in the tomographic reconstruction example in section 11.4.4. An alternative for boundary constraints for parameters is to quantify a positive parameter with an exponential, e.g. $T(x) = \exp(f(x))$ where $f(x)$ could be an unbounded spline representation.

The exponential of a spline is used at ASDEX Upgrade for the estimation of the temperature and density profiles within the IDA framework and the estimation of the effective ion charge $Z_{eff} = 1 + \exp(f(x))$ which lower bound is 1 [915]. An unbounded estimation of $Z_{eff}$ can easily go below 1 due to uncertainties in the data but also due to a deteriorating calibration of the data in case of, e.g. degrading optical components. The exponential representation of $Z_{eff}$ avoids values below one which is justified if the data are described reasonably well within their uncertainties. As an estimation of $Z_{eff} = 1$ is physically meaningful, it is frequently an indication of a problematic data set. At ASDEX Upgrade $Z_{eff}$ is estimated from the line-integrated bremsstrahlung background of CX recombination spectra (CXRS) [915]. A degradation of an optical component (coatings on lenses or mirrors, degradation of glass fibers) of the CXRS system is most sensitively detected with an estimated $Z_{eff}$ value at the lower limit for a clean, high-density discharge closely after boronization where $Z_{eff}$ is expected to be between 1.0 and 1.2. If, additionally to an estimated $Z_{eff} = 1$, the residuals between the measured and forward modeled bremsstrahlung data is systematically negative, this is a clear indication of a degradation of an optical component. This $Z_{eff}$ criterion is more sensitive to a deterioration of the calibration than monitoring impurity concentrations determined by CXRS. Future fusion devices working in a harsh environment might use the $Z_{eff} = 1$ criterion together with the data residuals for an early detection and quantification of a degradation of optical components and to specify the need for a re-calibration or a cleaning procedure.

Monotonicity constraints or penalty for non-monotonicity can easily be applied similarly to Tikhonov regularization

$$p(f) \propto \exp \left\{ -\sum_{i} \left( \frac{df(x_i)}{dx} \right)^2 / (2\sigma_m^2) \right\} \quad (11.4)$$

where the sum goes over positions $x_i$ where $df(x_i)/dx$ has the wrong sign. $\sigma_m$ quantifies the amount of tolerance from the monotonicity penalty. As $\sigma_m$ decreases, the penalty becomes a constraint. A strongly monotonic function can be obtained equivalently to the non-negativity constraint by using for the function derivative an exponential of, e.g. a spline. A subsequent integration with appropriate boundary conditions then yields a monotonic function without applying a non-monotonicity penalizing prior.

Another valuable prior information might arise from physical modeling. Examples are discussed in section 11.4.4 with the example of velocity-space tomography where, e.g. the velocity space is restricted or penalized due to simulations or the slowing-down physics is included as a regularizing prior.

### 11.2.6. Parameterization.
The assignment of the parameter space affects the results of data interpretation. As shown in section 11.2.5 the choice of parameters allows one to include physics knowledge as positivity, boundary or monotonicity constraints via parameter space reduction. Additionally, the choice of the parameter set determines the flexibility of the results. For example, the number and position of spline knots in profile reconstruction determines the spatial resolution. A reduction of the number of spline knots as well as an increase of the spline knot distance reduces the spatial resolution of data fitting. Similarly to the smoothness priors, a sparse parameter setting is suitable to reduce noise fitting as well as to mitigate fitting of problematic data if an outlier robust likelihood pdf is applied.

Comparable to the flexibility in the number of the parameters, Gaussian process regression (GPR) allows to reduce profile flexibility by introducing spatial correlation. Gaussian process regression is applied, e.g. in fits to electron density and temperature profile data and the estimation of impurity transport coefficients from Alcator C-Mod [938], in the reconstruction of various plasma parameters as in the estimation of ion temperature and rotation profiles at ASDEX Upgrade [920], for estimating $Z_{eff}$ profiles from line integrated bremsstrahlung spectra at Wendelstein 7-X [921], and tomography for SXR spectroscopy at WEST [939]. GPR is beneficial for linear problems, e.g. for interpolation and smoothing of noisy data. For these cases GPR is computationally fast because analytical formulas for the best estimate and for the estimation uncertainty are available. Additionally, with a Monte Carlo sampling approach any derived profile, e.g. logarithmic profile gradient and its uncertainties [920], can efficiently be calculated using the covariance matrix.

To estimate how much flexibility in the parameter setting is needed, e.g. how much spline knots to be chosen for the profiles, criteria are necessary for complexity estimation. The preferred criterion is to allow as much flexibility as necessary to describe the significant information in the data and reduce flexibility otherwise to avoid noise fitting (Occam's Razor). Various Bayesian and non-Bayesian techniques are available to (automatically) select the necessary flexibility [929, 938, 940].

### 11.2.7. Methods for parameter and uncertainty estimation.
The result of a Bayesian analysis is a posterior pdf for the parameters of interest given all the data and additional information. The posterior pdf quantifies how reliable a set of parameters is in the light of the information used. It contains all the parameter interdependencies.

Parameter estimates can be obtained with various methods distinguishing different properties of the posterior pdf. The most popular estimate is given by the maximum-a-posterior (MAP) solution where the posterior pdf is maximized with respect to the parameters. For numerical reasons it is preferred to maximize the logarithm of the pdf. For Gaussian likelihood and prior pdfs, this is equivalent to minimizing the sum of
all $\chi^2$-terms. The uncertainty of the estimate can be derived from the covariance matrix of the parameters at the MAP solution. This is equivalent to approximating the typically non-Gaussian posterior pdf with a Gaussian pdf at the MAP estimate (*Laplace approximation*) [929]. The parameter covariance includes the parameter dependencies but fails for strongly asymmetric pdfs as they occur, e.g. when non-negativity constraints are applied.

For an alternative estimate the mean of the posterior pdf can be used which is different from the MAP estimate for asymmetric pdfs. Asymmetric pdfs typically occur for non-linear FMs. Since usually the mean of a multidimensional pdf with non-linear parameter dependencies are not available analytically, Monte-Carlo (MC) sampling methods are used to explore the full pdf [929]. Among various sampling methods, Markov chain Monte Carlo (MCMC) sampling is frequently used because it is efficient and rather easy to implement. It allows to sample the full parameter space, to find multimodal pdfs with multiple estimate candidates, to visualize marginal distributions for finding an unresolved subspace or parameter correlations not resolved by the data. In case of an uni-modal posterior pdf, the mean of the parameter samples provide an estimate, which can be compared to the MAP solution, and the covariance of the samples provides information about the estimation uncertainty. Furthermore, any derived quantity from a parameter sample can also be averaged and its uncertainty estimated. As an example see [920] where the electron density and temperature profiles were estimated from MCMC sampling of the posterior pdf of an IDA approach of multiple diagnostics at ASDEX Upgrade. The uncertainties of the profiles as well as estimates for the profile gradient and the logarithmic gradients and their uncertainties were obtained applying MCMC sampling.

In any case when a new data inference problem is tackled, it is recommended to explore a posterior pdf with MCMC methods at least once to learn about the subtleties of the data analysis problem at hand.

### 11.2.8. Validation.
The validation of the results from a Bayesian analysis is closely related to the methods for parameter estimation and the estimation of the parameter uncertainties (section 11.2.3.3). Exploring the parameter space of the posterior pdf via MCMC sampling and comparing the mean and the MAP solutions and their uncertainties is recommended as a first validation step. Multi-modal pdfs with similar weights around the posterior maxima cannot easily be summarized by single estimates and uncertainties. Furthermore, they can result in misleading estimates in parameter ranges not supported by any of the diagnostics data [935]. Such a multi-modal posterior pdf can be obtained, e.g. for inconsistent diagnostics data when the individual analyses of the diagnostics result in distant estimates with non-overlapping uncertainties, for outliers within a set of data, or for a misspecified uncertainty level for the data [935]. As outliers of known or unknown source and misspecified uncertainties can be tackled with an outlier robust likelihood (section 2.4), inconsistent diagnostics need to be studied in

more detail. After a thorough inspection of sources for the inconsistency, candidate sources can be quantified with additional nuisance parameters, its uncertainties with a corresponding prior pdf, and marginalized (integrated out) from the posterior pdf. This way the uncertainty of the nuisance parameter propagates to the parameters of interest. If the posterior pdf becomes a unimodal distribution with parameter estimates and uncertainties capable of describing all diagnostics, a reasonable candidate for the inconsistency is found. This way various candidates for the inconsistency can be tested and compared for their success in explaining all data simultaneously. Please note, that with this method reasonable candidates can be identified, but the method does not guarantee to find the correct source of the inconsistency. Nevertheless, this probabilistic method puts any inconsistency study on quantitative grounds.

Similar methods as for inconsistent diagnostics are applied for diagnostics deterioration, e.g. degradation of optical components (see also section 11.2.5). An IDA method combining data from multiple diagnostics including calibration data provides a self-consistent approach to constrain uncertain and varying calibration nuisance parameters. This approach becomes important in any harsh environment of future fusion devices as DEMO.

An extension of the validation methods described so far is given by the combination of measured data with modeling information. Physical modeling allows to avoid non-physical prior information, to reduce the parameter space on physical grounds, and to validate the measured data. Transport analyses, e.g. given by ASTRA modeling, might help to identify diagnostics lack of strength, e.g. unresolved parameter dependencies, as well as, e.g. limiting profile gradients not restricted by diagnostics data within their uncertainty. Validation typically performs best if all relevant information, measured data and modeling information, are jointly analyzed. The most important criterion is given by reasonable data residuals. Successful validation needs data residuals within the uncertainties and data residuals scattering according to the likelihood pdf used. Again, successful probabilistic validation does not imply a physically correct description of the data and correct physical modeling, but it provides a quantitative framework for the validation process.

### 11.2.9. Numerical implementation.
Nowadays ample experience exists from applying IDA at various fusion devices (W7-AS, ASDEX Upgrade, JET, W7-X, TJ-II, and MST RFP), for various diagnostic combinations and for various parameter sets. Based on this experience and due to the conceptual clearly defined Bayesian approach an open-source IDA toolbox written in python and designed to be modular and flexible to be used at present and next generation fusion devices is presently under development. The code is intended to be highly modular in the set of diagnostics considered, in the type of likelihoods to address different uncertainty conditions, in the multi-fidelity FMs (synthetic diagnostics) to allow for fast analysis with reduced physics for real-time applications
up to post-plasma data analysis with highly-sophisticated diagnostics models, modular in the parameterization (splines, Gaussian process regression, ...), in the priors encompassing non-physical conditions (e.g. smoothness) or physical information from modeling codes, and modular in the evaluation and representation of results using MAP solutions or using MCMC sampling to explore the full probabilistic parameter space. A first implementation showing the combination of a synthetic set of interferometry, Thomson scattering and ECE diagnostics for the estimation of electron density and temperature profiles is described in section 11.4.2.

The IDA workflow is controlled by code parameters for, e.g. the selection of the set of diagnostics to be analyzed, the likelihood and FM to be used for each diagnostic, the equilibrium to be used, the time frame and temporal resolution with which the physical quantities are to be estimated, the parameterization of the physical quantities (profiles) to be estimated, the prior constraints to be applied (smoothness, physical models), or the parameter and uncertainty estimation methods (MAP, MCMC). A frequently used format for code parameters is given by the XML format. The present IDA implementation relies on the YAML format which is easier to be read and edited by humans.

## 11.3. IMAS

A multiple purpose data analysis framework should be adaptable to handle any data input and output method. Nevertheless, a standardized communication scheme between codes and databases is beneficial for an efficient workflow.

The ITER IMAS is the implementation of a physics modeling and data analysis suite for plasma operation and research. It provides standardized access to experimental and simulated data [397]. The data are organized in interface data structures (IDS) which are designed for high modularity and flexibility to be suitable for any fusion device. The IDS provide within a data dictionary a definition of data structures in a tree configuration and the names of the data to be used with the most popular programming languages. New IDS are continuously developed and existing ones are extended according to the needs of code developers and users.

IMAS is designed to provide workflows for plasma modeling, data analysis and data structures. The IDS encompass, e.g. the full description of the tokamak subsystems (diagnostic, heating system, etc) or the physical concepts describing the plasma (equilibrium, set of core plasma profiles, wave propagation, etc) [397]. IMAS is used within the IDA framework, at present, by reading the machine description data for the diagnostics properties (geometry), the diagnostics data, diagnostics FMs, and the equilibrium. The linkage with IMAS will be extended as further diagnostics and FMs will be provided.

For a diagnostic FM provided by IMAS to be used, the parameter representation internal to the IDA framework has to be mapped to the corresponding IDS needed as input to the IMAS FM. For example the spline representation of profiles within the IDA framework has to be mapped to the core-profile IDS defining the interface to the IMAS routines.

Eventually, the results of the data analysis, e.g. the estimated profiles and their uncertainties, and the forward modeled data and the residuals have to be written into the corresponding IMAS database for further usage. The residuals, which describe the misfit of the measured data or modeling prior information with the forward modeled data, is of central importance for a (later) validation of the estimation results.

FMs provided by IMAS ideally have to be provided in a numerically-efficient modular way since the estimation of physical parameters requires a fitting (MAP solution) or a sampling (MCMC approach) procedure where the FM is evaluated multiple times. Separate sub-functions for initialization and evaluation of synthetic signals, such that only the evaluation method is iterated in the IDA loop, have to be distinguished. Three instances of the FM are to be separated: First, the initialization of time independent (static) quantities such as reading the geometry of the interferometer LOSs from the IMAS machine database which has to be done only once for the complete evaluation of a plasma pulse. Second, the initialization of time dependent (dynamic) quantities such as the magnetic equilibrium and the magnetic coordinates along the interferometer LOSs, which has to be done once for each time point. Third, the evaluation of the FM (synthetic diagnostic signal) from the parameters to be estimated. The third and innermost part of the IDA iteration loop defines the most critical part for numerical efficiency.

## 11.4. Examples

### 11.4.1. Synergistic effect.
The result of a Bayesian analysis is a probability distribution of the parameters of interest. In case of a multidimensional probability distribution, the pdf contains the dependencies between the parameters. These dependencies allow one to obtain a synergistic effect where the result of a diagnostic set is more informative than the sum of the results of individual measurements. This is depicted in figure 186 where Thomson scattering data are analyzed together with SXR data [910].

The left panel shows the two-dimensional likelihood pdf as a function of density and temperature using only the TS data. The hyperbolic structure is typical for this TS diagnostics which was most sensitive to the electron pressure. The middle panel shows the pdf of a SXR analysis where only temperature information was obtained, to be seen in the structure-less shape with respect to the density. Assuming we are interested in the density only, the two-dimensional posterior pdfs have to be marginalized over the temperature. The result of this marginalization is shown in the right panel for the Thomson data only (dashed curve), SXR data only (dotted flat curve) and the joint analysis taken from the product of the two pdfs (solid line). Although the SXR data do not provide any information about the density, the joint analysis shows a 30% reduction of the estimation uncertainty (width of the marginal distribution) of the density. This example shows on the one hand the mechanism how a probabilistic synergistic effect is obtained, and, on the other hand, that exploiting the dependencies between the parameters are valuable for the combined analysis of heterogeneous diagnostics.
<figure><img src="image_198.png" /><figcaption>**Figure 186.** Synergistic effect by exploiting full probability distribution.</figcaption></figure>

**11.4.2. Profile reconstruction.** Various applications for profile reconstruction using IDA at the W7-AS stellarator [910], at the ASDEX Upgrade tokamak [914, 915, 920, 926], at the JET tokamak [912], at the TJ-II stellarator [916], at the MST RFP [917, 918], and at W7-X stellarator [921, 922] can be found.

Due to the conceptual clearly arranged Bayesian approach a general-purpose IDA toolbox, written in python, for present and next generation fusion devices was developed and will continuously be complemented as new diagnostics or parameterizations are requested. The ingredients are summarized in section 11.2. A first application of this IDA toolbox implemented at ITER combines synthetic diagnostic data from artificial ECE and TS diagnostics. These two diagnostics were augmented with a synthetic data set from the TIP [518]. The IDA software package allows for selecting (via the YAML parameter file) for the diagnostics individually among Gaussian and Student's t-likelihoods and for the profile parameterization between a spline representation optionally with non-negativity constraints or an exponential of a spline representation which is by definition positive. The profiles can be estimated in two ways, by finding the MAP solution of the posterior pdf or by evaluating the mean profiles from MCMC samples from the posterior pdf. Both estimation techniques allow to evaluate profile uncertainties.

The IDA software package reads from the ITER:IMAS database: From the ITER machine description database the interferometry geometry of 5 LOS (figure 187) and from the ITER scenario database an ITER equilibrium were taken. For the TIP a synthetic data set was generated by line-integrating a core density profile corresponding to profiles from the ITER scenario database. Random noise with a standard deviation of 5% was added to the TIP data. The ECE data and TS data were generated similarly at arbitrary positions within the plasma due to, at present, lack of realistic coordinates of the two diagnostics in the machine database. For the ECE FM the basic assumption of a thermal and optically-thick plasma (black-body radiation) is assumed where the radiation temperature equals the electron temperature ($T_{\text{rad}} = T_e$) at the cold resonance position. This frequently used, trivial ECE FM will be complemented with the radiation transport forward modeling using the ECRad code [930, 931]. For simulating TS data, $T_e$ and $n_e$ pair values are taken at various positions in the plasma

<figure><img src="image_199.png" /><figcaption>**Figure 187.** Toroidal plane of ITER (major radius 6.2 m, minor radius 2 m) and the 5 TIP LOSs.</figcaption></figure>

from the temperature and density profiles. Random noise of 10% for both ECE and TS data were added.

The profiles taken for generating the data sets for the three diagnostics are shown in figure 188 as black solid lines (original). The noisy data are shown as crosses (TS blue, ECE green, TIP orange) where the length of the vertical line corresponds to the uncertainty chosen. As the TIP data are line integrated, the data are normalized to the lengths of the LOSs as shown in figure 189. The 5 TIP data are plotted at arbitrary plasma position sorted according to the smallest (largest) length of the LOS to the largest (smallest) $\rho_{\text{pol}}$, correspondingly.

The profiles were parameterized with the exponential of a spline which ensures non-negativity. For the ECE and TS data the Student's t and for the TIP data the Gaussian likelihood were arbitrarily chosen. If sporadic fringe jumps in the TIP data are expected and routine (unsupervised) analysis
<figure><img src="image_200.png" /><figcaption>**Figure 188.** Simulated (black solid line) and reconstructed (red solid line) temperature and density profiles estimated from the noisy data from the ECE (green), TS (blue) and TIP (orange) diagnostics. The open diamonds depict the forward modeled TIP data using the fitted density profile. The dashed area covers the uncertainty band from a MCMC sampling method.</figcaption></figure>

is foreseen, the Student's t-likelihood is beneficial in downweighting the corrupted data, as routinely used within the IDA approach at ASDEX Upgrade. No smoothing prior is applied.

The profiles estimated from the set of noisy data using the MAP solution are shown as red solid lines (MAP) with uncertainties employing the Gaussian approximation as red dashed lines. The profiles from the mean of the MCMC samples hardly deviates from the MAP profiles (not shown). The uncertainty band estimated from the upper and lower standard deviations of the MCMC samples relative to the mean values are shown as shaded area (MCMC). Please note that the use of upper and lower standard deviations typically result in asymmetric uncertainty bands if the posterior pdf is not symmetric with respect to its mean value. As expected, the MAP and MCMC estimates for this test example agree within the evaluated uncertainties with the original profiles.

### 11.4.3. Equilibrium reconstruction.
A reliable magnetic equilibrium reconstruction is essential for stability and transport studies as well as for the development of advanced plasma operation or steady-state tokamak operation with high bootstrap current fraction and non-inductive current drive [941, 942]. Additionally, a reliable equilibrium is of major importance for the mapping of the diagnostics on a common

coordinate system in the IDA framework. Various equilibrium reconstruction codes and methods are available at the various fusion devices (see e.g. [943–948]). Frequently, for early availability and robustness equilibrium reconstruction is based on a reduced data set as, e.g. magnetic probe measurements only. But this usually results in reduced reliability especially of the core parameters (current and *q*-profiles and flux surfaces). Therefore, for best performance the equilibrium reconstruction is part of the IDA workflow where a lot of relevant information for an improved equilibrium can be provided.

Often abundant measurement and modeling information is available for an improved reconstruction of the magnetic equilibrium. This is exemplified with the ASDEX Upgrade equilibrium reconstruction using the IDE code package [948, 949]. This framework is based on coupling of a Grad–Shafranov solver with current diffusion modeling. The neo-classic current diffusion model (CDM) describes the temporal evolution of the equilibrium between two successive equilibrium reconstructions employing the Grad-Shafranov solver [950]. The CDM predicts the flux-surface averaged current density profile which provides data including their uncertainties additionally to all the other measurements to constrain the next equilibrium reconstruction. The free-boundary equilibrium solver employs data from magnetic measurements (field probes and flux measurements), diamagnetic measurements [951], pressure profiles from electron [914] and ion temperature and density measurements [920] and fast-ion pressure modeling (RABBIT [952] for NBI or TRANSP [953] for NBI and ICRH), effective ion charge $Z_{eff}$ [915], internal current measurements from MSE and IMSE [954] and polarimetry [955], tile (halo) currents for SOL currents, loop voltage measurements, *q*-constraints from mode analyses, topological iso-flux constraints from multiple measurements of $T_e$ or $T_i$ on the same flux surface [945, 956], and plasma rotation measurements for considering centrifugal effects in an extended Grad-Shafranov equation [945, 957]. For the neo-classical current diffusion the electron and ion temperature and density and the Zeff profiles are needed for the bootstrap current and the conductivity. Additionally, the EC and neutral beam driven currents are provided by the TORBEAM and RABBIT codes. Sawtooth reconnection events are described by two different sawtooth models for the sawtooth induced current re-distribution [949]. All these inputs provide redundant and complementary data for an improved and validated magnetic equilibrium.

The close interdependencies between the IDA profile estimation and the equilibrium reconstruction mutually influence also their reliabilities [920, 946]. As a fully integrated IDA approach covering profile estimation and equilibrium reconstruction simultaneously is still to be provided, a pragmatic approach is given by an alternating iteration of profile estimation and equilibrium reconstruction which was observed to converge within a few iterations. The uncertainties of the input data for the equilibrium reconstruction are taken into account in the fitting part of the Picard iteration, and, therefore, propagate to the uncertainties of the equilibrium quantities. The equilibrium uncertainties for the profile estimation can be considered by a MC approach sampling the base-function
<figure><img src="image_201.png" /><figcaption>**Figure 189.** Measurement of a fast-ion velocity distribution function [a.u.] in the center of a plasma heated by co-current and counter-current neutral beam injection at EAST. The tomographic inversion is based on (a) FIDA spectra using two detectors, and (b) additionally a NES spectrum. The expected ion densities to the right of the dashed line are low as expected from a calculation with TRANSP/NUBEAM. Reproduced from [958]. © EURATOM 2020. All rights reserved.</figcaption></figure>

equilibrium coefficients from their covariance matrix and evaluate a random sample of equilibria to be used for the study of equilibrium-induced profile uncertainties.

11.4.4. **IDA by velocity-space tomography.** An application of IDA, which has emerged in recent years, is the measurement of fast ion VDFs by velocity-space tomography [959–961]. As for any tomography application, IDA of all available measurements is essential. Position-space plasma tomography systems are usually designed with nominally identical or at least similar detectors. Velocity-space tomography uses any available detector monitoring the same spatial measurement volume, regardless of the type of diagnostic [960].

An example appears in figure 189 showing the VDF at EAST for a plasma heated by co- and counter-current NBI [941]. *E* is the energy and *p* is the pitch. The measurements are analyzed using (a) only two fast-ion $D_α$ (FIDA) spectroscopy detectors and (b) the two FIDA detectors and in addition neutron emission spectroscopy (NES).

The dashed line represents the upper boundary of a VDF computed with TRANSP/NUBEAM. Few ions are expected to the right of the dashed line because only NBI heating was used and no acceleration of ions is expected. If, on the one hand, only the two FIDA detectors are used to compute the tomographic image, large ion densities at energies significantly larger than the NBI injection energies are erroneously found. We additionally recognize these as artifacts since similar artifacts appear in tomographic inversions of synthetic measurements, where the true solution is known, for this diagnostic setup. If, on the other hand, in addition NES measurements are used, they force the distribution function to very small values at large energies. This works well since NES measurements are highly sensitive at large energies [962, 963]. This example shows that the IDA of FIDA and NES here suppresses the artifacts at large energies. A second example in addition to

figure 189 is velocity-space tomography based on γ-ray spectroscopy (GRS) measurements and NES measurements at JET [964]. The NES measurements are made by TOF, liquid scintillator and single-crystal diamond detectors [965], so that in total four different detector types were used in the tomographic inversion.

Until now velocity-space tomography has been applied at ASDEX Upgrade [961, 966–971], JET [964], MAST [972], DIII-D [941], EAST [973, 974] and TCV [975]. Various combinations of data from FIDA, NES, GRS as well as CTS with two to five simultaneous detectors have been used at these tokamaks. VDFs in plasmas heated by NBI as well as electromagnetic wave heating in ion cyclotron range of frequencies (ICRF) have been measured.

At ITER, velocity-space tomography of the α-particle distribution function based on GRS and CTS has been shown to be feasible for energies from about 1.7 MeV upwards [629]. However, since all currently foreseen diagnostics observe in a perpendicular direction with respect to the magnetic field, the sign of the pitch *p* of the α-particles cannot be determined. But the absolute value $|p|$ can be determined, so that the VDF $f(E, |p|)$ can be measured. If an oblique γ-ray detector is installed, the sign of the pitch can be found, too [629].

Velocity-space tomography is also applied to measure anisotropic deuterium temperatures $T_‖$ and $T_⊥$ as well as the deuterium density and drift velocity [976]. In this application, the full (fast and thermal) VDF is determined based on simultaneous measurements with several $D_α$-spectroscopy detectors, and then the lowest moments of the full VDF are computed [976].

Reviews of velocity-space tomography are available in [962, 977]. In the following we will focus on methods of velocity-space tomography and discuss the FM, the inverse problem, prior information, uncertainties as well as related 1D to 5D tomography problems.
<figure><img src="image_202.png" /><figcaption>**Figure 190.** Exemplary weight function showing the velocity-space sensitivity of a CTS measurement at a particular Doppler shift. Reproduced from [961]. © 2014 IAEA, Vienna. All rights reserved.</figcaption></figure>

**11.4.4.1. The FM: synthetic diagnostics.** To do tomography in velocity space, we need to quantify the sensitivity of the diagnostics in velocity space. This is analogous to modeling the lines-of-sight in traditional position-space tomography. Weight functions quantifying this velocity-space sensitivity have been developed for all major fast-ion diagnostics: FIDA [978, 979], NPAs [978], CTS [627], NES [980, 981], GRS [982, 983] and FILDs [984]. Recently, weight functions for 3 MeV proton diagnostics [985] and ion cyclotron emission spectroscopy weight functions [986] have been numerically computed, too. A weight function w relates a 2D fast-ion distribution function f to a measurement s through the integral equation [627, 978–983]

$$s(m_1, m_2) = \int_0^\infty \int_{-\infty}^\infty w(m_1, m_2, v_p, v_\perp) \times f(v_\parallel, v_\perp) dv_\parallel dv_\perp \quad (11.5)$$

$s(m_1, m_2)$ is the measured signal in the spectral bin $[m_1, m_2]$. FIDA measures spectra in wavelength [987], GRS in $\gamma$-ray energies [988], TOF NES in flight times [963], and CTS in wave frequency [989]. $(v_\parallel, v_\perp)$ are the velocities parallel and perpendicular to the magnetic field, respectively. $(E, p)$ coordinates are also often used but in $(v_\parallel, v_\perp)$ the geometrical shape of weight functions is often clearest. The weight function hence shows the quantity [signal/fast ion] where the units of the signal are particular to the instrument. An example of a weight function appears in figure 190. The colored regions are observable for the given measurement bin whereas the white regions are not observable.

Substitution of a $\delta$-function modeling $N_f$ ions at coordinates $(v_\parallel, v_\perp)$ into equation (11.5) and integration shows that the amplitude of a weight function at velocity-space position $(v_\parallel, v_\perp)$ is readily computed from

$$w(m_1, m_2, v_{\parallel 0}, v_{\perp 0}) = \frac{s(m_1, m_2)}{N_f} \quad (11.6)$$

using a standard synthetic diagnostic code for the diagnostic. The computation of the signal by weight functions neglects spatial effects, which is usually fairly accurate for the plasma

center where plasma profiles are flat and spatial effects are hence negligible.

Knowing the weight functions for all available measurement bins in a measured spectrum, we can write the FM of the diagnostic as the matrix equation

$$S = WF \quad (11.7)$$

which summarizes a discretization of equation (11.6) [959]. S is a vector holding the measurement data of all available diagnostics, F holds the VDF rearranged as column vector, and each line of the matrix W holds a weight function rearranged as a row vector. Given a simulation F and knowing the weight matrix W, we can rapidly compute the corresponding synthetic signals S for all diagnostics.

**11.4.4.2. Likelihood.** To determine F, given W and S, equation (11.7) has mathematically the same form as any traditional position-space tomography problem. However, velocity-space tomography often requires combinations of entirely different diagnostics or detector types. For practical reasons, to combine measurements with vastly different amplitudes by orders of magnitude, each individual measurement in S and its corresponding weight function is normalized by its uncertainty [960]. This is equivalent to the unnormalized data if likelihoods with the $\chi^2$-misfit between the data and the forward modeled data weighted with the measurement uncertainty are used as, e.g. for the Gaussian and Student's t-likelihood (equations (11.2) and (11.3)). In the present inverse problem of velocity-space tomography the Gaussian likelihood is employed.

**11.4.4.3. Prior information.** The amount of measured fast-ion diagnostic data is always small in fusion plasmas due to the limited access to the plasma and the often comparatively low SNR for tomography applications. Furthermore, there are never more than just a few detectors, such that we must always determine the 2D image from just a few projections (medical tomography uses hundreds of projection directions). Due to this limited amount of data and projection directions, the use of prior information for this ill-posed inference problem is often essential to reduce noise fitting and obtain meaningful images
[966], in particular in velocity-space regions observed by only one or two detectors [629, 919, 941, 972].

As in many tomography problems, the problem to find $F$ from $W$ and $S$ is ill-posed and must be regularized with additional (prior) information. The most successful regularization method in velocity-space tomography has been the Tikhonov regularization in which we solve a least-square problem of the form [966]

$$ \underset{F}{\operatorname{minimize}} \left\| \begin{pmatrix} W \\ \lambda L \end{pmatrix} F - \begin{pmatrix} S \\ 0 \end{pmatrix} \right\|_{2} . \qquad (11.8) $$

The upper row of this matrix equation seeks to fit the data whereas the lower row penalizes undesired features of the solution. $L$ is the regularization matrix. Velocity-space tomography usually uses zeroth order Tikhonov regularization, where $L$ is the identity matrix, or first-order Tikhonov regularization, where $L$ is a matrix effecting a gradient. This penalizes large absolute values or large gradients, reflecting our prior information that we believe the VDF to be smooth due to collisions. Equation (11.8) is equivalent to maximizing a posterior pdf given by the product of a Gaussian likelihood with a Gaussian prior pdf with the Tikhonov term in the exponent [919].

$\lambda$ is the regularization strength that balances data fitting versus the regularization requirement. $\lambda$ is a free parameter of the problem that must be determined as part of the solution. Various methods to choose $\lambda$ automatically have been tested, e.g. the L-curve or the generalized cross validation method [966]. However, no method is clearly always advantageous, and they usually produce similar $\lambda$'s within a factor 10. It is advisable to inspect a range of $\lambda$'s to make sure that no phenomena are missed.

This is the standard regularization technique in many plasma tomography applications. If no constraints are introduced, the solution is given by the so-called normal equation

$$ F_{\lambda} = (W^{T}W + \lambda^{2}L^{T}L)^{0.75[1.0]-1} W^{T}S. \qquad (11.9) $$

We write the index $\lambda$ in $F_{\lambda}$ to emphasize that the solution depends on the regularization strength. However, $F_{\lambda}$ computed with the normal equation usually becomes negative in some velocity-space regions, which is unphysical. This can be remedied by further prior information about non-negativity constraints. We are certain that the fast-ion VDF is not negative. This prior can be encoded by solving a least-square problem with non-negativity constraint [966]:

$$ \underset{F}{\operatorname{minimize}} \left\| \begin{pmatrix} W \\ \lambda L \end{pmatrix} F - \begin{pmatrix} S \\ 0 \end{pmatrix} \right\|_{2} \quad \text{subject to } F \ge 0. \qquad (11.10) $$

One can simply use a non-negative least-squares algorithm [990]. Alternatively, one may penalize negative values and hence force them to become small [967]. The non-negativity constraint also acts as a useful smoothing regularizer since it tends to dampen high-frequency spatial oscillations in the

<figure><img src="image_203.png" /><figcaption>Figure 191. The colored lines are boundaries of weight functions connected to null-measurements. The black line is their envelope, presenting a boundary to the velocity space region empty of fast ions. Reproduced from [966]. © 2016 EURATOM. All rights reserved.</figcaption></figure>

solution. Since the prior information of non-negativity is absolutely certain, we regard the non-negative Tikhonov problem as our standard method.

Several other constraints have been implemented in addition to non-negativity: isotropy, monotonicity, or restrictions on the target velocity space to be reconstructed. For example, a minimization problem with non-negativity, restricted velocity space, and monotonicity constraint in energy can be written as

$$ \underset{F}{\operatorname{minimize}} \left\| \begin{pmatrix} W \\ \lambda L \end{pmatrix} F - \begin{pmatrix} S \\ 0 \end{pmatrix} \right\|_{2} \quad \begin{array}{l} \text{subject to} \\ F \ge 0, \\ F(E_0, p_0) = 0, \\ L_{1,E} F(E_m, p_m) \le 0. \end{array} \qquad (11.11) $$

$F(E_0, p_0) = 0$ is the velocity-space region with negligible fast-ion densities according to null-measurements, as identified by weight functions [966]. A null-measurement in the measured signal $S$ is the measured absence of evidence for fast ions. An example of an experimentally determined null-measurement velocity space region at ASDEX Upgrade is illustrated in figure 191. It is advantageous to use null-measurements as they restrict the velocity space by reducing the number of unknowns [966]. Null-measurements are perhaps more intuitively understood in position-space tomography problems: A ray that misses the object altogether will measure the absence of any material, and thus this part of position-space does not need to be reconstructed.

A monotonicity constraint in one of the coordinate directions, in equation (11.11) the energy, can be advantageous if
<figure><img src="image_204.png" /><figcaption>Figure 192. $\kappa_1(E,p)$ encodes the NBI injection energies and pitch. Reproduced from [966]. © 2016 EURATOM. All rights reserved.</figcaption></figure>

one is confident that the distribution function is monotonous [941]. This is likely a good assumption for $\alpha$-particles or usually ICRF fast-ion tails. However, any local minimum in the distribution function may be physical, which would be missed when this mathematical constraint is enforced.

Prior information may also be encoded by modifying the penalty function to become dependent on the velocity-space coordinates. For example, to promote nearly isotropic solutions, we can penalize gradients in pitch direction much more strongly than in energy direction [919, 991]. This idea is similar to anisotropic regularization along flux surfaces in position-space plasma tomography. We may further enforce isotropy as constraint by assuming the solution to be constant in pitch direction [977].

Another way to modify the penalty function is to introduce a function $\kappa_1(E,p)$ acting with a first-order Tikhonov regularizer or another function $\kappa_0(E,p)$ acting with a zeroth-order Tikhonov regularizer [941, 966, 972, 973]. The minimization problem with a mix of zeroth- and first-order Tikhonov terms is written as

$$ \underset{F}{\operatorname{minimize}} \quad \left\| \begin{pmatrix} W \\ \lambda_1 \kappa_1(E,p) L_1 \\ \lambda_0 \kappa_0(E,p) L_0 \end{pmatrix} F - \begin{pmatrix} S \\ 0 \\ 0 \end{pmatrix} \right\|_2 \quad (11.12) $$

$\kappa_1(E,p)$ used with the first-order Tikhonov penalty term $\lambda_1 L_1$ can encode the velocity-space positions of the particle sources of an NBI. The velocity-space positions of the particle sources at the full-, half- and one-third NBI injection energies at a particular pitch are well-known. If $\kappa_1(E,p)$ is chosen to have minima at these well-known peak locations, as illustrated in figure 192, gradients are penalized less in the vicinity of the particle sources than elsewhere [966]. This can allow the formation of peaks in the image but does not force it. Observe that when the gradients are penalized less, a local minimum

is equally well formed as a local maximum. Data will usually dictate the formation of a maximum.

Instead of a formulation of null-measurements as a mathematical constraint, we can introduce a zeroth order Tikhonov penalty in the null-measurement velocity space as $\lambda_0 \kappa_0(E,p) L_0$ [972]. This method can be used if we are in doubt if the velocity-space is empty, e.g. if the null-measurements are too uncertain to set the related velocity space to zero. An example of a function $\kappa_0$ for a velocity-space tomography problem at the MAST tokamak appears in figure 193.

The increasing penalty with energy reflects our increasing doubt to find ions at increasing energies [972]. If the boundary between the null-measurement velocity space and the target velocity space cannot be found from measurements, we can use a numerical simulation, for example using TRANSP/NUBEAM, to restrict the velocity-space region considered for the inversion [972]. This assumes that there is no acceleration mechanism for fast ions to accelerate them beyond the boundary from the neoclassical simulation.

A recent idea is to expand the VDF into a series of slowing-down distribution functions $f_{SD}$ [973]. The tomography problem is then to determine the coefficients $a_i$ associated with the $i$th base function. In matrix form this expansion can be written as

$$ F = F_{SD}A \quad (11.13) $$

where the vector $A$ holds the expansion coefficients, and the matrix $F_{SD}$ holds the slowing-down distribution functions rearranged as columns. The forward problem becomes

$$ S = WF_{SD}A. \quad (11.14) $$
<figure><img src="image_205.png" /><figcaption>**Figure 193.** Prior information of unlikely velocity space for velocity-space tomography at MAST according to (a) TRANSP/NUBEAM and (b) null-measurements. The monotonously growing $\kappa_0(E,p)$ towards higher energies expresses our increasing doubt to find ions. Reprinted from [972], with the permission of AIP Publishing.</figcaption></figure>

Given A and knowing W and $F_{SD}$, we can calculate the signal S. Calculating A, given S, is an ill-posed problem, as the tomography problem with the expansion. We can then solve a zeroth-order Tikhonov problem in the expansion coefficients A of the form

$$ \underset{A}{\operatorname{minimize}} \left\| \begin{pmatrix} W F_{SD} \\ \lambda I \end{pmatrix} A - \begin{pmatrix} S \\ 0 \end{pmatrix} \right\|_2 . \quad (11.15) $$

If $F_{SD}$ is invertible, we can substitute $A = F_{SD}^{-1}F$, and equation (11.15) can be equivalently written as

$$ \underset{F}{\operatorname{minimize}} \left\| \begin{pmatrix} W \\ \lambda F_{SD}^{-1} \end{pmatrix} F - \begin{pmatrix} S \\ 0 \end{pmatrix} \right\|_2 \quad (11.16) $$

which shows that the expansion in basis functions can be formulated as a standard Tikhonov problem with $F_{SD}^{-1}$ as the regularization matrix L. This allows us to interpret this expansion in slowing-down basis functions as slowing-down regularization. This type of regularization reflects our prior belief that the usual slowing-down physics will in part determine the shape of the distribution function. However, if data dictates otherwise, deviations will appear due to the upper row of equation (11.16).

Lastly, if there is not enough data to do a full tomographic inversion, we can use a numerical simulation $F_{sim}$ as prior information and penalize any deviation from the simulation [966]. The penalty term becomes $\|L(F - F_{sim})\|_2$, and we write the problem as

$$ \underset{F}{\operatorname{minimize}} \left\| \begin{pmatrix} W \\ \lambda L \end{pmatrix} F - \begin{pmatrix} S \\ \lambda L F_{sim} \end{pmatrix} \right\|_2 . \quad (11.17) $$

Other prior information can still be added in the same way as described. However, observe that this Tikhonov problem pursues a less ambitious goal than a full tomographic inversion due to the use of the simulation. Our goal here is only

to identify regions in velocity space where the measurements suggest deviations from $F_{sim}$ which we can find by successfully decreasing $\lambda$.

We summarize the different types of prior information that has been used in velocity-space tomography:

* smoothness (zeroth- or first-order Tikhonov)

* non-negativity constraint or penalty for negative values

* restricted velocity space by null-measurements or according to a simulation (constraint)

* unlikely velocity space by null-measurements or according to a simulation (penalty)

* monotonicity constraint

* isotropy constraint or penalty for deviation from isotropy

* beam injection peak locations

* slowing-down physics as regularizer

* numerical simulation as prior.

#### 11.4.4.4. Uncertainties.
Sources for uncertainties in the estimated velocity-space distribution can be divided into four categories: (1) uncertainties due to (statistical) measurement noise [960], (2) bias uncertainties in the measurements (systematic uncertainties), (3) uncertainties in the weight matrix W (FM) due to uncertainties in nuisance parameters [970] and (4) bias uncertainties due to the regularization [970] (prior information).

Analytic formulas for estimating uncertainties due to measurement noise and uncertainties in the nuisance parameters can be given for the unconstrained Tikhonov problem [629, 969]. For the constrained Tikhonov problem, these uncertainties can be found by sampling. The fast-ion measurements and the nuisance parameters are sampled from their probability distributions. For each sample we obtain an inversion. Hence we generate a population of N inversions, $F_{\lambda,i}$. Its mean is the best estimate of the velocity-distribution function, and its standard deviation is the uncertainty due to uncertainties in the signal
and the nuisance parameters:

$$ \langle F_{\lambda} \rangle = \frac{1}{N} \sum_{i} F_{\lambda,i}, \qquad (11.18) $$

$$ \delta F_{\lambda} = \sqrt{\frac{1}{N-1} \sum_{i} (F_{\lambda,i} - \langle F_{\lambda} \rangle)^2}. \qquad (11.19) $$

Each pixel in the inversion hence has its own uncertainty [969, 970]. The two contributions can also be individually calculated if required.

The computation of bias uncertainties due to regularization and due to systematic errors in the measurements are open problems. Bias uncertainties make it impossible to reconstruct the true distribution function even with perfect, noise-free measurements. To quantify this bias, we would need to know the true solution, which we never do [919].

Systematic bias uncertainties in the measurement data are also notoriously difficult to detect. But such systematic measurement errors can lead to systematic artifacts which can sometimes reveal that some error is present. For example, errors in the calibration of the measurements lead to systematic artifacts that can give clues to what might be wrong.

### 11.4.4.5. Discussion.
To make optimal use of the diagnostic set at ITER or other tokamaks and stellarators, we must develop 1D to 5D inversion tools and be able to use prior information to deal with the sparsity of data on these devices. The methods presented here will allow measurements of α-particle VDFs for energies from 1.7 MeV upwards based on IDA of GRS and CTS [629]. Hence energy spectra in ITER, as requested by the ITER measurement requirements [4], can also be determined. Below α-particle energies of 1.7 MeV, CTS will be the only diagnostic for α-particles. If only one detector is available, 1D inversion techniques need to be used to determine energy spectra, for example by assuming isotropy or near-isotropy as prior [977, 991].

It is now also becoming possible to measure 3D phase-space distribution functions by orbit tomography [992, 993]. This approach is analogous to velocity-space tomography, but in 3D phase-space of constants of motion which covers the entire ion population in the tokamak. Each grid point in 3D phase space corresponds to an orbit in the tokamak. The FM computes the signal generated by fast ions on each orbit. In the tomography problem, the 3D phase-space distribution function of all fast ions in the plasma is inferred from the measurements of all detectors. The computed orbits constitute the prior information for orbit tomography. This approach has worked well at ASDEX Upgrade [994] and is being implemented at JET [993]. It requires many measurements to cover the 3D target phase space, but with appropriate additional prior information it will hopefully be useful at ITER.

Lastly, the presented method to expand the distribution function in 2D base functions is actually not restricted to 2D. The base functions can be 3D, 4D or 5D functions. For non-axisymmetric plasmas, the entire phase-space distribution function is described by 3D in position space and only 2D

in velocity space due to the fast gyromotion. 5D tomography would allow IDA of all measurements on stellarators or non-axisymmetric tokamaks.

## 11.5. Summary

IDA in the framework of BPT provides a method for improved results by a coherent combination of heterogeneous diagnostic measurements with physical prior and modeling information to restrict the parameter space of otherwise ill-posed inversion techniques. The concept of IDA is outlined and contrasted with conventional data analysis. The ingredients of this probabilistic approach is given by forward modeling, suitable likelihood pdfs with comprehensive uncertainty quantification of measurements, probabilistic quantification of prior information, and probabilistic quantification of nuisance parameters and their marginalization. The probabilistic approach enables us to obtain synergistic effects by exploiting the parameter correlation structure and diagnostics interdependencies.

A general purpose IDA toolbox was developed for present and next generation fusion devices and applied to a combination of ITER profile diagnostics. Profile estimation and equilibrium reconstruction is closely correlated and is recommended to be combined in an IDA approach. An example of IDA by velocity-space tomography highlights the benefit of combining various heterogeneous diagnostics with physical prior information including their uncertainties.

## Acknowledgment

All the ITPA TG on Diagnostics would like to express his gratitude to the strong and efficient support provided by the Guest Editors in particular by Professor Tony Donné for his very accurate comments and corrections who help us to improve the quality or our paper and to Dr David Campbell for his permanent support in preparing this paper, interacting with us with great efficiency and answering our numerous questions. We thank also very much Dr Axel Jardin for his active help in improving the layout of the document.

Subchapter 1: There are hundreds of contributors to the progress of ITER diagnostic measurement, including the authors of the subchapters that are listed here, but also their predecessors in the ITPA and ITER expert groups. The authors wish to acknowledge them all and those who helped with the editing of this chapter by providing internal and external critical review and Radija Bouhamou and Masanari Hosokawa for the maintenance of the measurement requirement and ITPA databases, respectively. For the magnetics section, the work reviewed is the work of the authors of [8–43, 395]. The views expressed in this paper do not necessarily reflect the views of the ITER Organization.

Subchapter 2: The work leading to this publication has been funded partially by Fusion for Energy under the Contract F4E-FPA-327. This publication reflects the views only of the author
and Fusion for Energy cannot be held responsible for any use which may be made of the information contained therein.

Subchapter 3: The work leading to this publication was initiated by the ITPA Diagnostic Group. This publication reflects the views of the authors only, and the ITER Organization is not responsible for any use that may be made of the information contained therein.

Subchapter 4: G. I. Pokol and O. Asztalos acknowledge the support of the National Research, Development and Innovation Office (NKFIH) Grant FK132134." The views and opinions expressed herein do not necessarily reflect those of the ITER Organization. J. Ko acknowledges the support from the Korean Ministry of Science and ICT under KFE R&D Program (Grant No. KFE-EN2301-14). Part of this work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No. 101052200—EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them. Parts of this work (the core-CXRS section) were supported by Fusion for Energy under the Framework Partnership Agreement F4E-FPA-408 (DG). The views and opinions expressed reflect the authors' views. Fusion for Energy is not liable for any use that may be made of the information contained herein.

Subchapter 5: The authors would like to thank the ITPA TG Diagnostic for his permanent support and fruitfull discussion.

Subchapter 6: This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200—EUROfusion) and from the EPSRC [Grant Numbers EP/W006839/1Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

This report supported in part Divertor Thomson scattering by Rosatom (contract—№ H.4a.241.19.19.1009) and by Ioffe Institute (Russian Federation state funding assignments 0034-2019-0001 and 0040-2019-0023) was prepared as an account of work for the ITER Organization.

Work supported by the U.S. DOE under Contracts DE-FC02-04ER54698 and No. DE-AC02-09CH11466 with Princeton University. All U.S. activities are managed by the U.S. ITER Project Office, hosted by Oak Ridge National Laboratory with partner labs Princeton Plasma Physics Laboratory and Savannah River National Laboratory. The project is being accomplished through a collaboration of DOE Laboratories, universities and industry. This work is supported by funds from Grant-in-Aid for Young Scientists (B) (Grant

No. 20760584) and by NIFS ULHH027. The views and opinions expressed herein do not necessarily reflect those of the ITER Organization.

The views and opinions expressed herein do not necessarily reflect those of the ITER Organization.

Subchapter 7: Acknowledgements for ECE section: Work of WLR and JPZ supported by the U.S. DOE under Contract No. DE-AC02-09CH11466 with Princeton University. All U.S. activities are managed by the U.S. ITER Project Office, hosted by Oak Ridge National Laboratory with partner labs Princeton Plasma Physics Laboratory and Savannah River National Laboratory. The project is being accomplished through a collaboration of DOE Laboratories, universities and industry. The views and opinions expressed herein do not necessarily reflect those of the ITER Organization. Acknowledgements for CTS section: The work leading to this publication has been funded partially by Fusion for Energy under the Framework Partnership Agreement F4E-FPA-393. This publication reflects the views only of the author, and Fusion for Energy cannot be held responsible for any use which may be made of the information contained therein.

Subchapter 8: Authors would like to thank Tonny Done and George Vayakis for carefull proof reading of the paper and for numerous suggestions which led to improvement of the resulting paper from the view point of scientific content as well as clarity of its presentation. Authors are also gratefull to Didier Mazon for his continuous support and for providing necessary organizational momentum along the paper preparation. The paper presents an overview of a rather extensive set of experimental results and research effort which was possible thanks to a dedication and enthusiasm of a scientific community engaged in the investigation of radiation effects in ITER diagnostic components. We would like to thank research and operation teams of SCK●CEN, Mol Belgium and CVŘ, Řež, Czech Republic where the most of the irradiation tests presented within this paper were conducted.

Subchapter 9: The authors are grateful to all colleagues who helped in compiling this paper. Specifically, we thank Dr Andrey Alekseev, Dr Ilya Orlovsky for graphic material on Hα diagnostic and Dr Yury Kapustin for his help in endorsing Figure 11. We are grateful to Dr Felix Klein and Dr Marcin Rasinski for performing analyses on diagnostic mirrors and Dr Arkady Kreter for reference plasma experiments, Dr Philippe Mertens for his enthusiastic advice on content. The author team acknowledges constant help and support from ITER Organization and from the ITPA. The experimental work was in part supported by the ITER Organization via purchase order 4100006576. Investigations were also partly supported by the Ministry of Science and ICT of Korea, through the ITER project contract RS-2022-00154842. The views and opinions expressed herein do not necessarily reflect those of the ITER Organization. In part, this work has been carried out within the framework of the EUROfusion Consortium,
funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200 (EUROfusion). Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them. This work was supported by the Swiss State Secretariat for Education, Research, and Innovation (SERI) under contract number 22.00424. Several studies reported in the contribution were supported by RSF grant No 22-12-00360 of the Russian Federation.

Subchapter 10: Former TU/e students Jochem Manders (presently at VDL ETG) and Mustahsan Majeed (presently at ASML) are kindly acknowledged for their work.

Subchapter 11: The authors thank S. Pinches from the ITER organization, K. Fujii from the Kyoto University and D. Mazon from CEA Cadarache for promoting and supporting this new WG.

This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200—EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

## ORCID iDs

D. Mazon ID 0000-0001-5560-2277

G. Yun ID 0000-0002-1880-5865

M.H. Aumeunier ID 0009-0009-6207-5079

A. Bultel ID 0000-0003-4792-9995

C. Klepper ID 0000-0001-9107-8337

D. Rasmussen ID 0000-0003-1949-3549

S. Oh ID 0000-0003-1233-676X

M. Scholz ID 0000-0002-7330-1782

B. Esposito ID 0000-0002-0005-5680

B. Coriton ID 0000-0002-0067-967X

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