Core ion measurements with collective Thomson scattering for DEMO burn control

DEMO burn control will require measurements of a range of plasma parameters, but the suite of feasible diagnostics for this purpose is limited. Here we assess the accuracy with which a collective Thomson scattering (CTS) diagnostic can provide key measurements for burn control in the planned European DEMO (EU-DEMO). This is based on estimated signal-to-noise ratios for a conceptual diagnostic design and trial fits to synthetic DEMO CTS spectra. We show that a diagnostic with a single probe- and receiver beam setup will be able to provide simultaneous measurements of core fusion alpha density and ion temperature to mean accuracies better than 5% and 10%, respectively, along with detecting intrinsic toroidal rotation velocities down to within ∼5 km s−1. Adding a second CTS receiver view furthermore enables inference of the core fuel-ion ratio, allowing discrimination between, e.g. a 50%/50% and 55%/45% D/T mixture, while also providing useful information on the thermalized He content. A DEMO CTS diagnostic would thus be able to monitor fusion alpha densities as well as anomalous transport of fast alphas and heat from the plasma core, quantify plasma rotation for confinement enhancement, and track the core isotope mix for optimum fusion performance. This versatility makes such a diagnostic a potentially valuable tool for real-time burn control on DEMO.


Introduction
As the next step beyond ITER, the purpose of DEMO will be to demonstrate the technology of a fusion reactor and the viability of nuclear fusion to deliver power to the grid.DEMO will therefore not represent a research device but will nevertheless require a carefully selected set of diagnostics for burning plasma control and machine protection [1].Measurements needed for basic burn control in DEMO are expected to include core ion density, ion temperature, and core isotope mix (D/T ratio), along with toroidal plasma rotation for MHD stabilization and confinement enhancement, and alpha particle velocity distribution functions for monitoring the fusion alpha heating and to identify any anomalous fast alpha losses [1][2][3][4].
Collective Thomson scattering (CTS) represents a versatile diagnostic that can potentially deliver all these measurements, also under reactor-relevant conditions [5].The conceptual feasibility of such a diagnostic at the European DEMO (EU-DEMO, hereafter DEMO for short) has already been demonstrated [6,7], with measurement scope and solutions for possible integration in DEMO discussed in [7].Furthermore, the capability of CTS to measure, e.g.fast-ion properties at reactor-relevant densities has been experimentally verified [8].
For a DEMO CTS diagnostic, a wide range of plasma measurements are being considered, including the above quantities as well as the core impurity content such as that of thermalized He ('He ash').
Here we discuss the physics basis and potential measurement capabilities of a CTS diagnostic at DEMO, significantly expanding on the results initially presented in [6,7].The aim is to assess the prospects for constraining relevant DEMO plasma parameters with CTS, and to quantify the expected accuracy on the measurements.This represents an initial exploration of the ability of a conceptual diagnostic setup to provide key measurements for DEMO burn control.It should not, however, be seen as a full performance assessment of a finalized diagnostic design.Focus is on measurements of the parameters mentioned above, in order to allow fusion performance estimates (via the core alpha density n α ), monitor the core ion heating (T i ), track the core fuel-ion ratio for optimum fusion performance, and quantify the toroidal rotation velocity v i .The latter will potentially be an operational parameter in DEMO, where operation without the detrimental impact of edge-localized modes will be essential, and confinement regimes such as quiescent H-mode, I-mode, or negative triangularity L-mode are consequently being considered [9,10].This may require a certain level of plasma rotation [11] as supplied by auxiliary torque input from heating systems.
This paper is organized as follows.In section 2, we outline the methods and assumptions underlying our analysis, including calculation of synthetic DEMO CTS signals and diagnostic background levels.Section 3 presents the results of inverting synthetic CTS spectra in terms of the predicted accuracy on relevant measurement parameters.We discuss these results in section 4 in the frame of requirements for DEMO operation and control, followed by our conclusions and outlook in section 5.
A general discussion of the principle of CTS and its capabilities for thermal-and fast-ion measurements can be found in, e.g.[5].

Methods
The recent demonstration of the feasibility of a CTS diagnostic at DEMO [6,7] has two main conclusions of relevance here.First, a diagnostic operating in O-mode and utilizing the planned 170 GHz electron cyclotron heating infrastructure (including in-vessel transmission lines and using one of the 170 GHz heating gyrotrons as a CTS probe source), would not be feasible, mainly owing to low resulting signal-to-noise ratios.Instead, detailed frequency and polarization scans suggest that an independent diagnostic operating at 60 GHz in X-mode would represent the optimum solution for a DEMO CTS diagnostic.This frequency is also the one adopted for the ITER CTS system [12], as was first proposed by [13].It avoids plasma cutoffs while representing a compromise between increased diagnostic background noise at higher frequencies and sensitivity of the diagnostic beams to refraction at lower ones.
A second result is related to the current measurement scope of the diagnostic, which involves the ability to contribute to measurements of both bulk-ion rotation velocity and fuel-ion ratio.This can only be achieved using two receiver geometries or movable steering mirrors for the gyrotron probe and a single receiver.The former option, with a fixed probe beam orientation and two receivers, can indeed be integrated in DEMO using front-end mirrors installed in an equatorial port plug [7].Raytracing-based geometry scans show that this can allow spatially localized measurements in the plasma core with projection angles of 76 • and 88 • to the magnetic field B, respectively, and provide sensitivity to both the above parameters.Based on these findings, we focus here on exploring the measurement performance of such a diagnostic incarnation.

Plasma scenario and raytracing
Our analysis is based on the DEMO 2019 Baseline plasma scenario, with parameters resulting from ASTRA simulations of a quiescent H-mode discharge.The scenario is broadly similar to the specifications underlying the EU-DEMO 'G1 baseline' machine configuration, with vacuum toroidal field on-axis of B t,0 = 5.74 T, a geometric axis at R = 8.94 m, plasma current I p = 18.2 MA, safety factor q 95 = 3.9, core fusion α density n α,0 = 4.2 × 10 18 m −3 , projected fusion power P fus = 1870 MW, and energy confinement time τ E = 2.6 s [10,14].
The ASTRA magnetic equilibrium extends to only just beyond the separatrix, so for the purposes of predicting the paths of CTS probe and receiver beams into and out of the plasma, a CREATE [15] magnetic flux distribution extending beyond the location of the poloidal field coils was superimposed on the ASTRA one.While this merged equilibrium comes with the caveat that the two individual equilibria are not necessarily fully consistent within the separatrix, this dataset is usable for the purpose of this study.The normalized poloidal flux grid and the associated relevant kinetic plasma profiles are shown in figure 1.For the purposes of raytracing, the electron density has here been extrapolated beyond the separatrix using a modified hyperbolic tangent function [16].The relevance of the q-profile will be discussed in section 4.
As mentioned, two possible scattering geometries for core measurements have been considered at this conceptual stage of DEMO CTS development: A geometry with a projection angle of ϕ ≈ 76 • to the magnetic field ('Geometry 1' in the following), and one with ϕ ≈ 88 • ('Geometry 2'), see also [6,7].Both result from microwave raytracing in the adopted DEMO equilibrium [6] using Warmray, which includes effects of relativistic electrons on the plasma refractive index [17][18][19][20].This is of particular relevance for DEMO plasma conditions, in which 13% of the thermalized electrons in the core (T e ≈ 40 keV) will have velocities v ≳ 0.5c.Geometry 1, illustrated in figure 1(c), is sensitive to bulk-and fast-ion parameters including toroidal rotation velocity, while Geometry 2 can provide measurements of the fuel-ion ratio n T /n D and He ash content n He4 /n e in addition to T i .Possible solutions for realizing these (or very similar) scattering geometries and for The q-profile has been multiplied by a factor of five for improved visibility.(c) Results of raytracing for our conceptual scattering geometry with ϕ = 76 • in a poloidal cross section of DEMO, overlayed on contours of ρ.The injected gyrotron beam with wave vector k i is shown in blue, and the receiver view with scattered wave vector k s in red.The yellow ellipsoid represents the resulting CTS overlap (measurement) volume.integrating them in DEMO are discussed in more detail in [7].
Here we focus on the corresponding measurement performance, which will vary only slightly for different configurations with similar values of ϕ.Table 1 summarizes the salient features of the two scattering geometries, based on assuming similar probe and receiver beam widths as adopted for ITER CTS.Here ϕ = ∠(k δ , B), θ = ∠(k i , k s ), and ψ = ∠(k i × B, k s × B) represent the scattering angles defined in terms of the plasma fluctuation wave vector k δ = k s − k i resolved by CTS and by the incoming and scattered wave vectors k i and k s representing the probe and receiver beams, respectively, in the scattering volume.Conceptual illustrations of these angles and the resulting overlap volume can be found in, e.g.[21].The CTS overlap factor O b in table 1 represents the volume integral of the product of the intensity distributions of incident and received microwave beams.Also listed is the central measurement location in cylindrical coordinates (R, z) and in the poloidal flux coordinate ρ, along with the spatial extent of the measurement volume in terms of the radial coordinate R and relative to the DEMO minor radius of a = 2.88 m.Neither mirror locations nor beam characteristics have here been optimized for spatial resolution, so the value of ∆R in table 1 is only indicative of that of a more mature diagnostic design.
Here we will focus primarily on Geometry 1, with discussion of Geometry 2 limited to a few special cases.We use a fully electromagnetic model of the collective scattering to generate synthetic CTS spectra in the two geometries.This assumes the plasma profiles provided with the 2019 Baseline equilibrium illustrated in figure 1, which includes thermalized D, T, and 4 He, fusion-born fast alphas, and 'impurities' in the form of H and 3 He from D-D fusion as well as Ar and Xe from impurity seeding.Since no fast-ion distribution functions are included with the equilibrium, we assume the fusion alphas to follow a classical slowing-down distribution, isotropic in velocity space (see also [22]).For simplicity, H and 3 He are assumed to be thermalized at the bulk ion temperature.Since their combined core density is only ~4% of that of the fast alphas, they anyway represent a negligible contribution to the total CTS signal from non-thermal ions.
No information on net toroidal plasma rotation v i is available in the adopted equilibrium, nor is any heating or current drive from neutral beam injection (NBI) envisaged in the adopted plasma scenario or in the current plans for the baseline heating system of DEMO in general [23].Some intrinsic turbulence-driven rotation might be expected in DEMO even in the absence of auxuliary torque input [24][25][26][27]; however, since this is challenging to predict quantitatively, we have here generally assumed v i = 0 when generating or inverting the synthetic spectra.We will revisit this assumption on v i in section 3.3.
Spectra are generated across a ±5 GHz frequency range from the probe frequency as in [22].Examples of resulting spectra for both scattering geometries can be found in [6,7], with a further case to be discussed in section 2.3.

Diagnostic background and signal-to-noise ratios
Electron cyclotron emission (ECE) represents the main contribution to the diagnostic background of existing CTS diagnostics.This will remain the case also for the diagnostics at ITER [20] and potentially DEMO, even if operating at frequencies below the fundamental electron cyclotron resonance.The ECE level affects the statistical noise σ CTS of the CTS signal through where P s and P b is the spectral power density of the CTS signal and ECE background, respectively, falling within a given frequency channel of width W, and ∆t is the total useful integration time (CTS operation usually employs on-off modulation of the probe gyrotron to allow background measurements [28]; ∆t here represents the combined gyrotron on and off period).Assessing and, if possible, minimizing P b through a judicious choice of operating frequency is hence a crucial component in estimating and optimizing the performance of a CTS diagnostic in any device.At the relevant frequencies of f ≈ 60 GHz, the DEMO plasma is optically thin.Consequently, any single-pass prediction for the ECE radiation temperature T rad = P b would represent a strict lower limit on the actual value, since it ignores the contribution from additional passes induced by wall reflections.To obtain more reliable estimates, we follow the procedure devised for estimating the ITER CTS background noise [20].This involves Monte Carlo-based multi-pass raytracing within the DEMO vacuum vessel, assumed toroidally symmetric, including randomized, diffuse wall reflections with polarization mode conversion.Upon each wall reflection, the component of a given X-mode ray that is subject to mode conversion generally does not re-enter the DEMO plasma but is instead reflected by the O-mode cutoff at the plasma edge.Adopting diffuse wall reflections is conservative in the sense that it leads to a higher estimated T rad in our procedure than do specular reflections [20].It can be justified on account of our imperfect knowledge of the detailed DEMO inner wall structure, which will contain indents, tile gaps, diagnostic apertures, antennas, and other irregularly angled surfaces not included in our simplified description of the vacuum vessel.
Following the discussion in [20], we consider a plausible range in wall reflectivity of R w = 0.6-0.9 at the relevant frequencies, along with a characteristic Gaussian width of the reflection angle distribution of σ = 20 • relative to the expectation from specular reflection.For σ larger than a few degrees, the exact choice of this parameter is not critical for the results due to the resulting randomization of reflection angles.While less than N = 50 reflections are enough for T rad to converge at f = 60 GHz, as shown in figure 2(a), adopting a larger N ensures low statistical uncertainties on the estimated T rad from our Monte Carlo procedure.Hence, we trace N = 1000 wall reflections of a ray entering a hypothetical CTS receiver aperture.This is also sufficient to ensure that the ray impacting on the receiver has traversed the entire vacuum vessel in all three dimensions as seen in figures 2(b) and (c).The final results for T rad are thus independent of the assumed CTS viewing geometry.
Figure 3 shows the resulting X-mode predictions for T rad for our default Baseline 2019 scenario with B t,0 ≈ 5.8 T. The predicted values of T rad imply sub-keV background levels across the frequency range of interest, with T rad ⩽ 20 eV at f = 60 GHz.However, the results are quite sensitive to the assumed value of the background magnetic field.To demonstrate this, the figure includes results for a lower toroidal field of B t,0 = 4.9 T, identical to the value assumed for the earlier 2017 Baseline scenario [10].In this case, the results suggest T rad ≈ 500 eV at f = 60 GHz for R w = 0.9.Note that the uncertainty on the actual B t in DEMO at this stage is a significant argument against increasing the CTS diagnostic frequency to, e.g.f = 65 GHz in order to reduce sensitivity to refraction.
If conservatively assuming the upper limit on T rad for the 2019 Baseline scenario at any given frequency, we obtain  the S/N ratios for Geometry 1 shown in figure 4.These results assume an integration time (total gyrotron on-and offtime) of ∆t = 10 ms and frequency bins W = 5 MHz, both smaller than the values of ∆t = 100 ms and W = 200 MHz assumed for the ITER CTS performance analysis [22].The adopted value of W would correspond to a setup involving 2000 frequency channels across a 10 GHz range, similar to the digitizer-based acquisition systems employed in contemporary CTS diagnostics [29][30][31][32][33].Note the significantly higher S/N at downshifted frequencies from the probe frequency, resulting from the pronounced frequency dependence of T rad .
The results imply S/N > 100 in the thermal bulk, including values up to S/N ≈ 100 at the downshifted frequencies dominated by fusion alphas.This suggests good sensitivity of DEMO CTS to both T i , v i , and alpha density.At frequency shifts >3.5 GHz from the probe gyrotron, only electrons contribute to the CTS signal (albeit at a level of <0.5 eV at downshifted frequencies).Arguably, one might not need to consider a wider frequency range than this, which would relax the requirements on diagnostic acquisition hardware.However, information on this electron contribution might still aid in constraining 'nuisance' parameters such as T e when inverting the spectra.At fixed integration time and probe frequency, the inferred S/N ratios would decrease by an order of magnitude if assuming the Baseline 2017 plasma scenario.In this case, figure 3 shows that it could be beneficial to reduce the planned CTS probe frequency from 60 to ~55 GHz, or alternatively increase the frequency bin width W or integration time ∆t, in order to maintain the above S/N ratios.

Inversion of synthetic DEMO CTS spectra
To assess the information that can be extracted from the synthetic spectra, we invert these using a Bayesian inversion scheme.The general procedure is based on that also adopted for the ITER CTS performance analysis [22].Here we adopt a uniform background noise level of T rad = 400 eV across the 55-65 GHz frequency range of interest.This corresponds to the upper limit predicted at any such frequency (figure 3) and so represents a highly conservative assumption.We further assume an integration time ∆t = 10 ms and-for computational reasons-a filterbank-like acquisition setup limited to 50 frequency channels covering a 10 GHz frequency range, corresponding to W = 200 MHz.
To mimic actual analysis conditions, the inversion ignores frequency channels within an assumed notch filter stop band around the probe frequency.This would be needed to protect receiver electronics from gyrotron stray radiation.For this, we note that the frequency accuracy specified to the manufacturer of the 170 GHz DEMO heating gyrotrons is f = 170 ± 0.3 GHz, including an anticipated frequency chirp at gyrotron start-up of maximum 500 MHz (e.g. from 170.3 to 169.8 GHz).If, highly conservatively, assuming that similar conditions apply for a 60 GHz CTS probe gyrotron, we would require a notch filter of total width 600 MHz, which is assumed in the following.
For each frequency channel in the synthetic spectra, additional noise contributions are added as in [22], such that the total noise estimate for each frequency channel, incorporates the ECE contribution from equation ( 1), an (anticipated) systematic uncertainty of σ sys = 1 eV per frequency bin, and a term σ sd that accounts for any significant variations in the signal within the relatively broad frequency bins assumed here.The fusion alpha velocity distribution is fitted using a classical slowing-down distribution, as also assumed when generating the synthetic spectra.The ITER CTS analysis in [22] showed that this approach provides reliable results also when the true distribution shows mild departures from classical slowing-down.In addition to the resulting alpha densities, the inversion considers a range of CTS 'nuisance parameters' in the scattering volume.Priors, assumed Gaussian, and uncertainties on these are summarized in table 2. These parameters include the densities of thermalized D-D fusion products and of He ash, the densities of heavy impurities Ar and Xe, and the CTS overlap factor O b .The latter acts as a scaling factor for CTS spectra according to the CTS transfer equation, where ∂P s /∂ω is the measured spectral power density at a given angular frequency ω, P i is the incident probe power, λ i 0 and λ s 0 are the incident and scattered vacuum wavelengths, respectively, r e is the classical electron radius, and Σ is the scattering form factor [17].
Unlike the case for ITER [22], target uncertainties on the plasma parameters in table 2 as measured by other diagnostics are not yet generally available for DEMO.An exception is the line-integrated value of the electron density, which is expected to be well constrained to within ~1% from interferometry [3].However, this uncertainty cannot be directly translated into that expected for our spatially localized CTS measurement volume.Furthermore, equation (3) shows that some degeneracy between O b and n e can be expected when inverting CTS spectra, so here we conservatively allow for a larger prior uncertainty on n e of ∼10% and on O b of ∼30%.For several other parameters in table 2, rough estimates of the required uncertainties can be obtained from extrapolation of the corresponding ITER requirements [3].Where relevant, our adopted accuracies are comparable to these estimates and can be refined once the specifications for the DEMO diagnostic suite are more fully defined.For the plasma rotation v i , assumed negligible when generating the synthetic spectra (section 2.1), we initially adopt a narrow prior distribution centered at v i = 0 km s −1 .Finally, we assume that the scattering geometry and plasma location of the CTS measurement volume can be reconstructed to an accuracy corresponding to that of existing CTS diagnostics [34].
The inversion allows for a non-parametric description of the velocity distribution of a non-thermal ion population in addition to alphas, arising from, e.g.auxiliary heating or fusion reactions.In the likely absence of neutral beam ions in DEMO [23], we here fix the phase-space densities of any such fastion distribution in the fit, assuming it to have a negligible total density of 10 14 m −3 (≈10 −6 n e ).This is a simplication relative to the ITER CTS performance analysis, [22], where the velocity distribution functions of alpha particles and NBI ions had to be inferred concurrently.Heavy impurities (Ar, Xe) are accounted for in the inversion but their densities are also not fitted, since they generally contribute to the CTS signal only within the assumed notch filter stop band.
Figure 5 shows part of the synthetic CTS spectrum for Geometry 1, as well as an example of the final spectrum to be fitted, based on rebinning and randomizing the original spectrum according to our default noise estimates for a ∆t = 10 ms acquisition period and W = 200 MHz frequency channels.The best-fit forward model evidently provides a good description of this perturbed spectrum.This applies in particular also at frequency shifts ∆f > 1 GHz from the probe gyrotron, where the fusion alpha contribution dominates the overall spectrum and the σ sys -term in equation ( 2) dominates the noise budget.

Inference of physics parameters
In the results to follow, it is generally instructive to consider the outcome of the inversion both when all fit priors are fixed at their true values (yet with their uncertainties taken into account), and when they are randomly drawn from a Gaussian distribution with characteristic width σ equal to the relevant uncertainty in table 2.

Core fusion alpha density
The core fusion alpha densities represent an important DEMO performance indicator and can be inferred using limited computational effort.For these, we adopt the particularly conservative case of assuming a largely flat prior centered at negligible density.This is feasible in light of the good S/N and dominance of the fusion alpha contribution at ∆f ≳ 1 GHz.
The alpha densities resulting from 100 trial fits to individually randomized synthetic spectra are shown in figure 6, including the impact of either fixing or perturbing the priors on other 'nuisance' parameters.On average, these fits recover the true alpha density very well.The mean and its 1σ error of the fit results using perturbed priors are ⟨n α,fit ⟩ = (4.14 ± 0.06) × 10 18 m −3 , showing that the inversion on average infers an alpha density lying within 3% of its true value, n α,true = 4.27 × 10 18 m −3 .The precision of the results based on the standard deviation σ around the mean fit result is σ/⟨n α,fit ⟩ = 14%, which is somewhat larger than the mean relative uncertainty on individual fit results of 8%.
As indicated by figure 6, the accuracy on n α does not improve if fixing all fit priors (except that of n α ) at their true values, as this results in a slightly lower ⟨n α,fit ⟩ = (3.93 ± 0.03) × 10 18 m −3 .This likely reflects our choice of a negligible prior on n α combined with the much reduced parameter space then allowed for the full parameter set in the inversion.Indeed, tests based on a further 100 trial fits with perturbed priors and with a prior on n α centered at twice the true value result in an ⟨n α,fit ⟩ that overestimates the true value by 2%.This indicates that adopting a sufficiently wrong prior can mildly bias the inferred n α in the corresponding direction.In all cases, however, the results suggest that core alpha densities can, on average, be well recovered with CTS at DEMO, even in the absence of useful prior knowledge of n α and of accurate information on other plasma parameters.

Core ion temperature
The above analysis was not optimized for accurate inference of the ion temperature, since the procedure assumes a filterbanklike data acquisition setup with the input spectrum binned into just 50 frequency channels (resembling the CTS diagnostic setup for fast-ion measurements at ASDEX Upgrade [35]).Assessing the full diagnostic potential for DEMO CTS measurements of bulk-ion parameters such as core T i , v i ,  and R i = n T /(n D + n T ) requires inversion of bulk-ion spectra with higher frequency resolution, using dedicated optimization algorithms running on high-performance CPUs [36,37].
Nevertheless, we can still obtain a conservative estimate of the accuracy with which T i may be inferred.Figure 7 shows the results for the inference of T i from the same 100 fits performed above.The distribution of fit results, even with perturbed fit priors, shows a standard deviation of 5.2 keV, which is significantly narrower than the 10 keV of the-intentionally fairly wide-supplied prior distribution, implying good convergence towards the true value.When allowing for perturbed priors, the average inferred ion temperature of ⟨T i,fit ⟩ = 35.1 ± 0.5 keV suggests a slight tendency to systematically overestimate the true value, T i = 32.6 keV, at a level of ~8%.This discrepancy is reduced to 2% if assuming correct fit priors.
This slight overestimation seems indeed to be related to the assumed frequency resolution.An additional set of 100 trial fits to spectra with slighly improved frequency resolution (obtained by retaining N = 50 frequency channels but considering a smaller frequency range of ±2 GHz around the probe frequency) yielded ⟨T i,fit ⟩ = 31.7 ± 0.2 keV.This is a slight underestimation, but one which is within 3% of the true value, supporting the need for high resolution of the thermal bulk for accurate inference of T i .The overall results seem highly encouraging for the prospects of constraining the core ion temperature in DEMO using CTS.We reiterate that these are conservative estimates of the diagnostic capability for T i inference at DEMO given the present assumptions, including that of limited frequency resolution and a wide receiver notch filter (masking the central thermal bulk of the spectra).

Rotation velocity and fuel-ion ratio
Additional key quantities in our analysis are the toroidal plasma rotation v i and the fuel-ion ratio R i .Based on the same fits described above, the results for these two parameters, shown in figures 8(a) and (b), indicate that both remain close to their prior value, with both the distribution and standard deviation of fit results mimicking those of the respective priors.In this case, there is no strong tendency of the fits to converge towards the true value, unless the prior is already chosen close to this value.
The sensitivity of DEMO CTS spectra to significant core rotation at the level of v i ≳ 100 km s −1 was demonstrated in [6].However, for the low values of v i considered here, a filterbank-only CTS diagnostic cannot distinguish cases with and without rotation for the assumed integration time.Nonzero rotation at these levels would only affect the signal outside the receiver notch filter by more than 1 eV per channel (equivalent to the adopted systematic uncertainty σ sys ) within a relatively narrow range of ∼±500 MHz around the probe frequency.This would at most be the case for 5-6 out of the assumed 50 frequency channels.For optimized estimation, it will be necessary to enhance the frequency resolution and apply a dedicated inversion algorithm for bulk-ion parameter inference [36].This point also applies to the case of the plasma isotope ratio parameter R i .Some degeneracy is present between this parameter and the densities of light impurities such as thermalized 4 He, see figure 4.This degeneracy can be lifted, and R i itself constrained, if adopting a different scattering geometry with ϕ close to 90 • such as Geometry 2 in table 1 [6].
In order to explore the ability to assess v i and R i in more detail, we conducted dedicated analyses for these two parameters.For v i , we generated two synthetic spectra assuming v i = 20 and 50 km s −1 , respectively.These values are at the low end of those in typical NBI-heated H-mode discharges in present-day devices [37][38][39] but roughly cover the observed range in intrinsic rotation velocities as discussed in section 4. The spectra were then resampled and perturbed as above.To aid the inversion of the resulting spectra, we narrowed the considered frequency range to ±1.5 GHz while maintaining N = 50 frequency channels, for an effective frequency resolution outside the notch filter of W = 48 MHz.Furthermore, we assumed a correct prior on n α = (4.27± 1.0) × 10 18 m −3 , along with a smaller prior uncertainty on T i of 10% [3].All other priors remained unperturbed from their values in table 2. However, the prior on v i was deliberately taken to be zero with a large uncertainty, 0 ± 300 km s −1 , so as to test whether a non-zero v i can indeed be recovered.
The results of 100 trial fits to the v i = 50 km s −1 spectra are shown in figure 8(c).Comparison to figure 8(a) shows that the inversion now clearly converges towards the true value of v i rather than coinciding with the wide but incorrectly centered prior.The fitted mean and its 1σ error of ⟨v i,fit ⟩ = 54 ± 4 km s −1 is indeed fully consistent with the true value and inconsistent with no rotation.A Kolmogorov-Smirnov (K-S) test corroborates this, yielding a negligible probability of p ∼ 10 −21 that the distribution of fit values has been drawn from a Gaussian with zero mean and the observed σ.Corresponding fits to the v i = 20 km s −1 spectra yield ⟨v i,fit ⟩ = 24 ± 4 km s −1 , again consistent with the true value but with a reduced relative accuracy.Hence, CTS can, on average, with high confidence identify net toroidal plasma rotation in DEMO, at least down to values of v i ∼ 20 km s −1 , with an absolute accuracy of ~5 km s −1 .These encouraging results arise despite the fact that the adopted scattering geometry and values of v i give rise to a frequency shift of the CTS spectrum of only δf ≈ cos(ϕ)v i k δ /(2π) ≈ 1-3 MHz, well below the assumed frequency resolution of W = 48 MHz.
For the fuel-ion ratio R i , we next consider Geometry 2 with ϕ ≈ 88 • as introduced in table 1. Synthetic spectra for this geometry, constrained to the frequency range ±0.55 GHz from the probe frequency, were generated for R i = 0.4 and 0.45.The spectra were binned into 40 channels outside the notch filter width (corresponding to W = 12.5 MHz), and perturbed as above.The corresponding inversion assumed unperturbed priors, again with a smaller prior uncertainty on T i of 10% as for the similar v i fit.The priors for this scattering geometry are generally quite similar to those in table 2, since Geometries 1 and 2 both involve measurements close to the plasma core.The chosen prior on R i of 0.5 ± 0.1 allows us to test whether the presence of a sub-optimal fuel-ion ratio can be correctly inferred if assuming an incorrect prior.
The associated results of 100 trial fits shown in figure 8(d) for the R i = 0.4 spectrum indeed indicate convergence towards the true value and away from the incorrect prior.The fitted mean and standard deviation are ⟨R i,fit ⟩ = 0.42 ± 0.03, with a K-S probability p ∼ 10 −46 that the fit results derive from a Gaussian distribution with a mean of 0.5.For the R i = 0.45 case, the corresponding results are ⟨R i,fit ⟩ = 0.46 ± 0.04.The conclusion is that deviations from the ideal core fuel-ion mix at the level of ∆R i = 0.05 (corresponding to, e.g. a 55%/45% D/T ratio) can be identified with DEMO CTS.
These estimated accuracies on measurements of v i and R i are on the one hand optimistic, since they assume correct (but uncertain) knowledge of the priors on various nuisance parameters in the analysis.However, they are at the same time conservative, since they are based on consistently assuming an incorrect prior for the parameter of interest, the highest plausible diagnostic background level, a sub-optimal frequency resolution, and possibly an unnecessarily wide notch filter.A detailed study of the inference of v i and R i at high frequency resolution under varying assumptions is beyond the scope of this work, due to the significant computational load.This will be conducted once the actual DEMO CTS geometry is more securely established.

Electrons and light impurities
The remaining plasma parameters listed in table 2 include the electron density and temperature, which are not usually target parameters for CTS measurements, and the densities of thermalized light impurities (H, 3 He, 4 He).The fit results for these under our 'default' assumptions (Geometry 1, W = 200 MHz, all priors perturbed) are shown in figure 9.As for v i and R i under the same assumptions (figures 8(a) and (b)), several of the results here again follow their corresponding prior distribution.
The two exceptions are the electron density and the diagnostic parameter O b , which show good convergence towards the true value.For both these parameters, the mean fitted value matches the true value to within ~4%, with a standard deviation of the fit results of only 35%-50% of that of the (perturbed) prior.This indicates that the inversion on average infers the correct normalization of the CTS spectra to good accuracy.Note here that the degeneracy between O b and n e in equation ( 3) is only apparent, since n e also enters in the form factor Σ, thus allowing the two parameters to be independently constrained.
The thermalized products of D-T and D-D fusion represent a combined core density of only ∼0.05n e , and their spectral contribution is thus largely masked by that of the fuel ions, cf figure 4. A diagnostic sensitivity analysis for these parameters, in particular that of He ash, must again exploit a scattering geometry with ϕ close to 90 • , combined with a frequency resolution well below the local cyclotron frequencies of these ions.Here we performed a preliminary study, based on inverting 100 spectra generated in Geometry 2 with a He ash content of n He4 /n e = 0.16, three times the default value of 0.055 that was also adopted as a prior.This yields a mean fitted ⟨n He4 /n e ⟩ = 0.090 ± 0.002.Although inconsistent with the true value, it is also significantly higher than the incorrect prior, indicating that departures from the expected thermal 4 He content in the plasma core can indeed by identified with DEMO CTS.

Discussion
The presented analysis demonstrates that a DEMO CTS diagnostic will be able to monitor properties of the DEMO plasma core such as the densities of fusion-born and thermalized alpha particles, ion temperature, rotation velocity, and fuelion ratio.We reiterate that all results in figures 6-9 have been inferred simultaneously in Geometry 1 using the uncertainties in table 2. The only exceptions are the fits underlying figures 8(c) and (d), which were optimized separately for inference of v i and R i in Geometries 1 and 2, respectively.As discussed in section 3.3, this optimization consists of increasing the frequency resolution of the thermal-ion CTS spectrum while adopting a smaller uncertainty of 10% on T i [3].This section discusses some implications of our results for DEMO burn control in the plausible event that realtime CTS analysis becomes feasible by the time of DEMO operation.It should be clarified, however, that our adopted inversion procedure presented in section 2.3 is currently too computationally expensive to allow real-time CTSbased plasma control, with typical computation times exceeding 10-20 s per trial fit on a standard laptop.Efforts are ongoing to significantly reduce these times, including inversion aided by machine learning, as already successfully demonstrated for CTS at Wendelstein 7-X [40], as well as parameter inference using digitizer-based data acquisition involving suitably configured field programmable gate arrays.
To inform the subsequent discussion, figure 10 summarizes the results for key parameters in our analysis, in all the cases where the prior is either assumed largely unknown or intentionally chosen incorrectly.The figure shows the relative accuracy ξ = (⟨p fit ⟩ − p true )/p true and its error for a given fit parameter p as a function of the total averaging time t av = ∑ ∆t i , where ∆t i = 10 ms is the adopted integration time for a single data acquisition.Hence, t av represents the effective total integration time required to obtain the plotted accuracies for a given plasma parameter.
Two general conclusions are apparent from figure 10.First, a reasonable estimate of any parameter is obtained for t av = 100 ms, which is also the integration time underlying the measurement requirements for the ITER CTS diagnostic [12].Second, the results generally converge towards their final value after ∼2-300 ms, after which further time averaging leads at most to modest improvements in the accuracy and precision of the estimates.This implies that the accuracies quoted on any parameter in section 3 can be obtained on timescales corresponding to ≈0.1τ E ∼ 0.1τ SD , where τ E ≈ 2.6 s is the energy confinement time (cf section 2.1) and τ SD ≈ 1.9 s is the fast-alpha slowing down time in the plasma core.The latter was here evaluated assuming an isotropic slowing down distribution, giving where ϵ 0 is the vacuum permittivity, m α and m e the alpha and electron mass, respectively, e the elementary charge, and ln Λ ≈ 23 is the Coulomb logarithm in the plasma core.
The DEMO burn control requirements dictate that the fusion power should generally remain within 20% of the nominal value [4].Any larger variations could be associated with changes in alpha heating and core T i and so should be understood.In this context, an important result of the present study is the ability of CTS to constrain the fusion alpha density in the DEMO core to better than ~5% on average (with the slight underestimation in figure 10(a) related to our choice of prior, cf section 3.1).In the present analysis, this relies on describing the fusion alphas simply using a classical slowing-down distribution.This is not a requirement, however, since the alpha velocity distribution can itself be inferred with CTS using a non-parametric description; this option has not been explored here but would form part of an extended DEMO CTS performance analysis.The inferred α densities can be translated into a local fusion power density S through and hence contribute to estimates of total fusion power.Here v b is the alpha birth velocity, v b ≈ 1.3 × 10 7 m s −1 , and v c is the critical velocity for the relevant core plasma composition (e.g.[41]).Naturally, CTS-based alpha particle measurements also offer a means of monitoring anomalous fast alpha losses from the core.This can be done either simply based on densities inferred under neoclassical assumptions as above, or through constraining the alpha velocity distribution function.The latter could provide direct evidence for non-classical slowing down in real or velocity space induced by, e.g.toroidal Alfvén eigenmodes and sawtooth instabilities.As shown in figure 1, the adopted q-profile has a minimum q min = 1.0 across the plasma core (possibly by construction).Minor perturbations in this profile could render the DEMO plasma prone to (n, m) = (1, 1) modes and sawteeth.In turn, this could redistribute heat and alpha particles from the core, potentially by up to ~50% [42][43][44] and so reduce the overall fusion power.The results in figure 10(a) suggest that such large changes in core alpha density are well within the measurement accuracy on n α even for very short CTS integration times.Hence, DEMO CTS should be able to track any such alpha redistribution on timescales below the several tens of ms typical of sawtooth periods.In addition, CTS-based estimates of the evolution in ion temperature could provide direct evidence of the sawteeth themselves, for subsequent suppression of these using current drive.
For any scattering geometry, CTS will parasitically provide spatially resolved estimates of the ion temperature, thus complementing estimates from DEMO x-ray and neutron spectroscopy.As shown in figure 10(b), the core T i can, on average, be inferred with CTS to better than ~2 keV (~8%), with useful estimates possible even on integration timescales of 10 ms.This level of accuracy assumes a filterbank-like acquisition system, and is sufficient to relate any observed variations in P fus to those in T i and to monitor anomalous ion heat transport from the core.In addition, it enables tracking the impact on T i of core fuelling with the proposed DEMO pellet launching system [45] on timescales below the anticipated maximum pellet delivery rate of ≳10 Hz.Furthermore, the accuracy on T i estimated here can be readily improved with longer integration times and/or by replacing the filter bank with a high frequency resolution fast digitizer, as discussed in section 3.2.
Plasma rotation and rotational shear can suppress instabilities and turbulence, thereby enhancing confinement.This can be provided by external momentum input from NBI, although the latter is not included in current plans for DEMO [23].Nevertheless, in case the adopted plasma scenario requires a certain level of rotation, or if v i becomes an operational parameter in DEMO for instability control, it will be necessary to monitor the toroidal rotation.In the likely absence of inclined x-ray views [4], CTS may be the only means of doing so in DEMO.Here we have demonstrated that any non-zero rotation in DEMO can be robustly identified with CTS, at least down to levels of v i ∼ 20 km s −1 .This is at the low end of the range in intrinsic rotation velocities inferred in existing devices (∼10-60 km s −1 ) for Ohmic or wave-heated plasmas with no external momentum input [24,26,27,[46][47][48].As demonstrated by figure 8, inference of v i would greatly benefit from the high frequency resolution afforded by a digitizerbased CTS system.
The above results can be achieved with a single CTS receiver having a projection angle ϕ ≈ 76 • to the magnetic field.With a separate CTS receiver viewing the same probe gyrotron beam but at ϕ ≈ 88 • , spatially resolved D/T measurements in the plasma core are possible and will allow even modest departures from the intended core fuel-ion ratio to be monitored.Such measurements will generally require digitizer-based data with high frequency resolution.The results can complement estimates based on neutron spectroscopy [49] for improved burn control and help inform the optimum edge fuelling rate as well as the pacing and size associated with core pellet fuelling.Again, this can potentially be done on timescales below the pellet delivery rate for continuous optimization of the core isotope mix.
A ϕ ≈ 88 • CTS setup can also track the core He ash content n He4 /n e , although this is more challenging and the exact accuracy of this must be established by a more detailed analysis.A preliminary analysis shows that core He ash levels exceeding the expected value by a factor of 2-3 can be safely identified.Detecting a higher or lower value of n He4 /n e than anticipated for a given fuel throughput might suggest unexpected issues with plasma particle exhaust, or could be a signature of nonclassical fast alpha slowing down.These possibilites could be distinguished using CTS-based evidence of anomalous fastion diffusion in the measured fusion alpha densities or their velocity distribution.

Conclusions and outlook
The diagnostic suite at DEMO will be far more limited than on ITER, due to the harsh radiation environment and the need to maximize the first-wall area for tritium breeding [2].The relevant diagnostics should be robust, powerful, and versatile while able to provide key measurements for plasma and burn control.Here we have demonstrated, using trial fits to synthetic spectra, that CTS can provide spatially resolved measurements of core fusion alpha densities and toroidal plasma rotation in the planned European DEMO (EU-DEMO), in addition to contributing to measurements of core ion temperature, fuelion ratio, and He ash content.
The best option for a CTS diagnostic at DEMO is a 60 GHz sub-harmonic setup, providing low diagnostic background [7].With this, a single-receiver CTS diagnostic will be able to infer core fusion alpha densities to an accuracy of better than 5%.This is enabled by the strong fusion-alpha signature in the CTS spectral wings.Core ion temperature can likewise be constrained to ≲10%, and this is a conservative estimate that can be improved by more sophisticated analysis of the synthetic spectra.Toroidal plasma rotation velocities can be constrained to ∼5 km s −1 , at least down to velocities of v i ∼ 20 km s −1 .Among planned or possible DEMO diagnostics, only CTS may be able to deliver such rotation measurements.This would be particularly relevant if v i becomes an operational parameter in DEMO.
With a separate (or alternative) receiver view, the core fuel-ion ratio R i = n T /(n D + n T ) can be inferred with CTS to within 5%, allowing discrimination between a 50%-50% and 55%-45% D-T ratio.Such a receiver view would also make CTS sensitive to core He ash content, although this is a more challenging measurement since the contribution by low levels of thermalized He tends to be masked by that of the fuel ions.A preliminary analysis shows that He ash levels exceeding the expected value by a factor of 2-3 can be safely identified.
These results are valid when averaging individual ∆t = 10 ms measurement pulses for an effective integration time of up to t av = 1 s.However, in all cases such averaging converges towards the final value already after ~100 ms, corresponding to ~5% of the energy confinement time or the core fusion alpha slowing-down time.With reduced accuracy, approximate results can be obtained also for individual measurement pulses, corresponding to timescales shorter than those associated with the proposed DEMO pellet fuelling system.As such, real-time analysis of DEMO CTS data could contribute to continuous optimization of DEMO core fuelling and heating.
Our results apply for a conceptual CTS diagnostic design that can indeed be integrated in DEMO, but the present analysis should be verified and expanded upon once any actual diagnostic configuration-and the planned DEMO toroidal field-are better established.This must include detailed analysis of the diagnostic performance with respect to all relevant measurement parameters, including inference of the velocity distribution function of fusion alphas and the accuracy with which a digitizer-based acquisition system can recover bulkion parameters.Such an analysis should also assess the need for a passive CTS view [28], which may be less pressing on DEMO than in existing devices owing to the low ECE background and good diagnostic signal-to-noise ratios predicted by our analysis.

Figure 1 .
Figure 1.(a) Normalized poloidal flux contours ψ N in a poloidal projection of DEMO.Red marks the separatrix (ψ N = 1), and black represents the DEMO limiter/inner wall.A cross marks the magnetic axis at (R, z) = (9.38,0.04) m.(b) Radial profiles of electron density ne, electron and ion temperature Te and T i , and safety factor q as functions of normalized poloidal flux coordinate ρ = √ ψ N .The q-profile has been multiplied by a factor of five for improved visibility.(c) Results of raytracing for our conceptual scattering geometry with ϕ = 76 • in a poloidal cross section of DEMO, overlayed on contours of ρ.The injected gyrotron beam with wave vector k i is shown in blue, and the receiver view with scattered wave vector k s in red.The yellow ellipsoid represents the resulting CTS overlap (measurement) volume.

Figure 2 .
Figure 2. (a) Contribution of individual 60 GHz X-mode ray segments to increases in T rad (green vertical lines) as a function of the number N of traced wall reflections.Black/blue solid lines and error bars show the cumulative value of T rad (N) until convergence and its final statistical uncertainty.(b) Paths of individual ray segments (magenta) and their reflection locations (cyan) for N = 1000 wall reflections in a poloidal and (c) toroidal cross section of DEMO.

Figure 3 .
Figure 3. Predicted X-mode ECE radiation temperatures for the DEMO Baseline 2017 and 2019 scenarios as a function of frequency.The range shown at a given frequency incorporates both variations in assumed wall reflectivity Rw, as labelled, and the relevant Monte Carlo-based uncertainties on T rad .

Figure 4 .
Figure 4. Predicted signal-to-noise ratios S/N for core CTS measurements in Geometry 1.The total contribution in the Baseline 2019 scenario is shown as a solid line, those of individual plasma species as dotted lines.For comparison, the total S/N for the Baseline 2017 scenario is also shown (dashed line).Gray region marks the frequency range of the assumed notch filter stop band; see section 2.3 for details.

Figure 5 .
Figure 5.Total CTS model spectrum (black curve) in Geometry 1 and the contribution of fusion alphas (dotted purple), along with an example of the associated rebinned and randomized spectrum to be fitted (red circles with errorbars).Green region shows the resulting best-fit forward model and its uncertainties.

Figure 6 .
Figure 6.Histograms of inferred alpha densities assuming either perturbed or unperturbed (i.e.true) priors on all other parameters in the inversion.Dashed black line marks the true (input) alpha density nα,true = 4.27 × 10 18 m −3 .

Figure 7 .
Figure 7. Histograms of inferred ion temperatures assuming either perturbed or unperturbed (i.e.true) priors on all other parameters in the inversion.Black curve shows the adopted prior distribution of T i , and dashed black line marks the centre of the distribution at the true (input) value of T i = 32.6 keV.The plotted range on the abscissa corresponds to the ±3σ range on the prior on T i .

Figure 8 .
Figure 8.As figure 7 but for (a) the toroidal rotation velocity v i and (b) the fuel-ion ratio R i = n T /(n D + n T ), both in Geometry 1. Panels (c) and (d) show results from dedicated fits of these parameters to spectra generated with (c) a non-zero v i = 50 km s −1 in Geometry 1 (here plotted only across the ±0.7σ range on the prior), and (d) an uneven D/T mix with R i = 0.4 in Geometry 2, see section 3.3 for details.

Figure 9 .
Figure 9.As figure 7 but for the remaining fitted parameters listed in table 2. Note that O b is not a plasma parameter.

Figure 10 .
Figure 10.Relative CTS measurement accuracy ξ (solid curve) and its precision (shaded) as a function of effective integration time tav for key parameters: (a) nα for a prior at 10 14 m −3 (see section 3.1), (b) T i for a prior of 32.6 ± 10 keV (section 3.2), (c) v i as labelled for a prior of 0 ± 300 km s −1 (section 3.3), and (d) R i as labelled for a prior of 0.5 ± 0.1 (section 3.3).Black error bars and labels indicate the characteristic accuracies for a ~1 s averaging time.

Table 1 .
CTS scattering angles, measurement location, and extent of scattering volumes in the two considered configurations.

Table 2 .
Free and fixed parameters and uncertainties on Bayesian priors in fits to synthetic spectra for Geometry 1.