Application of a metallic-magnetic calorimeter for high-resolution x-ray spectroscopy of Fe at an EBIT

The S-EBIT-I (also known as Stockholm R-EBIT) was originally developed by the Physics and Technology LLC Institute in Livermore, USA [25]. In 2005/06 the trap was installed in a dedicated laboratory at the AlbaNova University Center in Stockholm, Sweden where it was further developed [26]. Since its transfer to the campus of the GSI Helmholtz-Center for Heavy-Ion Research in Darmstadt, Germany, the S-EBIT-I is in operation at its experiment place in the X4 cave. The vacuum chamber surrounding the trap can be pumped to reach a pressure of below $1 \times 10^{-10}\,\mathrm{mbar}$ and the entire trapping area is shielded from ambient temperatures by an actively cooled heat shield at 60 K. The Helmholtz-coil pair used to focus the electron beam is operated at a temperature of 4 K using a pulse-tube operated cold-head. This way, a magnetic field of up to 3 T can be generated in the vicinity of the trap, which leads to an electron-beam diameter of around $70\,\mu\mathrm{m}$. At typical beam currents of 150 mA this corresponds to a beam current density in the order of 4 kA cm⁻². The acceleration voltage, thereby, can be adjusted up to 30 kV. X-ray emissions resulting from the continuous interaction of the trapped ions with the electron beam can be observed through a total of eight viewports around the approximately 2 cm long ion-target. Overall, electron densities up to $1 \times 10^{11}\,\mathrm{cm}^{-3}$ and ion densities of $1 \times 10^{9}\,\mathrm{cm}^{-3}$ can be achieved [27]. The element to be measured can be brought into the system via a dedicated gas-injection system [26]. It allows the transfer of an adjustable amount of gas-atoms or -molecules from a pre-vacuum chamber through a needle valve directly into the electron beam. Simultaneously, a second gas of a lighter element can be mixed into the gas-flow. This enables the exploitation of evaporative cooling effects of the trapped ions by the lighter ions [28].

X-rays emitted during the ion-electron collisions were recorded using a maXs-30-type detector array with sensors based on MMC technology. A detailed description of the detector can be found in [17]. It has an active detection area of $4\times 4\,\mathrm{mm}^{2}$ divided into $8 \times 8$ pixels (see figure 2). For stabilization of the signal baseline against temperature-drifts, two pixels each are connected to the same read-out and amplification stage in a gradiometric layout. The sensors' temperature-dependent change of magnetization in an external, static magnetic field is read out via inductively coupled dc-SQUIDs. A first amplification at low temperatures is applied to each of the signals utilizing a subsequent N-SQUID series array stage (see [18] for details). Finally, room temperature electronics further amplify the signal and provide a feedback signal to the read-out stage to fix the SQUID's operation point in a flux-locked loop (FLL). The design of the components is optimized for absorbers made from gold with around $30\,\mu\mathrm{m}$ thickness, to have a quantum efficiency of 80% at a photon energy of ${30}\,\mathrm{keV}$ and ${\gt}98\%$ below ${20}\,\mathrm{keV}$ [29]. The absorbers of the detector used in this experiment, had a thickness closer to $20\,\mu\mathrm{m}$, thus, slightly reducing its expected efficiency towards higher photon energies. However, in the spectral region of interest below ${10}\,\mathrm{keV}$, the impact on the quantum efficiency is negligible. Additionally, a smaller detector volume is expected to increase the signal-to-noise ratio of the calorimeter due to the fact that its sensitivity is inversely proportional to the thermal capacity of the detector and thus its overall volume. Under ideal conditions, an intrinsic energy resolution of about ${10}\,\mathrm{eV}$ full width half maximum (FWHM) at ${60}\,\mathrm{keV}$ and ${8}\,\mathrm{eV}$ in the low energy limit was reported for a comparable maXs-30-type detector (at 25 mK substrate temperature) [20]. The signal decay time of the utilized calorimeter was around 5 ms (time to reach the baseline level after the absorption of a photon). This is compatible with an average photon rate of around $10-20\,\mathrm{s}^{-1}$ observed during the experiments. The operation of the detector requires substrate temperatures of below 30 mK to exploit its full potential. By utilizing a ${}^3\text{He}/{}^4\text{He}$ dilution cryostat a continuous measurement at operation temperatures down to $\approx10\,\mathrm{mK}$ is achievable. Furthermore, the detection of magnetic flux changes in fractions of the magnetic flux quantum requires a good shielding against external magnetic fields. This is particularly important for a setup in the vicinity of the Helmholtz-coil pair of the EBIT. Therefore, the maXs-30 detector uses a soft metallic alloy shield as well as a superconducting shield made from Niobium to cover the detector and the SQUID read-out and amplification stages.

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The microcalorimeter was set up in front of the 90^∘ viewport of the EBIT with an air gap of ${\lt}2.5\,\mathrm{cm}$. The resulting distance of $\approx25\,\mathrm{cm}$ between the detector and the interaction area within the trap yields a total solid area coverage of 0.25 msr. Through the Be window of the EBIT and the x-ray entry window assembly of the maXs-30 (see [17] for details) a transmission of 65% of x-ray photons at $4\,\mathrm{keV}$ is expected. During the measurement, Fe ions were supplied to the trap in the form of gaseous Ferrocene $\text{Fe}(\text{C}_5\text{H}_5)_2$. By adjusting the anode voltage, several different electron beam currents between 11 mA and 25 mA were used throughout the measurement campaign. The acceleration voltage was fixed to 10 kV. In order to focus the electron beam, the Helmholtz-coil pair was supplied with a current of 17 A, resulting in a magnetic field strength of $\approx1\,\mathrm{T}$ in the trapping region. To prevent the accumulation of heavier ions in the trap over time the measurement was performed in cycles. First, the trap was closed for 500 ms to allow the successive build-up of Fe-ions with increasing charge states due to Coulomb-ionization through the electron beam. Afterwards, the trap was briefly opened to extract all contained ions and to prepare it for the next trapping cycle.

To extract the measured photon energies from the MMC signals, a finite response filter-based approach was applied. The procedure closely follows the analysis scheme described in [30] and consists of a combination of a moving window deconvolution-filter followed by a moving average filter. For the energy calibration of the recorded x-ray data, a ${}^{241}\text{Am}$ and a ${}^{55}\text{Fe}$ source were positioned in front of the EBIT viewport opposite to the MMC detector, each at a time. At first, x-rays and γ-photons from the radioactive sources were observed through the EBIT alternating with the measurement periods. Later, the calibration was performed simultaneously with photons from the trap. The calibration itself was performed by fitting Gaussian distributions to the peaks of several calibration lines, in order to determine their position in the spectra. A second order polynomial was then used to fit the measured line positions to their well-known calibration energies (for ⁵⁵Mn-Kα₁, ⁵⁵Mn-Kα₂, ⁵⁵Mn-Kβ₁, ²³⁷Np-Lα₁, ²³⁷Np-Lβ₁, ²³⁷Np–$\gamma_{2,1}$, and ²³⁷Np–$\gamma_{2,1}$) taken from literature [31].

The sensitivity of the MMC sensors is dependent on their substrate's temperature. Therefore, small fluctuation of the detector chip temperature (up to a few mK due to external vibrations of the cryostat) over time lead to corresponding variations of the measured energies, broadening the achieved instrumental resolution up to several ${100}\,\mathrm{eV}$ FWHM. This effect can be compensated by exploiting the fact, that asymmetries in the gradiometric pixel-pairs lead to a sensitivity of the signal baseline level to the substrate temperature as well [16, 17]. Although for most pixels this asymmetry is negligible, a dedicated pixel-pair with a deliberately imbalanced setup can be used as an on-chip thermometer. During the experiment, a temperature-drift correction procedure was implemented, that consisted of recording the baseline offset voltage of the temperature-sensitive pixel-pair for each triggered photon event. By performing a linear regression of the measured energies for events associated with the ${59.5}\,\mathrm{keV}$ calibration line to the temperature-dependent offset values, a compensation curve was determined. Applying the compensation to all events then eliminates most sensitivity-drift effects and improves the detector resolution greatly. Due to occasionally occurring sudden shifts of the read-out SQUID electronics' operation point (most likely due to external magnetic noise), the recorded temperature reference changes accordingly. These discontinuities need to be identified in software as well and respective temperature corrections must be determined for each stable interval in between. After individually drift-correcting and calibrating the photon energies measured for each pixel, events from all pixels can be accumulated and used to calculate the combined spectrum.

In the first runtime, an x-ray spectrum only containing transitions from Fe-ions was recorded, which can be seen in figure 3. During the interaction of the ions with the electron beam, electron impact excitation and ionization leads to the formation of K-shell vacancies leaving the ions in an excited state. The shown spectrum contains Kα photons emitted during the subsequent relaxation of an L-shell electron into the ground state. For neutral iron the Kα transition energy amounts to ${6.4}\,\mathrm{keV}$ [32] which coincides with the low-energetic boundary of the measured spectral distribution. By removing K- and L-shell electrons from the ions, their shielding effect on the nuclear Coulomb potential acting on the remaining electrons decreases. Therefore, the binding energy and, consequently, the transition energy between the bound states increases. The literature value for the ionization energy of Fe²⁴⁺ is given as ${8.8}\,\mathrm{keV}$ and ${9.3}\,\mathrm{keV}$ for Fe²⁵⁺ [33]. Thus, in principle, Fe ions could be fully ionized in collisions with an electron beam with ${10}\,\mathrm{keV}$ beam energy. At the same time, electrons from the beam are also being captured by the positively charged ions. The charge state distribution of the trapped ions therefore results in a time dependent equilibrium between ionization and radiative recombination (RR) [34] processes. It is defined by the electron beam-energy, and -density, as well as the target density and interaction time (see [35] for a detailed description of the dynamics). An approximation of the reaction cross sections using the flexible atomic code (FAC) [36] suggests that the removal of a L-shell electron is slightly more probable than the recombination for the given experiment parameters. The resulting accumulation of ions with increasing charge states over time matches the observed spectral behavior. Ionizing a K-shell electron, however, is two orders of magnitude less probable than the L-RR. After removing all L-shell electrons, it is significantly more probable for the ions to recombine with another electron than to remove a K-shell electron. Therefore, no charge states beyond Fe²⁴⁺ are expected to occur. A comparison of the Kα energy for He-like iron of ${6.7}\,\mathrm{keV}$ [8] with the high-energy boundary of the recorded spectrum agrees with this conclusion. During the experiment, a beam current of 11 mA was set. Based on the association of their most prominent transitions to the corresponding spectral features, the centroid position of the charge state distribution is approximated to fall between 18+ to 20+. The influence of the M-shell electrons on the binding energy of K- and L-shell electrons is weak. Thus, the change of Kα transition energies for charge states beyond neon-like iron is expected to vary significantly less. During the first run, the calibration utilizing the radioactive sources was performed in a brief periods before the EBIT measurements themselves. Due to changing read-out conditions (as explained in section 2.3), the sensitivity-drift behavior of the MMC sensors changed between measurement and calibration steps. Therefore, a direct correlation between the recorded temperatures and measured energies was difficult and remaining uncompensated sensitivity-drift lead to an overall instrumental resolution of ${40}-{50}\,\mathrm{eV}$ FWHM at ${6}\,\mathrm{keV}$. Compared to the expected ${8}-{10}\,\mathrm{eV}$ FWHM from previous measurements under ideal conditions, this proves the necessity of proper temperature correction procedures. The peak of superposed Kα transitions below ${6.43}\,\mathrm{keV}$ stemming from neutral iron up to Fe¹⁶⁺ could not be resolved.

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After the EBIT was damaged during a facility-wide power outage, it had to be disassembled, cleaned, repaired, and rebuild. During the setup phase of the reassembled EBIT, more x-ray photons were recorded in a spectrum shown in figure 4. Besides the expected iron Kα transitions it also contains several lines stemming from Ba$^{q+}$ ions. Barium is present inside of the trapping volume, because of the barium-oxide coating covering the cathode (used to improve electron emission characteristics). Recording the baseline voltage of the temperature-sensitive pixel-pair for every photon event and the simultaneous calibration using the ${}^{241}\text{Am}$ source during the entire measurement period made an efficient temperature-drift correction in software possible (as described in section 2.3), leading to a significant improvement of the achieved energy resolution to ${23.4}\,\mathrm{eV}$ FWHM at ${6}\,\mathrm{keV}$ (single pixel resolutions down to ${18}\,\mathrm{eV}$). This corresponds to a doubling of the achieved resolving power compared to the first run. Furthermore, temperature-drift related spectral artifacts as observed in previous measurements utilizing a maXs-30-type detector [23], could be suppressed entirely. The remaining uncorrected temperature drift effects still make up most of the difference to the measurement under ideal conditions (${8}-{10}\,\mathrm{eV}$ FWHM). The advantages of using a MMC detector becomes particularly obvious when comparing its spectrum with one, that was recorded by a conventional Si(Pin)-diode (XR-100CR by Amptec Inc.). The diode was also attached to one of the EBIT viewports and recorded x-rays at the same time as the MMC. However, in contrast to the results yielded by the semiconductor detector, spectral features from different charge states of Ba and Fe can be individually resolved utilizing the calorimeter based spectrometer. Using estimations for their transition energy from model calculations performed in FAC, transitions from the M- to the L-shell of Barium (see figure 5 top), as well as from the N- and O- to the L-shell (see figure 5 bottom) were identified. Due to the increase of ionization energy from ${3.6}\,\mathrm{keV}$ for Ba⁴⁵⁺ to ${8.3}\,\mathrm{keV}$ for Ba⁴⁶⁺ [33], FAC calculations of the corresponding cross sections suggest a similar imbalance between the M-RR and L-shell ionization as discussed for iron in section 3.1. This matches the observation that neon-like barium (Ba⁴⁶⁺) is the highest charge state present in the spectrum, despite that fact that the production of Ba⁵¹⁺ was energetically possible using ${10}\,\mathrm{keV}$ electrons.

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In order to estimate the charge state distribution of iron ions in the trap, a fit to a model function was performed. The model consists of a superposition of Gaussian peaks, with their mean energy fixed to the identified transition energies calculated for barium and previously measured for iron ions [8]. A least squares minimization to the spectral data yields the amplitudes of the individual x-ray lines. All peak heights for transitions belonging to the individual charge states are then accumulated and used as a rough qualitative measure for the abundance of that state. The resulting distribution can be seen in figure 6. It was later discoverd, that after the rebuild of the EBIT, electrical discharges between internal components lead to a feedback of voltage spikes into the surrounding electronics. This caused the controller responsible for the trap timing cycle to temporarily malfunction. As a result, the trap was closed significantly longer than expected. On the one hand, this explains why barium ions, which are around 2.5 times heavier than iron ions, were accumulated inside of the trap in the first place. On the other hand, it matches the observation that the centroid of the Fe ion's charge state distribution is shifted towards higher values compared to the first run.

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