Analysing the effects of heating and gas puffing in Proto-MPEX helicon and auxiliary heated plasmas

The Material Plasma Exposure Experiment (MPEX) is being constructed at Oak Ridge National Laboratory to investigate critical fusion reactor issues, such as plasma–material interactions (PMIs) under reactor-relevant conditions and time scales. The linear device Proto-MPEX was used as a test bed to address anticipated research and development issues associated with heating scenarios and establish the physics basis for MPEX. The SOLPS-ITER code suite has been applied to understand plasma and neutral transport in Proto-MPEX and to increase confidence in predictive simulations for MPEX. Coupling between COMSOL and SOLPS is performed to implement a 2D electron heating profile of the helicon source. The simulations show reasonable agreement with the experimental data for plasma with helicon and auxiliary electron cyclotron heating (ECH). Both Bohm and constant diffusion (D ⊥ : 0.5 m2 s−1 and χ⊥ : 1 m2 s−1) simulations show similar levels of agreement with respect to the sparse experimental data available, assuming a few per cent impurity concentration. ECH significantly increases the target electron temperature, however, the target electron density is reduced compared to helicon-only heated plasmas due to an increase in flow velocity and radial losses. The simulations show that further increasing the ECH power results in an increase in the target electron density due to increased recycling flux and ionization. The results indicate that ECH significantly enhances the target heat flux, with ECH power of 50 kW increasing the target heat flux from 0.4 to 17 MW m−2. It is found that a small amount of gas puffing (GP) near the target plate can further increase the target heat fluxes at the higher ECH power cases, but the target heat flux is reduced at higher GP conditions due to a significant reduction in electron temperature via radiation. ECH and GP scenarios can generate a higher target flux, facilitating improved PMI studies with more reactor-relevant plasma conditions.


Introduction
Plasma-material interaction (PMI) that may damage the first wall and divertor components represents a significant barrier to the development of a fusion reactor. Both in steady-state and during transient events, a huge amount of heat and particle fluxes strike the plasma-facing components [1,2], potentially causing significant damage, such as cracking, erosion, melting, and embrittlement. For this reason, exploring and understanding PMI at reactor-scale flux levels is an important research topic for present and future fusion devices. Linear plasma devices can reproduce the divertor conditions of a tokamak reactor, which allows for material development studies and validation of relevant predictive and interpretive simulations. Linear plasma devices also contribute to the understanding of critical fusion reactor issues, such as divertor detachment, plasma fuelling, confinement, heating, and PMI [3][4][5][6][7][8]. The plasma discharge time is relatively small for most current toroidal devices. Hence, it is necessary to construct a linear plasma device to address research issues in sustained steadystate conditions, closely resembling the fusion reactor scale.
The Material Plasma Exposure Experiment (MPEX) is a linear plasma device presently being constructed at Oak Ridge National Laboratory with the goal to investigate the physical mechanisms of PMI and divertor issues under reactor-relevant conditions [9,10]. The unique features of MPEX compared to present linear plasma devices will be (1) high plasma fluxes to the target, (2) long pulse steady-state operation up to 10 6 s, (3) a plasma heating system able to provide electron temperatures and ion temperatures in front of the target representative of those in a fusion reactor divertor, and (4) the ability to expose a priori neutron irradiated samples at relevant ambient material temperatures. In MPEX, long pulse operation will be achieved via a steady-state high power helicon antenna, electron cyclotron heating (ECH), and ion cyclotron resonance frequency (ICRF) [9,10]. This enables independent tuning of electron and ion temperatures. To address the RD issues associated with MPEX, a smaller device, Proto-MPEX, was constructed to study the heating scenarios and magnetic field configurations required to achieve fluxes that extrapolate to the MPEX design requirements [9][10][11][12][13][14][15][16][17].
The impact of auxiliary heating effects has been studied in other linear devices, such as GAMMA 10/PDX. In GAMMA 10/PDX, a short pulse (5 ms) of ECH significantly enhances the warm electron flow to the target plate and significantly increases the target heat flux from a few MW m −2 to 30 MW m −2 [3]. ECH experiments in Proto-MPEX have investigated the effect of plasma heating actuators on the target heat and particle fluxes [13][14][15][16][17]. These experiments raised an important research issue, in that ECH heating caused a plasma density drop towards the target. It is necessary to clarify the physical processes of these actuators to reduce the risks in achieving the MPEX design goals [9,10]. In this paper, plasma simulations with auxiliary heating are performed to better understand the impact of heating on achieving reactorrelevant target fluxes.
The SOLPS-ITER code (abbreviated as SOLPS) [18] has been applied to analyse and understand the plasma and neutral transport in Proto-MPEX for plasmas with helicon and auxiliary electron heating. SOLPS (referred to as B2.5-Eirene in [19]) code was previously used to understand the radial transport model for the helicon-only heated plasmas [19]. However, the sensitivity to GP and auxiliary heating actuators on the target plasma fluxes has, thus far, has not been studied. The current version of the SOLPS code has been updated in comparison with the previous study [19]. The current SOLPS implementation uses an improved EIRENE model (including additional molecular processes, neutral-neutral collisions, and a higher fidelity vacuum vessel), as well as a 2D heating profile from COMSOL [12]. The simulations presented here use a more recent Proto-MPEX geometry (target at 4.2 m) and magnetic field, while the previous simulations were performed for a different setup (target at 3.6 m) and magnetic field.
Here, we aim to understand the plasma and neutral transport processes in Proto-MPEX for helicon plasmas using SOLPS, and explore the effects of auxiliary heating (ECH+helicon) and gas puff actuators. The results are compared to Proto-MPEX experimental data with the goal of constraining SOLPS inputs for predictive MPEX modelling and future experiments. The GP rate and ECH power are varied over a wide range (Gas puff #2: 2 × 10 20 -7.5 × 10 20 atoms s −1 , ECH: 0-50 kW) to understand the impact of these actuators on the target plasma parameters. The constrained SOLPS simulations will be used in future work as background plasma conditions for other simulations, e.g. impurity transport analysis using the Global Impurity TRansport code (GITR) [20]. Figure 1 shows a schematic view of the Proto-MPEX device and the magnetic field along the axis. The red rectangles represent 13 magnetic coils that generate magnetic fields according to the Proto-MPEX operation scenarios. A dump plate is located on the left side of the device, while the target plate is located at Z = 4.2 m. The system has three pumps and a GP port as indicated. The helicon is shown in green at Z = 1.75 m, and the ECH location is at Z = 3.2 m. More detailed descriptions of the Proto-MPEX setup can be found in [13][14][15][16][17].

Experimental and simulation setup
The SOLPS (version 3.0.8) code is used to simulate plasma and neutral dynamics in Proto-MPEX. Numerical meshes are created according to the magnetic field and vacuum vessel structure as shown in figure 1(c). SOLPS is an integrated multi-fluid plasma and kinetic neutral transport code that couples the B2.5 and EIRENE codes [21,22]. The blue rectangular cells in figure 1(c) represent the plasma mesh aligned with the magnetic field while the black triangular cells represent the neutral particle mesh. Three pumps are added according to the Proto-MPEX experimental conditions. The GP port #1 (Z ∼ 1.5 m) is activated throughout all simulations presented here, but GP port GP#2 is only activated for section 6.3. In the SOLPS simulations, PMI is only considered at the target and the dump plate. Ions crossing the last radial plasma mesh are returned locally as neutrals (mimic a tight-fitting wall). The current setup includes only deuterium (D) ions, D atoms and molecules, and an artificial impurity term (discussed later).
A major part of this work is to constrain the plasma radial transport model, impurity radiation, and improve the description of the power deposition profiles which are inputs to the SOLPS simulations. In SOLPS, the radial transport is ad-hoc, with user-defined cross-field diffusivities. These can be adjusted to best reproduce experimental measurements, but this can introduce a large number of free parameters. Here, spatially constant and Bohm [23] transport models are considered. We have also modified SOLPS to allow a 2D heating profile calculated by COMSOL to be input.

Experimental results
Plasmas with helicon-only heating and auxiliary heating have been investigated in Proto-MPEX (shots 22 622-22 631). Significant uncertainties exist in the deposited power levels. For all shots, the source power was 125 kW while 100 kW was coupled to the plasma. However, only 8% to 43% of the coupled power is absorbed in the plasma with the rest reflected or absorbed by the walls [11,12]. The transmitted ECH power was 50 kW, with only a few per cent absorbed by the plasma [24]. The axial profile of electron temperatures (T e ) and densities (n e ) measured by the Langmuir probe are shown in figure 2 (radial profiles are shown in the appendix). The  peak T e is close to the helicon heating region (Z ∼ 1.25 m) for the helicon-only heating case. T e is strongly affected by ECH, with the peak T e near the ECH power deposition location (Z ∼ 3.2 m). The radial profile is also impacted by ECH (see appendix, figure 33), with the peak temperature occurring in the outer periphery region. n e is also significantly affected by ECH, with a reduction at the ECH power deposition location and downstream, and an increase upstream (see figure 2(b)).
The target heat flux was measured by an IR camera and is shown in figure 3. ECH increases the total target flux and the peak heat flux is shifted outward radially (note different colour scales). The dotted lines represent the Langmuir probe scan locations. The peak heat flux is shown to be off-axis with ECH, and the probes cannot measure the plasma at this position. Therefore, it is assumed that the probe measurements underpredict the peak 2D T e in ECH experiments. More specifically, it is roughly estimated that the probe measurements underpredict the peak 2D target T_e by nearly 2.8 times, while n e and ion saturation currents are overpredicted by nearly 2.3 and 1.5 times, respectively. This azimuthal asymmetry cannot be resolved using 2D (axial-radial) plasma simulations. Where possible, data from multiple azimuthal angles will be compared to the SOLPS radial profiles. E.g., the radial profile of T e at Z = 4.13 m is shown in figure 4. The black symbols represent the probe scan along the negative X direction, while the red symbol represents the probe scan along the positive X direction (see figure 3). Additional experimental radial profiles and comparisons to SOLPS data are shown in the appendix.

Helicon power deposition profile
Previous SOLPS simulations of Proto-MPEX used a simplified representation of the deposited heating power: a specified radial profile is multiplied by axial scale factors [19]. Here, a 2D heating profile is employed to elucidate plasma and neutral transport in Proto-MPEX. In this section and the next section, constant radial transport coefficients (D ⊥ : 0.5 m 2 s −1 and χ ⊥ : A cold plasma wave model was implemented in COMSOL [12] that computes the helicon electric fields and power deposition profile in Proto-MPEX based on a given density and magnetic field profile. In the COMSOL simulations, the density profile is assumed based on the following equation for the condition of r/a ⩽ 1 where n e−max is the maximum density, n e−min is the minimum density (10 16 m −3 ), a is the position of the first magnetic flux surface that intercepts the helicon antenna, and r is the radial coordinate. For r/a > 1, n e = n e−min is used. This profile was determined by an experimental fit (similar experimental conditions) to measured densities from Langmuir probes near the helicon source.
Here, three different peak plasma densities are used to check the sensitivity of the helicon heating profile on the plasma parameters as shown in figure 5. The SOLPS code was modified to accept a 2D power deposition profile, with the absorbed helicon heating power held constant at ∼16 kW suggested by the previous simulations and experiments [11,12,19]. Here, the input heating power is applied to electron while the ion exchange energy with electron via the electronion relaxation processes. The power is mostly deposited near the axial location at the lower density case (figure 5(a)) while the power is distributed radially with increasing plasma density (figures 5(b) and (c)), as higher electron density reduces the collisional dumping length of helicon waves (assuming constant magnetic field and T e ) [25]. Figure 6 shows T e from SOLPS corresponding to the heating profiles in figure 5. T e has a strong dependency on the input heating profile and follows the input heating profile.
The SOLPS n e are for the three COMSOL density profiles are compared to experimental data as shown in figure 7. The cases of n e−max = 2 and 3 × 10 19 m −3 show almost similar  agreement at Z = 1.14 m, however, the case with n e−max = 3 × 10 19 m −3 (figure 5(b)) shows better agreement with the probe data near the helicon heating regions (Z = 1.14 and 3.24 m). Therefore, the case with n e−max = 3 × 10 19 m −3 was selected and all subsequent results in this paper correspond to the power profile figure 5(b). In principle, the SOLPS-COMSOL coupling should be two-way and iterated until convergence, however this is beyond the scope of this paper.

Impurity fraction
Previous work has shown that a small amount (a few %) impurities exist in Proto-MPEX, generated from PMI with the helicon window [26]. These interactions are not directly simulated in SOLPS, and the self-consistent impurity source cannot be calculated until a wide-grid SOLPS [27] simulation is performed. Here, we employ artificial impurity radiation, where a spatially constant impurity fraction (f z = n z /n e ) is input, using a predefined radiation function. The result is applied as a cooling term in the electron energy equation. The electron energy loss increases with increasing f z , as the artificial radiation rate is a function of T e and f z , which is written below: where, T e is normalized to 15 eV. This radiation loss function has a peak at T e ∼ 18 eV and reduces before and after that temperature range, which is similar to carbon [28,29]. Figure 8 shows the axial T e and n e profile as a function of f z (radial profile is shown in the appendix, figure 25). The primary result is that T e is reduced as f z is increased, while n e is only weakly affected. While no spatially constant f z reproduces the full axial experimental profile, we focus on the measurement near the helicon source (Z ∼ 1.14 and 3.25 m), as the helicon window is considered to be the primary impurity source. At these locations, the best agreement is found for f z = 5%. All subsequent results correspond to this value. Beyond this impurity fraction level, T e is only weakly affected at Z = 1.14 m while deviating from experimental data towards the target. A more detailed representation of the impurity content will be explored in future work, including coupling to the GITR code.

Constant cross-field diffusion model
SOLPS solves a set of fluid transport equations which use adhoc radial transport coefficients [21]. Fluid simulations are widely used to describe plasma transport in linear and tokamak fusion devices, as kinetic simulations such as Particle-In-Cell [30] can be prohibitively computationally expensive and timeconsuming. Many linear device simulations use constant radial transport coefficients [31][32][33][34][35][36]. On the other hand, a recent turbulence study in the Large Plasma Device shows a reasonable agreement with a Bohm diffusion model (D ⊥ = kT e /16 eB) for the cross-field particle diffusivity, D ⊥ [37]. The plasma transport in GAMMA 10/PDX linear device is also simulated based on the Bohm diffusion model [38][39][40]. Therefore, it is necessary to test the sensitivity of radial transport coefficients in Proto-MPEX to minimize the number of free parameters for future MPEX simulations. Here, the SOLPS outputs are validated by experimental data and the transport model that best fits the experimental data is identified. Figure 9 shows the sensitivity to the radial particle transport on the integrated heat and particle fluxes to the vacuum vessel (wall) and the target plate. The plasma flux to the target decreases with an increasing D ⊥ , as more flux leaves the grid radially. The simulated target plasma heat flux for a range of D ⊥ is compared to IR camera measurements [24] in figure 10. The total energy flux is almost similar to the plasma heat flux, as neutral and radiation fluxes are very small on the target. The radial profile is similarly shaped for all the cases including both experimental and simulated data, with D ⊥ = 0.45-0.65 m 2 s −1 showing the best agreement to the experiment.
Simulation results are also compared to the n e profile measured by the Langmuir probe near the target plate (radial profile at 4.13 m) to further inform the transport model in Proto-MPEX. The electron density and temperature radial profiles are given in the appendix (figures 26 and 27). An error calculation between the simulation and experiments has been performed to identify the best transport model. The following equation is used to calculate the relative error between experimental and simulation data where, ϕ i,Exp is the experimental data, ϕ i,SOLPS is the SOLPS data, i is the position of each radial scan (at Z = 1.14, 3.25, 3.69, and 4.14 m), and N is the number of data point from each radial profile. Figure 11 shows the calculated error between the simulation and experimental results as a function of D ⊥ . The error is shown to be minimized for the diffusion coefficient cases 0.50-0.60 m 2 s −1 . The error for the T e is not shown in the figure 11, as T e shows weak dependency on the D ⊥ ( figure 27).
For the linear device plasma simulations shown here, the parallel transport is mostly convective, and the radial energy flux is shown to be small (see figure 12(a)). Therefore, the radial electron and ion energy transports show negligible effects on T e and n e (see figures 12(c) and (d)). The radial profiles of T e and n e are shown in the appendix (figures 28 and 29), and show negligible effects on the radial energy diffusion value. The target heat flux also shows weak dependency on the radial heat diffusivity (see figure 12(b)).  Based on these results, the best-fit constant cross-field diffusivity model corresponds to a particle diffusivity of 0.50 m 2 s −1 and a radial energy diffusivity of 1 m 2 s −1 . The next section investigates a Bohm model, while all subsequent constant diffusivity results correspond to these values (with χ ⊥,i = χ ⊥,e ).

Comparison between Bohm and constant diffusion models
Previous SOLPS simulations suggest that the Bohm diffusion model well describes Proto-MPEX plasma transport [19], motivating a comparison of Bohm and constant diffusion models. The axial profile of particle, electron and ion thermal diffusion value for the Bohm and constant model is shown in figure 13. The Bohm diffusion model describes both the particle and heat radial transport (χ ⊥ = T e /eB = D ⊥ /0.5), as in [19]. The constant model provides uniform radial diffusion  field. The Bohm model shows higher radial diffusion near the helicon heating and puffing region due to small B field profile (see figure 1). Here, SOLPS outputs (T e , n e , and target heat flux profile) are compared to the experimental data. Figure 14 shows simulated and measured axial T e and n e profiles for the Bohm and constant diffusion cases. Both the Bohm and constant diffusion models show a similar level of agreement to the probe data. To better evaluate the models, the full T e and n e radial profiles (see appendix, figures 30 and 31) are used to calculate the relative error for each model. The The measured and simulated radial profiles of target heat flux are shown in figure 15(a). The constant diffusion model shows a better agreement to the measurement, with the Bohm model overpredicting the on-axis heat flux. This is primarily the result of the small Bohm diffusion value towards the target plate (see figure 13), which provides a higher heat flux on the target.
Data from an experimental case with auxiliary heating (ECH + helicon) is used to further inform the transport model. The radial profile of T e and n e is shown in the appendix (figures 32 and 33). From these profiles, the Bohm model provides a global error of T e ∼ 27% while the constant diffusion shows a global error of T e ∼ 18%. The target heat flux is significantly enhanced by ECH (see figure 15(b)). The constant diffusion model shows a good agreement to IR camera heat flux profile, while the Bohm model again over-predicts the peak heat flux.
The Bohm and constant diffusion show similar global error levels, indicating that the model cannot be definitively identified in Proto-MPEX given the sparse experimental data currently available. Both transport models show qualitatively similar plasma profiles and level of agreement with the probe data. The major difference between the two transport models is the power deposited to the vacuum vessel. Bohm diffusion provides higher radial diffusion; therefore, the radial power loss is found to be significantly higher compared to constant diffusion. Bohm diffusion provides higher radial power loss, while the radial power is adjusted by radiation for the constant diffusion case. More experimental data (such as total radiation power loss and power deposition on the vacuum vessel) are needed to identify the radial transport model in Proto-MPEX. At present, we have freedom of choice using radial transport models in Proto-MPEX, as both the Bohm and constant diffusion show almost similar agreement to the experimental data.
The constant diffusion shows better agreement to the Langmuir probe and IR camera data near the target, while the Bohm model over-predicts the target heat flux and T e . On the other hand, the Bohm diffusion shows better agreement to the probe data near the helicon and ECH power deposition regions (Z = 1.14 m and 3.25 m). Since the Bohm diffusion model shows comparatively better agreement to the probe data near the heating regions, the Bohm diffusion model is used for detailed analyses in section 6, given that it has a physical justification and reduces the number of free parameters.

Impact of ECH and GP actuators on the target plasma parameters
To inform future operation of MPEX, the SOLPS simulations are used to evaluate the ability of actuators in Proto-MPEX to provide high particle and heat fluxes to the target plate. Specifically, the effects of GP and ECH are investigated. In this section, the effect of ECH on plasma transport is studied, and the simulations are compared to experimental data to validate the model. Figures 16(b) and (c) show the measured and simulated onaxis profiles of T e and n e with and without auxiliary ECH (helicon ∼16 and ECH ∼4 kW). The primary effect of ECH is an increase in T e and a reduction in n e near the heating region (Z = 3.2 m). As the n e reduction may affect achieving the desired target parameters, the mechanism for the density drop is investigated. In the current simulation, a constant power density (see figure 16(a)) over the region Z = 3.1 m to Z = 3.3 m profile is used, supported by as the nearly constant heat flux measured by the IR camera across the Langmuir probe sweep near the target (see figure 3(a)). Since significant uncertainties exist in the absorbed power levels, the ECH magnitude in SOLPS was adjusted to find the best fit to the experimental data. Radial profile data is given in the appendix (figures 32 and 33). Figure 16(d) shows parallel ion velocity for both the helicon-only heating and auxiliary heating case. The flow is accelerated near the target plate by ECH. A similar trend has been found during ICRF heating in Proto-MPEX and simulated by a 1D kinetic simulation PICOS++ , which shows that ions are accelerated to the target plate, while the density is reduced to maintain the particle balance [41].

Effect of auxiliary electron heating on plasma transport
The parallel particle flux along the axis is shown in figure 16(e). Γ ||i is shown to be similar near the upstream region with and without ECH. During ECH, however, the parallel ion flux is reduced for Z > 2.2 m. This can be understood from the Bohm diffusion model, which causes the radial loss to increase with increasing T e (see figure 17). As the radial particle flux to the wall is enhanced, the parallel ion Figure 17. Variation of (a) the on-axis Bohm diffusion coefficient for helicon-only and auxiliary heating case and (b) the particle flux along the last radial cell. particle flux is correspondingly reduced, Γ = nu || − D ⊥ ∇ ⊥ n. The plasma density is then reduced from these changes to the parallel particle flux (Γ || ∼ nu || ).

Impact of ECH power on the target plasma fluxes
The heating actuators in MPEX play a key role in generating the required conditions at target plate. Here, the effect of ECH power on the target conditions is investigated, while the helicon power is kept constant at ∼16 kW. Figure 18 shows the dependency of the target heat and particle fluxes, and on-axis target T e and n e on the ECH power. ECH power of 50 kW results in a peak target heat flux of 17 MW m −2 . For small levels of ECH power, the ion flux reduces slightly due to drops in the axial plasma density (discussed earlier). In contrast to this, the ion particle flux increases with ECH power because the density drop is counteracted via increased ionization. The target T e is increased as ECH power is increased. ECH power of 50 kW results in a peak target T e of 20 eV.
Although the on-axis target n e is drastically reduced at the lower ECH power (2 and 4 kW), but the target n e is increased with increasing the ECH power. The dependency of the ECH power on the target parallel ion velocity is shown in figure 18(e) to understand the physics of drastic n e drop during ECH. The target ion flow velocity is drastically increased when turning on ECH (2 and 4 kW) due to an increase in Te, which clearly explains the n e trend, as the target flux ( figure 18(b)) is weakly affected at the lower ECH power cases. Meaning that, the target n e behaviour at lower ECH power cases (2 and 4 kW) is directly correlated to the increase in u i|| and T e . The ion flow velocity is reduced with increasing ECH power because of increasing recycling flux, which enhances momentum loss processes during plasma-neutral interactions (see figure 20).
The radial losses are also investigated to additionally confirm the drastic drop behaviour of target n e at the lower ECH power cases. The radial particle losses show a positive correlation with the ECH power (see figure 18(f)), as more particles leave the system radially. The dependency of the source term (i.e, ionization-recombination) of continuity equation (S na ) on the ECH power is also shown in figure 18(f). S na is weakly affected at the lower ECH power (2 and 4 kW), while it continuously increases with higher ECH power, indicating that the ionization is significantly enhanced by ECH except for ECH power of 2 and 4 kW. Both the radial losses and S na increase with increasing ECH power. However, S na and radial losses appear comparable at the lower ECH power. Therefore, at the lower ECH power cases, the target n e is abruptly dropped due to an increase in the T e , u i|| , and radial losses.
Here, GP port #1 is only activated. Therefore, the only source for the neutral particles near the target is the recycling flux, which strongly depends on the incident plasma flux on the target. ECH enhances target plasma fluxes, which then enhances recycling flux. As a result, the ionization of neutral particles increases with ECH power, which then enhances target n e . The 2D profile of the ionization source (S ion ) as a function of ECH power is shown in figure 19. The primary result is S ion is increased significantly near the target, as ECH power is increased, which clearly clarify the trend of target n e and ion flux with ECH power. As a result, the target plasma parameters are strongly influenced by higher ECH power. These outcomes clearly indicate that the target plasma parameters can be strongly influenced by higher ECH power.
The source term of the parallel momentum equation is shown in figure 20 as a function of ECH power. The parallel flow velocity can be reduced by increasing momentum and friction losses. The momentum loss also increases with ECH power, as the recycling flux enhances the neutral density near the target plate. Thus, the ion parallel flow velocity is reduced at higher ECH power cases via plasma-neutral interactions. SOLPS outputs indicate that ECH will be an important actuator in MPEX to obtain high target heat and particle fluxes.

Impact of GP near the target (GP#2 ∼ 4.2 m) during ECH
ECH significantly enhances T e and fluxes to the target plate (discussed earlier). As a result, the GP during ECH can contribute to enhancing the target density and fluxes via ionization processes. Because of this, an additional GP port (GP#2 is added near the target plate (∼ 4.2 m, see figure 1) to understand the impact of plasma fuelling during ECH by SOLPS. Here, the magnitude of GP#1 is kept constant at 2.5 × 10 20 atom s −1 while the magnitude of GP#2 is varied over a wide range. Although higher GP increases the plasma density, plasma  temperatures are potentially reduced by energy loss processes, such as radiation, ionization, charge-exchange, and recombination losses. Therefore, it is necessary to identify the optimum puffing level that can increase both the target heat and particle fluxes. ECH and plasma fuelling scans have been performed to understand the optimum GP levels that can enhance both the target heat and particle flux.
The dependency of the target T e and n e on the GP levels is shown in figure 21. The target T e and n e have a strong dependency on both the ECH power and GP rate, which clearly indicates the importance of these actuators in controlling target plasma parameters. The target T e shows a negative correlation with the puffing rate due to increased energy loss processes. The order of ECH power in this plot is not linear (8 kW, 20 kW, 40 kW, and 50 kW). The T e is slightly increased when ECH power was varied from 40 kW to 50 kW, as the power difference is relatively small. As a result, n e shows a similar trend for the ECH power of 40 and 50 kW. Figure 22 shows the variation of heat and particle fluxes as a function of GP. SOLPS results indicate that the target fluxes can be effectively tuned by varying the neutral density as well as the electron heating power near the target plate. More specifically, it is clearly shown that the target heat flux has a strong dependency on the ECH power and GP levels. The target heat flux continually reduces with the increased GP rate at the lower ECH power cases (8 and 20 kW). During the higher ECH power scenarios (40 and 50 kW), the integrated target heat flux is initially increased with the GP peaking at 2× 10 20 atoms s −1 before decreasing. It is numerically demonstrated that a small amount of puffing can be useful to increase target plasma fluxes at the higher heating conditions. However, the target heat flux is reduced at the higher puffing conditions. The 2D profile of the ionization source is shown in figure 23 for the GP #2 conditions of 0.0 and 3 × 10 20 atom s −1 at the ECH power of 50 kW. The ionization is significantly increased near the target with GP, which enhances target n e . The dependence of the radiation and momentum loss terms on the puffing level is shown in figure 24 to understand the physical mechanisms of GP at the ECH power of 50 kW. The neutral radiation is increased with increasing the GP rate. As a results, the target T e is reduced via the radiation losses, with GP of 7.5 × 10 20 atoms s −1 reducing target T e from 20 to 6 eV. The  parallel momentum equation source term (charge-exchange and recombination loss terms) is enhanced with the increasing GP rate, meaning that the charge-exchange loss is enhanced, which reduces ion temperature and parallel ion flow velocity.
As shown in figure 21(b), n e increases significantly with increasing GP rate up to 6 ×10 20 atoms s −1 , and then n e becomes saturated with increased GP, as T e reduces from ∼ 20 eV to ∼ 6 eV via radiation, which then reduces ionization rate [5]. The ion energy is reduced by charge-exchange and recombination losses. Therefore, the target heat flux shows a roll-over phenomenon at a high puffing rate due to lower electron temperature.
The target ion particle flux shows a rollover phenomenon at the ECH power of 8 kW and 20 kW. The target ion particle flux significantly increases with GP at the higher ECH power cases (40 and 50 kW). For ECH power of 40 and 50 kW, the target flux becomes saturated at the higher puffing conditions. The optimum GP level has been identified in terms of target heat and particle fluxes under the conditions of the simulations. SOLPS outcomes indicate that a small amount of particle fuelling can enhance both the target particle and heat fluxes.

Summary
The SOLPS-ITER code has been applied to understand plasma transport processes in Proto-MPEX and provide a physics basis for MPEX. A direct comparison between SOLPS and experimental data has been performed to validate the model and constrain SOLPS inputs (radial transport, power deposition profile, and impurity fraction). The impact of GP and heating actuators on the target plasma parameters is also investigated to increase confidence in predictive simulations for MPEX. The main outcomes of the paper are summarized below.
• The SOLPS code has been coupled with the COMSOL code to import a 2D input heating profile. The impact of the helicon power deposition profile has been investigated. A sensitivity analysis shows a strong impact of the power deposition profile on the background electron temperature. • A small percentage of impurity fraction may exist in Proto-MPEX and a 5% artificial impurity fraction shows reasonable agreement to the probe data near the helicon regions. For increasing impurity fraction, the electron temperature is reduced, while the electron density is weakly affected. • The radial plasma transport has been investigated in Proto-MPEX. Both Bohm and constant diffusion simulations show reasonable agreement with respect to the sparse experimental data available. Bohm diffusion provides higher radial losses, while the radial losses are replaced by radiation for the constant diffusion model. • ECH significantly enhances the electron temperature, which then enhances the heat and particle fluxes to the target plate. The ECH reduces the plasma density near the ECH power deposition locations by increasing radial particle losses. • ECH power also shows a continual increase in the target electron temperature and heat flux. ECH powers of 50 kW significantly enhance the target heat flux from 0.4 MW m −2 to 17 MW m −2 . Higher ECH power increases the recycling flux, which enhances the target electron density via ionization processes. • The optimum GP rate near the target plate is also identified during ECH. It is found that a small amount of GP can further enhance both the target particle and heat fluxes at the higher ECH power cases. On the other hand, the target heat flux shows a negative correlation with the GP rate at the lower ECH power, as lower temperature leads to a plasma detachment state.
The simulation outcomes indicate that the ECH actuator can be used to generate reactor-relevant heat and particle flux in Proto-MPEX. Furthermore, a small number of GP near the target plate during higher ECH power further enhances the target heat and particle fluxes. Future studies will reveal the impact of additional ICRF heating on the target heat and particle fluxes, as well as the simultaneous heating of ICRF and ECH. We also plan to apply the obtained knowledge to predict the background plasma profiles in MPEX. We also plan to perform a self-consistent two-way coupling between COMSOL and SOLPS in the future.

Data availability statement
All of the data generated or analysed during this study can be made available by the corresponding author on reasonable request. All data that support the findings of this study are included within the article (and any supplementary files).