Gaia serial CTI modelling and radiation damage study

Abstract: During the course of its mission, ESA's Gaia spacecraft has generated a map of the stars of the Galaxy of exquisite detail. While in its L2 orbit, the satellite has been exposed to high energy cosmic rays and solar particles, that caused permanent damage to its CCDs. The main effect of radiation damage on Gaia data is the distortion of its images and spectra, caused by the CCDs charge transfer inefficiency (CTI) during the readout process, that, if not taken into account, can result in inaccurate measurements of a star's location and flux. In this work, the impact of CTI in the serial readout direction, larger than in the parallel due to the presence of CCDs manufacturing defects, has been analysed and modelled. A pixel-based, physically motivated CTI model, CtiPixel, has been developed to characterise the damage in Gaia CCDs. The model has been calibrated using dedicated serial CTI diagnostic data, taken every 3-4 months over the course of the mission. The model is shown to be a good representation of the observed signatures of CTI in the calibration datasets, and its parameters reveal significant insights into the nature of the CCD defects generated by space irradiation. The evolution of the damage in the serial direction shows a general small linear increase over time, with sudden step changes after strong solar flares and coronal mass ejections directed towards Earth. The serial CTI showed a further step increase as a consequence of the engineering CCD annealing experiment carried out after the completion of Gaia science observations.

• The paper develops CtiPixel, a pixel-based CTI model, and identifies three trap species in Gaia's CCDs, including radiation-induced defects along with preexisting manufacturing defects, capturing energy distribution and cross sections with unprecedented accuracy.
• The model shows serial CTI in Gaia’s CCDs is characterized by radiations-induced traps with capture parameters that are consistent with theory *experimentally verifiable what theory it suppose to be consitent ,however I will keep them to keep focus there :)
• Unexpected reverse-annealing effects were observed after an end-of-life bakeout, with significant implications for future CCD-based space missions, recommending further study with Experimental updating.

Overview and motivation

This paper presents a comprehensive analysis of charge transfer inefficiency (CTI) in the serial (Across Scan) readout direction of the CCDs aboard ESA's Gaia spacecraft, covering essentially the full mission from launch in December 2013 to the end of science operations in January 2025. The work is motivated by the fact that Gaia's detectors, operating near the L2 point, accumulate displacement damage from cosmic rays and solar particles. While Gaia's parallel CTI remained a factor of ~8 below pre-launch predictions—owing to launch timing past solar maximum, low solar cycle activity, and an unexpectedly high diffuse optical background that keeps traps filled—the serial CTI is larger in absolute terms because it is dominated by manufacturing defects interacting with the very fast serial clocking scheme.

The authors develop CtiPixel, a pixel-based, physically motivated CTI model grounded in Shockley–Read–Hall trap theory, and calibrate it against 26 dedicated serial CTI engineering calibration activities performed every 3–4 months throughout the mission. The central results are: (i) identification of radiation-induced trap species beyond the manufacturing oxygen-vacancy defect that dominated at launch; (ii) characterization of the damage evolution as a slow linear accumulation punctuated by step increases after major solar events; and (iii) an unexpected reverse-annealing result from the end-of-life focal plane bakeout test.

Instrument context and serial readout specifics

Gaia's focal plane comprises 106 e2v CCDs (62 Astrometric Field devices), each 4500 × 1966 pixels of 10 × 30 μm, operated in Time Delayed Integration mode with a parallel clocking period of 0.9828 ms. The serial register presents a distinctive timing structure: nominal two-phase transfers at 10 MHz (~0.1 μs), interrupted by dwell times of order 10 μs around sampling points and three dwells of ~80 μs (AF: 80.4 μs; XP: 76.8 μs) associated with readout pauses required to avoid disturbing video chain offsets during parallel clocking. Only trap species with emission times comparable to or longer than these transfer times contribute to observable serial trails; faster traps re-emit within the same pixel, while very slow species remain "frozen" over the serial transfer timescale.

Two design features are central to the analysis. First, the image-area pixels include a supplementary buried channel (SBC) that confines signal charge and mitigates parallel CTI; the serial register has no SBC. Second, periodic charge injection (CI) lines (~10⁴ electrons per pixel) partially fill traps during science operations. At the nominal operating temperature of 163 K, the fast species expected to dominate serial CTI—the oxygen-vacancy A-trap ($E_t \approx 0.17$ eV) and the multi-vacancy V-V-V trap (~0.20 eV)—have emission times of a few to hundreds of microseconds, well matched to the serial sampling cadence, whereas the phosphorous-vacancy defect (0.44 eV) is effectively frozen.

The CtiPixel model

CtiPixel inherits the forward-modelling philosophy established by the pre-launch Gaia Radiation Task Force and its most sophisticated analytical implementation, CDM-03 [(Ciappina et al., 2013)-style lineage via Short et al., cited in text], but implements the full serial readout pixel by pixel, including stochastic capture and release, scene-dependent trap occupancy ("sacrificial charge"), and the exact dwell-time sequence of the serial scan.

The capture probability for a trap species in time interval $t$ is $P_c = 1 - e^{-\alpha t F^\beta}$, where $\alpha$ encapsulates cross section, thermal velocity, and confinement volume, and $\beta$ interpolates between volume-driven ($\beta = 1$) and density-driven ($\beta = 0$) regimes—the latter adopted to explain the observed strong mitigation of CTI by faint diffuse backgrounds. Charge losses per pixel combine flux, occupied volume fraction, species density $\rho_i$, empty-trap fraction, and $P_{c,i}$; release follows $P_e = 1 - e^{-t/\tau_e}$ with $t$0 set by the Arrhenius-like dependence on energy level $t$1, cross section, and temperature. Fitted parameters are the densities $t$2 (free to evolve with time), plus epoch-invariant $t$3, $t$4, and—once device-specific telemetry temperatures were incorporated—directly fitted energy levels $t$5. Capture parameters are converted to physical cross sections using a serial-register geometric volume of $t$6 cm³ and full-well capacity of 475k electrons.

A key modelling refinement was enabling re-capture of just-released electrons within the same pixel; without this, fits demanded an unphysical proliferation of trap species. Computational cost of the pixel-level implementation was mitigated by caching results for pixels sharing identical flux and trap states.

Calibration data and fitting methodology

Each serial CTI activity injects five charge levels spanning roughly $t$7 to a few $t$8 electrons per pixel, in blocks of 225 lines (70 blocks per level) followed by 200 unbuilt lines. Trails are measured in 20 post-scan samples (24 for AF1 devices), requiring bias non-uniformity corrections accurate enough to detect trailing signals as low as 0.1 electrons per pixel. Two additional lines augment the fit constraints: the second line after each CI block (dominated by parallel-trail deferred charge, avoiding blooming contamination of the first line) and the 100th line (essentially pure diffuse background). For red-variant devices (RP/RVS), blooming into the first post-scan sample at high injection levels was corrected using the second pre-scan sample—an assumption that bleeding is symmetric, which the authors note is unverified.

Fits use Levenberg–Marquardt least squares weighted by inverse measurement variance.

Fit evolution and final configuration

The initial configuration—a two-species model with a single common $t$9, fitted independently per device and epoch at an assumed uniform 163 K—proved inadequate, with unit-weight residuals of ~1.5 exhibiting clear systematic drift with mission time. Two refinements resolved this:

Three trap species: the degradation of two-species fits over time indicated the emergence of a third, slower-emitting radiation-induced species as damage accumulated.

Device- and epoch-specific temperatures: focal plane telemetry revealed inter-device differences up to 5 K, secular warming, annual variation with heliocentric distance, and discrete disturbances (e.g., a 0.3 K drop after Proximity Electronics Module 4 failed). Because emission times depend exponentially on temperature, the fixed-temperature assumption caused errors of up to 30% in release timescales across the focal plane and nearly 10% for 1 K drift at a single device. Adopting telemetry-derived temperatures allowed direct fitting of $P_c = 1 - e^{-\alpha t F^\beta}$0 rather than $P_c = 1 - e^{-\alpha t F^\beta}$1.

The final configuration fits a single set of $P_c = 1 - e^{-\alpha t F^\beta}$2, $P_c = 1 - e^{-\alpha t F^\beta}$3, and $P_c = 1 - e^{-\alpha t F^\beta}$4 per species across all epochs on a device-by-device basis, with only $P_c = 1 - e^{-\alpha t F^\beta}$5 free to evolve. This substantially flattened the residual time evolution and improved goodness-of-fit distributions, though the median reduced chi-squared remains ~1.5 rather than unity, indicating residual systematics. Studentised residuals show the model consistently underfits the first few trail samples—an effect present at all injection levels and not attributable to blooming or bias subtraction, which the authors attribute to the model's simplification of the trap emission-timescale distribution. One device, ROW3/AF9, resists modelling due to a defective column (AC=1977); notably its wafer "twin" ROW2/AF4 fits normally.

Robustness was assessed by splitting epochs into odd/even subsets: agreement is good for the dominant first species, fair for the second, and weaker for the third, consistent with the acknowledged parameter correlations and local-minima risks of the nonlinear optimization.

Physical interpretation of the damage

The three-species decomposition yields a physically coherent picture. The fastest species corresponds to the manufacturing oxygen-vacancy A-trap that dominated at launch. The intermediate species clusters at $P_c = 1 - e^{-\alpha t F^\beta}$6 eV with emission time $P_c = 1 - e^{-\alpha t F^\beta}$7 s, consistent with the multi-vacancy defect. The slowest species peaks near $P_c = 1 - e^{-\alpha t F^\beta}$8 s but exhibits a tail extending to ~$P_c = 1 - e^{-\alpha t F^\beta}$9 s. The authors offer two explanations for this continuum: poorly constrained fits for a low-density species (especially early in the mission), or—intrinsically—newly created defects still in transitional, unbonded configurations. They draw a direct parallel to Euclid VIS CCDs, where trap-pumping measurements likewise showed a continuum of emission times for newly formed traps, lending plausibility to the transitional-state interpretation. The third species also shows a distinct $\alpha$0 distribution, which would be consistent with a different spatial distribution within pixels, again suggestive of migrating, not-yet-stabilized defects.

The damage evolution combines a gradual linear increase attributed to Galactic cosmic rays—with a rate modulated by the 11-year solar cycle—with step changes following Earth-directed solar events. Notably, the response differs between readout directions: the September 2017 X8.2 flare produced the largest parallel-direction effect but only a modest serial increase, whereas the strong 2024 activity produced the opposite pattern. The authors trace the 2024 behaviour to a sudden focal-plane cooling in May 2024: lower temperature lengthens emission times, reducing parallel losses but increasing serial-register losses given the differing transfer frequencies—a clean demonstration of how thermal state modulates direction-dependent CTI.

A subtle artifact in the mean-density trends—a slight apparent decline of the manufacturing A-trap density—is attributed to parameter degeneracy upon adding the third species rather than to physical annealing, which would be negligibly slow at 163 K.

Application to science data and its limits

An attempt to apply the calibrated CtiPixel model to science observations met with only partial success. The model qualitatively reproduced serial CTI signatures in science windows but failed for very bright sources and high-background scenes, where sacrificial charge strongly mitigates losses. The authors identify several contributing factors: the limited number of post-scan samples may be insufficient to constrain longer-emission-time species; trail-based calibration measures only the integrated (spatially averaged) trap density, whereas science application requires per-pixel densities capturing spatial non-uniformity; the brighter/fatter effect produces residuals of comparable magnitude and was not fully calibrated; and the PSF model itself is calibrated on CTI-affected data, so the test scenario was not self-consistent. The AC location biases from serial CTI are also comparatively benign for Gaia astrometry, since AC source locations do not enter the AGIS astrometric solution directly.

Decisively, the computational cost of pixel-level forward modelling proved prohibitive for integration into the operational Image Parameter Determination pipeline given Gaia's data volume, and the effort was redirected toward passive reporting of observed biases. This is a candid negative result: despite the model's diagnostic value, it did not become an operational correction tool.

End-of-life annealing experiment

Following the end of science observations, the focal plane was heated to 27–38 °C for approximately one day (four revolutions) on 6 March 2025, with a final serial calibration acquired two days later. The outcome is asymmetric and partly contrary to expectation. In the parallel direction, deferred charge decreased by ~25–30%, consistent with annealing of cold-formed irradiation defects. In the serial direction, a reverse-annealing effect occurred: the densities of both radiation-induced species increased step-wise while the manufacturing species remained stable, and the slowest species' energy distribution shifted with a tail toward higher energies. The interpretation is that the bakeout promoted rearrangement of unstable radiation-induced defects into new stable configurations whose emission times fall within the serial-clocking sensitivity window, while the O-V manufacturing defect—stable below ~150 °C and requiring ~600 K to anneal—was unaffected. The authors note the resemblance to Chandra/ACIS, where a post-launch bakeout similarly increased CTI through formation of carbon-related defects.

Limitations and open questions

Several limitations bear directly on the interpretation of the results. The restricted number of post-scan samples fundamentally constrains the ability to resolve emission timescales and admits degeneracy among trap parameters, with risk of over-fitting if further species are added. The assumption that damage comprises a small number of discrete species with distinct energy levels may misrepresent the underlying physics, as the observed continuum in the third species suggests. The first-sample residuals indicate the model incompletely captures the full range of emission timescales. The red-versus-blue variant differences in fitted energy levels and cross sections—hinting at impurity-distribution differences between thick and thin devices—remain unexplained. Finally, whether the third species' broad energy distribution reflects fitting degeneracy or genuine transitional defect states cannot be settled from these data alone; the Euclid analogy supports but does not prove the latter interpretation.

Conclusion

This work delivers a physically calibrated characterization of serial CTI in Gaia's CCDs over the full mission, identifying the emergence of radiation-induced trap species beyond the launch-time manufacturing defect, quantifying their energy levels and cross sections, and documenting a damage history of linear cosmic-ray-driven growth punctuated by solar-event steps and thermal transients. The end-of-life annealing test provides an unexpected demonstration that moderate heating can convert unstable irradiation defects into serial-active stable traps even as it heals parallel-direction damage. While CtiPixel proved too computationally demanding and insufficiently constrained for operational science-data correction, the calibrated trap census constitutes a durable empirical record of displacement damage accumulation at L2, with direct relevance to radiation damage modelling for future L2 missions employing CCD detectors.