Comparison of reduced model predictions for divertor detachment onset and reattachment timescales in ASDEX Upgrade and JET experiments

Building on prior analysis of ASDEX Upgrade (AUG) experiments (Henderson et al 2023 Nucl. Fusion 63 086024), this study compares simple analytical formula predictions for divertor detachment onset and reattachment timescales in JET experiments. Detachment onset primarily scales with divertor neutral pressure, impurity concentration, power directed to the targets, machine size, and integral perpendicular power decay length. JET experiments, focusing on seeding mixtures of Ne and Ar, align with the detachment onset predictions. Radiation efficiencies among the impurities show good agreement with the model predictions, contrasting with AUG observations which suggested higher efficiency for Ar and lower efficiency for Ne. The time taken to re-ionise the neutral volume in front of the outer target in fully detached divertor conditions was measured following both abrupt increases in injected neutral beam power and, separately, cutting of the impurity gas flow. Re-ionisation of the neutrals occurs within approximately 1 s on JET, which aligns with the simple model prediction derived from AUG data. While the AUG results are not new, their comparison with the JET results enhances understanding, reinforcing confidence in using simple models to predict future reactor scenarios.


Introduction
In future reactors capable of generating gigawatts of fusion power, with over 100 MW directed to the divertor, mitigation of the heat load on the divertors is imperative.This is primarily achieved through sustaining divertor detachment, initiated by maximising the volumetric losses through impurity injection.Although the selection of impurity is still under consideration, the leading contenders include Ne [1] and Ar [2] as the primary radiators in the scrape-off layer (SOL) on ITER and DEMO, respectively, with a heavier species, such as Xe [3], chosen to radiate in the plasma edge on DEMO.However, the amount of impurity injected into a reactor should generally be minimised to reduce dilution of fuel elements in the core plasma and to avoid exceeding core radiation limits set primarily by the H-L transition threshold [4].
Reduced SOL plasma models play a pivotal role in swiftly interpreting experiments [5][6][7], providing consistency checks for high fidelity simulations [8,9], and exploring different reactor design points [2,10].However, it is often hard to distinguish if trends found from reduced models developed on specific machines are machine-dependent and, therefore, experimental validation across machines of different size, geometry, and operational space is critical for improving confidence.This paper builds upon a recent study of impurity seeding experiments conducted on ASDEX Upgrade (AUG) [11] which provided evidence that a straightforward analytical formula, developed originally by Kallenbach et al [5,12], could predict the concentrations of Ne and Ar needed to induce detachment.The results further confirmed that the detachment threshold scaled linearly with the ratio of power and major radius, and inversely with the divertor pressure and the impurity concentration.The latter is scaled by a so-called radiation efficiency parameter which characterises the impurity's ability to radiate compared to D. It was concluded that the Ne radiation efficiency was slightly over-predicted by the formula, while, on the other hand, the Ar radiation efficiency was underpredicted.This implied that the impurity transport for each impurity may be different in comparison to the original model assumptions.
A control system is likely needed in reactor-class tokamaks to adjust divertor gas puffing rates for reaching the predicted steady-state detachment point and to react to relatively slow changes (e.g. on the order of the energy confinement time) in upstream conditions [5,13,14].Crucially, the system must be able to detect loss of detachment before a complete reattachment occurs [15].Experiments on AUG with both abrupt increases in injected neutral beam (NB) power and, separately, cutting of the impurity gas flow demonstrated that the divertor reattachment time in weakly detached conditions was primarily set by the timescale and magnitude of the power transient, but took longer to reattach when starting from a strongly detached condition [11].This delay was thought to be primarily driven by the timescales for recombination and ionisation of the neutrals in front of the target.A straightforward scaling method was developed to predict the time required to ionise the volume of neutrals between the X-point (XP) and outer divertor target.This model suggested the ionisation time should scale with the timescale and magnitude of the transient, as well the divertor pressure, electron density, volume of neutrals, and the connection length.
The findings presented in this paper, stemming from equivalent impurity seeding experiments conducted at JET, attempt to confirm the reproducibility of the observations made in AUG and to test the size scaling of both the detachment onset threshold and the reattachment timescales.The paper is structured as follows.Section 2 presents empirical evidence focusing on the validation of analytical formulas predicting detachment conditions.In section 3, the paper investigates the fundamental timescales governing divertor reattachment, drawing insights from abrupt power perturbations in both AUG and JET experiments.Finally, section 4 provides a conclusion discussing the findings and their implications for future devices.

Detachment scaling and radiation efficiency
The formula predicting the conditions required for detachment from Kallenbach et al [12], otherwise known as the detachment qualifier q det , was developed by comparing a 1D SOL model to an experimental scaling of the detachment threshold for N-seeded plasmas on AUG [5].It is written as: Here, P sep represents the power crossing the separatrix, R maj is the major radius, λ int = λ q + 1.64S represents the integral power decay length relating the peak heat flux and the deposited power, f Z c Z is the product of radiation efficiency and impurity concentration, respectively, for an impurity Z, and p 0 is the neutral pressure measured below the roof baffle on AUG (see figure 3 from [16]) which is primarily set by the gas puffing rate and the pumping speed.The detachment qualifier is normalised such that detachment is achieved when q det is close to or below 1.
The radiation efficiency characterises an impurity's ability to radiate in the SOL compared to D. f N = 18 was determined from a database of N seeding experiments, and the 1D model confirmed this using a non-coronal parameter n e τ = 0.5 × 10 20 m −3 ms to estimate radiation enhancement due to impurity transport.The weakly positive size scaling accounts for SOL and divertor radiation depending on the connection length.In theory, f Z could also depend on the upstream temperature (and thus power crossing the separatrix); however, this is also likely a weak effect, given that impurity cooling functions do not change significantly over the usual range 100-200 eV.
The model further revealed that detachment could be achieved with ≈2.5 times less Ne and ≈5 times less Ar compared to N, implying that f Ne = 45 and f Ar = 90, when using the same n e τ .Later measurements on AUG indicated that radiation efficiencies of f Ne ≈ 30 and f Ar ≈ 200 provided better agreement with the measured detachment state and radiation, highlighting variations from initial predictions [11].Differences in radiation efficiency in comparison to predictions could imply that different values of n e τ or atomic data for each impurity is required in the 1D model.
To assess the radiation efficiencies on JET, a series of ELMy H-mode experiments were conducted using injected powers of ≈25 MW at constant plasma current I P = 2.5 MA, toroidal magnetic field B T = 2.7 T, and major radius R maj = 2.9 m.The divertor was in vertical-vertical target configuration (similar to AUG), the D 2 gas puff flow rate was constant at Γ D = 6 × 10 22 elec s −1 , and different seeding levels of Ar, Ne, and mixtures thereof were puffed to induce varying degrees of detachment.Future work should assess the impact of changing the D puffing rate and the magnetic field.
Comparing experimental data to equation (1) requires measurements of P sep , λ int , c Z , and p 0 ; all of which are derived indirectly from various diagnostics.The following subsections details the methodology for deriving each of these parameters.

Divertor detachment state
The divertor detachment state was assessed through a combination of diagnostic techniques, including filtered camera tomography, to measure the 2D poloidal distribution of singly ionised Ne II or Ar II emission [17], and bolometry to measure radiation through and above the XP through horizontally viewing channels.
Figure 1 illustrates the evolution of the detachment state during JET pulse number (JPN) #101 925, a scenario with three increasing steps of Ne seeding.Firstly, the evolution of the ion saturation current, j sat , measured by the Langmuir probe (LP) closest to the outer divertor strike-point is shown in figure 1(a).The temperature measurements from LPs is typically not reliable in cold, detached divertor conditions; however, the roll-over in j sat is still a useful indicator of detachment.
Tomographic inversions of the divertor camera images, filtered to a narrow (1.37 nm) band-pass covering the Ne II (λ = 369.59nm) and Ar II (λ = 480.61nm) emission, are used to produce poloidal distributions of the emission in the outer divertor.The position of the ionisation front is gauged by the major radius of the region of 90% peak Ne II (or Ar II) emission closest to the target.The evolution of the ionisation front radial position is shown in figure 1(b), with the algorithm detection demonstrated in figures 1(e) and (f ).The detachment state is therefore getting stronger as the radial measurement gets smaller, with R ≈ 2.88 m representing attached conditions and R ≈ 2.77 m representing strong detachment and an XP radiator (XPR) [18].
The existence of edge localised modes (ELMs) causes the emission to swiftly transition back and forth as the emission begins to move away from the target.Different processes occur in the divertor at different stages of the ELM cycle [19].This paper considers only the average inter-ELM evolution of the detachment state when comparing against the detachment threshold and reattachment models.However, the suppression of ELMs in the fully detached phase, consistent with XPR formation [18], reduces the complexity of ELMs in understanding the reattachment timescales.Future experiments with ELM suppression in the attached phases are needed to quantify their impact.Once the XPR forms, the radial position measurement becomes steady at R ≈ 2.77 m.Although singly ionised impurity emission does not spread into the XP during the XPR phase, bolometry reconstruction clearly shows that the total radiation is localised within the XP.
Alongside this measurement, the equivalent radial measurement is made using the Ne IV (λ = 381 nm) line intensity measured using divertor spectroscopy.Since Ne IV emission is typically strongest at moderately hotter plasma temperatures than Ne II, this radial position measurement stretches closer to the XP and is moderately more sensitive in partially detached conditions than the equivalent Ne II radius.The evolution of this measurement during the seeding scan is shown in figure 1(c).
Finally, two bolometer channels viewing horizontally through and above the XP are used alongside the two measurements described above to gauge the detachment state.Taking the ratio of the radiation measured through the two channels provides a gauge of the position of the emission within the XP.The ratio is defined as P XP /P above XP − 1 such that negative values correspond to the emission predominantly from the XP.Given that the radiation is sensitive to ELMs and the temporal resolution is sufficient to resolve inter-ELM phases, inter-ELM values are evaluated by averaging all measurements occurring at least 5 ms after an ELM within 100 ms windows.Figure 1(d) shows that inter-ELM ratio reduces in tandem with the Ne II radial position; however, it also provides additional sensitivity after the XPR forms.
In summary, all four measurements described above can be used together to provide a tracking of the detachment state from partially detached to deeply detached conditions, including the XPR.Overall, the ratio of radiation from the two bolometer channels provides the widest sensitivity range and is available in most JET pulses; therefore, it is the primary measurement used in this paper to define the detachment state.A threshold value of 0.4 is selected to qualify the detachment, determined by the bolometry measurement before seeding and the corresponding changes in the front position after the ratio drops below 0.4.

Impurity concentrations
Impurity concentrations were determined using spectroscopy, analysing the chord-averaged intensities of near-VUV and visible Ne II and Ar II lines observed through vertically viewing sight lines from above the divertor.The impurity concentrations were derived using c Z = 4π I/TEC∆Ln 2 e where I is the radiance in ph s −1 m −2 per steradian, ∆L is the length of the emission region through the sight-line, TEC is the total atomic emission coefficients combining excitation and recombination photon emissivity weighted by their relative zero-transport ion abundancies, and n e is the electron density.The measurement technique follows the methodology described previously for N on JET [7], utilising the coefficients and line identifications established earlier on AUG as shown in the appendix of [11].The ∆L for Ne II and Ar II is determined by interpolating along the spectrometer path through the inverted 2D emission profiles, yielding values of approximately 0.15 m and 0.1 m for Ne and Ar, respectively.As in [11], n e is determined using Ne II line ratios for Ne and using Stark broadening measurements for Ar.

Divertor pressure
The prediction of q det necessitates knowledge of the divertor neutral pressure, p 0 .On AUG, this is measured by a baratron located underneath the high field side divertor.However, the equivalent measurement on JET does not exist.The divertor pressure is therefore estimated using the methodology outlined by Kallenbach et al [20], which establishes a link between the upstream (denoted by u subscript) and target (denoted by t subscript) conditions through simple two-point model considerations (i.e.f mom = 2T t n t /T u n u ).Furthermore, it replaces the dependency on target temperature by assuming it is proportional to the divertor pressure at the duct.The model, for clarity, is: Here, f rad and f mom are radiation and momentum loss factors, respectively, γ represents the sheath energy transmission factor (typically ≈ 7), L c is the connection length, α inc is the impact angle of the field line at the outer target which is typically ≈ 3 o , q ||,u is the upstream unmitigated parallel heat flux, b = λ int /λ q , and κ 0 κ Z signifies the normalised electron parallel thermal conductivity with non-unity Z eff correction.The divertor pressure is replaced with ∆p t-d p duct , where ∆p t-d is the ratio of the pressure between the outer divertor target and the pump duct.On AUG, the duct and divertor pressure were similar (i.e.∆p t-d ≈ 1) in detached L-mode conditions [21], however there has been no equivalent study on JET.The pump duct pressure can be calculated assuming particle balance: where Γ D2 is the total injected D 2 flux and v s represents the effective pumping speed, assumed to be 130 m 3 s −1 on JET [22].A molecular flux at T D2 = 300 K is assumed at the pump duct.It is shown later in section 2.5 that ∆p t-d ≈ 1.5 provides the most consistent agreement between the separatrix density and the pump duct pressure.The separatrix density, n e,u is obtained from Thomson scattering diagnostic measurements, with the separatrix position determined by matching the separatrix temperature to the twopoint model prediction.For simplicity, it is assumed that the ratio of f rad and f mom is approximately unity in equation ( 2), and that the broadening factor is proportional to b ∝ p 0.25 0 as found on AUG [20].

SOL power and width
The power crossing the separatrix is determined using P sep = P in − P rad,core − dW/dt where P in is the total injected power, P rad,core is the total radiation in the core above (but not including) the XP measured using bolometry, and W is the plasma stored energy.Notably, emission within the XP region is excluded from P sep , which is consistent with the previous study on AUG [11].Finally, λ q is determined using an experimental scaling [23], approximating it to be 2 mm.Equation ( 1) is simplified by replacing λ int with λ q and using a normalisation factor of 2.5 instead of 5.The broadening of the SOL at the target is unlikely to change significantly in the JET database, since the fuelling rate (and hence divertor pressure) is kept constant.

Detachment onset
The paper analyses data from JPNs #101 924, #101 927, #102 592, #102 597, #102 598, #102 945, #102 946, #103 281, and #103 371. Figure 2 presents time traces from a selection of these scenarios seeded with Ne-only, Ar-only, and a mixture of Ne and Ar.Typically, values of P sep fall within 10-15 MW during the seeding phase, with Ar-seeded scenarios generally exhibiting lower P sep compared to Ne-seeded scenarios.The stored energy and line-integrated density tend to remain relatively constant during the seeding phase, providing the injected power remains constant.
Impurity concentrations, obtained through spectroscopy, are displayed alongside approximations derived from the ratio of gas injection fluxes, represented as Γ CZ = (Γ Z /Z)/(Γ D + Γ Z /Z).Similar to AUG measurements, the spectroscopyderived impurity concentrations agree with the simple gas valve ratios after sufficient time has passed to reach equilibrium.However, there are certain cases where the two measurements differ by up to a factor two in steady state, as shown for Ar and Ne in figures 2(g) and (k), respectively.This could be due to wall pumping effects or incorrect calibration of the gas injection flux.
The detachment state progresses from attached or partially detached divertors to full detachment in all scenarios, as evidenced by the drop in the bolometry-measured ratio of radiation below 0.4, as shown in bottom panels of figure 2. However, there is also a consistent rise in the ratio preceding this drop, particularly noticeable in figure 2(h).The reason for this is not yet fully understood, but it could be attributed to a more pronounced reduction in inner divertor radiation measured by the channel viewing above the XP compared to the channel measuring through it.This interpretation aligns with experimental observations indicating that seeding leads to a reduction in high-density regions on the high-field side [24].ELM suppression is observed as the bolometry ratio approaches zero, consistent with the formation of an XPR.
Figure 3(a) displays the derived divertor pressures using equation (2) as a function of the bolometry ratio indicating the detachment state.Each point is time-averaged over 400 ms during intervals in each shot with steady conditions.On average, the pressure calculated with ∆p t-d = 1.5 is ≈1.5 Pa.The pressure at the pump duct, derived using equation ( 3) is ≈1 Pa in all scenarios (i.e.constant Γ D2 ).Note, a lower average pressure is found when using a higher value of ∆p t-d (and viceversa); hence, the value of ∆p t-d = 1.5 provides best agreement overall.
For the calculation of q det , an average value of 1.5 Pa is used for all impurity mixtures.Radiation efficiencies are set as f Ne = 45 and f Ne = 90 to align with the 1D model estimations.The measurements are time-averaged over the same interval as the derived divertor neutral pressure.In figure 3(b), the resulting values of q det for different mixtures of seeded impurity are presented.These results reveal a notable decrease in q det to ≈1.5 as the bolometry measurement of the detachment state falls to values <0.4,corresponding to fully detached conditions.There is consistency in values of q det among cases with different impurity mixtures in equivalent detachment states.It is noted that there is some scatter of low q det values existing in ratios above 0.4.This is likely due to the moderate increase in ratio observed just before detachment occurs.Moreover, q det does not fall below unity, even in the most extremely detached scenarios, despite the original model calibration factor being chosen such that detachment occurs for q det < 1 [5].However, this is consistent with later measurements shown on AUG [11], which also lie around 1.5 in deeply detached conditions.There are two potential reasons for this.Firstly, the original equation was based on estimations of the impurity concentration using the ratio of valve fluxes, while the latter used concentrations derived from spectroscopy.While the two tend to agree in scenarios with fully saturated wall conditions, there are cases where the spectroscopy measurements are significantly lower.Secondly, the latter measurements use a new technique on AUG to define the core radiation [25], which can provide core radiation excluding the radiation around the XP.If the radiation from the XP were included, then the q det values would be lower on both AUG and JET.It is difficult to accurately measure whether radiation is from inside or outside the core plasma around the XP, hence it was not included in this analysis.
In summary, these results provide evidence that the detachment qualifier can predict the conditions required to achieve detachment in two different sized machines with relatively similar divertor design.Furthermore, it suggests that the impurity radiation efficiencies are similar to the original model predictions, contrary to results from AUG, which suggested that Ar had a greater radiation efficiency (f Ar ≈ 200) and Ne was less efficient (f Ne ≈ 30).These radiation efficiencies are sensitive to the SOL impurity transport, which may differ between the two scenarios studied on AUG and JET.

Reattachment timescales
To investigate the fundamental timescales for divertor reattachment, impurity seeding experiments were conducted on AUG, involving the abrupt injection of an additional 5 MW of NB power.This led to a 1.5 fold rise in P sep over ≈ 200 ms, the timescale set by the fast ion slowing down and core energy confinement times.These increases in power were initiated under varying divertor conditions.
When the divertor was only weakly detached, the divertor temperature increased almost immediately and reached its maximum (steady-state) value of ≈10 eV within 100-150 ms, on a timescale similar to the transient itself.However, in cases where the divertor was strongly detached with an XPR, there was a delay of ≈100 ms before the target temperature started to change, which was thought to be due to the finite time required to ionise the neutrals in front of the target.Similar results were observed when the abrupt power increase was replaced by a cut in impurity gas injection.

Reduced model
A reduced model was proposed to predict the time required for re-ionisation of the volume of neutrals.This model was formulated to track the decay of the XPR position above the XP (measured by AXUV diodes on AUG) following a power transient [11]: and then simplified to a provide a single ionisation time by the following equation E ion ≈ 30 eV is the effective ionisation energy loss for deuterium including radiative losses, n 0 is the average neutral atom density, τ resid is the residence time of an ion, and τ ionis is the ionisation timescale.V represents the volume of the neutrals in the outer divertor leg, and L X is the connection length from the XP to the target.The value of 12 m used to normalise L X corresponds to the flux surface ≈1 mm away from the separatrix at the midplane.While the full model in equation ( 4) includes the time dependence of P sep , the simplified expression in equation ( 5) assumes that P sep is constant in time.However, given that the time dependence of P sep plays a crucial role, the simplified expression is improved by assuming a linear dependence with time, such that P sep = tP max sep /t max .The superscript 'max' indicates the maximum power increase of the transient and the time to reach the maximum.With this addition, the simple expression becomes: ) ( P max sep 0.2 s t max 4 MW To a first approximation, if all the terms in the brackets of equation ( 6) are close to unity except for those involving V, L X , and t max , then the time required for the re-ionisation of the volume of neutrals following a relatively slow transient on JET, on the order of the energy confinement time and hence around 4-5 times longer than AUG, can be simplified to t ≈ 0.09 √ (t max /0.2)(R maj /1.65) 4 ≈ 1 s.Faster transients, such as ELMs, will lead to much faster re-ionisation, which is captured by the time dependence of P sep .

Experimental observations
To validate the reduced model predictions, similar experiments were conducted on JET.Figures 4(a)-(h) compares the temporal dynamics of an XPR on JET and AUG following cuts of the impurity gas, where JPN #103 371 includes a cut in both the Ne and Ar gas for 2.5 s, followed by the reinstatement of the original impurity injection rates.Notably, on both machines, the stored energy decreases after the impurity gas cut.Time traces for the scenarios with 5 MW increases of NB injection (NBI) power are shown for both JET and AUG in figures 4(i)-(m).However, for JPN #103 281, the pulse disrupts after 1 s.
The timescale of the power transient following the impurity gas cut depends on the impurity decay rate, which is sensitive to the impurity enrichment (divertor over core impurity concentration ratio).The dynamics following the gas cut are highlighted in figure 5, which shows the Ar concentration starting to decay around 300 ms after the cut, exhibiting an exponential decay rate of ≈450 ms.In contrast, the Ne concentration starts to decline ≈500 ms following the cut, with an exponential decay rate of ≈600 ms.The delay after the gas valve closes appears to be consistent with the delay in the impurity concentration rising after the gas valve is initially opened at the beginning of the seeding phase (see figures 4(c) and (k)).In contrast, the impurity concentration rises and falls almost immediately after the gas valves open and close on AUG.The trend in decay rates between Ne and Ar on JET is consistent with AUG measurements, which showed a slower decay rate for Ne compared to Ar. Ne is also typically observed to have a lower enrichment on AUG [26], and this evidence on JET is consistent with that hypothesis.After the gas cut, there is a clear change in the detachment state, as shown by the detachment indicator in figure 4(d).
In the case of the NBI power increase, there is no obvious change in the detachment state following the power increase on JET, as shown in figure 4(l).However, the ELMs do reappear after ≈200 ms, which suggests that the XPR is reduced.Reattachment is more clearly observed on AUG for the similar power transient.However, the power increase on JET was a factor ≈1.2, in comparison to a factor ≈1.5 on AUG.A moderately higher factor of ≈1.33 was observed following the impurity gas cut on JET.This likely indicates that equation (4) needs to account for the fact that small increases in power increases may not lead to steady state reattachment.Furthermore, it was already highlighted that the model does not account for radiation in the SOL, which will impact the amount of power reaching the divertor.

Model validation
Figure 6 provides closer examination of the divertor timescales on JET following both power transitions, comparing all three detachment state indicators.Firstly, following the impurity gas cut, there is a ≈300 ms delay between the gas valve being closed and the impurity concentration beginning to decay; therefore, timescales are compared accounting for this additional delay.Both the Ne II radiation edge and the bolometry ratio lose sensitivity ≈700 ms after the impurity begins to decay.The Ne IV radiation edge position loses sensitivity ≈200 ms later.
The full model to predict the evolution of the neutral ionisation is re-formulated to predict the bolometry detachment indicator as follows: Given that the plasma conditions and magnetic equilibrium are similar between the AUG and JET experiments, the leading order difference is assumed to be the major radius.Therefore, the volume is scaled to the AUG result by a factor 8 (determined by taking typically quoted plasma volumes of JET and AUG as 100 m 3 over 13 m 3 ) and the ratio τ resid /τ ionis ∝ L X is scaled by a factor ≈2 determined by the ratio of major radii.The resulting evolution is shown by the red dashed line in figure 6(d) and shows good agreement to the measurement.The Ne II and Ne IV both confirm that very little movement of the emission is observed during the NBI power increase.This is in disagreement to the model, which would have predicted ionisation of the neutrals within a similar timescale to the scenario with an impurity gas cut.This indicates that SOL radiation plays an important role; however, it is challenging to measure the SOL radiation with such fine precision.Alternatively, it is not clear if the front would have re-ionised if the plasma had not disrupted.
It is noted that previously published JET data did observe re-ionisation of the neutral front within ≈1 s when the heating was increased to 15 MW over a baseline of 8 MW [19].While this resulted in a similar rise in P sep , the relative factor increase in power was significantly greater than the scenario described above.It is therefore expected that the model for reattachment is only valid if the fraction increase in power is sufficiently high (i.e.>1.3).
Nonetheless, despite these caveats, the model successfully predicts the reattachment timescale on JET during the impurity gas cut.Table 1 provides an overview all relevant timescales from AUG and JET together.Further work is required to validate the model at significantly different divertor pressures, perturbation timescales, and in machines with alternative divertor geometries.However, Ar is also observed to achieve a greater level of enrichment than Ne on AUG, primarily due to its lower first ionisation potential [26].This observation strengthens the argument for Ar as a preferred SOL radiator in reactors.
Injection of Ne and Ar both act to increase the core radiation and the average core charge (Z eff ).However, on JET it is observed that Ar acts more strongly on the core radiation, while Ne mostly impacts the Z eff .For ITER, which is expected to operate near the L-H threshold, the use of Ar could lead to a transition to L-mode due to reduced power crossing the separatrix.In DEMO, which is expected to operate at high core radiation fraction, high Z eff may be a bigger problem due to fuel dilution.
In current machines, mixing the impurities can provide benefits.For instance, on AUG, introducing a baseline level of N alongside Ne helps to maintain the ELM frequency which, in turn, assists in removing impurities from the core.On JET, seeding with Ne-only tends to lead to transitions back into L-mode, while seeding with Ar-only can cause issues with NBI neutral re-ionisation.Seeding with an Ne and Ar mixture avoided both of these issues.However, there is no evidence that shows a benefit of mixing impurities that is directly scalable to a reactor.The most optimal mixture may depend on where the margin exists in the operating scenario (i.e. on fuel dilution or core radiation) or it may be dictated by engineering limits.
Finally, the investigations reveal that the time required for full re-ionisation of the neutral volume between the XP and outer divertor target under fully detached conditions is approximately 1 s on JET.This aligns well with the simplified model predictions derived from AUG data.Future research should aim to further validate these model predictions by exploring reattachment in scenarios with varying neutral pressure conditions and in alternative divertor geometries.

Figure 1 .
Figure 1.Divertor detachment state measurements over time, including (a) the jsat signal through the outer target probe (as shown by the red circle in (e), (b) the edge radius of the Ne II emission zone tracked by an algorithm analysing inverted camera images (as shown by symbols in (e)-(h)), (c) the edge radius of Ne IV emission zone measured by the vertically viewing divertor spectrometer, and (d) the ratio of the total radiation through the X-point and above the X-point measured using bolometry.Subfigures (e)-(h) show tomographic inversions Ne II emission from inverted camera images on JET, normalised to the peak emission in each frame and then artificially saturated to emphasise the outer divertor radiation location.The horizontal (b)-(c) and vertical (f )-(g) dashed lines are shown for reference to visualise where the radial measurements correspond to in 2D poloidal space.The upstream location represents where the Ne II and Ne IV radiation saturates in XPR.

Figure 2 .
Figure 2. Time traces from JET scenarios with Ne-seeding, Ar-seeding, and a Ne-Ar mixture are shown in (a)-(l).An example of the Ar seeding scenario from ASDEX Upgrade, used for comparison, is shown in (m)-(p).The horizontal dashed line in (d), (h), and (l) indicate the choice of bolometer chord ratio to qualify the detachment.

Figure 3 .
Figure 3. Time-averaged predictions of (a) divertor neutral pressure and (b) detachment qualifier as a function of bolometry-measured detachment state.

Figure 4 .
Figure 4. Time traces from equivalent JET and AUG scenarios demonstrating divertor dynamics following prompt changes in upstream power driven by a cut to impurity gas flows, as shown in the first two columns (a)-(h) and an increase in neutral beam power, as shown in the last two columns (i)-(p).

Figure 5 .
Figure 5. Measured divertor impurity residence times for Ne and Ar following the gas cut in JPN #103 371.Equivalent measurements of Ne and Ar from AUG are shown for reference.The red lines represent the fitted decay rates.

Figure 6 .
Figure 6.Comparison of all detachment state indicators (see figure 1) for the JET scenarios, with the time axis normalised to the power transient time.The dashed black line in (d) and (h) corresponds to the simple model predictions described in the text.

Table 1 .
Overview of experiments analysing the timescale for neutral ionisation at the divertor following perturbations in power.