2.1. Physics model

A one-dimensional fluid model of the plasma available in the Dream code is applied. This is a finite-volume numerical simulation framework that has been developed for tokamak disruption modelling, with a particular focus on the runaway electron dynamics. It evolves the plasma current self-consistently, along with the thermal bulk of electrons, and charge states of the relevant ionic species – all in a realistic toroidally symmetric magnetic geometry. In this section, the relevant equations and physical assumptions are described in detail.

2.1.1. Plasma current

The plasma current density $j_\parallel$ consists of an Ohmic component $j_\Omega$ , and a component $j_{\textrm {re}}$ carried by runaway electrons. Other non-inductively driven currents, such as the bootstrap current, are not included in this model as these are expected to convert to Ohmic current during a disruption. The total current density is related to the poloidal magnetic flux $\psi _{\textrm {p}}$ , as described by Ampère’s law

(2.1) \begin{equation} 2\pi \mu _0\left \langle \boldsymbol{B}\cdot \boldsymbol{\nabla }{\varphi }\right \rangle \frac {j_\parallel }{B} =\frac {1}{V'}\frac {\partial }{\partial {r}}V'\left \langle \frac {|{\boldsymbol{\nabla }{r}}|^2}{R^2}\right \rangle \frac {\partial {\psi _{\textrm {p}}}}{\partial {r}}, \end{equation}

where $\mu_0$ is the permeability of free space,  $\langle \cdot \rangle$ denotes flux surface average, $\boldsymbol{B}$ the magnetic field, $R$ the major radius and $V'$ is the spatial Jacobian ( $\textrm {d}{V}=V'\textrm {d}{r}$ being the volume between two infinitesimally close flux surfaces). These depend on the particular magnetic equilibrium $\boldsymbol{B}(r, \theta )$ used in the simulation set-up, which is treated as static in this model. Note that radial coordinate $r$ is defined as the distance on the midplane from the magnetic axis $R={R_0}$ to the corresponding flux surface on the low-field side.

The poloidal magnetic flux $\psi _{\textrm {p}}$ is evolved using a modified version of Faraday’s law of induction

(2.2) \begin{equation} \frac {\partial {\psi _{\textrm {p}}}}{\partial {t}} =-2\pi \frac {\left \langle \boldsymbol{E}\cdot \boldsymbol{B}\right \rangle }{\left \langle \boldsymbol{B}\cdot \boldsymbol{\nabla }{\varphi }\right \rangle } +\mu _0\frac {\partial }{\partial {\psi _{\textrm {t}}}}\psi _{\textrm {t}}\varLambda \frac {\partial }{\partial {\psi _{\textrm {t}}}}\frac {j_\parallel }{B}. \end{equation}

This is the loop voltage, of which the first term on the right-hand side is proportional to the component of the electric field $\boldsymbol{E}$ parallel to the magnetic field driving the Ohmic component of the current according to Ohm’s law $j_\Omega /B=\sigma \langle \boldsymbol{E}\cdot \boldsymbol{B}\rangle /\langle B^2\rangle$ . The parallel electric conductivity is modelled as outlined in Redl et al. (Reference Redl, Angioni, Belli and Sauter2021). It is a neoclassical correction of the Spitzer conductivity $\sigma \propto T_e^{3/2}$ accounting for trapped particle effects at arbitrary collisionality.

The second term in (2.2), derived by Boozer (Reference Boozer1986), involves a second-order derivative in the toroidal magnetic flux $\psi _{\textrm {t}}=(2\pi )^{-1}\int V'\textrm {d}{r}\langle \boldsymbol{B}\cdot \boldsymbol{\nabla }{\varphi }\rangle$ , which is used as a radial coordinate. Given the relation in (2.1), this term is in fact a fourth-order radial derivative, and thus describes the hyperdiffusion of $\psi _{\textrm {p}}$ . Whenever $\Lambda$ is greater than zero, this term acts to relax $j_\parallel /B$ while conserving the helicity content of the plasma. This leads to a transient increase in $I_{\textrm {p}}$ as the current density radially redistributes in what is referred to as the ‘ $I_{\textrm {p}}$ -spike’. This emulates the effects that the break-up of magnetic field lines has on the current density, and is used to model the enhanced transport event during the thermal quench phase of a disruption with strong field stochastisation. This is explained in more detail in § 2.2.

As boundary condition for the plasma edge flux $\psi _{\textrm {p}}(a)$ , we couple it to an ideally conducting wall at $r=b\gt a$ . By doubly integrating (2.1) over the vacuum region $a\lt r\lt b$ , in which $j_\parallel =0$ , we can relate the plasma edge flux to that of the wall $\psi (b)=\psi (a)+M_{\textrm {ab}}I_{\textrm {p}}$ , where $M_{\textrm {ab}}=\mu _0{R_0}\ln (b/a)$ is the edge–wall mutual flux inductance taken in the cylindrical limit $a/R\to 0$ . We consider a wall that is perfectly conducting, meaning no electric field is induced in the wall and thus the wall flux remains constant in time.

In addition to the Ohmic component, the plasma current can also contain a component driven by runaway electrons. Without resolving the electron distribution in momentum space, the runaway electrons are assumed to travel at the speed of light $c$ , and their contribution to the total plasma current density is given by $j_{\textrm {re}}=ecn_{\textrm {re}}$ , with $e$ being the elementary charge. The evolution of the runaway density $n_{\textrm {re}}$ also includes diffusive transport with the diffusion coefficient set to $D_{\textrm {re}}=1\,\textrm{m}^2\,\textrm{s}^{-1}$ , and a set of source terms accounting for the runaway electron generation mechanisms. These include Dreicer generation, which is calculated by a neural network that has been trained on kinetic simulations (Hesslow et al. Reference Hesslow, Unnerfelt, Vallhagen, Embreus, Hoppe, Papp and Fülöp2019b ; Ekmark et al. Reference Ekmark, Hoppe, Fülöp, Jansson, Antonsson, Vallhagen and Pusztai2024); hot-tail generation, as calculated in § 4.2 of Svenningsson (Reference Svenningsson2020); and a model for the avalanche growth rate, which accounts for the effects of partially screened nuclei in non-ideal plasmas (Hesslow et al. Reference Hesslow, Embréus, Vallhagen and Fülöp2019a ). A negligible generation of runaways is expected for the plasma scenarios considered in this work, but the respective terms are included for completeness as these models are readily available in Dream and are relatively inexpensive computationally. Runaway electrons were so far not observed in ASDEX Upgrade SPI experiments with neon and deuterium–neon injections. Our simulations help explain that this is due to insufficient generation, rather than due to runaway seed losses preventing avalanche.

2.1.2. Ions and SPI dynamics

Ions and neutral atoms are characterised both by a temperature $T_i$ , and a set of densities $n_i^{(j)}$ for every species $i$ with atomic number $Z_i$ , and charge state $j=0,\ldots, Z_i$ . The densities are evolved according to

(2.3) \begin{align} \frac {\partial {n_i^{(j)}}}{\partial {t}}&=\mathcal{I}_i^{(j-1)}n_i^{(j-1)}n_e-\mathcal{I}_i^{(j)}n_i^{(j)}n_e +\mathcal{R}_i^{(j+1)}n_i^{(j+1)}n_e-\mathcal{R}_i^{(j)}n_i^{(j)}n_e\nonumber\\ &\quad{} +\delta _{0j}\sum _{k=1}^{N_{\textrm {frag}}}\mathcal{G}_k \frac {\delta (r-r_k)}{4\pi r^2{R_0}} +\frac {1}{V'}\frac {\partial }{\partial {r}}V'\bigg(A_in_i^{(j)}+D_i\frac {\partial {n_i^{(j)}}}{\partial {r}}\bigg). \end{align}

The first four terms describe ionisation and recombination processes, for which the coefficient $\mathcal{I}_i^{(j)}$ denotes the rate of ionisation between the two charge states $j\to j+1$ , and $\mathcal{R}_i^{(j)}$ the rate of recombination between $j\to j-1$ . These coefficients are extracted from the OpenADAS database (Summers Reference Summers2004).

The fifth term describes a source into the neutral state $n_i^{(0)}$ of the injected material, as the fragments travel along their trajectories $r_k(t),\, k=1,\ldots N_{\textrm {frag}}$ , depositing ablated material. The rate at which a fragment decreases in diameter $d_k(t)$ is $\dot {d}_k=-2\mathcal{G}_k\mathcal{M}/(\pi d_k^2 \rho N_{\textrm {A}})$ , where $\mathcal{M}$ is the pellet molar mass, $\rho$ the pellet mass density and $N_{\textrm {A}}$ Avogadro’s number. The rate of the deposition of neutrals per unit time $\mathcal{G}_k$ is calculated using a version of the neutral gas shielding (NGS) model, first derived by Parks and Turnbull (Reference Parks and Turnbull1978) and further extended upon by Parks (Reference Parks2017) to allow for mixed deuterium–neon pellets. The NGS model provides the scaling law $\mathcal{G}_k\propto \lambda n_e^{1/3}T_e^{5/3}d_k^{4/3}$ , where $\lambda$ (along with $\mathcal{M}$ and $\rho$ ) is a function of the neon fraction of the pellet $f_{\textrm {Ne}}=N_{\textrm {Ne}}/(N_{\mathrm{D_2}}+N_{\textrm {Ne}})$ .

The sixth and final term in (2.3) describes both advective and diffusive particle transport, for which the transport coefficients $A_i$ and $D_i$ are active during the thermal quench (similarly to $\Lambda$ ). More on this in § 2.2.

For each ion species, a temperature $T_i$ , which is assumed to be same for all charge states, is evolved via collisional heat exchange with the bulk electron population and other ion species present in the plasma, according to

(2.4) \begin{equation} \frac {3}{2}\frac {\partial {{n_i}T_i}}{\partial {t}} =\sum _{i'}Q_{ii'}+Q_{ie}, \end{equation}

with the total density ${n_i}=\sum _{j=0}^{Z_i}n_i^{(j)}$ . Here, $Q_{\alpha \beta }$ is the collisional heat exchange between Maxwellian species $\alpha$ and $\beta$ , which is is proportional to their temperature difference, as further detailed in Hoppe et al. (Reference Hoppe, Embreus and Fülöp2021).

2.1.3. Thermal electrons

The evolution of the electron temperature $T_e$ is modelled using an energy balance equation

(2.5) \begin{align} \frac {3}{2}\frac {\partial {n_eT_e}}{\partial {t}}&= \frac {j_\Omega }{B}\left \langle \boldsymbol{E}\cdot \boldsymbol{B}\right \rangle -n_e\sum _i\sum _{j=0}^{Z_i-1}L_i^{(j)}n_i^{(j)} +\mathcal{P}_{\textrm {ion}}\nonumber\\ &\quad{} +\frac {j_{\textrm {re}}}{B}E_{\textrm {c}}\left \langle B\right \rangle +\sum _i Q_{ei} +\frac {1}{V'}\frac {\partial }{\partial {r}}V'\frac {3n_e}{2}{\chi _e}\frac {\partial {T_e}}{\partial {r}}, \end{align}

in which the first term on the right-hand side describes Ohmic heating, and the second radiative cooling due to line radiation, recombination radiation and bremsstrahlung. Integrating this term over the plasma volume yields the total radiated power, which we will denote as $P_{\textrm {rad}}$ . Typically, this energy balance is dominated by Ohmic heating and radiative cooling, both of which are nonlinear functions of the electron temperature. The rates of energy loss $L_i^{(j)}(n_e, T_e)$ for neon are retrieved from OpenADAS (Summers Reference Summers2004). Deuterium is instead assumed to be opaque to Lyman radiation, which reduces the radiative losses at temperatures below $10\,\textrm {eV}$ ; for this the loss rates are extracted from the AMJUEL database (Reiter Reference Reiter2020).

The third term, $\mathcal{P}_{\textrm {ion}}$ , represents the change in potential energy due to the electron–ion binding energy removed by the electron bulk during ionisation and added during recombination. With the ionisation threshold energies $\Delta W_i^{(j)}$ obtained from the NIST database (Kramida et al. Reference Kramida, Ralchenko and Reader2020), this contribution to the energy balance is calculated by adding up the terms $\Delta W_i^{(j)}(\mathcal{R}_i^{(j)}-\mathcal{I}_i^{(j)})n_i^{(j)}n_e$ over all charge states.

Collisional heat transfer from the runaway electrons is accounted for with the fourth term, for which $E_{\textrm {c}}=n_e e^3\ln {\Lambda }/(4\pi \varepsilon _0^2 m_e c^2)$ , where $\ln\Lambda$ is the Coulomb logarithm, $\varepsilon_0$ the permittivity of free space, and $m_e$ the mass of the electron. The fifth term is the collisional heat transfer between electrons and ions $Q_{ei}=-Q_{ie}$ , and the final term describes diffusive heat transport, with $\chi _e$ being the heat diffusivity. A baseline value of ${\chi _e}=1\,\mathrm{m}^2\,\mathrm{s}^{-1}$ is used throughout.

2.2. Enhanced transport event

To emulate the effect of the magnetic field stochastisation during the thermal quench that causes the thermal energy loss, an enhanced radial transport of heat, particles and poloidal magnetic flux is applied at a time $t_{\textrm {relax}}$ . As previously done in ITER studies by Vallhagen et al. Reference Vallhagen, Hanebring, Artola, Lehnen, Nardon, Fülöp, Hoppe, Newton and Pusztai(2024a), we take $t_{\textrm {relax}}$ to be the time when the electron temperature drops below $10\,\textrm {eV}$ somewhere inside of the resonant $q=2$ surface. The choice of this particular criterion for triggering the enhanced transport event is motivated by the fact that the conductivity at $10\,\textrm {eV}$ is sufficiently low to likely trigger a resistive MHD instability at the resonant $q=2$ flux surface on a millisecond time scale.

In the simulation the transport event is emulated by increasing any transport coefficient $\mathcal{Y} \in \{ \Lambda , A_i, D_i, {\chi _e} \}$ from their baseline value $\mathcal{Y}_0$ up to some maximum value $\mathcal{Y}_{\textrm {max}}$ , which then exponentially decays over a time scale of $\tau _{\textrm {decay}}=1\,\textrm {ms}$ , according to

(2.6) \begin{equation} \mathcal{Y}(t) =\mathcal{Y}_0 +(\mathcal{Y}_{\textrm {max}}-\mathcal{Y}_0)\exp \left (-\frac {t-t_{\textrm {relax}}}{\tau _{\textrm {decay}}}\right )\!\varTheta (t-t_{\textrm {relax}}), \end{equation}

where $\varTheta$ denotes the Heaviside function. In particular, this concerns the hyperdiffusivity $\Lambda$ in (2.2), the ion and neutral particle advection and diffusion coefficients $A_i$ and $D_i$ in (2.3) and the electron heat diffusivity $\chi _e$ in the energy balance (2.5). We omit the enhanced transport of runaway electrons, as all simulated cases considered here yield already negligible runaway currents. We have conducted a sensitivity study for the impact of $\Lambda _{\textrm {max}}$ on current quench evolution in the range of $\Lambda _{\textrm {max}}=[1\times 10^{-7}-1\times 10^{-3}]\,\mathrm{Wb^2}\, \textrm{m}^2\,\textrm{s}^{-1}$ . By selecting $\Lambda _{\textrm {max}}=6.3\times 10^{-5}\,\mathrm{Wb^2}\,\textrm{m}^2\,\textrm{s}^{-1}$ , we observe an increase in the plasma current during the $I_{\textrm {p}}$ -spike similar to the experiment ( $\Delta I_{\textrm {p}}\sim 20\,\textrm {kA}$ for the cases studied here). The impact of $\Lambda _{\textrm {max}}$ in this range on the radiated energy fraction is between $\pm 2\,\%$ and $\pm 5\,\%$ , depending on the pellet composition. The maximum value of the other transport coefficients are set to $A_{i,\textrm {max}}=-100\,\textrm{m}\,\textrm{s}^{-1}$ , $D_{i,\textrm {max}}=100\,\textrm{m}^2\,\textrm{s}^{-1}$ and $\chi _{e,\textrm {max}}=100\,\textrm{m}^2\,\textrm{s}^{-1}$ . Similar values were used in ASTRA simulations of massive gas injection scenarios in AUG by Linder et al. (Reference Linder, Fable, Jenko, Papp and Pautasso2020) to reproduce the evolution of line-integrated electron densities from experiment.

2.3. Fragment sampling

The generation of the fragment plume is performed in two steps: a rejection sampling of fragment sizes, utilising an analytical distribution function $f(d)$ for the characteristic fragment diameter $d$ following the pellet break-up; and then assigning velocities $\boldsymbol{v}$ to the individual fragments. This results in a set of tuples $\{(d_k, \boldsymbol{v}_k)\}$ , with $k=1,\ldots, N_{\textrm {frag}}$ .

The fragment size probability distribution stems from a statistics-based model for the shattering of brittle materials, initially derived in the context of exploding munitions by Mott and Linfoot (Reference Mott and Linfoot1943), and then more recently by Parks (Reference Parks2016) in the context of shattered cryogenic pellets. This has subsequently been correlated with relevant injection parameters to experimentally measured fragment distributions to yield a modified analytical distribution for the fragment size (Gebhart et al. Reference Gebhart, Baylor and Meitner2020a ,Reference Gebhart, Baylor and Meitner b ), which is used in this paper. For a cylindrical pellet of diameter $D$ and length $L$ injected with an impact velocity $v_\perp =v_{\textrm {inj}}\sin \theta _{\textrm {s}}$ (component of the injection velocity $v_{\textrm {inj}}$ normal to the shatter plane at an angle $\theta _{\textrm {s}}$ ), this fragmentation model yields the characteristic size distribution

(2.7) \begin{equation} f(d) =\alpha d K_0(\beta d). \end{equation}

Here, $\alpha =X_{\textrm {R}}/D$ , $\beta =X_{\textrm {R}}/LC$ and $X_{\textrm {R}}=v_\perp ^2/v_{\textrm {thres}}^2$ , the latter of which is the ratio of the impact energy and the threshold energy required to initiate fracture in the pellet and $K_0$ is the modified Bessel function of the second kind accounting for the energy propagation through the pellet. The material parameters $C$ and $v_{\textrm {thres}}$ depend on the neon–deuterium content ratio $f_{\textrm {Ne}}$ of the pellet, both of which are obtained from Gebhart et al. Reference Gebhart, Baylor and Meitner(2020b). Fragments are sampled from (2.7) in sequence until the sum of all fragment volumes exceeds the pellet volume, after which the final fragment is shrunk such that the total volume equals that of the pellet. In doing so, $N_{\textrm {frag}}$ will depend on the specific random seed used during the sampling process.

The next step concerns assigning velocities to each fragment. For simplicity, the magnitude and direction are sampled independently from one another and uncorrelated to the corresponding fragment’s size. The velocity magnitude $v_{\textrm {frag}}$ is sampled from a normal distribution, where the mean fragment speed $\overline {v}_{\textrm {frag}}$ is assumed to be given by the average of the injection speed $v_{\textrm {inj}}$ and its component parallel to the shattering surface at an angle of $\theta _{\textrm {s}}=12.5^\circ$ , i.e. $\overline {v}_{\textrm {frag}}=v_{\textrm {inj}}(1+\cos \theta _{\textrm {s}})/2$ , and the spread is set to be $\Delta v_{\textrm {frag}}/\overline {v}_{\textrm {frag}}=20\,\%$ (see Peherstorfer Reference Peherstorfer2022). Finally, each fragment is assigned a direction in which it traverses through the plasma at constant speed that is sampled uniformly within a circular cone with an opening angle of $20^\circ$ (Peherstorfer Reference Peherstorfer2022).

2.4. Simulation set-up

Each simulation presented in this paper uses initial conditions from the representative AUG discharge no. 40655, which is an H-mode deuterium plasma with a major radius of the magnetic axis ${R_0}=1.74\,\textrm {m}$ , minor radius $a=0.39\,\textrm {m}$ (midplane low-field side distance from $R_0$ to the last closed flux surface) and on-axis toroidal magnetic field $B_0=1.81\,\textrm {T}$ . Reconstructed magnetic equilibrium data and relevant initial plasma profiles are taken at $t=2.3\,\textrm {s}$ , which is approximately the time of the SPI trigger, all of which are obtained from the integrated data analysis (IDA) framework (Fischer et al. Reference Fischer, Fuchs, Kurzan, Suttrop and Wolfrum2010, Reference Fischer2016, Reference Fischer, Giannone, Illerhaus, McCarthy and McDermott2020). The IDA framework applies Bayesian probability theory to the combined analysis of multiple diagnostics and physical modelling to obtain the most cohesive profile reconstructions and uncertainty estimates.

The reconstruction of the initial electron density profile $n_e$ is based on both deuterium cyanide laser interferometry and Thomson scattering spectroscopy, and the electron temperature $T_e$ is based on the latter. The initial thermal ion temperature $T_i={T_{\textrm {D}}}$ is based on charge exchange recombination spectroscopy. Furthermore, neutral beam injection (NBI) provides a non-negligible population of super-thermal fast ions, for which IDA makes estimates of the fast ion density $n_{\textrm {fi}}$ and pressure $p_{\textrm {fi}}$ profiles based on kinetic modelling using the RABBIT code (Weiland et al. Reference Weiland, Bilato, Dux, Geiger, Lebschy, Felici, Fischer, Rittich and van Zeeland2018). With the fast ions being made up of ionised deuterium, and assuming the pre-SPI plasma is ideal, the quasi-neutrality criterion implies that the initial thermal ion density can be expressed as $n_{\textrm {D}}=n_e-n_{\textrm {fi}}$ . The total plasma pressure $n_eT_e+n_{\textrm {D}}{T_{\textrm {D}}}+p_{\textrm {fi}}$ is then used to solve for the magnetic equilibrium in the Grad–Shafranov equation, which is done iteratively since these profiles themselves depend on the equilibrium (see Fischer et al. Reference Fischer2016).

In this model we do not resolve the momentum space distribution of any of the particle species involved. Instead, the thermal and fast ions are incorporated into a single Maxwellian distribution, with density $n_{\textrm {D}}=n_e$ and a rescaled temperature as to maintain the total plasma pressure. By doing this, it is effectively assumed that these fast ions instantaneously thermalise at the start of the simulation. It is also assumed that NBI is turned off at this point in time, meaning no further fast ions are introduced.

The corresponding flux surface geometry, with the SPI plume indicated, and the relevant plasma profiles are shown in figure 1. Note that the total current density from experiment includes bootstrap current and the NBI-driven current, which is here incorporated into the Ohmic current, as shown in figure 1(d). This is motivated by the fact that the bootstrap current quickly becomes Ohmic as a result of the relaxation of the pressure profile during the enhanced transport event. The NBI-driven current is turned off by the control system as soon as insufficient absorption is detected, and since we do not model the complex control system logic, this contribution to the total current is omitted.

Figure 1. Input data based on the reference AUG discharge no. 40655, used in all simulations presented. The illustration in (a) shows the flux surface geometry and the SPI plume, within which all fragments travel in straight lines originating from the shatter point. The particular shatter head considered in this study has a square cross-section with $22\,\textrm {mm}$ side lengths, and a shatter angle $\theta _{\textrm {s}}=12.5^\circ$ . Flux surfaces are indicated in red, and the $q=2$ surface is marked in blue. The initial plasma profiles used in this work consist of (b) density and (c) temperature profiles of the bulk electrons (blue), thermal ions (red) and fast ions (green) and (d) the initial current density.

The radial coordinate is discretised on a grid with $n_r=11$ points, and for the time coordinate we use an adaptive time step based on the assumption that the shortest time scales are those of ionisation $\tau _{\textrm {ionis}}\sim |{\partial \log n_e/\partial t}|^{-1}$ . It sets the next time step according to $\Delta t=\min (\Delta t_{\textrm {max}}, \alpha \tau _{\textrm {ionis}})$ , where we set $\Delta t_{\textrm {max}}=10^{-6}\, \textrm {s}$ as the maximum allowed time step and $\alpha =10^{-3}$ . With this set-up, depending on the pellet neon content, the typical wall-clock time for the simulations considered here is between 5 and 15 minutes on a computer running on an AMD EPYC 9354 processor.

2.5. Experimental cases selected for comparison

The SPI system installed for the 2022 AUG SPI experimental campaign is highly flexible, with three different shatter heads, of which two have a square cross-section at a $\theta _{\textrm {s}}=12.5^\circ$ and $25^\circ$ shatter angle, respectively, and the third has a circular cross-section at $\theta _{\textrm {s}}=25^\circ$ . With two different shatter angles it is possible to isolate the normal impact velocity $v_\perp =v_{\textrm {inj}}\sin \theta _{\textrm {s}}$ , which sets the fragment size distribution as given in (2.7), and the velocity distribution of the fragments $v_{\textrm {frag}}$ . A detailed description of the SPI system is provided by Dibon et al. (Reference Dibon2023) and Heinrich et al. (Reference Heinrich, Papp, de Marné, Dibon, Jachmich, Lehnen, Peherstorfer and Vinyar2024).

In the 2022 AUG SPI campaign, approximately 180 SPI shots were carried out with this same H-mode scenario, of which no. 40655 was selected as the representative discharge. To represent a scan in injected neon quantity, we have chosen a small subset of discharges from the same scenario, each of which have relevant plasma parameters (such as plasma stored energy or pedestal top temperature) within ${\lesssim}5\,\%$ of the reference shot. In this paper, all the considered cases are pellets injected via the square shatter head with $\theta _{\textrm {s}}=12.5^\circ$ (GT3). With input conditions all based on the reference AUG discharge no. 40655, as described in § 2.4, only the injection parameters are modified when modelling the various discharges, mainly the fraction of neon $f_{\textrm {Ne}}$ in the injected pellet. An overview of the different set-ups is shown in Table 1. The values for the pellet length $L$ , diameter $D$ and injection speed $v_{\textrm {inj}}$ are based on image processing analysis by Peherstorfer (Reference Peherstorfer2022). Note, that the 40 % neon case has a higher injection velocity than the rest. There were no experiments executed in 2022 with 40 % neon and a matching velocity, but we nevertheless wished to include a neon fraction case between 10 % and 100 % in the experimental comparison. For each discharge we run 40 otherwise identical simulations with varying random seeds, resulting in a variation in the number of fragments sampled between the simulations. The last column in Table 1 includes the average and standard deviation in the number of fragments.

Table 1. The SPI parameters used in the simulations of the considered AUG discharges, being the pellet neon fraction $f_{\textrm {Ne}}$ , number of injected neon atoms $N_{\textrm {Ne}}$ , pellet length $L$ and diameter $D$ and pellet injection speed $v_{\textrm {inj}}$ . All injections use the $\theta _{\textrm {s}}=12.5^\circ$ shatter head with a square cross-section – corresponding to guide tube 3 (GT3) in the 2022 experimental set-up – as indicated in figure 1(a). The final column shows the mean and standard deviation in the number of fragments generated using these parameters, based on 40 samplings of the fragment size distribution (2.7).