In this paper, we investigate the use of a Mylar filter to eliminate VUV PPU in SDD signals. Section II. describes the pulse-pileup issue in PFRC-2 x-ray measurements and introduces the Mylar filter along with its properties as a potential solution to resolve VUV PPU. The details of how the Mylar filter fits into the x-ray data analysis along with the calibration of x-ray spectra with the Mylar filter are described in Sec. III. Section IV. describes results enabled by the implementation of the Mylar filter, including elimination of pulse pileup in RMF_o plasmas and the ability to measure bremsstrahlung with even higher power RMF_o.

Under certain conditions, the x-ray spectra measured from the PFRC-2 exhibit behavior that we attribute to PPU. An example can be seen in Fig. 2, which shows x-ray spectra for various apertures that limit the x-ray flux into the SDD because of their different aperture areas. If there were no PPU, increasing the aperture area would result in the same spectral distribution, albeit with an augmented spectral count rate. However, we observe that increasing the aperture area causes the spectrum to extend to higher energies, which is indicative of PPU. The “noise” spectrum region (10–200 eV) correspondingly decreases with increasing aperture size, also consistent with PPU. Pileup would alter the x-ray spectrum’s slope, which thus affects the measurement of electron temperature T_e.

Figure 3 shows the transmission curve for the Amptek C1 window installed with the SDD and that for the C1 window plus 850 nm PET/Mylar filter. In our analyses, Mylar is assumed to be pure polyethylene terephthalate (PET) with unit formula C₁₀H₈O₄. The C1 window has an aluminum coating with Al L-edge at 70 eV, which results in a transmissive energy range with centroid at 61 eV.

In the energy range E < 200 eV, the values of the x-ray transmissivity are only approximately known.⁵ Because of this, it is not possible to say definitively that bremsstrahlung from Maxwellian electrons produces enough x-ray flux around 61 eV to cause the inferred pileup. Taking the NIST model at face value, the amount of pileup inferred is consistent with bremsstrahlung from n_e ∼ 5 × 10¹³/cc, T_e ∼ 60 eV.

A removable Mylar window, shown in Fig. 4, was installed in front of an SDD to significantly reduce pulse pileup. The Mylar attenuates the photons in the 60 eV region by a factor of 1000 while transmitting higher energy photons, those of interest for x-ray measurements, such as of T_e. The implementation of the Mylar filter requires only a hoop on a Wilson seal, the ease of which makes the Mylar filter a practical approach.

Figure 5 illustrates the x-ray path from plasma emission to detector measurement and where the Mylar filter fits into the x-ray data analysis. Analyzing the effect of the Mylar filter on the spectra requires knowledge of the matrices for each step in the figure.² From left to right: The PFRC-2 plasma with a given electron energy distribution function (EEDF) emits x rays with a corresponding x-ray energy distribution function (XEDF); the bremsstrahlung transformation matrix M_Brems converts the EEDF to XEDF. The X rays then pass through the Mylar filter, then through the Amptek C1 window, and finally are recorded by the SDD. The corresponding matrices for these transmission steps are the Mylar transmission matrix M_Mylar, the C1 window transmission matrix M_Win, and the detector resolution matrix M_res. The bremsstrahlung, window, and resolution matrices are described in Ref. 2. A first approximation comparison multiplies the XEDF with no Mylar filter by M_Mylar, while a more detailed comparison includes convolution with the detector response M_res.

Calibration of the effects of the Mylar filter were conducted in an x-ray tube with a graphite target. In the x-ray tube, thermionically emitted electrons are accelerated to 5 keV by a DC voltage source. Figure 6 compares the measured x-ray spectra with no Mylar filter to that measured with the Mylar filter and additionally plots the no-filter measurement multiplied by the NIST transmission model⁵ for 850 nm of Mylar. There is good agreement between the data taken with the Mylar filter and the no-filter data corrected by the transmission model for energies above 600 eV. The Gaussian peaks at 277, 392, and 525 eV are narrow lines corresponding to the carbon, nitrogen, and oxygen K-α lines, respectively, blurred by the detector’s (mostly Gaussian) response. The peak at 1.7 keV is due to Si, most likely fluorescence of the C1 window. Figure 7 shows the ratio of with-filter to no-filter measurements, the NIST transmission model for 850 nm, and the NIST model convolved by the SDD response, for energies less than 1500 eV. The sharp edges of the NIST model are blurred by the SDD response, bringing the curve closer in behavior to the measurement data. The calibration results show that 850 nm of Mylar is the best fit with transmission data.

In this section, we describe various x-ray measurements made with the Mylar filter. The first results described are for a quasi-Maxwellian tenuous plasma (n_e ∼ 10⁹ cm⁻³), known to contain a hot minority component reaching T_e ∼ 1500 eV. X-ray spectra from this plasma, also called the PFRC-2 “seed” plasma, are shown in Fig. 8. Measurements without the Mylar filter were compared to measurements with the Mylar filter divided by the Mylar transmissivity; good agreement is found. Sharp jumps in the “corrected” data are artifacts of analysis, as the measurement is subject to the broad response of the SDD while the transmissivity correction factor has discontinuities at the electron shell edge energies associated with the carbon and oxygen atoms contained in the Mylar. The broad peaks of the spectral lines are found to agree.

We now consider the impact of the Mylar filter on PFRC-2 RMF plasmas. In Fig. 9, x-ray spectra are recorded from PFRC-2 RMF plasma in a high-UV-flux condition. The spectrum measured with no Mylar filter shows a broad range of x-ray energies, heavily distorted by pileup, while the same spectrum measured with the Mylar filter shows a drastically different behavior—the x-ray spectrum behind the pileup is revealed. The Mylar filter window successfully eliminates the pulse pileup. This spectrum is included for illustration purposes; the plasma was formed using helium gas fill.

The Mylar filter’s ability to eliminate pulse pileup enables measurements of electron energies in the PFRC-2 RMF plasma, undistorted by VUV PPU. Maxwellian fits were performed on the x-ray spectra to obtain electron number density and temperature. Two cases are now presented. Figure 10 shows an x-ray spectrum from hydrogen plasma in the PFRC-2 with 70 kW RMF. The electron density (top part of Fig. 11) decays from 4 × 10¹² to 1.2 × 10¹² cm⁻³. (Density was extracted from the line-averaged interferometer measurements and assumed an 8 cm plasma radius.) Often, when n_e decays in an RMF_o-heated plasma, the x-ray count rate (bottom part of Fig. 11) increases. The x-ray spectrum shown is attributable to bremsstrahlung and an oxygen K-α line at 525 eV. The fit in Fig. 10 is valid above 400 eV. Extrapolated down to 0 eV, the maximum inferred Maxwellian fit density during the pulse (corrected for pressure drop) would be 6.5 × 10¹¹ cm⁻³.

Finally, we consider x rays from higher power, 100 kW, RMF_o-heated plasmas, observed by an SDD equipped with a Mylar filter. (The gas fill pressure was high, to increase the UV flux and lower T_e, in order to test the Mylar filter under extreme conditions.) Fig. 12 shows the x-ray spectrum from a single RMF_o pulse along with a Maxwellian fit. At this power level, the count rate has reached 2 × 10⁴ s. The oxygen K-α line is visible at 525 eV. The broad energy spread around the oxygen K-α line led to the choice of fit range before this region: 300–400 eV. X-ray Maxwellian fit parameters are n_e = 8.5 × 10¹¹ cm⁻³, T_e = 57 eV. Figure 13 shows the interferometer electron density time trace and x-ray time histogram for the RMF pulse. The full pulse is 40 ms. The maximum n_e is 2.7 × 10¹² cm⁻³. X-ray measurements are not contaminated by PPU in this high-count-rate regime, thanks to the Mylar filter.

To test its ability to ameliorate UV-emission-generated pulse-pileup effects in pulse-height x-ray detectors, an 850 nm Mylar filter was fabricated, calibrated, and operated on the PFRC-2 device. X-ray measurements were made under high-UV-flux conditions. The Mylar filter permits x-ray spectrum measurement in regimes previously distorted by pulse pileup caused by low-energy photons. The filter is an accessible solution, requiring only a hoop on a Wilson seal for implementation. The measured XEDFs in 50–100 kW discharges are described by Maxwellian extrapolations approaching bulk density and Maxwellian fit temperatures of 50–75 eV.

This work was supported by the U.S. Department of Energy under Contract No. DE-AC02-09CH11466. The United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.

This work was also supported by ARPA-E Award No. DE-AR0001099 (Princeton Fusion Systems) and the Princeton Program in Plasma Science and Technology, Princeton University. We are grateful to M. Paluszek for support and to B. Berlinger and C. Brunkhorst for excellent technical work.

The authors have no conflicts to disclose.

C. A. Galea: Data curation (equal); Formal analysis (equal); Writing – original draft (lead); Writing – review & editing (equal). C. P. S. Swanson: Conceptualization (equal); Data curation (lead); Formal analysis (equal); Writing – review & editing (equal). S. A. Cohen: Conceptualization (equal); Investigation (equal); Writing – review & editing (equal). S. J. Thomas: Data curation (equal); Formal analysis (supporting); Funding acquisition (equal); Writing – original draft (supporting); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.