<figure><img src="image_171.png" /><figcaption>**Figure 159.** Bismuth Hall sensor before installation into the ITER OVSS probe.</figcaption></figure>

were used while proper layout of sensor electrodes was shaped by etching. Sensitive layer was encapsulated by ~4 µm thick layer of Al₂O₃, prepared by reactive magneto sputtering, with a few millimeters of Al₂O₃ ceramic paste on top. Copper wires were resistively welded to the sensor electrodes and the bond areas were further mechanically reinforced by Al₂O₃ ceramic paste. Detail view of the resulting sensor is shown in figure 159.

The sensors were subject to extensive testing, characterization and qualification [685-688] including neutron irradiation testing [689]. Here, the sample sensor inside Cd shield was exposed to the total neutron fluence of 2.5 × 10¹⁸ cm⁻² with the fast (0.1–20 MeV) neutron fluence of 6 × 10¹⁷ cm⁻². This neutron irradiation dose exceeds by a factor of 2 the expected maximum life time neutron fluence of the sensors on ITER. Sensor sensitivity before and after irradiation was measured in the temperature range from room to 220 °C. The sensitivity changes at 100 °C (operational temperature on ITER) was 1.3% which is compatible with overall required stability of the sensors.

Moreover, impact of transmutation on periodic *in-situ* recalibration of N type thermocouples embedded inside OVSS sensors was assessed using nuclear inventory code FISPACT [690]. Thermocouples within OVSS units will be periodically recalibrated using integrated e-beam welded capsule containing high-purity indium with well established melting point. Transient flat top on the thermocouple signal evolution along the periodic heat up of OVSS during ITER VV baking occurring at indium melting temperature will be employed as one point periodic recalibration. FISPACT simulations confirmed that changes of indium material composition due to transmutation over the ITER life time will not compromise accuracy of the thermocouple recalibration beyond acceptable margins.

Later after manufacturing process of the OVSS probes, the follow up calibration revealed the issue with gradual increase of bismuth Hall sensors resistances for a fraction of assembled OVSS probes along long storage time (~year) which separated probes assembling from their calibration. It was concluded that the most probable cause of the observed phenomena were

imperfections in Al₂O₃ encapsulation layers for some of the OVSS sensors and consequent gradual oxidation of bismuth layers which was manifested by gradual resistance increase. Long term exposure of the order of years at ambient atmosphere cannot be avoided for OVSS sensors due to long time interval between installation on ITER VV segments and the first pump down of ITER cryostat. These findings highlight the fact that although assessment of radiation induced effects is indeed very important for reliable operation of fusion reactor diagnostic components, other aspects like chemical stability, diffusion processes or aging over very long time scales can be equally important particularly for the components not allowing any maintenance along their operation on ITER.

Consequently, the R&D was focused on antimony which is another perspective material for ITER OVSS sensors [691, 692]. Antimony is much less prone to oxidation compared to bismuth, it offers wider temperature margin with melting temperature 630.6 °C versus 271.4 °C for bismuth and independence of sensitivity on magnetic field which simplifies calibration and data evaluation. The drawback of antimony is about 20 times lower Hall coefficient resulting in lower sensitivity of the sensors though, this can be partly compensated by sensitivity gain due to lower thickness of the sensitive layer and higher gain of the first stage amplifier. New generation of OVSS sensors based on Antimony was prototyped and tested in order to refurbish those OVSS sensors with manifested long-term drift of resistance. Recent technological advancements were implemented in sensors design namely change of DBC metalized AlN substrates and following etching process by thick printed copper metalized Al₂O₃ substrates where the required shape of sensor electrodes is screen printed without the need of follow up etching process. Resistive welding of sensor output wires was changed to ultrasonic bonding and contacting electrodes were moved further away from the sensitive layer in order to eliminate the risk of sensor damage during wire bonding.

Neutron irradiation test of the antimony-based Hall sensors at LVR-15 fission reactor where the sample was exposed to a total neutron fluence of 9.3 × 10¹⁷ cm⁻² with fast (E > 0.1 MeV) neutron fluence of 5.7 × 10¹⁷ cm⁻² demonstrated comparable radiation hardness of antimony sensors compared to previously tested bismuth ones [693].

Following the successful qualification of the new antimony Hall sensors, ITER VV sectors number 5 and 2 will be instrumented by the new antimony-based Hall sensors while the originally installed bismuth-based sensors are kept at sector 8.

In parallel, there is an ongoing R&D activity toward development and qualification of new Hall effect-based sensors for future DEMO fusion reactor where sensors will be exposed to about two orders of magnitude higher neutron fluences and potentially also to higher temperatures. Assessment of transmutation under DEMO relevant neutron loads was done for a set of candidate sensitive materials including bismuth, antimony, chromium, gold, carbon (in form of graphene) and others [692]. Initial neutron irradiation test of a chromium Hall sensor was conducted on LVR-15 fission reactor up to the total neutron fluence of 4 × 10¹⁸ cm⁻². Change of the sensor sensitivity of the order of a fraction of percent was measured
<figure><img src="image_172.png" /><figcaption>**Figure 160.** FOCS basic scheme. The arrows indicate the linear light polarizations at the light source output and the detector input rotated by angle θ as a result of the Faraday effect.</figcaption></figure>

at 100 °C which shows good potential of these sensors for DEMO from radiation stability point of view. On the other hand, drawback of chromium is about two orders of magnitude lower sensitivity compared to antimony [694]. Sensors based on golden nanolayers are also being developed [695]. They were successfully tested in a fission reactor up to neutron fluence of $10^{20} \text{ cm}^{-2}$ [695], but gold has in terms of transmutation rather low radiation resistance [692] which might compromise stability of the sensors at still higher fluences. Moreover, the tested sensors had a weaker signal than the chromium sensors reported in [694]. The first tests of graphene Hall sensors contemplating their application on fusion reactors were presented in [696]. These sensors would offer extremely high sensitivity and potentially very good radiation hardness but unfortunately, their technology is currently limited to operational temperatures only up to 150 °C [697].

### 8.4.4. Fiber optic current sensors (FOCS).
FOCS is another steady-state magnetic diagnostic. The FOCS must satisfy the standard requirements defined for the ex-vessel plasma current diagnostics on the plasma current measurements [698], p 96: 'for plasma currents below 1 MA the accuracy must be better than 10 kA, and for 1–20 MA plasma currents, the accuracy must be better than 1%. The time resolution for FOCS is 10 ms. The ranges are ambipolar'.

FOCS operation relies on the Faraday effect experienced by light travelling in optical fibers exposed to a magnetic field; a rotation of the plane of polarization is induced by the magnetic field component aligned to the fiber's propagation axis. If a fiber with no intrinsic birefringence makes a loop around a current, the polarization rotation angle θ of a linearly polarized light is directly proportional to the enclosed current I [699]:

$$ \theta = NVI, $$

where V is the Verdet constant, and N is the number of fiber turns around the current. For silica fibers V ~ 0.7 rad MA⁻¹ at 1550 nm [700]. The wavelength dependence of the Verdet constant can be approximated as ~λ⁻². The basic scheme of typical FOCS experimental arrangement is shown in figure 160.

In practice, the situation is complicated by the presence of intrinsic and induced birefringence [699]. The Verdet constant dependence on temperature [701] and on wavelength [700] creates an additional calibration issue.

FOCS is included into ITER research plan as an upgrade beyond the 2016 baseline. However, FOCS requires installation of components on the VV, which means that the FOCS design must be completed before the closure of the cryostat.

The ITER FOCS system includes three major components: the sensing fiber, the transport fiber, and the DAQ installed in the cubicle area, see figure 161. The sensor can operate in transmission regime or in reflection regime with the Faraday mirror. The DAQ components are selected based on the availability of preferably commercial components and the compatibility with the ITER requirements. The sensing fiber placed on the VV must sustain the combination of vacuum, nuclear radiation, and high temperature. The ITER FOCS system design allows to replace the fiber. However, performing this operation during the nuclear operation of ITER would be technically challenging due to safety requirements. Using a fiber, which maintains its performance under radiation is by far the preferable option.

The part in the cryostat area will be irradiated at low temperatures. This sensing fiber will be replaceable.

Taking account of radiation effects has a significant impact on the FOCS design. Radiation flux estimations in table 34 relevant for the VV external surface are reproduced from [702].

For the energies relevant for the FOCS location, ionization is the most important mechanism of radiation damage. The equivalent dose rate is ~0.5 Gy s⁻¹, corresponding to a total dose of 8.5 MGy for 4700 h of operation. It is also proposed in [702] that a 20% margin should be added in the design. Therefore, 10 MGy is a conservative upper limit for the FOCS life-time dose.

A known radiation effect is an increase of attenuation due to RIA. The RIA in the FOCS sensing fiber decreases the useful signal, making measurements inaccurate or even impossible. For the polarimetry detection scheme a 40 dB dynamic range of the analyzer at a +3 dBm detected signal is a reasonable estimation. A standard light source power is up to 13 dBm, which increases the dynamic range by 10 dB. The FOCS performance can be improved by operating it in reflection with a Faraday mirror [703]. In this case the optical length exposed to intense radiation is the double length on the VV, ~56 m. Therefore, the acceptable RIA is up to 0.9 dB m⁻¹.

This estimation puts an immediate constraint on the system design. In any available optical fiber, the RIA levels in the visible and shorter wavelength at ~MGy are significantly higher than 1 dB m⁻¹. Therefore, the system must operate at wavelengths in the IR range. As a result of the Verdet constant wavelength dependence, a change of the operation wavelength from 633 nm to 1.55 µm means a sensitivity decrease by a factor 6.

Typical absorption values for Ge-doped fibers at the 1.55 µm are below 0.3 dB m⁻¹ at a 1 MGy dose of 20 keV x-rays [704], and should remain below 0.6 dB m⁻¹, when extrapolated to 10 MGy. The results presented in [704] are obtained for continuous high dose rate irradiation, while ITER operation is extended over 20 years with multiple interruptions. The ambient temperature of the FOCS fibers during ITER operation will be ~100 °C, which will promote RIA annealing [705], additionally accelerated during baking periods, when
<table><caption>**Table 34.** Irradiation conditions for the FOCS.</caption><thead><tr><th></th><th>&lt;0.1 MeV, n</th><th>14 MeV, n</th><th>Total n</th><th>γ</th></tr></thead><tbody><tr><td>Flux cm<sup>-2</sup>s<sup>-1</sup></td><td>1.7 × 10<sup>8</sup>–3.3 × 10<sup>10</sup></td><td>4.3 × 10<sup>6</sup>–2.6 × 10<sup>9</sup></td><td>3.8 × 10<sup>8</sup>–7.7 × 10<sup>10</sup></td><td>2 × 10<sup>8</sup>–4.2 × 10<sup>10</sup></td></tr><tr><td>Fluence cm<sup>-2</sup> for 3000 s pulse</td><td>Up to 10<sup>14</sup></td><td>Up to 7.8 × 10<sup>12</sup></td><td>Up to 2.3 × 10<sup>13</sup></td><td>Up to 1.3 × 10<sup>14</sup></td></tr><tr><td>Fluence life (4700 h)</td><td>Up to 5.6 × 10<sup>17</sup></td><td>Up to 4.4 × 10<sup>16</sup></td><td>Up to 1.3 × 10<sup>18</sup></td><td>Up to 7.1 × 10<sup>17</sup></td></tr></tbody></table>

<figure><img src="image_173.png" /><figcaption>**Figure 161.** ITER FOCS data acquisition diagram.</figcaption></figure>

the temperature will rise to 200 °C with a 20 °C margin [706]. Therefore, the actual RIA levels at 10 MGy should remain acceptable.

An additional improvement can be obtained by using radiation-hard pure silica core fibers instead of standard Ge-doped fibers. For example, RIA levels of 16 and 27 dB km<sup>-1</sup> after Co60 at 5 Gy s<sup>-1</sup> dose rate for doses of 1 and 3 MGy, respectively, were reported in [707] for high-temperature acrylate-coated fibers. It is also important to notice that a ~Gy s<sup>-1</sup> dose rate relevant for ITER is a value that is common for such tests.

A ~6 m length of the fiber in the cryostat penetration (FOCS bridge) can be exposed at temperatures below 0 °C and possibly down to 80 K. The radiation loads on the fiber in this area are smaller than on the VV surface thanks to the cryostat shielding effect and the geometrical factor. Still, a temperature decrease down to 80 K results in a very strong fiber radiation sensitivity increase: a dose of only several hundreds of Gy may result in an unacceptable RIA increase above 10 dB m<sup>-1</sup> [708, 709]. 80 K temperatures are expected only in accidental conditions. During normal operation the temperature of the fiber in the bridge area should be higher. However, an accurate estimation of the temperature during operation is required.

The presence of neutrons should not change the estimation of the RIA. Usually, in case of fission reactor irradiations, the RIA contributions of neutrons and gammas for a same dose of radiations have similar scales [710–713]. Figure 162 shows the RIA measured in a pure silica core single mode optical fiber exposed at a temperature of 100 °C in the BR2 fission reactor [714] to a total gamma dose of 7 MGy and a fast (E > 1 MeV) neutron flux of 5 × 10<sup>16</sup> cm<sup>-2</sup>. The RIA level remains below 0.9 dB m<sup>-1</sup>. The dose rate and the flux were up to 6 MGy h<sup>-1</sup> and 10<sup>13</sup> cm<sup>-2</sup>s<sup>-1</sup>, respectively. The ITER radiation environment is less severe.

Still, the impact of 14 MeV neutrons characteristic for the ITER nuclear phase cannot be addressed in a fission reactor. FOCS systems installed at JET should provide an answer to

<figure><img src="image_174.png" /><figcaption>**Figure 162.** RIA evolution in a pure silica core single mode fiber irradiated in the BR2 fission reactor.</figcaption></figure>

this question [703]. In terms of the dose-rate the radiation exposure during D–T operation will be completely relevant for ITER.

Ionizing radiation also changes the refractive index, and can consequently modify the fiber Verdet constant. This question is not addressed in literature. Off-line tests performed at SCK CEN demonstrated that both for gamma doses up to 5 MGy and fission reactor (BR1) irradiation up to a total neutron fluence of 10<sup>15</sup> cm<sup>-2</sup> changes were within the measurement accuracy, which was probably close to ±10% [711]. The low accuracy does not allow to draw conclusions relevant for ITER. Regular re-calibration of the FOCS during ITER operation using other plasma current measurement systems can be a simple yet reliable mitigation measure.

The exposure to high temperature and intense radiation may compromise the mechanical reliability of the sensing fiber. The temperature of the VV surface will be ~100 °C during normal operation and 200 °C–220 °C during baking periods. The use of polyimide coated fibers seems relevant in this situation because the standard acrylate fiber coating is rated up to 85 °C. Polyimide is also considered as radiation resistant material. Unfortunately, the use of polyimide results in a significant degradation of the fiber polarization characteristics. On the other hand, the experience shows that the temperature limit of acrylate coated fibers can be increased if the fiber is exposed to elevated temperature in an inert atmosphere. For example, the sensing fiber of the FOCS installed at JET was exposed to ~200 °C during operation and 320 °C during baking periods [703, 715]. The system is operational for more than five years. The coating probably deteriorated, but that did not prevent the system from performing current measurements. The actual state of the coating is unknown as the systems
continue operation. Unfortunately, this example is not completely representative for ITER because of the low radiation levels at JET.

## 8.5. Bolometers

In ITER, bolometers will be used to obtain information on the total radiated power and its spatial distribution from the main plasma and in the divertor region. Bolometer arrays will be installed in selected locations on the VV, and on the divertor [716]. Operation of a bolometer is based on the absorption of radiation. The absorbed power is determined by measuring the corresponding temperature increase, which is derived from changes of the electrical resistance of a meander shaped metal conductor on the back side of the absorber. The bolometers are directly open to plasma and have to withstand high neutron fluxes as well as ambient temperatures exceeding 200 °C, which presents a serious challenge with respect to maintaining their characteristics.

The ITER bolometers are an example how taking into account radiation effects may influence the design. Initially, it was supposed to use JET type high-temperature bolometers, which employ a thin mica substrate as the support for a gold meander shaped electrical resistor. However, a reactor experiment performed at the Japan Materials Testing Reactor (JMTR) in Oarai, Japan, indicated that such bolometers may not sustain the 0.02 dpa [Al] dose of neutron radiation expected for ITER due to both the mica instability and the transmutation of gold into mercury [717]. To answer those problems several modifications in the bolometer construction have been proposed. First, mica was replaced with aluminum nitride or alumina ceramics, which were expected to be stable under radiation and which have the added advantage of considerably increasing the upper temperature limit for continuous use above the 500 °C recommended for mica. To mitigate the transmutation Au was replaced with Pt. The new development was done at IPP in Garching [718].

A prototype of the radiation hard bolometer with the bolometer bridge formed by a thin Pt-meander sputtered on a $Si_3N_4$ foil was exposed in a reflector channel of the BR2 fusion reactor up to a total dose of ~0.02 dpa. The bolometer remained operational during the 19 d of irradiation at a temperature of ~400 °C [719]. The four bolometer bridge resistances were continuously measured during irradiation. The measured values closely followed small temperature and neutron flux variations related to the reactor operation. Two meander resistances showed a small drift under irradiation, while two other meanders experienced first an increase in their resistance and then after almost two weeks of irradiation the resistances returned to values close to the initial ones.

Although, the post-irradiation examination indicated possible problem with the Pt meander adhesion on the substrate, see figure 163, it was concluded that the design could be considered as a solution for an ITER-compatible device.

Following significant work, an improved version of the bolometer with $Si_3N_4$ substrate and a Pt resistors was proposed [720]. This prototype bolometer successfully passed reactor irradiation test up to a 0.3 dpa dose with an acceptable increase

<figure><img src="image_175.png" /><figcaption>**Figure 163.** Delamination of Pt tracks from the $Si_3N_4$ substrate observed during dismantling of the irradiated bolometer in a hot cell.</figcaption></figure>

of the resistance [721]. A new reactor irradiation test is being planned where the bolometer meander resistivity and the time constant will be measured under irradiation at temperatures in the range 225 °C–275 °C.

The power deposited onto the absorber is expected to be in a range 0.5 µW–2 mW. The maximum noise level of the voltage measurements of 50 µV is acceptable, which is based on the requirement for the dynamic range of the diagnostic and the noise budget for signal cables of 0.3–3 µV m⁻¹ and it corresponds to a noise level of 2.5 µW [716]. For bolometers, the intrinsic noise level is ~20 µV. A comparison with the relevant power levels shows both a need for optimizing this diagnostic and reducing the noise levels in the connecting cables.

The question to what extent the results obtained at JMTR are relevant for ITER was considered. The neutron capture cross-section for gold is maximal for thermalized neutrons (<2.5 eV). A significant flux of thermal neutrons in the JMTR test explains the high transmutation yield. In ITER, the bolometers will be open to the main plasma, with a harder neutron energy spectrum and the thermal neutron flux will be significantly lower than that at the JMTR. As a consequence, the transmutation rate will also be significantly lower. It was concluded that after 5 years of ‘hot’ ITER operation the transmutation level should not exceed 2%, which has acceptable impact on the reliability of the bolometers.

## 8.6. Needs for future research and standardization of the testing approach

### 8.6.1. R&D for refining the ITER design for suppressing radiation effects (neutron calculations, irradiation test of samples and prototypes, neutron shielding development).
To allow for long-term operation of plasma diagnostics at ITER, combination of radiation resistant components and systems while providing efficient radiation shielding against gamma and neutron fluxes from the hot plasma is necessary. This means that it is necessary to evaluate the gamma and neutron fields, identify radiation-resistant materials and elements, and determine the levels of their permissible exposure in ITER. Three areas of the researches have been identified, in this regard, almost from the very beginning of the ITER diagnostics development.
The first area is the calculation of neutron fluxes and gamma dose rates in which diagnostic elements will be located. For this purpose, methods for calculating of the gamma and neutron fields in ITER were developed. ITER diagnostics should be worked out in detail to obtain reliable results of the calculations, including the materials and geometry of the individual elements. In parallel with the design development of the diagnostic systems, three-dimensional models of the ITER installation were created. Neutron calculations were performed using a Monte Carlo method. Specialized numerical methods (MCNP code) and libraries for cross sections of the nuclear reactions in construction materials were used. The results of these calculations give the gamma and neutron fields with a high accuracy, at least inside the vacuum part of the ITER installation, provided that the geometry and materials are specified precisely. In turn, this makes it possible to set conditions for particular radiation tests. In addition, the data obtained must (or can) prove that the diagnostic design meets the ITER nuclear safety requirements.

The second research area is the experimental investigation of materials and critical diagnostic elements under irradiation. To perform experiments at conditions that are close to ITER attention should be given to radiation dosimetry. Early experiments were performed at high radiation levels, based on the assumption of a high load under ITER conditions. For example, for optical glasses it was shown [722, 723] that only pure silica for the visible range can withstand long-term intense gamma and neutron irradiation, but even such glasses quickly lose transmission in the UV range. This made it clear that the optics needs to be protected from radiation, to minimize the fluxes of the neutrons and secondary gamma radiation where the optical elements need to be placed. But even with the use of the neutron shielding in port plugs, radiation levels remain high. Subsequent irradiation tests [674] have shown that it is practically impossible to use silica glass for collecting and transmitting UV radiation to detectors in ITER.

The third area is the neutron shielding development and modifications in ITER port plugs. Neutron calculations have shown that when boron carbide blocks are placed in the port plugs together with an iron-water neutron shield and periscope channels are used to collect light from the plasma, the radiation loads become less critical beyond the vacuum boundary. As a result, the critical diagnostic elements shall be located as much as possible far from plasma, e.g. in the Port Interspace & Cell. It should be noted that drastic measures to strengthen neutron shielding requires changes in the design of diagnostics.

### 8.6.2. Refinement of the ITER design.
DSMs design was changed in 2016 due to the insufficient effectiveness of the previous neutron shielding relatively to nuclear facility licensing requirements. So-called ‘LEGO design’ of the DSM was developed for maximum reduction of weight of the steel parts and filling of all voids with a light but effective neutron absorber, in which boron carbide blocks were used to weaken neutron fluxes. The neutron flux was decreased significantly, which led to reduced radiation loads on optics and detectors in the Port Cell area. Such refinement of the DSM design was

forced and led to an increase of the project cost. As a rule, diagnostic characteristics (measurement accuracy, spatial and temporal resolution) have suffered as a result. On the other hand, without these changes, diagnostics would simply not be able to function for both physical reasons (degradation of optical characteristics, too high background from gamma and neutron fluxes to the detectors) and formal reasons (violation of the nuclear safety requirements).

### 8.6.3. Other examples of the design changes.
Some other refinements were made in the design of the plasma diagnostics due to radiation problems. Here are the main ones: using of the mirror telescopes for plasma light transmission in Port Interspace and Port Cell, the periscope legs lengthening in the DSM neutron shielding, shifting of the entrance pupil of optical diagnostics deeper into the port plug further away from the plasma, reducing of the solid angle of the plasma light collection, using of the fiber optics to transmit light to remote diagnostic rooms, etc.

## 8.7 Summary

Overview of the impact of recent radiation effect studies on design and qualification of various ITER diagnostic systems is presented. Compatibility with ITER radiation fields is highlighted as one of the main design drivers for diagnostics. Experimental testing of diagnostic functional components in radiation fields with parameters as close as possible to the target ones is still seen as the main approach to their qualification. This shall be accompanied with numerical simulation of radiation effects whenever technically feasible. Significant progress in development and qualification of various ITER diagnostic systems from radiation-hardness point of view is reported.

Sufficient radiation hardness of the vacuum window assemblies based on silica glass was successfully demonstrated during irradiation tests using nuclear reactor, a Co-60 gamma source, and a NG. In particular, such assemblies were irradiated in the BR1 reactor of SCK●CEN in Mol at 150 °C during 5.5 months up to a total fast ($E > 0.1$ MeV) neutron fluence of $\sim 2 \times 10^{16} \text{ cm}^{-2}$ with positive outcome of post-irradiation thermo-mechanical and He-leak tests.

Borosilicate glass inserts of the ITER vacuum electrical feedthroughs were irradiated at LVR-15 reactor of CVŘ Řěž up to the total fast ($E > 0.1$ MeV) neutron fluence of $5 \times 10^{17} \text{ cm}^{-2}$. It was concluded that radiation induced dimensional changes of these borosilicate glass inserts pose no risk with respect to the potential loss of vacuum accident on ITER.

Radiation hardness of ITER in-vessel LTCC magnetic sensors was investigated using Co-60 gamma source up to 72 MGy and also at LVR-15 fission reactor up to neutron fluence $\sim 10^{20} \text{ cm}^{-2}$ with positive outcome.

New technologies potentially applicable for magnetic sensors future designs were highlighted. In particular, samples of ceramic substrates metallized by copper using TP technology were irradiation by total neutron fluence of $4 \times 10^{18} \text{ cm}^{-2}$ at LVR-15 reactor while the samples showed satisfactory
adhesion of copper layer to ceramic substrates better than 35 N mm⁻².

Steady state magnetic field sensors based on Hall effect which use both bismuth and antimony sensitive layers were also successfully qualified at LVR-15 reactor with respect to their expected total neutron exposure on ITER.

Compatibility of FOCS fibers, to be used for plasma current measurement on ITER, with gamma radiation, neutron fluxes and elevated temperature was investigated. Silica core single mode optical fiber was exposed at a temperature of 100 °C in the BR2 fission reactor to a total gamma dose of 7 MGy and a fast (E > 1 MeV) neutron flux of 5 × 10¹⁶ cm⁻². The RIA level remains acceptable below 0.9 dB m⁻¹. Operation of FOCS in inert atmosphere was suggested as solution to achieve compatibility of fibers with elevated temperatures even up to 320 °C as demonstrated during operation of FOCS prototype on JET.

ITER bolometers are presented as an example of a diagnostic where taking into account radiation effects had significant impact on its design. Bolometer with Si₃N₄ substrate and a Pt resistors successfully passed reactor irradiation test up to a 0.3 dpa dose with an acceptable increase of the resistance.

Finally, three main directions of R&D to be continuously pursued are identified, namely, 3D modeling of radiation fields using real fusion reactor geometry and materials, experimental qualification of diagnostic functional components in radiation environment as close as possible to the target one and optimization of neutron shielding and overall engineering design of implementation of various diagnostic components on ITER in order to minimize their radiation exposure.

# 9. Diagnostic mirrors for ITER: status and perspectives

A. Litnovsky⁴⁰, L. Moser²,⁴¹, N. Babinov²⁹,

A. Dmitriev⁴¹,²⁹, B. Kim⁵, L. Marot⁴¹, A. Razdobarin²⁹,

A. Rogov⁴², D. Samsonov²⁹, C. Seon⁴³, K. Soni⁴¹,

M. W. Walsh², R. Yan²⁶ and E. Yatsuka⁴³

## 9.1. Diagnostic mirrors in ITER

**9.1.1. Role and mission of mirrors.** The ITER international experimental fusion reactor being built in Cadarache, South France by the EU, Russian Federation, Japan, South Korea, the United States, China and India will be equipped with highly sophisticated and versatile diagnostic systems. Diagnostic overviews are provided in [4, 724] and an update can be found in [725]. Among others, there will be twenty-three optical diagnostics monitoring crucial physics and engineering parameters of the reactor, such as the temperature of divertor plates, electron and ion densities and temperatures [724, 726]. Due to harsh neutron environment, optical systems will be based on reflective optics using mirrors to guide plasma radiation towards spectrometers and detectors. The plasma-facing mirror (FM) will be affected at most from the plasma particles and intensive radiation. The lifetime of a first mirror will affect the entire performance of the corresponding mirror-based

diagnostic and hence, have a direct impact on ITER operation. Maintaining the lifetime of diagnostic mirrors is a significant physics and engineering challenge. There will be about 80 first mirrors employed in optical and laser-based diagnostics operating in a wide wavelength range spreading from 2 nm, for the VUV spectrometer in the divertor [96] up to 118 micrometers as foreseen for the polarimeter system [727, 728]. An example of the first mirror for ITER Hα diagnostic system is shown in figures 164(b) and (c). According to the design regulations, the lifetime of the mirrors has to be guaranteed for the entire service life of the reactor. Maintenance and servicing of diagnostic mirrors are to be avoided whenever possible. These critical requirements have triggered a significant international research and development (R&D) program on diagnostic mirrors.

**9.1.2. Phasing of diagnostics.** In the course of the planning of ITER diagnostics, there was a clear understanding that the simultaneous delivery of the entire diagnostic set to ITER is not feasible due to logistics, engineering and budget constraints. Therefore, it was decided to make a prioritized list of diagnostics based on their impact on machine commissioning, operation and physics program. This list is also known as diagnostic phasing. The first diagnostics in the list had to be procured earlier. In total, there are three categories of diagnostics in the list:

### Category 0

* Diagnostics required for machine start and commissioning.

### Category 1

* Diagnostics required for machine operation.

and

### Category 1a

* Diagnostics required for fulfillment of the physics program in ITER.

The detailed list of diagnostics according to each category (phase) can be found e.g. in [729]. As can be seen from the list, among optical-based diagnostics, there are several which are required for the basic machine operation. For instance, divertor thermography is an inevitable instrument for detection of dangerous operation conditions in the divertor target area.

## 9.2. Risks and issues

The initial stage of the coordinated research and development program on diagnostic mirrors involved dedicated and accompanied experiments with special mirror assemblies to address the specific environmental conditions in ITER diagnostics. These studies were complemented by the analyses of mirrors in existing diagnostics in present-day tokamaks. The respective overviews of results are available in [730–741].
<figure><img src="image_176.png" /><figcaption>**Figure 164.** ITER Hα as an example of mirror-based diagnostic and its first mirror: (a) diagnostic locations in ITER equatorial port plugs (EPP) and upper port plugs (UPP), (b) the reflecting surface of the first mirror and (c) rear view of the mirror. The single crystal molybdenum reflecting surface has dimensions of 164 × 60 × 42 mm and a radius of 364 mm.</figcaption></figure>

These studies were aimed at identifying the major risk factors for diagnostic mirrors. The major risk factors expected for diagnostic mirrors in ITER are summarized below.

### 9.2.1. Erosion.
Erosion of the mirror surfaces was treated as a major risk for diagnostic mirrors from the beginning of research and development (R&D). Under the term ‘erosion’ usually two different processes are meant: chemical erosion in the reactive environment and physical sputtering.

Chemical erosion played the major role in defining the mirror performance at an early stage of the ITER project. The deposition of volatile hydrocarbon radicals on the mirrors originating from the carbon-based old divertor was treated as a critical risk factor for e.g. divertor mirrors [740, 742–745]. In the current ITER design, the plasma-facing materials will be beryllium at the first wall and tungsten in the divertor. Carbon was excluded mostly due to safety considerations related to chemical erosion of first walls and subsequent transport of tri-tiated carbon radicals. Therefore, the chemical erosion issue does not represent a major concern anymore.

Sputtering of the mirror surface currently represents the major risk for the mirror performance. Physical sputtering is expected in ITER due to energetic neutrals originating from the CX reactions in the core DT plasmas. The CX-fluxes to the first wall of ITER were assessed by modeling by several research groups. Modeling results predict quite intensive fluxes reaching $10^{19}$ atoms m$^{-2}$ as reported in [724]. Recent modeling assessment based on SOLPS 4.2 code provided a detailed overview of CX fluxes for different operation scenarios of ITER. The flux of CX neutrals with energies of about 200 eV will cause sputtering of the mirror surface. Sputtering may provoke a drastic increase of mirror roughness and unfortunately, the abrupt and rapid degradation of mirror reflectivity. The natural CX fluxes in modern tokamaks are rather

small making the experimental reproduction of the sputtering environment expected in ITER challenging. An effective way of addressing the mirror performance under sputtering conditions formed by fusion plasmas, was to perform the sputtering exposures in tokamak SOL plasmas and substituting the CX fluxes with plasma ion fluxes of nearly the same energy featuring much higher flux density. These studies [746] allowed making estimates of the mirror lifetime under erosion conditions in ITER.

However, CX neutrals originating from the regular plasma operation of ITER is not the only sputtering source. An experiment made in the Tore Supra tokamak brought a remarkable result [747, 748]. Here, a copper mirror was severely sputtered, almost losing its reflectivity in the visible range. The accompanying research has demonstrated non-ambiguously, that the sputtering of mirror surfaces has been caused by wall conditioning discharge. The wall conditioning based on a radio-frequency stimulated glow discharge can produce high-energy ions which can penetrate several tens of centimeter deep into the diagnostic ducts while sputtering the mirrors. One respective estimate has been made e.g. in Litnovsky et al [749]. Photographs of mirrors suffered from sputtering are provided in figure 165(a).

Studies of the effects caused by sputtering made a decisive impact on the choice of mirror material described later in this paper.

### 9.2.2. Deposition.
Deposition is another crucial factor degrading the mirror performance in ITER. Plasma impurities sputtered or molten from the plasma-facing components may be transported by plasma particles toward mirrors and become deposited on mirror surface. The formed deposition layer has its own reflectivity drastically affecting the reflectivity of the mirror. A mirror with a deposit formed in the course
<figure><img src="image_177.png" /><figcaption>**Figure 165.** Diagnostic mirrors affected by (a) sputtering, as seen on the shiny part of a mirror exposed in TEXTOR [743] and rough surface of a mirror exposed in the JET divertor (inlay, Reprinted from [739], Copyright (2019), with permission from Elsevier), (b) deposition, as seen on the mirror exposed in the divertor of the ASDEX Upgrade. Reproduced from [750]. © 2013 IAEA, Vienna. All rights reserved, (c) water leak/steam event affected mirrors in the Tore-Supra first wall. Reprinted from [747], Copyright (2006), with permission from Elsevier and (d) wall conditioning leading to severe sputtering of a mirror located in Tore Supra first wall. Reproduced with permission from [751].</figcaption></figure>

of exposure can be seen in figure 165(b). General information on erosion and deposition is reported in the dedicated chapter devoted to the first wall diagnostic in this issue.

Intensive research program has been made within the ITPA on several major tokamaks worldwide to study the effect of deposition [730, 734, 739, 740, 742, 747, 750, 752, 753]. The key adverse feature of deposition of impurities are identified to be the following:

1. The deposition pattern is usually highly inhomogeneous i.e. no systematic correction of reflectivity is possible for the affected mirror.

2. Even a very thin deposited layer of 10 nm is enough to have a dominating effect on the reflectivity in the visible range.

3. Deposits are mostly rough, inevitably leading to the reflectivity degradation.

4. Deposition is a process in part involving volatile radicals and/or atoms. Therefore, deposition can be expected even at far distance from plasma.

5. In the presence of energetic plasma particle, e.g. from neutral beam, deposition can be accompanied with the implantation of impurities into the mirror substrate and/or formation of mixed layers with substrate material.

These adverse properties of deposition underline the severity of the problem. As in the case of sputtering, the regular plasma operation is not the only source of deposition in ITER.

Wall conditioning sometimes plays a decisive role in mirror surface contamination, as can be inferred from the following sub-sections.

9.2.3. *Steam ingress.* In ITER, diagnostic mirrors are also vulnerable to a 'Vacuum Vessel Ingress of Coolant Event' (VVICE, where VVICE category IV also called Loss-of-Coolant Accident) in ITER [754–756], also known as a steam ingress. The in-vessel components of ITER are cooled with water. A large number of tubes connected by welding are located inside the vacuum chamber. Vibration of in-vessel components, high thermal and electromagnetic loads on the structural elements lead to an increased probability of depressurization of the water-cooling system and water ingress into the VV. A steam event is anticipated in case of an accidental rupture of the cooling loops inside the VV or due to damage caused to the cooling pipes by runaway electrons generated during plasma disruptions. As a result, several negative factors can simultaneously affect the in-vessel mirrors: increased temperature of 250 °C during baking, and up to 400 °C in case of accidents during regular plasma discharges, and a contact with steam at an increased pressure. As a result of the interaction of steam with a reflecting mirror material, a volumetric degradation of the mirror surface can occur along with the formation of hydroxide layers on it. These processes will lead to degradation of optical properties of affected mirrors. A
photograph of the mirror assembly exposed in Tore-Supra
tokamak and suffered from steam and water ingress is
provided in figure 165(c).

During a steam ingress event, the FMs will be exposed to
steam at pressures of up to 1.5 bar [755, 757] at temperature up
to 250 °C—the maximum temperature during the ITER baking
process [756, 757]. The steam may also mobilize dust, which
could eventually be deposited on the mirror surfaces further
degrading the optical properties of FMs [758].

9.2.4. Wall conditioning. Wall conditioning necessary for plasma and particle control in ITER, represents an additional risk for the lifetime of diagnostic mirrors. The effect of wall conditioning has been assessed in a number of dedicated experiments. These studies show that the wall conditioning effect on diagnostic mirrors can be manifold. An experimental campaign undertaken at Tore Supra tokamak [747, 751] demonstrated a severe sputtering effect caused by the glow discharge wall conditioning to mirrors located at the first wall, figure 165(d). This effect may be relevant to the mirrors in ITER that are closest to burning plasma.

At the same time, the results of a reference experiment per-
formed in the KSTAR tokamak [759] demonstrate explicitly
that wall conditioning and baking can also lead to deposition
of impurities on mirrors. In this experiment the deposition mit-
igation assembly (DeMi) was installed into the midplane loc-
ation of the machine. The DeMi is a system of tubes imitating
the diagnostic ducts with sensors at their ends, acting as mir-
rors in real duct systems. A detailed description of the DeMi
system can be found in [759].

To measure the *in-situ* deposition or erosion effect on the mirror surface with the baffle duct, QCM's were installed in KSTAR. The first QCM-1 located 1.5 m away from the plasma measured the deposition quantity *in situ* through the short-baffled duct. QCM-2 is positioned near QCM-1 inside an enclosure case. The QCM-2 provided a reference signal for the compensation of the error in QCM-1 signal due to temperature or noise effects. The net amount of deposited mass was derived by subtracting QCM-2 signal from the QCM-1 signal. The result of the deposition measurement during the 2015 KSTAR campaign is depicted in figure 166. The experimental data explicitly shows that the wall recovery operation with the GDC and baking resulted in heaviest deposition on the QCM surface, while the plasma operation and the sole GDC have resulted in ten-fold less deposition rate. Impurity deposition conditions caused by wall conditioning may be expected for mirrors in ITER located in diagnostic ducts far away from plasma.

9.3. *Risks evaluation and mitigation*

Adverse factors affecting diagnostic mirrors were discussed
and analyzed in numerous expert meetings, conferences and
dedicated seminars involving the ITER Team and represent-
atives of domestic agencies. In the course of these meet-
ings, all aforementioned aspects were thoroughly and critically

<figure><img src="image_178.png" /><figcaption>**Figure 166.** The net accumulated mass (deposition) data from the QCM measurement in the 2015 KSTAR campaign. The major deposition on QCMs occurred during wall recovery period including baking and the GDC. A maximum value of 170 pm h⁻¹ was found during the GDC+ baking condition assuming graphite for deposition material. Reprinted from [759], Copyright (2018), with permission from Elsevier.</figcaption></figure>

assessed leading to a number of crucial decisions. Important
decisions, influencing the entire diagnostic mirror philosophy
are shortly outlined below.

In the course of evolution of the ITER diagnostic systems,
the position of the first mirrors was changed with time. For
more than fifteen years, the FMs were close to the first wall
position [760]. After a careful assessment of major risks for the
first mirrors imposed by the deposition of impurities and sput-
tering of the reflecting mirror surfaces, it was finally decided
to use any possibility of moving the FMUs of all diagnostics
whenever possible, far away from the plasma. In this decision,
the persisting uncertainty in predicting transient events which
are supposed to have an instant and devastating impact on mir-
rors, was considered as a high risk. However, transient heat
loads which are unfortunately, not fully predictable till now,
could momentarily damage the mirror terminally.

Diagnostic mirrors positioned close to the plasma, will
be exposed to a high heat load from the neutron flux which
induces deformation even for a water-cooled FM [761].
Moreover, being close to the first wall and having a large area
open to the plasma lead to physical sputtering of the surface
due to CX neutrals [725]. These considerations have triggered
the re-positioning of the FM, whenever possible, further away
from the first wall [504]. In addition to moving away from the
plasma to the farthest distance possible, additional engineer-
ing measures, such as using diagnostic pupils with a possibly
small aperture for viewing the plasma were prescribed for dia-
gnostic engineers.

The a wide scope of options has been assessed to allevi-
ate the diagnostic mirror challenge. A possibility of a general
change of the probing wavelengths from the UV and VIS range
toward the less vulnerable IR range [762] was assessed along
with a possibility of substituting the optical diagnostics with
ones not using any optics in ITER [763]. In general, how-
ever, this assessment did not lead to a significant change of
the projected diagnostic suite and its principal parameters as planned for ITER.

It was decided to develop a solution for the first mirror problem using a coordinated R&D effort with several well-defined focus areas. Attaining progress or a solution in the dedicated area contributes to a solution of the entire diagnostic mirror problem. These areas were initially defined in the Work Plan of the First Mirror R&D [764] and then further evolved [732, 764]. Based on initial critical assessment of mirror risks provided in e.g. [765], five crucial areas of first mirror R&D were identified as follows:

1. mirror material choice

2. predictive modeling of mirror performance

3. mirror surface recovery (MSR)—a crucial set of measures for a prolongation of mirror lifetime comprising the passive mitigation of mirror contamination, the use of engineering tools for mirror protection and active mirror cleaning. The MSR will be described later in this paper in more detail.

4. Tests under harsh environmental conditions involving studies under neutron, gamma and steam conditions

and

5. engineering solutions for ITER mirrors.

In the past decades experimental and theoretical predictive modeling efforts were aligned along these main topics. Significant progress was attained in all these directions. At the same time, as the project evolved, several crucial decisions remained actual for the present diagnostic mirror R&D, while others had to be discarded due to a major change in design and because of other boundary conditions.

Here, the authors feel it necessary to briefly list decisions which were despite success in their elaboration, discarded from the further consideration due to reasons mentioned above.

1. Engineering solutions using retractable diagnostic tubes with mirrors. Tubes were discarded from the design of optical diagnostics as being too complex.

2. Mirror cleaning using lasers was discarded as a prime generic cleaning technique due to the complexity of realization in ITER geometry.

3. Feeding deuterium in front of the mirror to stimulate chemical erosion of carbon impurities. Discarded due to reason mentioned above.

In addition to the mentioned ‘grand’ decisions, such as moving mirrors further away from plasma, there are crucial specific achievements and decisions that remained fully in power and actual in ITER design. Among those decisions are:

* The use of single crystal and possibly nano-crystalline materials instead of any polycrystalline mirrors including those made through powder metallurgical route

* The use of *in-situ* mirror cleaning system

* The use of shutters and flaps

* The use of so-called ‘gas shutters’ a gas, usually helium or argon feeding across the plasma particle flow in order to intercept the contamination flow toward the mirror.

Interestingly, the mirror heating initially proposed for stimulating the chemical erosion of carbon impurities was preserved. The use of mirror heating, active and passive was found useful and effective for reduction of deposition of plasma impurities on the mirror surface.

These decisions are described in detail in the following section. Certainly, this list is not full and several prospective mirror solutions are under consideration. Authors, however, believe that providing both lists is a necessary aide for physicists and engineers working on mirror solutions, possibly saving an extra effort on discarded directions and allowing a more efficient R&D on the priority topics.

## 9.4. Solutions

### 9.4.1. Mirror material.
The choice of mirror material is one of the key topics of the ITER Research plan, see e.g. Task A.8 [56]. In the course of an intensive R&D [732, 734, 746, 766–769], the prime candidate mirror materials were identified. Currently, molybdenum (Mo) and rhodium (Rh) are two main candidate materials for the FM. Molybdenum, due to its low sputtering yield, is more advantageous under sputtering conditions [504, 734, 746, 751, 753–772]. Rhodium, on the other hand, provides a better reflectivity (between 70% and 80%) in the visible range [773] as well as near-IR and IR ranges (around 85% at 1 µm). Rh also has low chemical reactivity, suppressing oxide and carbide formation [774]. In the case of polycrystalline mirrors composed of many grains with random orientation of faces, the sputtering yield can vary strongly over the material surface depending on the crystallographic plane of each individual grain and its orientation with respect to the incoming particle flux. It is also important to keep the surface relief pattern i.e. the roughness of a polycrystalline mirror small compared to the wavelength of the reflected light in order to minimize the effect of diffuse reflection on the measurements. Generally, this indicates that the mirrors must have small grain sizes and preferably similar crystal orientations to be homogeneously sputtered. These requirements can be fulfilled, for instance, by using a single crystal [302, 734, 775] or by coating the surface with nanometer-sized crystallites [766].

The advantages of single crystals under sputtering conditions were extensively studied under laboratory conditions in e.g. subchapter 5 and [734, 776], a direct comparative test in a tokamak was performed in TEXTOR [746]. The series of dedicated sputtering tests revealed the outstanding ability of both single crystal molybdenum and rhodium to preserve their optical reflectivity despite the severe sputtering [768, 769]. At the same time, the availability of large single crystals and high price of rhodium presently make the mirror solution based on nano-crystallite coating particularly attractive for several diagnostics [766, 777, 778].

For several diagnostics, there are diagnostic-specific mirror materials addressing the performance requirements of
these diagnostics. An example is the ITER VUV spectrometer operating at an extremely short wavelength range of several nanometers [96]. Here, several materials such as silicon carbide and Ni-P plated stainless steel substrate mirrors along with gold (Au) coated stainless steel mirrors were tested. The steam ingress event as well as thermal cycling played a crucial role in the selection of mirror material for this diagnostic. Based on results of thermal cycling from room temperature up to 240 °C for 100 cycles, silicon carbide was selected as a prime mirror material for the VUV spectrometer.

**9.4.2. Predictive modeling.** Modeling was initially anticipated to provide a crucially important estimate of the main mirror risk factors, such as sputtering and deposition rates. These rates had to be used during the e.g. engineering and design of cleaning systems. Several approaches to modeling the effects on mirrors were pursued so far [779-782]. Among the most prominent is the so-called conservative approach followed in the modeling studies of Kotov *et al* [780-783], also known as ‘Kotov model’. The main characteristic feature of the model is in providing conservative estimates for expected effects—the extreme results on erosion and deposition rates were taken and multiplied by conservative factors, reaching 10.

In this model, the B2-EIRENE [784] codes were used to calculate the plasma parameters: electron and ion temperature, ion and neutral density at the vicinity of diagnostic ports. Later, the model was extended towards the inside of diagnostic ducts and was using the unified interface with engineering CAD programs [783]. In the latest stages of development, the Kotov model was extended to 3D geometry and incorporated among others, 2.5D plasma parameters. According to modeling, the calculated worst case gross deposition rate of beryllium in the middle of the port plug faces reaches almost 0.1 nm s⁻¹. At the same time, the Be erosion to deposition ratio at those locations is always larger than 5, indicating a high probability of net erosion conditions there [780].

Another approach was followed by Rode *et al* [785] later. Here, like in the Kotov model, the 3D distributions of particle fluxes at the surface of the mirrors were used. Contrary to Kotov’s model, the precise balance between erosion and deposition was the focus of the modeling. The results of the modeling using the new model are pending and will be the subject of a dedicated publication.

At the same time, there are dedicated modeling efforts ongoing for addressing the issues of the specific ITER diagnostics. As an example, the modeling using the domestic-made code KITe [493] is underway at the Ioffe Institute (Russia) along with a use of the German particle-in-cell (PIC) Monte Carlo (MC) code package Fraunhofer IST [786] (Germany). The results of these diagnostic-specific efforts are reported later in this overview.

**9.4.3. Shutters and ducts.** Shutters and ducts are vital elements in the passive protection of diagnostic mirrors from the adverse factors degrading their performance. The shutters minimize the undesirable fluxes of plasma particles

towards the mirrors by reducing the exposure time, leaving the diagnostic ducts open only for the time necessary for measurements.

Diagnostic ducts may provide a sink of particle fluxes by depositing these particles on the duct walls and hence, minimizing the amount of particles reaching the mirror. Some modeling codes have predicted a positive effect of duct shaping in order to reduce particle fluxes towards the mirrors. In order to address it experimentally, a dedicated task within the International Energy Agency (IEA)—ITPA Joint eXperiment (JEX) program was initiated. In the framework of this task performed in large and medium-scale tokamaks, duct systems of different shapes and lengths, such as Mirror Station [749] were exposed in several tokamaks, including TEXTOR, ASDEX Upgrade, DIII-D and JET [739], whereas the Deposition Mitigation (DeMi) system following a similar intrinsic design was exposed in KSTAR [759]. The results are summarized in e.g. [739, 742, 759]. A positive effect of the duct length on suppression of deposition was experimentally confirmed, whereas the predicted advantages due to duct geometry, revealed only a slight practical positive effect. At the same time, during the recent experiment in KSTAR [759] the mitigation efficiency was tested using three different baffled duct geometries: short, long and short with extended volume via fins. Mirror degradation was evaluated *ex-situ* by measuring the reflectivity of the mirror samples using Dα line at 654.9 nm wavelength. The baffled duct with the expanded volume before the mirror sample did show the most effective mitigation effect. Therefore, the investigations of the effect of fins needs to be continued.

**9.4.4. Mirror cleaning.** The FMs, being the initial elements in the optical path in the diagnostic systems, will be vulnerable to several effects influencing their optical properties. In addition to deposition of the first wall materials (Be and W) [738, 739], they are also vulnerable to surface oxidation following long-term maintenance (LTM) [504, 787] as well as oxidation and structural damage from steam ingress events [757]. As the only technique for an active recovery, mirror cleaning is envisaged [500, 504, 732]. Following the requirement of the minimum service to be applied to diagnostic mirrors in ITER mentioned earlier, the *in situ* cleaning by plasma is currently seen as the only option [788]. In the course of the cleaning, particles from the cleaning plasma sputter the contaminants from the mirror surface along with a part of the mirror material, possibly affected by e.g. contaminants diffused into the mirror bulk.

Such a cleaning technique, despite its relative complexity, allows avoiding the time and resource-consuming pull out of the entire diagnostic port plug needed for mirror service and replacement—as required by the ITER maintenance procedure [787].

There are two main techniques currently under consideration for achieving the desirable ions with energies specific to plasma cleaning: radiofrequency (RF)-based along with pulsed direct current (DC) plasma cleaning techniques. In both
<figure><img src="image_179.png" /><figcaption>**Figure 167.** Scheme of a capacitively coupled radiofrequency cell.</figcaption></figure>

these techniques, the mirror acts as an electrode and the RF or DC plasma is ignited around the mirror. There are several particular advantages as well as technological challenges for both techniques, which will be described in detail later.

The capacitively coupled RF (CCRF) discharge comprises applying an RF-voltage with the frequencies varying in the range 10–100 MHz to the mirror serving itself as a plasma source [500–502, 789, 790]. CCRF-discharge has been widely used due to its ability to treat both dielectric and metallic electrodes. The CCRF-discharge is generated between two electrodes, one of which is grounded and the other one is RF-powered, see figure 167. Electrons oscillate in the electrode gap at the applied frequency while ions are mostly immobile in the bulk RF-plasma column. Electrons located near the electrode are captured by the electrode surface. Areas of positive spatial charge, the so-called near-electrode sheath, are formed in front of each electrode. Depending on the RF voltage phase each sheath is filled with plasma or represented as a gap. Ions are accelerated in the gap and impinge on the electrode surface providing physical sputtering of the surface of the electrode.

The ability of a cleaning system to remove the contaminants from the mirrors on a regular cyclic basis is of crucial importance for the validation of mirror cleaning in ITER. Cyclic contamination—cleaning cycles were performed on single crystal molybdenum (SC Mo), rhodium (SC Rh) and Rh-coated mirror with coating thickness exceeding 10 µm. For SC Mo, the specular reflectivity was not changed after 100 cycles. However, after the subsequent air storage and the following new cleaning cycles, it was observed that pits and ripples formation induced a rapid decrease of the reflectivity [791].

In a symmetric discharge when the surface areas of both electrodes are equal the average sheath thickness and voltage drop are equal for each of electrodes. However, most CCRF-reactors are asymmetric due to the grounded vacuum chamber walls. Their surface plays the role of a grounded electrode. In this case the smaller (driven) electrode is automatically biased negatively with respect to the larger (grounded) electrode to ensure zero direct current. Consequently, the voltage drop near the powered electrode becomes equal to sum of the so-called

<figure><img src="image_180.png" /><figcaption>**Figure 168.** Scheme of a mirror cleaning system based on a DC/p-DC discharge: 1—VV walls; 2—mesh hollow cathode; 3—contamination; 4—mirror; 5—water cooled grounded mirror body; 6—insulating thermal interface (for insulated mirror cleaning mode only); 7—surface for the deposition of impurities sputtered during the cleaning process; 8—discharge area; 9—anode; PS—DC/p-DC power supply; S1 opened—mirror insulated mode, S1 closed—mirror grounded mode (insulator 6 not required).</figcaption></figure>

DC-bias and plasma potential. Usually DC-bias is in the range of hundred volts. The voltage drop at the grounded electrode in this case is almost equal to the plasma potential and takes values of 20–40 V for low-pressure CCRF-discharges.

The realization of the RF-based mirror cleaning system should enable compatibility with mirror cooling system. Currently cooling of the mirror can be realized using different approaches. The first one is by passive radiation cooling of the mirrors which is used in $H\alpha$ and VS diagnostics [792]. Most of the mirrors are however, actively water-cooled due to fine tolerance requirements, see [793]. In this scenario the mirror is connected to the grounded cooling lines directly by welding or indirectly by a ceramic spacer between mirror and cooled carrier [250]. Ceramic solution can provide good electrical insulation, but it can lead to additional heating due to RF-losses in the spacer. Direct connection of the mirror to cooling system pipes requires grounding of the mirror to be done using $\lambda/4$ coaxial lines—the so called notch filter, described later integrated with the water pipes [500, 790].

The pulsed-direct current (p-DC) systems represent an alternative class of local plasma generators suggested for mirror cleaning. In the case of a DC/p-DC cleaning system, a contaminated mirror will be treated in a low-pressure DC or p-DC gas discharge localized near the mirror surface [794, 795]. The application of a gas discharge with oscillating electrons (hol-low cathode) additionally increases the cleaning efficiency. The scheme of a mirror cleaning system based on a DC/p-DC discharge is shown in figure 168.

The use of the medium-frequency pulse mode of the gas discharge in the frequency range from 10 to 200 kHz, as well as the RF mode, ensures the sputtering of thin dielectric impurities with a thickness of up to 100 nm [796]. During the negative pulse, DC sputtering mode is implemented. Therefore, the use of matching devices in the power supply line is not required, which greatly simplifies the first mirror assembly. The duration of the interval between pulses should ensure full compensation of the accumulated charge. Thus, the choice of DC cleaning mode depends on the size, thickness, and permittivity
of the contamination. The optimum choice of the operating fre-
quency and pulse duty cycle can ensure high sputtering effi-
ciency. When removing conductive contaminants, the max-
imum efficiency is provided by the DC sputtering mode. This
technology provides cleaning of both grounded and insulated
mirrors. The generalized electrical scheme of the discharge
cell connections of a mirror cleaning system based on a DC/p-
DC discharge is also shown in figures 168.

Mirror and a mesh represent there a cathode and its surface is sputtered by ions emitted from the discharge. The energy of sputtering ions depends on the discharge voltage and the working gas pressure and is usually several hundred eV. It exceeds the threshold sputtering energy for any type of contaminants expected in ITER.

The main cleaning mode is a DC mode without magnetic
field, B_t = 0, which is used to remove conductive contam-
inants. It can also be used effectively to remove impurities
formed during steam ingress [797]. The applicability of this
method of removing contaminants in a strong magnetic field
has also been confirmed experimentally. At the same time, the
cleaning efficiency significantly depends on the orientation of
the mirror relative to the magnetic field and the design of the
discharge cell. The maximum contaminant removal rate was
obtained with the orientation orthogonal to the direction of tor-
oidal magnetic field [798]. The disadvantages of DC/dc clean-
ing systems include the inability to remove thick (more than
100 nm) dielectric contaminants and a need in increased pres-
sure needed to start a discharge.

**9.4.5. Mirror activation and neutron-related effects.** A sig-
nificant factor affecting the mirrors installed inside the ITER
VV is heating caused by intense fluxes of neutron and gamma
radiation [499, 799]. In [793], the thermal calculation of the
first mirror is given under conditions of radiation heating. The
specific power incident on the mirror surface was limited up
to 16 kW m⁻², which corresponds to the total ITER thermo-
nuclear power of 500 MW. The study of the effect of the cool-
ing method on the maximum temperature of the mirror and on
its deformation caused by temperature gradients demonstrated
the advantage of using a water-cooling system [793, 799, 800].

Exposure to intense ionizing radiation also negatively
affects the optical parameters of metal mirrors. To simulate
neutron radiation characteristic of a tokamak, irradiation of
targets with their own ions is often used in experimental
studies. It was shown [801] that irradiation of polycrystal-
line molybdenum mirrors with ⁹⁸Mo⁺ and ⁴He⁺ ions with
an energy of 350 keV and fluences corresponding to radiation
exposure of 1 dpa (displacement per atom) leads to an insig-
nificant (2%–3%) decrease in the reflection coefficient. In this
case, irradiation of mirrors with helium ions with a fluence
above 3 × 10¹⁷ cm⁻², corresponding to the effect of 30 dpa,
leads to a significant drop of the reflectivity [802]. Considering
the estimate, that the impact on the first wall of the ITER is
about to 1–2 dpa, it can be assumed that ionizing radiation
and fluxes of CX atoms will have an insignificant effect on the
characteristics of mirrors, in comparison to other effects.

Dielectric first mirrors for some laser diagnostics possess
altering layers of high-*n* and low-*n* materials deposited on a
glass substrate. Such mirrors are proven to withstand neutron
radiation worse than metallic mirrors. In [803] it was shown
that high neutron doses (1 dpa for HfO2/SiO2 and 4 dpa for
Al2O3/SiO2) resulted in a drastic drop of optical reflectance
due to failure of the multilayer coating. Lower neutron fluxes
(up to 0.1 dpa), which are expected in ITER at dielectric mirror
location [804], lead to modification of the multilayer coating
as well, but do not result in degradation of optical performance.

**9.4.6. Engineering of mirror systems.** Engineering and qual-
ification of the diagnostic-specific mirror systems is the
final step toward the implementation of mirror solutions into
respective ITER diagnostics. This is also a challenging step
comprising not only the mirror itself, but the whole com-
plex mirror infrastructure. There are several aspects which are
being compulsory addressed by the diagnostic designers and
engineers:

1. detailed design of the first mirror system with all necessary *in vacuo* and *ex vacuo* interfaces to the ITER infrastructure;

2. scaling-up the diagnostic mirrors to the sizes required;

3. design and construction of the *in-situ* mirror cleaning sys-
tem for the specific diagnostic;

4. mirror cooling system;

5. *in-situ* mirror characterization—calibration system with a
   ‘cleaning stop’ indicator;

6. shutters, flaps and diagnostic ducts;

7. performance testing of the mirror system including mech-
   anical tests.

In the course of addressing the engineering aspect, a com-
mon way was identified to be building the so-called FMU
[302, 504, 777, 805]. Usually, the FMU contains all the vital
elements of the mirror infrastructure of the particular dia-
gnostics. The FMU is sometimes equipped with mock-ups of
diagnostic mirrors. The FMUs provide an efficient platform
for multiple qualification tests in the relevant environment. In
the course of this chapter, the majority of engineering chal-
lenges is described and addressed in detail. The example of
FMU of an ITER diagnostic is provided as well.

**9.4.7 Generic mirror solution for maximum performance and durability.** As can be seen from the previous sections of the paper, the proposed risk mitigation strategies are dependent, synergistically complementing each other toward attaining the maximum mirror performance and endurance of the service life. The combination of risk mitigation strategies represents the so-called ‘generic mirror solution’. This solution is a desirable (and maximum) set of measures prescribed as far as it is feasible, for every mirror—based diagnostic.

The generic mirror solution prescribes using prime mirror
candidate materials, such as single crystals and nano-crystal
coated mirrors. The choice of mirror position should be made
involving modeling calculations. This can be done by adapting
<figure><img src="image_181.png" /><figcaption>**Figure 169.** ITER infrared thermography diagnostic [806]: (a) an overall view of the optical design for divertor IR thermography, (b) the side view and the (c) first mirrors system installed in the DSM, where M1 and M2 are the first and the second mirror respectively.</figcaption></figure>

the existing modeling tools as it has been made for core CX (ccXRS) diagnostic system [783]. Alternatively, dedicated modeling tools can be developed and applied to a specific diagnostic as described later.

The set of MSR tools comprising both passive: shutters, flaps and diagnostic ducts should be supported by the application of in-situ mirror cleaning system. Preferentially, such a cleaning system should use the RF-stimulated or pulsed-DC discharge for local cleaning plasma source.

Certainly, an intensive prototyping, building the working mockup of the FMU should be done beforehand. This unit should be tested in the environment that is as close as possible to that in ITER, prior to the final FMU design of ITER diagnostic.

As an example of implementation of the generic mirror solution to ITER IR thermography system is described in the next section.

## 9.5. Practical application on example of ITER IR thermography diagnostic

The ITER divertor IR thermography system (55.G6) is intended for measurements of the temperature distribution of the divertor plates using passive observation of thermal radiation [806]. The system is located in an equatorial port while LOS is directed towards the divertor plates, see figure 169 for details.

The aforementioned solutions were applied in the ITER IR thermography system. Here in general, we will follow the structure of the previous section to go through this example of a particular application in a simplest way.

The FMU of the diagnostic consists of two plane mirrors M1 and M2, forming a dog-leg structure inside the equatorial port neuron shielding, see figures 169(a) and (b). Both mirrors should be water-cooled as they are located close to the main ITER plasma causing a high level of volumetric radiation heating while the diagnostic operating in the IR range is sensitive to the parasitic thermal radiation of the mirrors. At the same time, the mirrors do not require an adjustment during ITER

operation thus greatly simplifying the design and integration as no movable parts, as actuators etc are needed.

### 9.5.1. Mirror material.
Plane and relatively small 50 cm² to 100 cm² mirrors make it natural to use single-crystal materials for the reflective surfaces as the most reliable solution for optical surface survivability during cleaning. Currently single-crystal molybdenum has been chosen as the main candidate as it has high reflectivity in the IR range, good thermal and mechanical properties while the manufacturing technology for this kind of mirror is relatively well developed.

### 9.5.2. Predictive modeling.
As mentioned in section 3, numerical simulations were performed in order to evaluate the required performance of the candidate mirror cleaning system and to generate estimates necessary for the FMU optimization. The approach was applied to address RF-discharge cleaning in the IR thermography FMU. The following processes are included in the simulation workflow: the discharge itself, surface erosion of all plasma-wetted surfaces (including FMU walls), particles transport in ambient gas and corresponding re-deposition.

The CCRF discharge was simulated by means of the PIC-MC Fraunhofer-IST code [786], while materials transport, sputtering and re-deposition was simulated using the KITe MC software [493]. Ion fluxes and ion energy distribution functions (IEDFs) from the Fraunhofer-IST code have served as input data for the KITe.

Simulations have shown the presence of the deposition dominated areas near the edges of the mirrors. This deposition is associated with shaded areas formed by the mirror and surrounding structures. Based on simulation results it was possible to define necessary geometry modification to ensure that the entire mirror surface is in an erosion-dominated area. Figure 170 shows the net erosion profile simulated at 2 Pa background pressure He with 20 W of input RF power. The deposition dominated areas can be clearly seen near the edges
<figure><img src="image_182.png" /><figcaption>**Figure 170.** Simulated patterns of beryllium deposition (blue colors) and erosion (red and orange colors) on the 2nd mirror of 55.G6 FMU during the cleaning at 20 W of RF power in helium.</figcaption></figure>

with a large zone in the right bottom corner which is shaded by the surrounding FMU walls.

### 9.5.3. MSR for diagnostic mirrors in ITER IR thermography system.

#### 9.5.3.1. Passive mitigation techniques.
As the 55.G6 IR Thermography system should observe a large area on the divertor plates, figure 169(a), it requires a relatively large aperture in the DFW. To prevent deposition on the mirrors during ITER wall conditioning (very large contaminant fluxes are expected in these regimes), a diagnostic shutter is absolutely necessary for this system. It is to be designed yet, the required space is reserved in the current FMU design.

A stainless-steel diagnostic duct is equipped with a socket in the DFW providing a direct path from the plasma to the M1.

#### 9.5.3.2. Active recovery technique: in situ cleaning system.
In the ITER Thermography Diagnostic 55.G6 FMU utilizes two mirrors: first (M1) and the second (M2) mirrors serving as water-cooled RF-electrodes. The CCRF discharge will operate to alternately clean M1 or M2 [501, 502, 790]. As the two mirrors are located close to each other, both of them require an RF cleaning system as cleaning of one mirror will affect the other. The two mirrors are to be cleaned in a series. They have independent power circuits and while RF power is supplied to one mirror, the second one is grounded.

The 55.G6 IR thermography FMU consists of two mirror assemblies (MAS), electrical distribution circuit, water distribution circuit and the support structure (housing), providing structural/optical stability and Remote Handling compatibility. The general view of the MAS developed following the principles above is shown in figure 171(a). Each mirror

<figure><img src="image_183.png" /><figcaption>**Figure 171.** First mirror assembly: (a) general view of the FMU housing containing mirror itself (1), water cooling pipes combined with RF notch filter (2), combined with electric shields (3), RF and electrical connectors (4), (b) FMU inside the test chamber with RF discharge operation.</figcaption></figure>

<table><caption>**Table 35.** Set of mechanical and environmental tests of the FMU mock-up.</caption><thead><tr><td>Test No.</td><td>Test title and description</td></tr></thead><tbody><tr><td>1</td><td>Demonstration of the plasma generation in the FMU mock-up</td></tr><tr><td>2</td><td>Delivering at least 100 W of RF power to the mirrors for at least 1 h</td></tr><tr><td>3</td><td>Baking in vacuum better than 10<sup>-3</sup> Pa</td></tr><tr><td>4</td><td>DC high-voltage (≤1 kV) breakdown test</td></tr></tbody></table>

assembly is equipped with an RF plasma cleaning system and consists of the mirror itself, water cooling pipes combined with an RF notch filter, a housing combined with electric shields and RF electrical connectors. The RF components utilize planar RF design concept and are implemented as printed circuits on a ceramic substrate. Two mirror assemblies are installed in a housing which is to be connected to the DSM. The photo of plasma cleaning operation in the FMU is presented in figure 171(b).

The requirement for water cooling makes it almost unavoidable to use the RF cleaning with DC coupling where a quarter-lambda filter is used to detach the mirrors from the ground at the RF cleaning frequency. In the FMU water pipes are combined with such a filter enclosed into rectangular housing filled with AlN ceramics to prevent the parasitic breakdown. After the grounding point, there is no need in further shielding the water pipes.

#### 9.5.4. Engineering solutions.
Preliminary mechanical and environmental tests of the designed FMU mock-up were conducted to ensure the FMU integrity. Tests are listed in table 35 below, in the order they were conducted. The order was selected considering potential risks of the FMU damage during tests, allowing to perform successive tests even in case such damage would occur.

Tests No. 1 and 2 were combined since they require the same experimental conditions. Only one of the mirrors was fed by RF power at a time whereas the second one was grounded. The RF discharge plasma was generated and successfully sustained for 1 h in Ar at 2 Pa. The power delivered to the RF
vacuum feedthrough was 150 W at 81.36 MHz, a fraction of about 100 W was expected to be delivered to the RF discharge.

## 9.6. Open questions and issues

**9.6.1. Physics issues.** The remaining issues and open questions of design and procurement of reliable and efficient diagnostic mirrors can be divided into two main classes: physics issues and engineering issues. Physics issues are mostly not related to mirrors directly, but originate from external factors which may nevertheless affect the mirror performance. Environmental effects of plasma operation, and the impact of ITER commissioning on mirrors are good examples of such external factors.

**9.6.1.1. Early (unstable) ITER: list of actions.** Presently, the commissioning of ITER and its first plasma (FP) are treated as significant risks for diagnostic mirrors. The following stages of an early ITER can be identified already:

* commissioning risks

* risks caused by the wall conditioning actions, and

* risks during the FP and initial plasma operation.

Under commissioning risks the mechanical damage during e.g. installation of the components can be understood. During the integrated commissioning of ITER, the plasma-facing modules for instance, will not be installed for the FP. Their subsequent installation can mechanically damage the mirror assembly. Also, unpredictable damage such as failure of the water-cooling supply system, may dramatically affect the mirror performance.

Wall conditioning will precede the FP [807]. As was shown in previous sections, the impact of wall conditioning on non-or badly protected mirrors can be highly detrimental.

Finally, risks caused by initial plasma operation should not be underestimated. ITER is planned to attain the FP with a very basic set of magnetic diagnostics and without many components installed. The first plasma operation will not be NBI-powered, but will feature ECH heating [807]. During the initial plasma operation, the risk of e.g. plasma disruption and loss of control is the highest. An extensive work ongoing on plasma-control system of ITER [808] including modeling of possible plasma scenarios involving unpredictable and sudden events. Nevertheless, the sudden risks due to faulty plasma controls, initial errors of operators etc cannot be excluded.

The general strategy to address the aforementioned challenges during the early ITER operation should include:

* Favor the later installation of mirror-based systems.

* When possible, avoid commissioning with mirrors open to plasma. Pragmatically, if possible, only mirror-based systems directly involved to commissioning should be involved.

* The mirror-based diagnostic should not be operated, unless it is absolutely needed for the FP and subsequent initial plasma operation.

**9.6.1.2. Modeling level.** Several modeling approaches were pursued in order to estimate mirror risks and provide guidelines for engineers [779-783]. Generally, however there is neither a unified modeling code nor modeling results which are widely accepted by the diagnostic community. Mostly, this is due to the remaining large uncertainties in modeling results and vulnerability of predictive codes to a change of boundary conditions. It is believed that modeling of mirror performance needs to be intensified in order to be pragmatically useful for the diagnostic mirror R&D.

At the same time, the diagnostic-specific modeling efforts are proven to be rather successful. Modeling of the cleaning system of the ITER IR Thermography diagnostic pursued at Ioffe institute by using the KITe [493] and Fraunhofer IST [786] codes, has delivered important results. These results are implemented into the design of the mirror-cleaning system already.

**9.6.1.3. Thermal cycling.** During the operation, mirrors in ITER diagnostics will be subjected to intensive thermal cycling. This will originate from e.g. inter-discharge phases and during wall conditioning and VV baking operation. Technical shutdowns due to installation of new equipment will cause a change of temperature conditions. Therefore, the study of operation of diagnostic mirrors under varying and cyclic temperature conditions are important. An example of a thermal cycle test on diagnostic mirrors is provided below.

A temperature cycle test was performed on mirrors having rhodium films formed on SS316 substrates. The mirror samples have outer diameters of 25 mm and substrate thickness of 5 mm with rhodium film thickness of 5 and 10 µm respectively. To form rhodium films with good adhesion, chromium inter-layers between the rhodium and SS316 are applied. The surface roughness after rhodium film formation was 10–13 nm depending on the location. A temperature of the cooling channel at the start of plasma operation of ITER is 70 °C. Baking temperature of the divertor cassette is 350 °C and those in port plugs and lower port racks are 240 °C. Temperature cycle from 70 °C to 350 °C was repeatedly applied 500 times. The period of one cycle was approximately 2500 s. A SS316 substrate (dummy mirror) having the same dimensions as the mirror sample was also installed. Figure 172 shows the surface temperature of the dummy mirror measured with a thermocouple up to the 9th cycle.

As shown in figure 173, the thermal cycle did not degrade spectral reflectivity. It looks as if the reflectivity is slightly improved. However, the tested samples had lower reflectivity in the UV region than the one reported in [809]: reflectivity of rhodium coating at 200 nm was 25% in experiments, while the reference value for rhodium revealed 55%.

In a similar manner the thermal cycling was made for several mirror materials of the ITER VUV divertor spectroscopy diagnostic [96]. The procedure of thermal cycling test followed the ITER baking scenario, and the change of the mirror surface condition was measured between each cycle. The
<figure><img src="image_184.png" /><figcaption>**Figure 172.** Time history of mirror surface temperature.</figcaption></figure>

<figure><img src="image_185.png" /><figcaption>**Figure 173.** Reflectivity of Rh film mirrors after 500 temperature cycles in the wavelength range of (a) 200–900 nm measured by spectrophotometer and (b) 900–2500 nm measured by Fourier transform infrared spectroscopy.</figcaption></figure>

appropriate candidate materials of the first mirror for the VUV wavelength range are chosen to be gold (Au)-coated stainless steel substrate mirrors, bare coated Ni-P plated stainless steel substrate mirrors, or silicon carbide (SiC) mirrors considering their mechanical strength and optical performance in VUV wavelength range. From the thermal cycling test, however, the Au coated stainless steel mirror was found to be damaged since its Au coating peeled off in case with a Cr inter-layer. For the case of Au coated Ni-P plating mirror without Cr inter-layer, peeling-off of the coating did not occur, however the mirror roughness of the Au coating surface was increased up to ~10 nm (rms) due to the aggregation of Au in the baking temperature of approximately 240 °C. For this reason, Au-coated mirror was found not to be appropriate for the VUV wavelength range. In the following tests, bare Ni-P plated stainless steel mirror without Au coating and SiC mirror were tested, and both showed good results meeting requirement for the thermal cycling test. The roughness change over 100 cycles was measured to be ±0.2 nm on Ni-P plating surface of the mirror sample. The other thermal cycle test with SiC mirror showed a mirror surface roughness change of ±0.1 nm after 100 thermal cycles.

9.6.1.4. *Steam event.* Steam ingress, mentioned earlier in our chapter, significantly deteriorates the optical properties of diagnostic mirrors [810]. In most cases, the ability to recover the specular reflectivity after the steam event leads to the down selection of the mirror material. For instance, the mirrors for the ITER VUV Divertor Spectroscopy System qualified after the thermal cycling tests described in the previous section, were subjected to the steam ingress event testing. The conditions of a steam ingress event VVICE IV [754, 756] were reproduced during the testing. After steam ingress test, bare Ni-P plating on the stainless-steel substrate was found to be oxidized and it peeled off as inferred from analyses of scanning electron microscope (SEM) images. On the other hand, the roughness and topology data on the silicon carbide mirror surface evidenced no change or damage after the steam ingress test. As an outcome of the series of qualification tests, the material of the first mirror for the ITER VUV spectrometers was chosen to be silicon carbide.

For some first mirror materials, it was possible to recover reflectivity almost entirely using the RF-plasma cleaning. The nano-crystalline Rh samples had developed 'voids' along the thickness of the mirror coating after a steam ingress, which increased their diffuse reflectivity. However, it was also possible to remove these voids by the RF plasma cleaning [811].

There are still several open questions in the topic including the impact of a steam event when the mirrors are already polluted by first wall deposits, steam induced risk on the FM substrate interface for coatings and the impact of irradiation. For the mirror material itself, nano-crystalline rhodium is considerably better in resisting the surface oxidation than single crystal molybdenum [245, 764, 810, 811], giving it a larger estimated lifetime in ITER. Mo mirrors in particular have been shown to degrade in all considered scenarios of exposure to water and steam, however they can be made less sensitive to water/steam by reducing the operating temperature of the mirrors [798]. A recent study [812] outlined the detailed consequences of a steam event that occurred in ASDEX Upgrade during the baking procedure. The water condensate was found all around the torus as well as alt-like remnants from reaction of steam with first wall deposits as well as rust around the welding seams. In order to minimize the risk of a steam event during baking, it was suggested increasing the pH of hot water to 8.5 to avoid erosion of copper-containing components as well as increasing pressure for routine leak testing before infill of water from 10 bar to 20 bar. Furthermore, a control logic was defined to stop the baking of the vessel in the event of a leak (i.e. when a pressure increase of $10^{-1}$ mbar is detected) and prompt conditioning/drying of vessel to avoid further erosion in remote areas. Similar steps can also be adopted for the baking procedure for ITER to mitigate steam event effects.

It should be noted that steam ingress conditions will affect all in-vessel mirrors, and not only the first mirror equipped with a cleaning system. Therefore, it is necessary to select the materials carefully for the both the first and secondary mirrors. To date, several studies of candidate materials for the role of in-vessel mirrors have been carried out [813]. The best
steam resistance was shown by mirrors made of Rh and Cr (figure 168), as well as mirrors with a protective dielectric coating including multilayer dielectric mirrors and Al + SiO₂, Al + Al₂O₃, SiC + Al + SiO₂, SS + Ag + SiNₓ/SiOₓ mirrors. Here, a precise evaluation of the given steam ingress scenarios and their consequences for diagnostic mirrors is needed.

**9.6.1.5. Re-deposition during cleaning.** As mentioned in section 4.4, a high plasma potential associated with DC-grounding of FMs poses a significant challenge towards plasma cleaning of the mirrors accompanied with a massive re-deposition of sputtered material on the FMs [814]. The redeposition of the wall material ends up competing with the erosion of the FMs, making the plasma cleaning process inefficient. Hence, mitigation strategies are necessary to minimize the wall redeposition and promote FM cleaning.

Four different techniques were pursued to reduce the sputtering and re-deposition of wall material on the FMs as follows:

1. Mechanically profiled walls. It was observed that using a 'saw-tooth' shaped wall introduced a significant asymmetry (over 40%) in the ejected distribution profile— effectively moving the sputtered material away from the mirror. However, this technique does not reduce the wall sputtering itself and a resultant re-deposition on the FMs while reduced, is still not negligible.

2. Metallic GGs: in this technique, GGs with transparency of 70% were placed a few centimeters above the walls to act as 'interim' walls for the plasma. This technique has a great potential for application in ITER, however its benefits may not be as pronounced in the presence of B field [815].

3. Floating walls: in this technique, the walls of the FMU were isolated from the ground and remained at the floating potential in the plasma discharge. The ion energy at the floating walls was constant at 30 eV, while the ion energy at the grounded FMs could be increased by several times keeping the FMs are in a net erosion regime. This technique is potentially of crucial importance for ITER, as specific wall regions in the FMU initially prone to sputtering can be isolated to minimize re-deposition [816].

4. Wall material of FMU: the choice of materials with high sputtering threshold can minimize re-deposition. However, the threshold is greatly influenced by the presence of native oxides on the surface and needs to be taken into consideration for selection of ITER relevant wall materials [816].

Single or multiple solutions could be implemented in FMUs, depending on their size, orientation to B-field, etc. It must be noted that those solutions are not universal, and their application needs to be assessed for each particular diagnostic. Generally, wall geometry, competing with redeposition of contaminants can be treated as an extension of the passive mitigation techniques, such as shutters and diagnostic ducts described earlier in section 4.3.

**9.6.1.6. Adverse effects caused by high deuterium and helium fluxes.** Within their lifetime, the first mirrors are naturally subject to deuterium, tritium and helium fluxes originating from the fusion plasma. In addition, cleaning plasma will inevitably affect the surface of mirrors. The most process gases used for cleaning plasmas are those which allow removal of light elements such as beryllium while preserving rhodium or molybdenum mirrors [817-819]. Yet, the atoms and molecules of those gases, such as deuterium (D₂) or helium (He) likely will pass along the boundaries of sub-grains and grains accumulating at the grain boundaries, vacancies, dislocations or ion-induced defects, see e.g. [820, 821]. Accumulated D₂ or He can then form bubbles and blisters [791, 801, 821-824] at the inter-grain boundary due to interstitial diffusion through the grain body [825], as well inter-grain boundary diffusion [826]. Material structure, plasma species, surface temperature, ion flux and fluence can influence the blister formation. Blister nucleation was found on polycrystalline Mo, which was polished with diamond paste, after exposure to D₂ plasma with an incident ion energy of 30-80 eV at the fluence exceeding 10²³ m⁻² [827]. Besides, the large size blisters were found to form on the surface of the first mirror made of TZM substrate with 100 µm Ni layer after exposure in a (H₂ + 10%Ar) plasma with a fluence of 6 × 10²⁵ m⁻² [828]. Helium blisters can be formed only at temperatures higher than about 0.2 times the melting point, about 600 °C with incident energy higher than several hundred eV. As the FMU should operate in the temperature range of 100 °C-300 °C for actively cooled single crystal mirrors in ITER, the risk of blister formation is relatively small. At the same time, understanding and prevention of blister formation on e.g. nanocrystalline mirror material is important.

The formation of blisters during mirror cleaning leads to irreversible destruction of the mirror surface. This effect is observed when mirrors are exposed to He or D atoms or ions in the course of the mirror cleaning. Formation of nanoscale bubbles was observed during bombardment of single crystal molybdenum mirrors with He ions [795]. Blistering and bubble formation changes the spectral reflectivity of the mirror. At the same time, it was found that the mirror polishing procedure has a large effect on blistering [829].

Recently, the formation of pits was observed during sequential exposure of single crystal polished Mo mirrors to helium and argon ions. At the same time, the use of single crystal material with a particular orientation can mitigate formation of blisters [821, 830]. Adverse factors due to mirror preparation and *in situ* cleaning processes must be taken into account when choosing working gases and the cleaning mode with using cleaning systems in optical diagnostics [797].

**9.6.1.7. Mirror in magnetic field.** The magnetic field of ITER can reach 5.3 T on the magnetic axis of the machine [831]. Currently, cleaning of diagnostic mirrors in the presence of B field is envisaged to minimize the dedicated service time.

The uniformity of first mirror cleaning by plasma sputtering using 81.36 MHz RF discharges was studied in a 0.05 T field [501]. An enhanced sputtering rate within the center of the
electrode was reported and it was noted that the longitudinal field improved sputtering uniformity along the edges. Results of the study gave evidence that the net sputtering profile in magnetic fields is determined not only by the ion flux distribution but also by the re-deposition process. Mirror cleaning experiments performed in a magnetic field up to 0.5 T with Penning discharges in helium gas were reported in [795]. The efficient removal of aluminum (Al) contamination coatings from molybdenum mirrors was observed. In these studies, aluminum was used as beryllium proxy. The maximum thickness of removed Al was up to 200 nm. Mirror cleaning was accompanied with recovery of the optical properties. Cleaning of Mo mirrors from $Al_2O_3$ films with 13.56 MHz RF argon (Ar) discharges in a magnetic field of 0.35 T was reported in [832]. In particular, the cleaning performance was enhanced when the field lines were nearly parallel (within a few degrees) to the mirror surface. In another study, sputtering cleaning experiments with RF plasma in 3.5 T field were performed. The formation of filaments and strong inhomogeneities due to erosion profile drifts on the FM surface were detected, whereas the maximum and minimum erosion rate ratio on the FM sample was as high as 14 [833]. CCRF plasma cleaning experiments on the ETS mock-up in a 1.7 T magnetic field were conducted in the EAST tokamak [834]. The presence of the magnetic field reportedly decreased the self-bias on the FMs up to 10 times, and the cleaning rate was increased by 40 times compared to those in identical experiments without a magnetic field. A complete recovery of the total reflectivity of the FMs was reported, whereas the diffuse reflectivity and surface roughness at the center of the mirror assembly were enhanced. Experimental results describing the impact of an axial 0.5 T field on CCRF discharges in the DC-coupled scheme were presented in [504]. Here, a similar decrease in the DC current with magnetic field was observed as reported above. Furthermore, the effect of the field was more pronounced for the low-pressure discharge at lower excitation frequencies and at fields >0.3 T, where ions and electrons are both magnetized [835, 836]. For RF-cleaning plasma this would mean that for both ions and electrons the Larmor radii are much smaller than the characteristic length scales of a plasma and the cyclotron frequency is much smaller than the collision frequency leading to momentum transfer. Ion energies obtained were identical both in the presence as well as in absence of the notch filter. In a recent study, an RF plasma cleaning with notch filter in a 3 T magnetic field using the mock-up of a FMU was investigated [837]. The areas of sputtering and net deposition on the FM surfaces were dependent on the angle between the FM surface and the magnetic field. Remarkably, the net deposition could be eliminated completely at certain angles. This also has implications for the design of FMs in ITER. Since the plasma extends in the direction of B field, the FMs need to be oriented in such a way that the sputtering of wall surface from the extended plasma column is far from the mirrors in the FMU to minimize the probability of redeposition.

Regarding the efficiency of a particular discharge type used for the mirror cleaning: CCRF or pulsed DC, the current results look promising for both discharge schemes. The

CCRF-discharge is known to successfully operate in the presence of an external magnetic field. The presence of longitudinal magnetic field is known to symmetrize the CCRF-discharge due to particle magnetization already at a weak magnetic value of ~0.3 T. The spatial inhomogeneity of the sputtering in this case was found to be decreased even in moderate B-field providing magnetization of the electrons only. The concept of CCRF-cleaning of inclined mirror in high magnetic field of 1.7 T was successfully tested in the EAST tokamak for angles to magnetic field of 5° and 20° [834]. The experimental results give evidence of the remaining DC-bias due to building up the discharge symmetry. The 5° case revealed a high asymmetry of sputtering. A study of the CCRF-discharge application in magnetic field is underway.

As for the pulsed DC-based cleaning system, experiments have demonstrated its feasibility and efficiency in a magnetic field $B_t \le 3$ T. The highest cleaning rate was obtained for the orthogonal orientation of the magnetic field to the mirror surface ($R \approx 0.2 \text{ nm min}^{-1}$ at a power of $P_d = 100 \text{ W}$). With the same discharge power and a parallel orientation of the magnetic field to the mirror surface, the cleaning rate significantly decreases ($R \approx 0.01 \text{ nm min}^{-1}$). The use of a fully closed discharge cell, however, can significantly increase the sputtering rate and uniformity of cleaning.

### 9.6.2. Engineering issues.
In contrast to physics issues, engineering issues are most likely caused by internal factors, parts of construction, design or an assembly directly related to the mirror itself. The mirror material, its availability, machinability, and scale-up forecast are good examples of such internal factors. Below are engineering issues which were identified as having a high importance.

#### 9.6.2.1. End of cleaning indicator.
Operational feedback should be implemented in a mirror cleaning system, which stops the plasma discharge as soon as the deposits have been removed to prevent sputtering of mirror surface.

The most obvious parameter indicating the complete recovery of the mirror surface is mirror reflectivity. The *in-situ* measurement of the absolute reflectance requires, however, a calibrated light source and a light collection and transmission scheme, stable throughout the ITER operation. The optical scheme is preferably to be the same as the diagnostic one, since any additional optical components located close to the first mirror will be subjected to deposition as well. The use of plasma discharge emission as the light source seems to be troublesome because of uncontrolled variation of discharge parameters resulting, among others from the increase of power loss in feeding lines with their heating. The idea to compare the optical emission of fast hydrogen atoms with that reflected from the FM has been suggested in [250, 838]. The ability to measure absolute values of mirror reflectivity was demonstrated. The validation of this technique is necessary for RF cleaning discharge operating at higher pressures in FMU geometry. Alternatively, a retroreflector can be used, being hidden during ITER operation. This can be done e.g. by mounting the reflecting surface on the back side of the shutter allowing the
<figure><img src="image_186.png" /><figcaption>**Figure 174.** Discharge voltage evolution during cleaning in DC mode: $P_{Ar} = 2$ Pa, $I_{d} = 200$ mA, current stabilization mode.</figcaption></figure>

usage of the same diagnostic optical path for light input and collection [839, 840].

Another technique suggested to monitor the plasma-cleaning process is optical emission spectroscopy of sputtered species in the discharge column. Potentially, the intensity of spectral lines of both deposited and mirror material can be taken as an end-of-cleaning indicator. Experiments with an CCRF discharge at 13.6 and 60 MHz, Ar and self-bias of 140–280 V revealed the presence of Mo and Rh and absence of Be lines in plasma emission spectra [841]. The technique also should be tested in schemes with notch filter and/or in B-field with a much smaller (or even zero) value of self-bias and, consequently, smaller sputtering yields.

For the RF-based cleaning system, monitoring of plasma and voltage/current parameters is widely used to control the process in a number of RF sputtering/deposition techniques [842]. In particular, the evolution of higher harmonics of the applied frequency in the current and voltage characteristics of the discharges was shown to be a sensitive tool to monitor changes in plasma conditions and composition. These studies were performed both in inductively coupled plasmas and during reactive magnetron sputtering [843, 844]. However, it is not clear whether the effect will be observable for metal pairs Be/Rh or Be/Mo and in a symmetric discharge in the presence of the B-field.

In a DC-based mirror cleaning system, it is possible to control the presence of impurities on the cathode elements of the discharge cell. A change in the composition of the sputtered surface leads to a change in its ion-electron emission coefficient. Therefore, at a fixed discharge current, the end of cleaning can be determined by the discharge voltage reaching a new stable level, corresponding to that measured on a clean mirror. An example of the discharge voltage evolution during the cleaning process is shown in figure 174.

With the sound progress made in end-of-cleaning indicator research and development, presently, there is no clearly favorable generic solution suitable for all diagnostic systems. The final decision should be based on the geometry of the FMU,

space available, cleaning regime, power feeding scheme and should be qualified for each particular diagnostic.

9.6.2.2. **Notch filter.** The necessity of the notch filter was discussed earlier in the chapter. However, an application of such a filter increases the plasma potential significantly allowing for an enhanced sputtering of FMs. At the same time, this could also trigger an increased sputtering of walls surrounding the FM and its re-deposition on the FMs during the cleaning process, for which additional coping strategies might be necessary [816].

In the case of a capacitively coupled discharge, application of the notch filter results in vanishing of the DC-bias and increase of the plasma potential [790]. The discharge non-symmetry reveals itself in this case as direct current flowing through the circuit. Due to absence of DC self-bias the energy of ions bombarding both powered and grounded electrodes become equal. This leads to comparable sputtering rates of the RF powered and grounded surfaces [790, 814]. Hence, the redeposition of the material sputtered from the grounded constructions is non-negligible for the case of notch filter as it is for the case of the insulated RF-powered electrode. Therefore, the redeposition phenomena also need to be taken into consideration in the design of the RF cleaning systems for ITER.

9.6.2.3. **Power delivery issue.** For the DC-coupled RF discharge scheme, considered as one of the primary-candidate for mirror cleaning in ITER, the RF power density of $1–4$ W cm$^{-2}$ at a frequency of 10...100 MHz is required to achieve effective cleaning [502, 790]. Depending on the size and shape of electrodes, the total RF power delivered to the discharge should be in the range of 0.5–2.5 kW. One of the feeder candidates for solving this problem in ITER is mineral insulated (MI) cable. However, due to overheating caused by high insertion losses, applicability of a single MI cable for feeding RF power for all cases may be limited. The most important parameter for this MI cable type is the dependence of its attenuation on frequency and temperature [845]. As a result of these studies, the following options for attaining the required power were proposed:

* RF Power Modulation by HF pulses (~10 kHz);

* using a heat sink at the beginning section of the MI cable;

* RF Power combiner/splitter devices.

The modulation of RF power results in an increase of power in the pulse linearly with the reverse value of the duty factor while keeping the mean power value constant [846]. A low-frequency RF power modulation is an effective tool, which allows to decrease the supplied RF power required for mirror cleaning from hard-to-sputter deposits in ITER. An acceptable sputtering rate ~1 nm min$^{-1}$ of both Be and BeO can be achieved in the case of pulsed RF power feeding in B-field at power density of approximately 0.6 W cm$^{-2}$. Without B-field the much higher power is needed to remove BeO in DC-coupled scheme.
9.6.2.4. Scale-up of mirrors. The dimensional requirements for mirrors in ITER are dictated by the corresponding design solutions. In general, however, there are several mirrors with dimensions reaching several tens of centimeter that are required. As an example, the mirror unit of the ITER core CX recombination spectroscopy has a projected length of 30 cm [778], whereas the dimensions of the second mirror in the VUV DIM can reach 100 cm [96].

Significant R&D was performed for several ITER diagnostics in order to find a suitable solution for the required size of the mirror. Here, two approaches were investigated: making a large single crystal or nanocrystalline mirror out of many pieces or attaining a one-piece mirror solution [847]. Although the single-piece mirror solution was favored in [847], the largest size molybdenum single crystals commercially available to date, does not exceed 200 mm. A possible way to overcome such a limitation is assembling a large reflective surface from a set of smaller single crystal molybdenum plates. These plates can be bonded to a full-size base plate made of polycrystalline molybdenum by brazing, electron beam- or diffusion welding [847]. This was demonstrated for mirror dimensions of 100 × 80 mm. In this design, the reflecting part was produced from several parts of single-crystal molybdenum with the same orientation in the crystallographic planes. The mirror part was joined by diffusion welding with the base of a mirror made of non-magnetic material with a heat conductivity coefficient and a linear thermal expansion coefficient similar to those of molybdenum. As structural materials for molybdenum tiled mirrors, a diffusion bonding to the titanium—aluminum—vanadium (Ti-6Al-4V) and vanadium-chromium-titanium (V-4Cr-Ti) alloys acting as substrate plates [848] was proposed.

Recently a Rh coating with a thickness exceeding 10 µm was deposited by magnetron sputtering technique. As a structural element for rhodium, the tungsten-copper (W-Cu) alloy was chosen [778] in order to attain the required mirror dimension. Presently, industrial-type ITER water-cooled first mirror mock-ups with up to 109 mm in diameter with Rh and Mo reflecting coatings have been manufactured. The mirror scale-up efforts are ongoing.

## 9.7 Summary and outlook

In this chapter we provided a concise overview of the main results of the structured and coordinated international R&D in the field of diagnostic mirrors for ITER during the past decade. An important element of the overview is that the major decisions on mirrors taken by the international groups of mirror experts with an active interaction with ITER Team and domestic agencies are described to the knowledge of authors, for the first time. These decisions can be found in the section ‘Risk evaluation and mitigation’.

Another important aspect of this overview, which is different from the research published earlier [730–732], is a list of successful, but in the course of evolution of ITER project, presently irrelevant studies. The authors believe that providing such a list will help to streamline the current mirror R&D.

The list of past milestone results of the R&D which are valid for ITER diagnostic mirrors is presented as well in the section ‘Risk evaluation and mitigation’. The use of single crystal and possibly nanocrystalline mirrors, the use of shutters, the necessity of MSR are viewed as necessary measures for ensuring the longest mirror service life possible.

A high priority research on mirror surface recovery is presented in the dedicated section on MSR. Here, the importance of the in-situ mirror cleaning is clearly presented along with the currently favorite mirror cleaning solutions including the RF and pulsed DC discharges. Generally, a set of measures, technologies and scenarios allow issuing the optimistic forecast for the mirror lifetime for majority of ITER diagnostics. An application of the envisaged solutions was demonstrated on the FMU of the ITER IR Thermography system, used as an example.

At the same time, there are several still unresolved questions needing immediate attention. Among those, the impact of a steam event and addressing its consequences needs more thorough investigations. Especially, an applicability of an in-situ cleaning system to recover a mirror from a steam event must be evaluated. If necessary, the cleaning system must be made capable of recovery after a steam ingress. The use of steam-resistant mirror materials, such as silicon carbide used e.g. in the space VUV systems [849], must be assessed. Such an assessment is especially important for mirrors in ITER which are distant from burning plasma. Several urgent engineering solutions, among others, the use of a notch filter, the robust and reliable cleaning-stop indicator need to be finalized. The capability of modeling for making robust and reliable predictions still reveals significant doubts. Here, the opportunity of conservative estimates necessary for outstanding engineering must be evaluated at the cost of discarding the predictive feature.

The resolution of the mentioned outstanding open questions will surely employ the most coordinated R&D efforts in the field of ITER diagnostic mirrors in the nearest future.

As for a longer-term perspective, thorough thinking must be given to address the late stage of ITER exploitation. The research and engineering program in the late ITER phases will need to be focused on preparation for the exploitation of a fusion power plant, such as the DEMOstration power plant. We can assume that during commissioning and at early stages of operation, a power plant will possess a diagnostic suite similar to that of ITER. Later, the plant-relevant aspects, resembling those in ITER significantly, will be inevitably introduced. A quasi-stationary operation, the orders of magnitude higher neutron fluences on the in-vessel components are among factors which will define the future use of diagnostic mirrors in DEMO. A possible and logically understandable approach will be in limiting the use of diagnostic mirrors in DEMO to necessary diagnostics only, providing reserve mirror channels and backup mirror units. An example of critical thinking on the first mirror application is given in e.g. [298]. Addressing the coming long-term challenges relevant to a fusion power plant will certainly employ the first mirror research and development efforts in a longer-term perspective.
# 10. Synthetic diagnostics for real time plasma control studies and diagnostic design

M. R. de. Baar$^{44,45}$, D. Mazon$^1$, L. Zabeo$^2$, M. de Bock$^2$, M. Schneider$^2$, Th. Blanken$^{44,45}$, Th. Bosman$^{44}$, T. Ravensbergen$^2$, B. van de Boorn$^{44}$ and C. Orrico$^{45}$

## 10.1. Introduction

The purpose of ITER is the study of plasmas with significant alpha particle heating. In addition to an extensive science and technology programme, ITER has two ultimate deliverables: (1) the development of an inductive plasma scenario (in which the plasma current is driven with a set of primary transformer coils) with a power multiplication factor (the ratio between the fusion power and coupled input power required to sustain the conditions) of $Q = 10$ and (2) a non-inductive scenario (in which the current is driven without transformer action) with $Q = 5$.

The topic of plasma control is a branch of the field of system and control research with a few peculiarities. First, a fusion plant is operated close to operational and machine limits. A second complication is the use of actuators that are shared between various control tasks, while these in turn are strongly coupled. The optimization of the fusion reactivity is associated with the control of a number of distributed parameters. The sensor and actuator park is distributed poloidally and toroidally as well as radially. The interpretation of the sensor data and the actuator input is plasma state dependent. To deal with these complexities, the design of a PCS relies on model-based approaches.

ITPA diagnostics and ITER-IO have started and activity on the development of synthetic diagnostics for IDA and validation (IDAV) and application Real Time (RT) control systems. The purpose of this activity is to develop, adapt and validate synthetic diagnostic models with associated test cases for their use in the ITER Integrated Modeling and Analysis Suite (IMAS) to make them available prior each phase of the ITER Research Plan. An IDA workflow will be implemented at ITER, starting with a rudimentary IDA workflow based on just a few diagnostics (those already available). In addition, a subset of synthetic models will be defined to be used for control applications, namely for the development of the ITER PCS simulation platform (PCSSP).

Examples of the use of synthetic diagnostics in diagnostic design validation are given throughout this special issue, with special emphasis on integrated data-analysis in the next subchapter 11. This subchapter presents one example of diagnostic design and design validation for the VSRS, but mainly focusses on the use synthetic diagnostics in real-time forward modeling for real-time control.

A significant part of this activity consists of validating the models onto existing fusion devices. As a starting point, AUG and WEST have committed to provide the data for model validation but the list of contributing devices is expected to grow.

A workflow to run and combine Synthetic Diagnostics together has been developed. It is written in python following the same spirit as the python H&CD workflow. The Minerva

platform to apply Bayesian techniques for deducing the best answer from combining models together has been installed on ITER cluster. Specific synthetic diagnostics have been under development in this context: magnetics, VSRS, H-alpha, etc. A prototype workflow for IDA combining ECE, Thomson Scattering and interferometry is being developed. In this context, specific methods are defined for physics models to be exploitable in the context of an IDA iteration loop. To provide the required input for each synthetic diagnostic, a machine description database has been developed and populated, which contains the geometry of the various diagnostics. It completes the already existing scenario database that provides the plasma conditions (equilibrium, kinetic profiles) for the models to be executed. The plan is to continue the development described above and to get new contributors/new models to cover all the synthetic diagnostics for each phase of the ITER Research Plan.

In this contribution, it is discussed how of synthetic diagnostics are used for diagnostic design and design validation and for the formulation of model-based plasma control for ITER.

This paper is organized as follows. First we classify the plasma control topics and discuss their interactions, and the evolution of modern systems and control methods is summarized. Notably, it is explained how models of the input-output dynamics can be used in real time for optimal data analysis. Then we give a number of examples of synthetic diagnostics models and their application in ITER diagnostic design and model-based control design: Iterative learning control (ILC) for discharge optimization, model predictive control (MPC) for current density and temperature, observation and sensor fusion of the density profile and MPC for the density distribution, synthetic diagnostics for the magnetics with application to neo-classical tearing modes (NTMs) suppression and a model of the VSRS diagnostic with the view to design an optical dump and to simulate spectra.

## 10.2. Systems and control perspective on nuclear fusion

10.2.1. *Classes of control tasks.* Traditionally, most of the plasma control of reactors is done in feed-forward. In feed-forward control the waveforms for the actuators are pre-programmed by the tokamak operator. In spite of modeling support, the feedforward waveforms are often not optimized against multiple requirements and constraints. Moreover, the feed-forward waveforms are intrinsically not able to deal with varying limits, varying plant conditions, disturbances or actuator failure.

A case where feed-forward control maybe essential is the start-up optimization, consisting of the breakdown, the burn through and current ramp phase. Start-up must be carried out with a high success rate, and low loads on the central solenoid and heating systems. A key issue is that during the start-up phase the current and density are low, and associated quantities such as plasma position are difficult to diagnose as the signals are small. Moreover, given the realistic path lengths of the gas-feeds, long time lags are introduced. Consequently, stable position, current and density feed-back control is hard to
achieve in this phase. This introduces the first control category: determination of optimal start-up feed-forward waveforms.

Once the plasma is established in feed-forward, the magnetic configuration control needs to take control of the plasma shape, boundaries to the wall, location of the X-point and strikes and total current while rejecting the vertical instability. This is the second control category. The poloidal field coils are the actuators while the central solenoid is used to drive the Ohmic current in the plasma. Mathematically, the dynamics associated with these control tasks can be formulated as ordinary differential equations [846]. Magnetic configuration control has one unstable mode, associated with the vertical position and velocity of the plasma centroid. Key challenges for the magnetic configuration control in ITER and DEMO are the sensors and the coupling with confinement physics. The traditional magnetic pick-up coils used in fusion research are prone to thermal gradients and neutron fluxes. These will give rise to drifts. The coupling to the confinement physics, such as during LH back transitions, could give rise to variations in beta and li that are too fast to be rejected by the magnetic control system.

The SOL (with open field lines that intersect the machine walls) interfaces the plasma with the reactor wall. It is used to shield the core plasma from undesirable impurity influxes and to abate the fluxes of heat and particles to the PFCs and to guide the heat fluxes to regions in the tokamak designed to deal with these fluxes. Tungsten components with active cooling can tolerate up to $10 \text{ MWm}^{-2}$. However, in ITER, if no measures were taken the steady state and dynamic heat fluxes would well exceed this. These fluxes would damage the reactor wall components.

Detached plasmas are likely to drive the fluxes down to acceptable limits. Plasma detachment can be induced by a high neutral gas density in the divertor, a high electron density, low temperatures and the introduction of low-Z radiative impurities (such as Nitrogen and Neon) in the plasma periphery and possibly radiating high Z impurities (Argon, Krypton) within the last closed flux-surface. Under these conditions, loss processes are introduced leading to a pressure gradient along the field lines. Radiative instabilities may emerge from the non-monotonic relation between temperature and radiative power losses per unit volume. In some temperature ranges, radiative power losses decrease with temperature leading to instabilities. It follows that to actively control the edge radiative power it is required to ensure sufficient dissipation of energy and momentum. This introduces the third category: Exhaust control. This entails the controlled introduction of low Z radiating impurities in the plasma periphery, and the control of their distribution.

The exhaust control is strongly coupled with the core plasma. First, the required radiative power is subject to the total heating power, including the fusion power. Second, the inward transport of low and high Z impurities depends on gradients lengths in the ion temperature and the ion density distributions. This introduces constraints on the distributions of $T_i$ and $n_i$ that can be formulated to ensure neo-classical shielding of high Z-impurity and falls into the group for profile control and the need for active control density profile control.

The core plasma is organized in concentric surfaces with constant toroidal and poloidal flux, magnetic winding number $q$ and magnetic shear $s$, pressure $p$ and electron and ion temperature $T_{e,i}$. Strictly speaking, the particle density is not a flux-surface quantity, but in most ITER relevant cases with low toroidal rotation and low effective ion charge $Z_{\text{eff}}$, this quantity can be treated in good approximation as a flux-surface quantity. The consequence is that for the closed flux-surfaces, the abovementioned quantities are functions of the flux surface label $\rho$ only. The transport of these quantities is perpendicular to the flux-surfaces, and subject to 1D diffusion, or diffusion-convection equations. It is very important to note the various couplings between the transport channels, such as the couplings between pressure and bootstrap current, temperature and resistivity, magnetic winding number distribution and transport, temperature and density gradient-length and heat diffusivity and neo-classical impurity fluxes. The heating and fueling systems deposit power and particles at various radial locations. Non-linear coupled transport equations with a single spatial coordinate ($\rho$) describe the relations between the deposition locations, the fluxes and the distributions and the gradients therein. The fourth category of control challenges is often referred to as profile control. The challenge here is to simultaneously maintain optimal distributions for the above-mentioned quantities using the limited set-of actuators.

The profile optimization strongly couples to operational limits associated with maximum density, maximum pressure and current density gradients. Magnetohydrodynamic (MHD) instabilities limit the achievable pressure and current density gradients. NTMs can form at flux surfaces where $q$ takes on a simple rational value, such as $q = 3/2$, 2/1 and 3/1 in the pressure gradient zone. The sawtooth instability (ST) develops at the surface with $q = 1/1$ and reorganizes the complete plasma core. The fifth control category is MHD control and suppression. This entails NTM suppression, ST amplitude control, or in general, control of resistive MHD modes often using ECRH as an actuator. Control-oriented models for the sawtooth evolution are often based on current diffusion, Porcelli conditions for the crash and a profile reset. Models for the NTM evolution are often based on the generalized Rutherford equation.

The sixth class of control challenges emerges where the control system interfaces with the plant safety system and must induce a safe shut down. There are three typical examples. Reactive, in which the controller tries to reject an event but cannot and triggers a shut-down, pro-active, in which a MPC anticipates problems and ramps-down the plasma, or blind/lame, in which the controller has to ramp-down the plasma with less than the nominal actuator and sensor availability.

These are special cases of event driven control. In the general case, a supervisory controller needs to be designed that can switch controller functionality and allocate actuators to various control tasks in a plasma state dependent and objective and tractable manner. The design of such a supervisory control represents the seventh ITER controller challenge.

In addition to controller functionality, there is the aspect of sensor and actuator design. The overall schematics is shown in figure 175.
<figure><img src="image_187.png" /><figcaption>**Figure 175.** Plasma control functions. Three continuous domains (magnetics, kinetics and exhaust) as well as two domains of events (preprogramme and stochastic) need to be controlled. This calls for controllers in the domains, coordination between the domains, and supervisory control. This requires a systematic, model based design approach.</figcaption></figure>

It will be now discussed how these challenges connect to advances in the development of the field of system and control.

### 10.2.2. Overview development control technology.

Classical control engineering was developed between 1940 and 1960. The applications were controlled by single input single output controllers (SISO). A reference was set, outputs were measured and compared to the reference. The residual was then used in a control law to calculate the control input. A typical method to do this is by making the control law a function that simultaneously has a Proportional, an Integral and a Derivative term (PID).

Between 1960 and 1980 the state-space formalism was introduced. This formalism introduces the state. The state contains all information of the evolution of the unperturbed and unactuated system. In general, the variation of the state $x'$ is a function of the state itself, the actuation $u$ and the external disturbances $d$, $x' = f(x,u,d)$. The output $y$ is a static projection of the state and the input, $y = h(x,u)$. Linearization yields the state space equations $x' = Ax + Bu$ and $y = Cx$, in which A, B and C are the system, the actuator and sensor matrices, respectively. The state-space formalism is highly relevant for the analysis and optimization of SISO systems and essential for large-scale systems with MIMO's.

As shown above, the measurements only provide a static projection of the state. However, the state-space formalism allowed for an iterative process for the estimation of the state, known as Kalman observation. In Kalman observation, a model of the input-output dynamics is interfaced with synthetic diagnostics. The model is subjected to the same inputs as the plant and outputs of the plant and the synthetic diagnostics can be compared. The residual is used to update the state. As Kalman observation is a statistical procedure, it deals with uncertainties in the measurements and can assess how much confidence has to be put on the measurements. Advanced implementations can deal with multiple sensors that measure various aspects of the state at various locations.

Also the field of robust control emerged in the seventies and eighties. This is a branch of linear control theory that explicitly takes bound uncertainties into account. In $H_\infty$ methods, control problems are expressed as a mathematical optimization problem, and the controller is the result of this optimization. $H_\infty$ techniques are used to synthesize controllers to achieve stabilization with guaranteed performance and are readily applicable to multivariate systems with cross-coupling between channels. Robust control requires a priori information about the bounds on these uncertain or time-varying parameters; if the changes are within given bounds the control law needs not be modified. This is in contrast with adaptive control, which is concerned with changing the control laws to adapt to a controlled system with varying (or initially uncertain) parameters. The foundation of adaptive control is parameter estimation. A common method of estimation is gradient descent, providing an updated control law, which is then used to modify estimates while the system operates.

The field of system identification (SI) arose between 1980 and 1990. In SI, statistical methods are applied to build mathematical models of dynamical systems from measured data. SI also aims at the optimal design of experiments for efficiently generating informative data for fitting such models as well as model reduction. A common approach is to start from measurements of the behavior of the system and the inputs to the system, the disturbances and noise, and try to determine a mathematical relation between them.

Very relevant for nuclear fusion is the identification of partial differential equations, notably transport equations. This is a field that is being developed now. Also very relevant for our discussion is that the quality of parameter observers depends on many factors such as the SNR of the measurements, sensor availability, sensor locations, quality of the models available, time scales of the processes, and if the operational regime features non-linearities, transitions between regimes. As we discussed above, many of the parameters in DEMO that need to be observed are distributed quantities (time-spatial), e.g. density, temperature, current density. This implies that both the temporal evolution and the spatial distribution are important.
This also affects the sensor placement and choices in time-
spatial ratios.

Another problem which is highly relevant is the case
in which different sensors are used to observe a quantity
not measurable by either of the individual diagnostics. This
requires a dynamic model describing how the measurements
indirectly describe this parameter. Identification methods need
to be applied to build such an accurate dynamic model, and
the dynamic model needs to be implemented in a real-time
environment.

From 1990–2000, MPC, was developed. MPC optimizes a
finite time-horizon, but only implementing the current timeslot
and then optimizing again. The merit of this approach is that
a process can be controlled while satisfying a set of limits
and constraints and anticipating future events. MPCs rely on
dynamic (typically linear) models of the process. These can
be from white or grey box modeling or from empirical models
obtained by system identification.

From 2000–2010 hybrid (event-driven) system theory was
developed. Hybrid systems combine discrete logics with con-
tinuous controllers. For our purposes, the relevance is that
this enables a systematic analysis of the class of control prob-
lems in which control tasks need to be modified. This can be
due to a limit in the plasma (e.g. an instability emerged in
the plasma) or varying constraints (e.g. because less actuators
become available during the experiment).

In the same period, the field of distributed control emerged.
Normally, control is developed for systems that can dynamic-
ally be modeled with ordinary differential equations, only tak-
ing the time evolution of the control parameters into account.
Distributed control deals with the control of systems in which
both time and location need to be taken into account. These are
described by partial differential equations such as the transport
equations for flux or temperature.

In the last decade, the use of artificial intelligence and
machine learning have been applied in controllers, often
in situations where there are ample modeling results avail-
able. Recent developments suggest that reinforcement learn-
ing allows for direct inference of complex controllers from
modeled data.

Control theory is not only involved with feedback con-
trol. ILC is an active field of research with the view to find
optimal feed-forward control for systems that work in a repet-
itive mode. In each of these tasks the system is required to
perform the same action over and over again with high preci-
sion. Repetition allows the system to improve tracking accur-
acy from repetition to repetition, in effect learning the required
input needed to track the reference exactly. The learning pro-
cess uses information from previous repetitions to improve the
control signal ultimately enabling a suitable control action can
be found iteratively. The internal model principle yields con-
ditions under which perfect tracking can be achieved but the
design of the control algorithm still leaves many decisions to
be made to suit the application.

10.3. Model based plasma control and synthetic diagnostics for ITER

**10.3.1. Magnetic configuration control.** The control of the plasma boundary, the plasma current and the radial and vertical position of the plasma centroid, as well as the suppression of the vertical instability all fall in the frame work of magnetic configuration control. This was the first domain in tokamak physics that was cast in a proper control theoretical framework [850]. Although the theoretical framework is mature, the field is still under development as a consequence of the requirements that a fusion reactor poses to the controller. These are associated with the development of new sensors for the plasma boundary (such as Hall probes (see e.g. [851], reflectometers [852] or visible imaging [853]) and [854] or with more stringent safety margins that require more precise controllers that can deal with limits and constraints (see e.g. [855] or [856]. The field is also driven by new divertor configurations such as the super-X with flaring strike points, or new, reactor relevant, plasma dynamics that needs to be rejected (see e.g. [857] or [858] by modifying the plasma volume and shaping to off-set undulations in the plasma burn. State of the art in reinforcement learning in plasma control is the development of controllers for the magnetic configuration [859].

10.3.2. *Profile control and confinement optimization.*

Predicting and controlling turbulent energy transport is a
grand challenge in nuclear fusion science. Control of the
spatial distribution profile of the toroidal plasma current dens-
ity distribution helps realizing improved confinement and
MHD stability. A high fraction of non-inductively driven
plasma current, could enable steady-state reactor operation
with high fusion gain. The dynamic evolution of the current
profile is nonlinearly coupled with several plasma paramet-
ers, motivating the design of model-based control algorithms
that can exploit knowledge of the system to achieve desired
performance.

Models for the input output dynamics using different actu-
ators were developed, see e.g. [860]. RAPTOR is a fast
dynamic model for the non-linear evolution of the coupled
distributions of the current density, the electron density and
the electron temperature. RAPTOR can be run in interpretat-
ive mode, as an extended Kalman filter [861–864].

Boyer [865] uses a first-principles-driven, control-oriented
model of the current profile evolution in low confinement
mode (L-mode) discharges in DIII-D to design a feedback con-
trol law for regulating the profile around a desired trajectory.
The model combines the magnetic diffusion equations with
empirical correlations for the electron temperature, resistiv-
ity, and non-inductive current drive. To improve tracking per-
formance of the system, a nonlinear input transformation is
combined with a linear-quadratic-integral optimal controller
designed to minimize a weighted combination of the tracking
error and controller effort.
Maljaars [866–869] exploited the fact the tokamaks are typ-
ically operated in scenarios and showed that, using RAPTOR
to estimate the non-linear state, a MPC can be synthesized to
achieve the optimal distribution of the current density in ITER
plasmas [866]. The MPC was set-up to use the four Upper Port
ECH systems, the neutral beam injector and the primary pol-
oidal field coil as actuators to avoid the current density profile
peaking in ITER hybrid scenarios.

The density profile is notoriously difficult to control. Initial
real-time density control schemes were based on PID schemes
with interferometers as sensors and gas introduction valves as
actuators. This scheme is associated with a number of com-
plications: The interferometers may suffer from fringe jumps,
which may be difficult to compensate in real-time. New gen-
erations interferometers use multiple wavelength to become
robust against fringe jumps. In some case, mm-wave heating
systems distort the sensor signal e.g. [870]. The interaction
with the wall varies per discharge or even during the discharge.
This is particularly relevant in long pulses, with or without
on-line wall conditioning using lithium power [871]. Heating
schemes can affect the particle transport and the pumping of
the divertor cryo-pumps is plasma configuration dependent.
PID density controllers may respond to confinement back-
transitions by increasing the fueling rates, which may further
deteriorate the confinement. These effects may render the PID
tuning ineffective or even unstable. Gas introduction valves
have only a limited particle deposition depth. Other actuators
such as NBI and pellets have a deeper deposition but the depos-
ition location is plasma state dependent.

To deal with these complexities, RAPTOR was extended to
include the distribution of the electron density. It is assumed
that for cases with low torque input and low plasma rota-
tion, the electron density distribution is with sufficient accur-
acy a flux surface quantity and that also the transport equation
for the electron density is dependent on the radial location ρ
only. RAPDENS is a 1D + 0D multi-inventory model of the
particle transport in a tokamak. The particles inside the vessel
are attributed to one of three inventories: the plasma, the wall,
or the vacuum.

The model contains a 0D representation of the particles
contained in the wall and the vacuum surrounding the plasma,
a 1D representation of the flux surface averaged electron dens-
ity in the plasma. The evolution of the density distribution is
represented by the 1D particle conservation law. The particle
transport Γ(ρ, t) is modeled by a drift-diffusion equation with
empirical transport coefficients. The particle sources and sinks
S(ρ, t) include particles injected via NBI and pellet injection,
particles entering the plasma due to ionization of neutrals at
the edge of the plasma and the loss of particles due to recom-
bination of ions at the edge of the plasma.

Blanken validated this model for the density evolution
(a.k.a. RAPDENS) off-line and showed that the model man-
aged to reconstruct the evolution of the central density as
well as the distributions of the density right in both TCV
and ASDEX Upgrade [872, 873]. Closed loop density control
experiments were successfully carried out in ASDEX Upgrade
and TCV with RAPDENS in observer mode [874].

Highly relevant for fusion reactors is the control of the distributions of the deuterium and tritium densities n_D and n_T. At present, experimentation at JET [875] and gyrokinetic modeling [876] suggest that the transport from the LCFS to the core is quite equal for D and T and in fact it suffices to guarantee n_D(ρ = 1) = n_T(ρ = 1) to achieve n_D(ρ = 0) = n_T(ρ = 0). If, however, a significant isotope effect would emerge in DEMO, the distributions of D and T must be controlled to ensure n_D(ρ = 0) = n_T(ρ = 0).

10.3.3. MHD control and suppression. The control of NTMs requires an intense micro-wave beam to be focused and deposited at the location where the magnetic island crosses the EC wave deposition resonance. The island’s radial location as well as the mm-wave ray propagation and resonant absorption condition are plasma state dependent and difficult to estimate. Moreover, the island rotates, and can be attributed a frequency and a phase. The power has to be deposited when a poloidal deficiency in current density (the O-point) crosses the resonance condition. The frequency and phase of the rotating island must be determined in real-time and used to modulate the ECCD system.

DIII-D [877] and ASDEX Upgrade teams [878] have set-
up an NTM control scheme that use multiple sensors. As an
example, the DIII-D implementation uses ECE and Mirnov
coils, magnetics, and MSE as sensors. Multiple real-time
estimators for the mode rational surface location and real-
time raytracing are required to identify the optimal launcher
angle to aim the ECH beam to the mode rational surface. This
scheme is the ITER reference [879].

An alternative scheme uses deep (120 dB) and narrow
(1 GHz) notch filter around the gyrotron frequency. This
allows for measuring the plasma temperature with ECE in
close vicinity of the ECCD deposition, along the same optical
path as the heating beam. This concept eliminates the equilib-
rium and the ray-tracing from the problem.

The challenge for in-line ECE is to design a notch filter
with 120 dB suppression of the ECCD frequency (140 GHz
on TEXTOR and ASDEX Upgrade) with a quality of bet-
ter than 1 GHz. This then isolates the ECE channels from
the ECCD and allows for measuring the temperature fluc-
tuations associated with the island [880]. An ITER relevant
notch was designed and constructed based on the mm-wave
cavity FADIS. A mover coil was used for cavity tuning, in
particular to couple the ECE to the radiometer and the resid-
ual ECCD to a dump [881]. A prototype, designed for 500 kW
ECCD power was mounted on ASDEX Upgrade [882]. A sim-
ilar set-up was achieved on DIII-D [883]. The EU DEMO
concept for NTM suppression (also known as quasi in-line
ECE) is derived from this concept [884, 885].

Hennen used in-line ECE for closed loop MHD track-
and-kill experiments in TEXTOR. A linear control technical
analysis was set-up by casting the Rutherford equation for
the island evolution into a state-space formalism [886]. Also,
the control performance analysis of the ITER NTM suppres-
sion system was done by casting the generalized Rutherford
equation in state-space formalism for typical ITER high performance discharge conditions with the view to sustain islands that have sizes below the critical island width [887].

Van de Brand demonstrated on ASDEX Upgrade that the fluctuations associated with small magnetic islands could be observed after correlation of the in-line ECE system with the interferometer and that interferometer was associated with the correct alignment of the radial location of the tearing mode could be identified [888].

Various methods were tried to determine the phase and frequency of the rotating modes in real time: Hilbert transforms on FPGA, a phased locked loop [887] and various variants of Kalman filters [889].

Another intriguing aspect of magnetic islands is that the rotating magnetic perturbations induce mirror currents in the conducting walls of the tokamak. The slower the islands rotate, the easier the mirror currents are induced. The mirror currents, however, lead to a deceleration of the plasma rotation, which promotes further growth of the islands. This mechanism, known as mode-locking is responsible for violent events, known as disruptions. La Haye coupled the equations for the island-wall interaction with the generalized Rutherford equation to study the combined dynamics. Van de Brand used this modeling to derive the requirements of the ITER NTM stabilization system [890].

Witvoet developed a control-oriented model for the sawtooth. This is based on the evolution of the current density profile, leading to varying magnetic shear at the $q = 1$ radius. If the magnetic shear exceeds a threshold, the profiles are reset to their starting condition. This model has been used to successfully tune SISO [891, 892], MISO [893] and adaptive [894] controllers and to test their performance.

Paley et al [895], Van Berkel et al [896] and van den Brand et al [897] developed advanced real time sawteeth period estimators.

A particular aspect of Witvoet's control-oriented sawtooth model is that it predicted strong non-linear response to modulated ECCD input, a phenomenon called locking [891]. The relevance of locking is that it allows for a very strong response of the plasma state to feed-forward waveforms. Witvoet and Lauret obtained corroborating experimental evidence for locking in the TCV tokamak [898]. Lauret described the sawtooth locking phenomenon with a simple model for the evolution of the magnetic shear. Lerche applied the concept of sawtooth locking on JET discharges using ICRH [899].

Lennholm did control and physics experiments in which the energetic ion population was varied by Ion Cyclotron Heating. Lennholm derived a control-oriented model for sawteeth with the destabilizing magnetic and stabilizing fast particle effects [900]. Alexandre Gomes (IST Lisbon) set-up a heuristic model for the fast particle generation and losses and interfaced this with Lennholm's sawtooth model. Gomes derived an adaptive controller for two actuators (ICRH and ECCD). The ICRH is used to pump destabilizing ion orbits at the inboard of the $q = 1$ surface while the ECCD acts on the magnetic shear.

#### 10.3.4. Edge dissipation control, radiation and plasma exhaust control.
ASDEX upgrade team tuned a PID controller to keep the radiation induced with nitrogen seeding in high performance H-modes in close proximity to the X-point while remaining detached. The sensing was done with real-time x-ray tomography [901].

MANTIS is a ten camera multi-imaging spectroscopy system that allows for the observation of a single field of view with multiple real-time cameras, while each camera has a different filter for line-radiation. The first MANTIS system was mounted on the TCV divertor. The TCV divertor area can be imaged in real-time, in different wavelengths [902].

Ravensbergen adapted the optical boundary recognition procedure from Hommen [854, 903, 904] to find fronts in the divertor region [905]. Assuming the CIII emission front as a proxy for detachment, Ravensbergen and van Berkel applied a system approach to identify the input output dynamics and derived a controller to position the radiation front in the TCV divertor in both L-mode and H-mode. Controllers were derived and successfully applied [906].

Recently, the control of the x-point radiator was improved by applying system identification [901]. Multi-input-multi output system identification was done to achieve simultaneous core density control as well as radiation front control in TCV [907].

#### 10.3.5. Break-down optimization.
Ravensbergen developed ILC for the gas introduction system in ITER [908] and shows that optimal feed-forward waveforms can be obtained for the breakdown and burn-through phase.

As a conclusion, we see a development towards state-controllers rather than output controllers. This is motivated by the need to deal with limits and constraints, as well as managing the complexity of the plasma by coordinated control and supervisory control.

All these methods rely on the availability of the complex plasma state, rather than a physics parameter. This motivates the development of state-observers, which are forward models (FMs) of the plasma dynamics interfaced with synthetic diagnostics.

### 10.4. Synthetic diagnostics and applications

#### 10.4.1. VSRS.
The VSRS is a passive optical diagnostic. Its primary purpose is to provide measurement data of the Bremsstrahlung continuum radiation in the visible light range. From this data, the line-averaged effective ion charge ($Z_{eff}$) can be determined, which in turn can provide information on the impurity content of the plasma. Also, $Z_{eff}$ is used to provide an early warning on HNB shine-through. In case of neutral beam shine-through a part of the beam power passes through the plasma and is deposited on the wall of the tokamak which may damage the wall.

Decreasing $Z_{eff}$ or $n_e$ in the plasma core increases the beam shine-through fraction. The back-up role of the VSRS
is therefore to provide a value for the line-averaged electron density, in case the designated diagnostic for electron density, the system for toroidal interferometry and polarimetry fails. The continuum emission measured by the VSRS scales with electron density squared $n_e^2$, square root of the electron temperature $T^{-1/2}$ and the effective ion charge $Z_{\text{eff}}$. In case of measurement failure of the former, the latter two are set at their current value and the VSRS is used to measure ne. This role is strictly meant to shut down the plasma in an orderly manner and not as a means to keep the experiment running.

The VSRS diagnostic collects line integrated data on a single line-of-sight that passes through the plasma from Equatorial Port #8 to Equatorial Port #3 at a height just above the midplane of the tokamak, corresponding to a height of about $Z = 0.60$ m measured from the mid-plane. Coincidentally, the VSRS line-of-sight also crosses the DNB in the core of the plasma. Therefore, also active exchange occurring in the beam at the cross section is measured. Both of these emission measurements are supplementary roles of the VSRS diagnostic. The first mirror, that forms the start of the line-of-sight, is positioned Equatorial Port #8 and at the other end in Equatorial Port #3, a viewing dump is located. The purpose of this viewing dump is to decrease the reflections from the divertor region of the tokamak that are measured by the VSRS. The functioning of the viewing dump plays an important role in achieving the main purpose of the VSRS. Both the first mirror and viewing dump are positioned relatively far behind the port plug in order to decrease reflections and damage from incoming particle fluxes. The viewing dump is visible from inside of the vessel through a hole in the port-plug and is encased in a cavity of which the final design is not yet determined.

A synthetic diagnostic for the VSRS has been developed in python. This model produces representative output of the diagnostic, in the form of emission spectra in the visible light range, using raytracing simulations. The raytracer module Raysect is used as a framework upon which the synthetic diagnostic is built, as it is used for the definition of geometry, light sources and detectors within the model. In order to use a plasma as light source and to allow for the implementation of other physics properties, Raysect is used in conjunction with the CHERAB spectroscopy modeling framework. Atomic Odata is provided by the ADAS database.

The synthetic diagnostic is developed such that VSRS spectra can be modeled see figure 176 based on plasma simulations stored in IMAS scenarios and used to investigate the functionality of the viewing dump of the VSRS diagnostic, for which use of the retroreflector of 55. FA, the DIP, is projected. It is main purpose is to decrease reflections of radiation on the inner vessel wall of ITER from the divertor region of the plasma. These reflections cloud the measurement results and should be suppressed.

The functionality of the viewing dump is determined in two representative cases see figure 177: a case with reflections, but without viewing dump and a case with reflections and with viewing dump. The information on the reflection sources is of major importance to the VSRS. The diagnostic should be able to measure small changes in the continuum radiation in the

<figure><img src="image_188.png" /><figcaption>Figure 176. Plasma model for core (left) ad edge (right) radiation.</figcaption></figure>

<figure><img src="image_189.png" /><figcaption>Figure 177. Modeled Bremsstrahlung spectrum for visible spectroscopy reference system with reflections without a viewing-dump (top figure) and with a viewing dump (bottom figure).</figcaption></figure>

core of the plasma. Reflections from the edge of the plasma can cloud this measurement and would make it almost impossible to know whether measured bremsstrahlung changes are caused by the core or the divertor. Separate simulations of these two areas of the plasma provide a positive result in this regard; only 0.39% of 2.34% reflections stem from the edge and divertor region while the majority comes from the core. This edge/divertor value is lower than the desired 1% overall accuracy for the VSRS Bremsstrahlung measurement and can therefore effectively be disregarded.

The impact of changing the reflectivity of the retroreflector surface is investigated see figure 178. It is discovered that
<figure><img src="image_190.png" /><figcaption>Figure 178. Effect of roughness on the viewing dump efficiency.</figcaption></figure>

a more mirror-like surface decreases the reflections, while a more ‘rough’ surface has negligible impact. Due to the small improvement, the standard DIP retroreflector does not require adaptation for the VSRS system.

The geometry of the enclosure in which the viewing dump is positioned is not set. The two most extreme case shapes are analyzed, a large box around the viewing dump and a cylinder that closely wraps viewing dump. The reflections are slightly decreased when using the cylinder shape, but it is questioned whether this slight impact warrants the increase in manufacturing complexity of this shape. The VSRS Synthetic diagnostic is currently too slow for real-time control and the model structure is not suited for a Kalman filtering approach.

### 10.4.2. RT analysis of magnetic signals for NTM suppression.
The poloidal magnetic field is measured by a system of high frequency multiple magnetic pick-up coils. These coils are used to measure the time resolved MHD perturbed poloidal component of the magnetic fields The individual pick-up coils are mounted on cooled mounts and distributed both poloidally and toroidally, as indicated in figures 179(a) and (b).

A model is set up of the dynamic magnetic fields due to rotating NTMs. The island width growth dynamics for w is modeled by the Modified Rutherford Equation (MRE), $\frac{\tau_r}{r_s} \frac{dw}{dt} = -r_s \Delta'_0 + r_s \Delta'_{BS} - r_s \Delta'_{CD}$, in which w is the island width, rs is the mode-rational surface, $\Delta'_0$, $\Delta'_{BS}$ and $\Delta'_{CD}$ are the contributions to the mode growth due to the nominal tearing mode stability, the Bootstrap current and the stabilizing non-inductive current drive from the Upper Port ECCD systems.

The MRE is coupled to the Lahaye equation for the island rotation frequency dynamics $\omega$ which is dependent on both w and $\omega$, $\frac{d\omega}{dt} = \frac{\omega_0}{\tau_{ED}} - \frac{\omega}{\tau_E} - \frac{1}{mC_w \tau_{A0}^2 \omega \tau_w} \left(\frac{w}{a}\right)^3$. Although this is very much a simplified representation, it provides a good basis for the synthetic HF pick-up coil diagnostic and a good test case for the unscented Kalman filter frequency tracker and the extremum seeking control (ESC) algorithm. In particular, it does not contain the effects of other MHD activity, such as the sawtooth instability or edge localized modes. As methods

<figure><img src="image_191.png" /><figcaption>Figure 179. (a) Poloidal and toroidal distribution of HF pick-up coils (b). For the analysis presented here, all coils have been modeled at a single toroidal location.</figcaption></figure>

have been discussed in the literature to filter spike-like disturbances from continuously varying signals, this omission was not expected to be a problem. Moreover, the MRE is well-studied and could therefore conveniently be extended with the efficiency maps for modulation and misalignment necessary for the ESC scheme. The parameters used in the NTM model can be validated and tuned to match the simulated NTM development, once ITER is operated experimentally.

Synthetic HF pick-up coil signals are generated by modeling the magnetic perturbation in the plasma as a result from the NTM dynamics using the following equation:

$$ \frac{dB}{dt}(r_{m,n}, \omega_{m,n}, \theta, \phi) = -\omega_{m,n} \tilde{b}_{\theta} \left(\frac{r_{m,n}}{r_c}\right)^{m+1} \sin\left(m\theta - \frac{mr_{m,n}}{R_0}\right) \times \left(\beta_{\theta} + \frac{l_i}{2} + 1\right) \sin(\theta) + n\phi + \omega_{m,n}t $$

These signals are used to test the unscented Kalman filter for frequency tracking (UKFFT). The UKFFT is an instantaneous, computationally inexpensive algorithm for signal property estimation. It is shown that the UKFFT algorithm is robust and able to track both synthetic and actual coil data. The output of the UKFFT are the frequency, the amplitude and the phase of the mode. Phase differences that have not been incorporated in the synthetic diagnostic could exist due to eddy currents in the metal structures surrounding the diagnostic. These should be experimentally determined and incorporated in the diagnostic afterwards. This would have acted as added noise to the UKFFT algorithm, which was synthetically applied in simulations.
<figure><img src="image_192.png" /><figcaption>**Figure 180.** Synthetic signals from NTM model with 10% white noise and 0.2 ms input delay, estimated with UKFFT. 10 ms to converge. Max. error $e_f < 3\%$ and $e_\theta < 1\%$, Expected noise level for HF pick-up coil in ITER as given in [698].</figcaption></figure>

The UKFFT algorithm has proven to have robust signal estimation capabilities with fast convergence ($<10$ ms) for both the synthetic and actual coil data, figure 180. When the algorithm is applied to the synthetic data, it shows strong performance with disturbances well over the ITER requirements (tracking achieved for signals with SNR of 10.45 dB and 12 mm measurement delay). The performance of the algorithm is for these reasons deemed satisfactory and could be useful for the tracking of harmonic signals found in other diagnostics as it is a computationally inexpensive method for signal property estimation.

The estimates from the UKFFT are utilized for the application of NTM suppression with ECCD. The ESC scheme is self-optimizing and does not rely on a model to achieve performance. The scheme is used to autonomously steer the ECCD to drive current at the optimal location in the plasma, which lies at the center of the magnetic island. Besides the misalignment, the ECCD modulation is successfully optimized as well.

The extremum-seeking control scheme applied here follows the approach applied in [906] and the references therein. An harmonic perturbation $y_p$ is mixed with the input of the controller. This leads to a variation of the cost function, which can be used to estimate the gradient in the cost-function, and the size and direction of the control action, see figure 181.

In the noise-less case, see figure 182, this scheme proved able to optimize both the modulation frequency and phase as well as the radial misalignment of the ECCD deposition. The scheme does not converge to the optimal modulation when subjected to ITER noise levels. The reason for this is that the scheme cannot distinguish the effect of the modulation from the added noise. Also, as the extremum-seeking control scheme only converges to a local minimum, convergence might fail in cases of too significant initial misalignment.

#### 10.4.3. Detachment diagnostics.
Reliable diagnostics that measure the detached state of the ITER divertor plasma will be necessary to adequately control heat flux to the ITER divertor targets during steady state operation. The feasibility of the ITER shunt diagnostic as a lightweight, robust, and real time detachment sensor has ne. The ITER shunt diagnostic is a set of shunt lead pairs affixed to the body of the ITER divertor cassette that measures the voltage drop along the CB.

This measurement is combined with impedance modeling of the divertor cassette assembly to calculate the current flowing through the divertor, which is equal to the current flowing through the plasma SOL. The relationship between the SOL current and the detached state of the divertor plasma is established using several SOLPS-ITER boundary simulation cases for control-relevant ITER plasma scenarios. Across all simulation data studied, there is a clear and significant decrease in thermoelectric current through the SOL coinciding with the onset of partial detachment at the outer divertor target. Preliminary electromagnetic modeling of a simplified divertor cassette assembly was set-up to develop a control-oriented resistance-inductance circuit model, from which SOL currents can be calculated given shunt pair voltage measurements. The reliability of this model-based approach is then verified. The sensitivity and frequency-response of the resulting system to evaluate the availability of the diagnostic system is determined. Due to modeling limitations, we conclude that physical impedance measurements of the ITER divertor cassette are necessary to calculate accurate SOL current values from divertor shunt measurements. Given these measurements, combined with further development of time dependent SOL plasma simulations and inclusion of future SOLPS-ITER data, the ITER shunt diagnostic will adequately reconstruct the detached state of the divertor plasma for steady-state control purposes [29].
<figure><img src="image_193.png" /><figcaption>**Figure 181.** The added perturbation $y_p$ induces a perturbation of the cost function (w), from which the unbiased signal is extracted by applying a second-order high-pass filter. The filtered cost function output $J_f$ is multiplied by the perturbation signal for these signals. The gradient is obtained using a moving average.</figcaption></figure>

<figure><img src="image_194.png" /><figcaption>**Figure 182.** Noiseless case. The UKFFT extracts successfully the phase, amplitude and frequency of the NTM. The power deposition and modulation of the ECCD system are varied to estimate the gradient of the cost function and suppress the NTM.</figcaption></figure>
<figure><img src="image_195.png" /><figcaption>**Figure 183.** Dynamic state observer using multiple diagnostics on ITER, including real-time Thomson scattering. The top box presents the time evolution of the core density. The predicted density is wrong in terms of absolute value and does not correlate with the reference (green), while the state estimation follows the reference very well. The middle box shows the discrepancy between the reference and the estimated value. After an initial discrepancy of ~15%, the discrepancy decreases to ~3%. The bottom box shows the estimate of the density distribution at three instances. The inclusion of Thomson scattering profile yields very good estimates, including the pedestal.</figcaption></figure>

**10.4.4. Density distribution control.** Initial ITPA diagnostic focused on the control of the line-integrated density with interpretation of the interferometry. Recently, the control of the density distribution has been extended in two ways. First, a multi sensor Kalman state estimator was developed which also includes real time TS. Simulations show that high quality density profile estimation can be achieved with this Estimator, see figure 183.

Second, an ITER relevant robust MPC is developed as a strategy to regulate the density profile while avoiding limits associated with the total density (Greenwald limit) or gradients in the density distribution (e.g. neoclassical impurity transport). Simulations show the controller is capable of regulating the distribution as desired, including the observation of the limits [909].

**10.5. Summary and conclusions**

For the systematic development of the various controllers taking the various couplings into account, a model-based controller design is required. An activity has been started within the ITPA diagnostics group to provide the synthetic diagnostic needed for the design of diagnostics, the optimal interpretation of the physics experiments and for real time control.

After giving a rudimentary introduction in systems and control theory and an overview how control engineering has been

applied to nuclear fusion plasma research and operation, it is shown how sensor models or synthetic diagnostics are used in model based controller synthesis.

A plasma and synthetic diagnostic have been set-up for the VSRS have been set-up, and used for the design optimization of the viewing dump.

A synthetic diagnostic of a section of high frequency pick-up coils for MHD characterization. The signals of these coils can be interpreted using an UKFFT to estimate the frequency, amplitude and phase of a rotating NTM. The UKFFT can be interfaced to an extremum seeking controller to optimize the radial deposition, the modulation frequency and phase. In the noiseless case, this approach works for the deposition, phase and frequency. In case of realistic noise, the gradients in the cost function for the phase are shown to be too shallow for convergence.

An robust MPC has been developed for control of the density distribution with gas feed and pellet injection as actuators, taking limits and constraints into account. This scheme relies on a Kalman filter for the real-time estimation of the density profile. The addition of the TS data in the Kalman filter gives fast and very good convergence.

A synthetic diagnostic has been set up for the divertor shunts and tested numerically.

As we have seen from e.g. the observer for the density, the requirements of the presented models for control and
observation are not very stringent in accuracy. It is critical
that the model formulation is such that it can be cast into the
Kalman observation framework. Then the real-time constrain-
ing of the model by multiple measurements will ensure con-
vergence. In this context, a key requirement is that the models
are tractable, and can be evaluated on timescales that are faster
than the dynamics that needs to be controlled. For physics
interpretation or diagnostic design, the fidelity-requirements
of the models are more stringent.

10.6. Outlook

The development of synthetic diagnostics for real time control
will be further pursued. Focus will be put on the diagnostics
needed for 1st plasma. Special attention will be put on the real
time estimation of the pellet fueling efficiency, the optimal
control of the density distribution and the impurity transport.
Finally, we will focus on data integration aspects. Multiple
diagnostics with similar outputs need to be integrated. The
associated control capabilities and robustness against failure,
degradation, and limitations due to long pulses need to be
assessed. The real-time WG has just started an effort to set-up
an Multi-Domain Matrix of the elements of the control sys-
tem, including the plasma. This approach will be pursued to
model the structure of the control system including aspects of
real-time sensor or actuator failure and the real-time diagnosis
thereof.

11. Integrated data analysis and validation

R. Fischer⁴⁶, A. Bock⁴⁶, S. S. Denk⁴⁷, A. Medvedeva⁴⁸,
M. Salewski⁴⁴⁹, M. Schneider² and D. Stieglitz⁴⁶

11.1. Introduction

In present and future fusion devices huge amounts of meas-
urements coming from many diagnostic systems have to be
analyzed. The information obtained from these measurements
are and will be used for machine control and safety as well as
for physics studies. The goal of the IDA method is to integ-
rate measured data and their analyses to optimize informa-
tion available for plasma operation and physics studies. The
measured data from diagnostics providing redundant or com-
plementary information are combined, together with available
physics knowledge and modeling information within a prob-
abilistic framework.

The IDAV specialist WG within the ITPA diagnostics TG
was founded in the year 2020. It was motivated by the useful-
ness of IDA applications at present day machines [910–922].
The goal of the IDAV specialist WG is to provide and apply an
IDA framework for present and next generation fusion devices
such as ITER and DEMO for self-consistent data analysis and
validation procedures.

A comparison of the concept of IDA with a traditional
approach for data analysis, based on the analysis of individual
diagnostics data and a subsequent combination of the results,
can be found in [923].

IDA in the framework of Bayesian probability theory (BPT) provides a concept to analyze a coherent combination of measured data from heterogeneous diagnostics and to combine them with physics knowledge and modeling information [924]. Since every piece of information from measurements and modeling are subject to uncertainties, quantification and processing of uncertain information is central to this probabilistic approach. Complex error propagation is obtained automatically combining data in a concise probabilistic one-step analysis. The extended set of measurements and modeling information allows for an improved treatment of ill-posed inversion problems of, e.g. profile reconstruction, tomography or equilibrium reconstruction. Different techniques for measuring the same subset of physical parameters provide complementary and redundant data for, e.g. improving the reliability of physical parameters, increasing the spatial and temporal resolution of profiles, resolving data inconsistencies, and for reducing the ambiguity of parameters to be estimated without employing non-physical constraints.

IDA was developed and first applied to reconstruct elec-
tron density n<sub>e</sub> and temperature T<sub>e</sub> profiles from a probabil-
istic analysis of Thomson scattering (TS) data [925] in com-
bination with interferometry and SXR measurements at the
W7-AS stellarator [910]. A corresponding application at the
ASDEX Upgrade tokamak includes additionally to the TS and
interferometry data also data from ECE and the lithium beam
(LIB) diagnostic for which an improved FM was developed
[914, 926]. This LIB FM was additionally used in a prob-
abilistic analysis of the JET LIB diagnostic [913]. At W7-
AS, Bayesian graphical models were introduced for integ-
rating diagnostic data analyses [927]. IDA was then applied
at ASDEX Upgrade to reconstruct the effective ion charge
Z<sub>eff</sub> profiles from various CXRS measurements [915]. A non-
Maxwellian electron energy distribution function in the pos-
itive column of a neon dc-discharge was reconstructed from
the visible emission spectrum using IDA [911]. At JET the
Bayesian combined analysis of LIDAR, edge LIDAR and
interferometry diagnostics provided n<sub>e</sub> and T<sub>e</sub> profiles [912].
At the TJ-II stellarator the n<sub>e</sub> profile was reconstructed in an
IDA approach using data from interferometry, reflectometry,
TS, and the helium beam [916]. At the Madison symmetric
torus (MST) reversed field pinch (RFP) the T<sub>e</sub> profiles were
estimated in the probabilistic framework from a combination
of the double-foil SXR system and the TS diagnostic [917].
Additionally, at the MST RFP Z<sub>eff</sub> profiles were determined
by the integration of SXR tomography and CXRS impurity
density measurements [918]. The ion temperature T<sub>i</sub> and rota-
tion profiles v<sub>rot</sub> were reconstructed at ASDEX Upgrade in a
probabilistic integrated approach from various CXRS meas-
urements using Gaussian process regression [920]. Recent
Bayesian analyses combining various diagnostics can be found
at W7-X [921, 923], at ASDEX Upgrade and JET [919], and
the MST RFP [928].

The present paper aims at showing the basic ingredients of
IDA in the Bayesian framework, reviewing the work previ-
ously done, and some examples highlighting typical realiza-
tions. More details of the implementation of IDA can be found
in publications which are cited as appropriate. The references
<figure><img src="image_196.png" /><figcaption>**Figure 184.** Simplified flow-charts for typical data analysis steps inferring electron temperature $T_e$ and density $n_e$ profiles for magnetic confinement fusion experiments from the Thomson scattering and electron cyclotron emission (ECE) diagnostics in (a) a conventional approach and (b) within the IDA concept.</figcaption></figure>

in this paper cannot be exhaustive as they should only provide an entrance point for the interested reader.

Section 11.2 compares IDA with a conventional data analysis approach for multiple-diagnostic data analysis and summarizes the main ingredients of IDA: BPT (section 11.2.1), FMs (11.2.2), uncertainty quantification (11.2.3), likelihoods (11.2.4), prior information (11.2.5), parameterization (11.2.6), methods for parameter and uncertainty estimation (11.2.7), validation (11.2.8) and numerical implementation (11.2.9). Section 11.3 addresses the ITER IMAS for physics modeling and data analysis as a standardized way to access and process data. Section 11.4 shows examples applying IDA to obtain synergistic effects (11.4.1), profile reconstruction (11.4.2), equilibrium reconstruction (11.4.3) and velocity-space tomography (11.4.4). Section 11.5 summarizes.

## 11.2. IDA

The IDA approach in the framework of BPT is conceptually different from an often used sequential (conventional) data analysis approach. Frequently, due to the large amount of diagnostics available at fusion devices, in conventional data analysis the individual diagnostics are analyzed by the responsible diagnosticians familiar with the hardware, physics and analysis details (figure 184(a)). To obtain a unique (linked) result the various results of the heterogeneous diagnostics are mapped on a common, typically magnetic, coordinate system and fitted with a joint parameter set. Often the analysis of the single diagnostics are augmented with additional information to regularize ill-posed inversion problems and obtain, e.g. smooth and well-defined results. The linked result might then be used as input for the equilibrium (mapping) estimation, the analysis of other diagnostics or for result validation and consistency checks.

Various challenges of this conventional approach arise from the parametric entanglements involved. In this iterative procedure it might be difficult to obtain a (self-)consistent result, in particular if many diagnostics are involved as is the case for present and future fusion devices. An automation of this analysis chain is challenging if a huge amount of data has to be analyzed. The propagation of information between diagnostics might be incomplete if single estimates from one diagnostic are used as input for other diagnostics, neglecting complex parameter interdependencies. Error propagation is frequently neglected, resulting in an underestimation of the estimation uncertainties. Data and result validation and overall consistency checks between coupled diagnostics might be a non-trivial task because a quantitative and unified description and processing of statistical and systematic uncertainties is missing. Furthermore, often backward inversion techniques are used which might be prone to noise fitting or numerical instabilities necessary to be regularized by additional constraints or data binning. The estimated parameters (linked result) and their uncertainties often miss a description of the non-linear dependencies.

These difficulties are resolved by the IDA approach using a probabilistic combination of different diagnostics (figure 184(b)). The scheme starts with a complete set of physical parameters (section 11.2.6), as a function of a common coordinate system, which is sufficient to describe all diagnostics data. Only forward modeling is used which allows one to evaluate the diagnostics data given the parameters of interest (11.2.2). Forward modeling is known to be numerically stable. The measured data of a diagnostic is compared to the forward modeled data with a likelihood probability distribution function (pdf) (11.2.4) describing the distribution of the data uncertainties (11.2.3). Additional physical information and its uncertainty can readily be integrated with a
probabilistic description and is used only once in the analysis of the combined set of diagnostics (11.2.5). Systematic effects are described with nuisance parameters. Their uncertainties are quantified with probability distributions. The nuisance parameters are integrated out (marginalized) such that the uncertainty in these parameters propagate to the uncertainty of the parameters of interest. Uncertain nuisance parameters can arise from calibration constants, atomic data, or quantification of systematic effects which are candidates for diagnostic inconsistencies. Quantification of inconsistency effects might help to resolve the reason for diverging diagnostics results. Finally, the result of the Bayesian approach is a multidimensional probability distribution which quantifies how reliable a certain set of parameter values is in the light of all measured data and the additional information provided (11.2.1). This posterior probability distribution includes all parameter interdependencies. Low-dimensional properties of this posterior pdf allows for estimating the parameters (maximum or mean), their dependencies (covariance) and their uncertainties (variance) (11.2.7).

### 11.2.1. BPT.
The interpretative and numerical framework of IDA is given by BPT. BPT provides a unique interpretation of probability as a measure of uncertainty and rules to combine and process (uncertain) information. Uncertainty in the Bayesian framework is lack of knowledge. An introduction to Bayesian inference and further references can be found in [929]. Measured data as well as most information used to describe the measured data or constrain the parameter space of interest suffer from uncertainties. Therefore, a unique framework to handle any kind of uncertainty is mandatory if different sources of information have to be analyzed jointly. An overview of various types of uncertainties encompassed by BPT is given in section 11.2.3.

Additional to the unique quantification of information and its uncertainty, BPT provides rules to combine and process information. Bayes' theorem in its most reduced form relates the posterior pdf $p(f|d)$ for the parameters of interest $f$ given the data $d$ with the likelihood pdf $p(d|f)$, the prior pdf $p(f)$ and the evidence $p(d)$:

$$p(f|d) = \frac{p(d|f) \times p(f)}{p(d)} \qquad (11.1)$$

$p(A|B)$ means probability that A is true given (assuming) B is true. The power of Bayes' formula is that it provides what we actually want to know from what the FM by themselves can produce. The likelihood pdf with the FM of the measured data provide the probability of the measurement data, given the parameters of interest, $p(d|f)$. But we actually want to know the probability (reliability) of the parameters of interest, given the diagnostic data, $p(f|d)$.

The Bayesian scheme can be expanded by taking the product of all likelihood pdfs describing all diagnostic measurements and prior pdfs describing any kind of additional physical information used. Therefore, the likelihood $p(d|f)$ in the IDA framework consists of the product of the likelihoods of the various diagnostic data to be analyzed jointly,

$p(d|f) = \prod_k (p_k d_k | f)$, where the data of diagnostic $k$, $d_k$, are described with the likelihood $p_k(d_k|f)$. The functional form of a likelihood pdf depends on the uncertainty distribution of the measured data and might differ for the various diagnostics (see section 11.2.3.1). As a likelihood pdf describes the probability of measuring a certain data value assuming one knows the underlying physics, the likelihood links the measured data with a FM of the measurement process $D_k(f)$ (2.2), which typically also varies for the heterogeneous diagnostics. The likelihood for each diagnostic, $p_k(d_k|f)$, is typically a product of likelihoods of the measured data points if the data uncertainties are uncorrelated or a multi-dimensional likelihood if the uncertainties are correlated.

The prior pdf, $p(f)$, describes what we know about the parameter of interest independent of the measurements. Typical information to be encoded in the prior are non-negativity constraints for, e.g. temperature and density, monotonicity constraints, smoothness constraints, constraints from physics modeling such as for profile gradients. More examples for useful prior information can be found in the velocity-space tomography section 11.4.4.3.

### 11.2.2. FMs.
A FM evaluates synthetic data to be compared with the measured data within the likelihood pdf. Various fidelity levels of FMs for a diagnostic might be available for various purposes. High-fidelity FMs are typically used for post-plasma analysis where the most reliable results are aimed at. For post-plasma analyses numerical resources and time restrictions are less crucial. Low-fidelity FMs are typically used for time critical applications as real-time analyses or if numerical resources are limited. An example for a low-fidelity FM is given by ECE analyses where optically thick thermal plasmas are assumed. For optically thick plasmas black-body radiation can be assumed which results in a radiation temperature which equals the electron temperature, $T_{rad} = T_e$. This ECE FM belongs to one of the simplest FMs where the parameter of interest, here $T_e$, is proportional to the measured intensity. A high-fidelity ECE FM is given by solving the radiation transport equation [930, 931]. An implementation of the radiation transport FM can be found in the ECRad code [931]. The ECRad FM is capable of analyzing optically thin plasmas with broadened EC emission regions due to high temperatures, as expected for ITER, or due to low-density scenarios. Additionally, it is capable to describe oblique ECE measurements, harmonic overlap, different polarizations and emission from non-thermal electron energy distribution functions [932]. For the analysis of ECE data with this sophisticated model electron density $n_e$ profiles are necessary. Therefore, a combination of the ECE diagnostic with density diagnostics, e.g. Thomson scattering or interferometry, within an IDA framework is mandatory.

Another example for a multiple-fidelity FM is given by CXRS. Frequently, ion quantities as ion temperature $T_i$ and rotation velocity are pre-evaluated and available from databases. These data allow for low-fidelity FMs as the parameter of interest, a profile of the ion parameter, can easily be evaluated at the measurement positions. Ideally, the database
provides also information about the uncertainties of the measured values. A high-fidelity FM for CXRS data describes directly the measured spectra [933]. Although numerically more expensive, this high-fidelity FM would allow to incorporate nuisance parameters describing, e.g. uncertainties in calibration quantities or in the atomic data [911].

The preparation of a FM and its combination with other diagnostics FMs in a probabilistic framework is typically less challenging than developing and combining inversion techniques which additionally might suffer from noise fitting or numerical instabilities as for, e.g. Abel inversion techniques. An example of a multiple-purpose FM for velocity-space tomography (weight function) can be found in section 11.4.4.

### 11.2.3. Uncertainty quantification.
Uncertainties in the Bayesian framework are interpreted as lack of knowledge covering any type of uncertainty. Statistical uncertainties are distinguished from systematic uncertainties which, in contrast to statistical uncertainties, cannot be reduced by increasing the data sample. As the results of data analysis depend critically on the uncertainties associated with the data, the quantification of uncertainties of measured data (likelihood) and of additional information (prior) is a major part of a parameter estimation problem. Uncertainties determine the absolute amount of information available and determine the weight of measurements of various diagnostics and prior information relative to each other. Especially for the detection and resolution of inconsistent measurements, uncertainties play a major role as consistency is obtained if all data and prior information are reasonably well described within their uncertainties. Details about the interpretation and definition of uncertainties can be found in *Evaluation of measurement data—Guide to the expression of uncertainty in measurement (GUM)* [934].

#### 11.2.3.1. Uncertainties in measured data.
Statistical measurement noise is always quantified with the likelihood pdf (section 11.2.4). A systematic measurement uncertainty is typically described with a prior pdf (2.3.2). For example, a calibration uncertainty can be quantified with a prior pdf on a calibration nuisance parameter. In special cases this systematic uncertainty can be propagated to the likelihood pdf (see (11.2.4) and [925]).

The distribution of measurement noise is frequently described with a standard deviation. Higher moments are often neglected. This defines the use of a multivariate Gaussian distribution suitable for normally distributed measurement errors. Depending on the measurement scheme other distributions such as the Poisson distribution for counting measurements might be suitable. The measurement uncertainty of the lithium beam diagnostic at ASDEX Upgrade was estimated by assuming a Poisson distribution for the photon counts with unknown offset and amplification factor of the measured signal [926]. In case of unknown measurement uncertainties, contributions to the measurement with unknown source or contributions not described in the FM, or in case of data failure, robust estimation techniques are mandatory as described in (11.2.4).

#### 11.2.3.2. Uncertainties in physics models.
FMs describing measured data or physical models providing prior knowledge to constrain the parameter space frequently are not exactly known and are, therefore, subject to uncertainties. Typical uncertainties arise from uncertainties in calibration ‘constants’ from calibration measurements, from degrading effect of, e.g. optical components or glass fibers, or from atomic data which themselves are determined by measurements or uncertain modeling. An example for this is given in section 11.4.4.4 for uncertainties in the FM (weight matrix) for the velocity-space tomography.

Such systematic uncertainties are tackled in the Bayesian framework by nuisance parameters which describe the variability of the model due to the unknown systematic effect. The uncertainty of the nuisance parameters are quantified with prior distributions and marginalized (integrated out). This way the uncertainty of the nuisance parameter propagates into the uncertainty of the parameter of interest. A systematic (bias) uncertainty might arise due to uncertainties in the prior information as, e.g. the functional form and weight of the regularization term (see section 11.4.4.4).

#### 11.2.3.3. Uncertainties in estimated quantities.
Uncertainties in estimated quantities should describe the reliability with which parameters can be inferred from measured data and modeling information. These uncertainties arise due to statistical and systematic measurement uncertainties, uncertainties in the FM and uncertainties in the prior information used. Various methods for uncertainty estimation exist which are summarized in section (11.2.7).

#### 11.2.4. Likelihoods.
The likelihood pdf quantifies the probability of measuring a certain data set given the FM which links the parameters of interest and the measured quantity. Since the probability of measuring certain data is closely related to the measurement uncertainties, the likelihood quantifies the uncertainty distribution of the data. The most often used likelihood is given by the Gaussian pdf with the familiar $\chi^2$-misfit between the data d and the forward modeled data D(f)

$$p(d|f) \propto \exp\{-\chi^2/2\} \\ \chi^2 = \sum_i \chi_i^2 = \sum_i (d_i - D_i)^2 / \sigma_i^2 \quad (11.2)$$

given here in its most simplified version. The use of the Gaussian likelihood is justified for normally distributed measurement errors $\in$ with variance $\langle\epsilon^2\rangle = \sigma^2$ and mean error $\langle\epsilon\rangle = 0$. Frequently only the measurement uncertainty describing the statistical distribution of the measurement error is considered. The Bayesian interpretation of measurement uncertainties additionally comprises systematic uncertainties from, e.g. calibration or modeling uncertainties which can be considered in the likelihood pdf in special cases. An example of the use of the Gaussian likelihood with an extended interpretation of the uncertainty can be found in the analysis of Thomson scattering data measured at the stellarator
<figure><img src="image_197.png" /><figcaption>Figure 185. Comparison of a Gaussian with a Cauchy distribution appropriate for outlier robust estimation.</figcaption></figure>

Wendelstein 7-AS, see subchapter 8. The statistical uncertainties of the TS data are augmented with the uncertainties of the background-estimation data, the uncertainty of the calibration measurement, uncertainties of physical model parameters and uncertainties of measured nuisance parameters. A sensitivity analysis of the uncertainties and model parameters allows for finding the crucial uncertainties which have most impact on the diagnostic performance [925].

If measurements suffer from outliers, e.g. due to unspecified uncertainties, measurement failure or physical contributions not included in the FM, an outlier robust likelihood is recommended. The Student's t-distribution treats outliers leniently due to its heavy tails [935]

$$p(d|f) \propto \prod_i / \{a + \chi_i^2 2\}^{-(a+1/2)}. \quad (11.3)$$

The Cauchy pdf is obtained for $a = 1/2$ and the Gaussian pdf in the limit of $a \to \infty$. The heavy tails give outlying data less weight in the fitting process than the Gaussian pdf (figure 185). The Student's t-distribution can also be used if the standard deviation of the uncertainty is not known [935]. The parameter $a$ of the Student's t-distribution allows one to select the weights of the wing, and therefore the weight outlying data have in the fitting process.

This outlier robust likelihood is used routinely at ASDEX Upgrade for estimating electron temperature and density profiles in the IDA framework [914]. Examples for outlying data are given in the following examples: Fringe jumps in interferometry measurements, remaining after a fringe-jump correction procedure, typically occur for rapid density changes due to, e.g. pellet injection or signal cross-over due to ICRH. ECE data might be deteriorated, e.g. from cut-off, non-thermal electron distributions or harmonic overlay when not described properly by the standard black-body radiation assumption or the more sophisticated radiation transport modeling [930–932, 936]. Thomson scattering data might be affected by non-Gaussian calibration uncertainties, low SNR especially at the

low-density edge of the plasma, or by transient events such as filaments which are resolved in the TS diagnostic, which typically has a temporal resolution of about 20 ns, and which are not resolved with other diagnostics. Lithium beam data might be deteriorated by beam drifts typically not covered by the calibration procedure performed after a plasma discharge, local filaments not measured simultaneously at the positions of the interferometry or TS channels, or background subtraction uncertainties due to frequent events (ELMs) during the beam-off phases [926]. The emission profile of the thermal helium beam data is typically located at the plasma edge with low SNR at the far scrape-off-layer with low density and temperature values and within the separatrix where the neutral helium beam diminishes due to ionization [937]. This low SNR in the intensities easily produces outlying data in the line-ratio data when the denominator comes close to zero destroying any Gaussian assumption about the error distribution.

11.2.5. Prior information. The Bayesian approach allows to combine measured data from multiple diagnostics with additional information from physical considerations. In the Bayesian terminology the data independent information and its uncertainty/reliability is quantified with the prior pdfs.

Ubiquitous in profile or tomographic reconstruction is the assumptions of some degree of smoothness, non-negativity or monotonicity. Smoothness constraints are typically applied using Tikhonov regularization. Most often Tikhonov regularization is used to penalize the amplitude (zeroth-order), gradient (first-order) or curvature (second-order) of distributions. An example for Tikhonov regularization can be found in section 11.4.4 with velocity-space tomography.

Non-negativity constraints are less frequently applied due to its degrading performance in the optimization steps. Nevertheless, optimization routines for estimating best fitting parameters providing boundary constraints are available although at the expense of increased computation time. An example for the use of a non-negativity constraint can be found