On the accuracy of measurements of electron temperature by Thomson scattering diagnostic in the plasma core of the ITER tokamak

Technical Summary: Reassessment of Electron Temperature Measurement Accuracy in ITER Thomson Scattering

Problem Statement
The ITER tokamak project relies on a Thomson scattering diagnostic system to measure electron temperature ($T_e$) and density in the plasma core. The system is designed to operate with a 1064 nm Nd:YAG laser and filter polychromators, targeting a measurement accuracy of 10% across a temperature range up to 40 keV at electron densities ($n_e$) as low as $3 \times 10^{19} \text{ m}^{-3}$. A previous feasibility study [6] concluded that these requirements were achievable. However, the current work identifies a fundamental error in that prior analysis: the calculation of the number of photoelectrons ($N_{pe}$) generated in the avalanche photodiodes (APDs) was based on energy scattering spectra rather than photon-number spectra. This dimensional inconsistency led to a significant overestimation of the signal yield, particularly in the short-wavelength (ultraviolet) region where high-temperature spectra broaden. Consequently, the measurement errors reported in the earlier study were significantly underestimated, casting doubt on the feasibility of meeting the 10% accuracy requirement for $T_e > 20$ keV under the current diagnostic configuration.

Methodology
The author re-evaluates the measurement accuracy by correcting the photoelectron yield calculation and incorporating realistic background radiation effects. The methodology involves:

1. Correction of the Photoelectron Yield Equation: The study corrects the integral expression used to calculate $N_{pe}$. The previous formulation (Eq. 4 in [6]) integrated the Thomson scattering energy spectrum weighted by quantum efficiency. The corrected formulation (Eq. 2) divides the energy spectrum by the photon energy ($h\nu$) to obtain the photon number spectrum before integration. This introduces a critical correction factor of $\lambda/\lambda_0$ (where $\lambda$ is the scattered wavelength and $\lambda_0$ is the probing laser wavelength), which accounts for the difference between energy and photon distributions, especially at high temperatures.
2. Re-evaluation of Detector Quantum Efficiency (QE): The study critiques the assumption in [6] that avalanche gain is independent of wavelength for semiconductor APDs. Using manufacturer data, the author demonstrates that the gain of the Hamamatsu S8664 detector varies with wavelength, leading to an overestimation of QE by approximately 5% in the short-wavelength region. Similarly, the QE of the Excelitas C30956EH detector is inferred to be lower than previously calculated, potentially overestimating the signal by up to 10%.
3. Error Propagation Analysis: Using the corrected photoelectron numbers and the original background radiation data from [6], the author recalculates the relative temperature measurement errors using a least-squares regression (LSR) approach. Two background scenarios are analyzed: a "low" background level and a "high" background level (5 times the low level).
4. Background Radiation Sensitivity: The study further assesses the impact of assuming constant background levels across the temperature range. It posits that in realistic scenarios, bremsstrahlung intensity scales as $T_e^{-1/2}$, meaning background radiation would be significantly higher at lower temperatures, further degrading accuracy.

Key Results
The revised analysis yields the following findings regarding the accuracy of electron temperature measurements:

• Correction Factors: At high electron temperatures ($T_e = 40$ keV), the total number of photoelectrons predicted by the corrected equation is approximately $1.3 \times 10^4$, compared to $2.1 \times 10^4$ predicted by the erroneous equation. This represents a reduction in the expected signal yield.
• Accuracy under Low Background: With low plasma background radiation, the corrected system can achieve the required 10% accuracy only up to approximately 20 keV. At 40 keV, the error rises to nearly 20%, double the required limit.
• Accuracy under High Background: Under high background radiation conditions, the 10% accuracy limit is breached at approximately 1 keV. At 40 keV, the error reaches roughly 40%.
• Impact of Variable Background: If the background radiation is assumed to increase at lower temperatures (scaling as $T_e^{-1/2}$), the measurement error is predicted to exceed 10% across the entire temperature range (100 eV to 60 keV).
• Detector Characteristics: While the incorrect QE assumptions for the APDs contribute to the overestimation of the signal, their impact on the final error budget is secondary compared to the fundamental error in the photon-number spectrum integration.

Proposed Mitigations and Limitations
To achieve the required 10% accuracy across the full temperature range (up to 40 keV) while maintaining the current diagnostic configuration, the paper identifies two necessary adjustments:

1. Increase Laser Pulse Energy: The probing laser pulse energy would need to be increased by a factor of 2–4. However, the author notes this is likely impractical due to the risk of damaging optical components with the intense 4 ns pulse.
2. Raise Minimum Electron Density: The minimum electron density at which the required accuracy can be achieved must be raised from $3 \times 10^{19} \text{ m}^{-3}$ to $6 \times 10^{19} \text{ m}^{-3}$.

The paper also addresses the proposal in [6] to use an additional 1320 nm laser to shift the spectrum. The author concludes this would not suffice, as the probing power of such a laser would remain an order of magnitude lower than the standard 1064 nm laser.

Significance and Claims
The paper's primary significance lies in correcting a critical dimensional error in the modeling of Thomson scattering signals for the ITER diagnostic. It demonstrates that the previously claimed feasibility of measuring core electron temperatures up to 40 keV with 10% accuracy at low densities is not supported by the corrected physics. The work establishes that under the current configuration, the diagnostic is limited to temperatures up to 20 keV (under low background) or 1 keV (under high background) to meet accuracy standards. The findings necessitate a re-evaluation of the diagnostic requirements, specifically suggesting that either the laser energy must be increased (with associated risks) or the operational density range must be restricted to higher values to ensure reliable temperature measurements.