Parametric study of midplane gas puffing to maximize ICRF power coupling in ITER

Midplane gas puffing close to the ion cyclotron range of frequencies (ICRF) antennae has been demonstrated to be robust in improving ICRF power coupling in current tokamaks. It is also shown in a previous study (Zhang 2019 Nucl. Mater. Energy 19 364–71) that in ITER, midplane gas puffing with a puff rate of ∼4.5 × 1022 electrons s−1 can increase the antenna loading/coupling resistance by about a factor of two. In this paper, a comprehensive parametric study has been carried out to characterize the influence of midplane gas puffing on ICRF power coupling in additional and broader range of parameter scans. The new parameter scans include the gas puff rate, the poloidal location of the gas pipe orifices (GPOs), the separatrix density, the particle perpendicular diffusion coefficient, the radial distance between the plasma and antenna as well as the antenna phasing. The 3D edge plasma fluid and neutral transport code EMC3-EIRENE code has been used to simulate the 3D distributions of plasma density in the presence of gas puffing, which are then used in the antenna code ANTITER II to calculate the antenna coupling. The simulation results indicate that the ITER ICRF local midplane gas injection layout (with the GPOs located on one side of each antenna port) increases the ICRF power coupling significantly in all studied plasma scenarios and antenna parameters. We are hence confident that the chosen layout for the ICRF local gas injection on ITER is appropriate. We are also confident that the ITER local gas injection will allow boosting the ICRF coupling with all studied plasma conditions and antenna phasings.

Midplane gas puffing close to the ion cyclotron range of frequencies (ICRF) antennae has been demonstrated to be robust in improving ICRF power coupling in current tokamaks. It is also shown in a previous study (Zhang 2019 Nucl. Mater. Energy 19 364-71) that in ITER, midplane gas puffing with a puff rate of ∼4.5 × 10 22 electrons s −1 can increase the antenna loading/coupling resistance by about a factor of two. In this paper, a comprehensive parametric study has been carried out to characterize the influence of midplane gas puffing on ICRF power coupling in additional and broader range of parameter scans. The new parameter scans include the gas puff rate, the poloidal location of the gas pipe orifices (GPOs), the separatrix density, the particle perpendicular diffusion coefficient, the radial distance between the plasma and antenna as well as the antenna phasing. The 3D edge plasma fluid and neutral transport code EMC3-EIRENE code has been used to simulate the 3D distributions of plasma density in the presence of gas puffing, which are then used in the antenna code ANTITER II to calculate the antenna coupling. The simulation results indicate that the ITER ICRF local midplane gas injection layout (with the GPOs located on one side of each antenna port) increases the ICRF power coupling significantly in all studied plasma scenarios and antenna parameters. We are hence confident that the chosen layout for the ICRF local gas injection on ITER is appropriate. We are also confident that the ITER local gas injection will allow boosting the ICRF coupling with all studied plasma conditions and antenna phasings.
Keywords: ITER, ICRF coupling, local gas puffing, scrape-off layer, 3D simulations (Some figures may appear in colour only in the online journal) 5 Dr A. Messiaen was passed away in 2021. * Author to whom any correspondence should be addressed.
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Introduction
Radio frequency heating with waves in the ion cyclotron range of frequency (ICRF) relies on the fast wave to transport the energy from the antenna to the plasma core. The amount of ICRF power coupled to the plasma critically depends on the width of the evanescent layer, a layer where the plasma density is lower than the cut-off density and the fast wave decays exponentially. To maximize the ICRF power coupling, it is important to increase the local density in front of the antenna and decrease the fast wave evanescent distance, i.e. the distance from the position of the cut-off density to the antenna. One of the most effective methods to achieve this goal is to puff the working gas (same gas as the plasma) locally close to the antennas. Previous experiments and simulations in many devices, such as ASDEX Upgrade (AUG) [1][2][3][4][5], JET [6][7][8], DIII-D [9,10], EAST [11,12], TORE SUPRA [13] and TEXTOR [14,15], have shown that compared to divertor gas puffing, midplane gas puffing increases the antenna loading/ coupling resistance significantly. This increase is in a level of 100% (i.e. by a factor of two) in AUG and JET H-mode plasmas, for example, when all the working gas is puffed from the midplane.
Encouraged by these results, it has been proposed to introduce midplane gas puffing close to the antennas to maximize the ICRF power coupling in International Thermonuclear Experimental Reactor (ITER). This strategy is very important since large uncertainties exist in the ITER scrape-off layer (SOL) density profiles. Studies show that a low ITER SOL density can lead to a poor ICRF power coupling [16]. A significant limitation of ICRF power coupling could seriously compromise the achievement of the ITER objectives, in particular the aim of using a total 73 MW auxiliary power to achieve Q = 10 burning plasma in long pulse. Previously, simulations with the 3D edge plasma fluid code EMC3-EIRENE [17] and the antenna code ANTITER II [16] were carried out to compare different local gas puffing strategies in ITER [18]. It was shown that compared to divertor gas puffing, outer top gas puffing increases the coupling resistance in a moderate level for the antenna which does not have good magnetic field line connections to the gas pipe orifices (GPOs), by 30%. In contrast, midplane gas puffing with GPOs located close to the antennas increases the coupling resistance most significantly, by up to 150% [18]. Thus, it is highly advisable to use midplane gas puffing to maximize ICRF power coupling in ITER. Considering possible engineering constraints and available space for gas pipes and GPOs, the final proposed GPO locations for midplane gas puffing are both on the right side of the two antennas (viewing from inside the torus to the outside). This means one GPO will be installed near Port 13 (close to the ICRFA antenna) and the other one will be installed near Port 15 (close to the ICRFB antenna). ICRFA and ICRFB represent the two ICRF antennas located in Port 13 and Port 15, respectively. A schematic design view of the gas pipes and GPOs is shown in figure 1.
Thus it was shown in the previous studies that midplane gas puffing close to the antennas is the best strategy to increase ICRF power coupling in ITER [18]. A review of the previous gas puffing study of ITER is given in the following section. To further confirm this strategy, and to characterize the improvement of ICRF power coupling by the midplane gas puffing method in various plasma conditions, a comprehensive parametric study for ITER has been carried out. These new results are reported in the present paper. The investigated parameters include the gas puff rate, the poloidal location of the GPOs, the separatrix density, the particle perpendicular diffusion coefficient, the radial position of the antenna and the antenna phasing.

Review of previous work
Previously, dedicated simulations were performed for ITER to find the optimal gas injection locations to maximize ICRF power coupling. The EMC3-EIRENE [17] code was used to calculate the density in the presence of different local gas sources, while the FELICE [19] and ANTITER II [16] codes were used to calculate the antenna coupling resistances and the coupled powers, for assumed maximum RF voltages on the system. In these simulations, the particle and energy diffusion coefficient profiles were modified so that the density profiles of the reference case (i.e. divertor gas puffing) are fitted to ITER 'low' or 'medium' density profiles [18]. For other gas puffing cases, only the gas injection location was changed while other settings were kept the same as the reference case. Various cases were investigated, including the divertor gas puffing, outer top gas puffing and midplane gas puffing with the GPOs located toroidally close to the two ICRF antennas. It was found that with the same amount of injected gas (4.5 × 10 22 electrons s −1 ), the local midplane gas puffing increases the ICRF power coupling considerably more than the divertor or even top gas puffing. Such an example is given in figure 2 which uses the data set from [18]. In the figure the coupled ICRF power is compared for the lower divertor gas puffing, for the top gas puffing and for the midplane gas puffing (i.e. local ICRF gas puffing). The result clearly shows that midplane gas puffing increases the ICRF power coupling very significantly (about three times as much as the divertor gas puffing case) for both antennas and for all studied antenna phasings. For top gas puffing, this increase is more prominent for the antenna in Port 15 than the antenna in Port 13. The magnetic field lines from the puffing location are mostly connected to the antenna in Port 15.

Simulation setup
In our study, the EMC3-EIRENE code [17] is used to calculate the 3D SOL density in the presence of local gas puffing. In front of each antenna, the resulting 3D density profiles are averaged in the poloidal and toroidal directions to construct 1D density profiles for the ANTITER II code [16] which calculates the coupling resistance. EMC3-EIRENE is a 3D edge plasma fluid and neutral particle transport code which couples  the EMC3 and EIRENE codes self-consistently. It is particularly robust in calculating 3D inhomogeneous plasma parameters by taking into account arbitrary 3D magnetic field and 3D realistic wall geometries. Thus, it has been widely used to study 3D physics in stellarators and tokamaks [20]. ANTI-TER II is a semi-analytical antenna code which considers simplified 3D antenna structures but uses 1D radial density. The modelling is made in plane geometry with Fourier analysis along the z (toroidal) and y (poloidal) directions. It integrates numerically a system of two first order differential equations derived from the Maxwell's equations and forms the cold plasma dielectric tensor along x (radial) direction of the plasma profile.
In the EMC3-EIRENE simulations, the computation grid is extended to the wall, so that the influence of atomic processes (such as recycling) on the SOL density is taken into account. The wall, which is composed of a beryllium main chamber wall and a tungsten divertor, acts as a boundary condition for the plasma. In addition, the grid is built to have a toroidal extension of 360 • (with 18 identical segments in the toroidal direction). To correctly describe the 3D toroidal inhomogeneous density induced by a local gas puffing, a toroidal 360 • grid has to be used in the study. This is firstly because the density perturbation in the SOL induced by the local gas puff on a given set of field lines is still strong 360 • toroidally away from the gas source. The simulation results in section 4 (figures 4 and 8) as well as the 3D magnetic field line tracings (figure 3(b)) clearly show this. Secondly, since EMC3-EIRENE enforces a periodic boundary condition in the toroidal direction, simulating a limited toroidal sector would systematically introduce spurious midplane gas injection sources. This would result in a larger number of perturbed flux tubes and would grossly misrepresent the localized density perturbation produced by the actual local antenna gas puff.
Since the parallel transport (motion along field lines) of charged particles is much stronger than that in the perpendicular direction, the structure of field lines determines the distribution of SOL density in the presence of local gas puffing. Typical field lines traced in the ITER plasma edge (figure 3(b)) show that field lines starting from points located in the injected gas cloud are mostly connected to the nearby antenna. This suggests that the injected gas cloud will significantly impact the density in front of the antennas. In addition, part of field lines starting from the gas cloud near Port 15 are connected to the top of ICRFA antenna. As a result, the density increase in front of the ICRFA antenna is expected to be reasonably larger than the ICRFB antenna when using the same gas puff rate for the GPO near Port 13 and Port 15. In the simulations, five antenna phasing are considered: [0, π, 0, π], [0, 0, π, π], [0, π, π, 0], [0, π/2, π, 3π/2] and [0, −π/2, −π, −3π/2].
In the EIRENE setups, the GPOs are radially retracted by ∼0.26 m to approximate the poloidal and toroidal spreading of the gas. In reality, the injected neutral gas enters the main chamber through the (horizontal) toroidal gaps between the blanket modules. However, in the simulations, a toroidal 360 • slot is set in the outer midplane wall to allow the gas entering the main chamber. The reason for this setting is to reduce the EMC3 grid resolution near the first wall and to save computation memory for EIRENE when more than 2 × 10 6 Monte-Carlo particles are used. A series of validation simulations show that the toroidal spreading of the gas is nearly the same whether using a toroidal 360 • slot or using a toroidal 0.3 • gap (of the same order as the gap between the blanket modules). This is because the gas rapidly spreads as soon as it leaves the toroidal gap, and immediately creates a neutral gas cloud with a toroidal extent of ∼10 • in the main chamber.
To enforce an accounting of particles consistent with a stationary equilibrium, a toroidal symmetric pumping surface with a reflection coefficient of 0.96 is set at the bottom of the divertor to approximate the effects of pumping and keep the amount of pumped gas equal to the puffed ones. In addition, the EMC3-EIRENE code itself could keep strict particle balance through adjusting the recycling flux at the divertor. It was observed in the simulations that removing the pumping surface hardly influences the results. The simulated plasma is purely deuterium H-mode using the ITER baseline Q = 10 magnetic equilibrium with q 95 = 3. The puffed gas is also deuterium gas. No impurity is considered in the simulations. Both the magnetic field (B t ) and plasma current (I p ) are in the clockwise direction when viewing from the top of the machine. Please note that in reference [18] and in Fig. 2 of this paper, simulations were performed with B t in the counter-clockwise direction.
The studied parameter scans in the paper include: (a) scan of gas puff rate; (b) scan of poloidal location of GPOs; (c) scan of separatrix density; (d) scan of transport parameter (diffusion coefficient); (e) scan of radial distance between plasma and antenna; (f) different antenna phasings. The initial separatrix density is set as 4. In the parameter scan of separatrix density, transport parameter and poloidal location of GPOs, the separatrix density, transport diffusion coefficient D ⊥ and poloidal location of GPOs will be modified, respectively. In each parameter scan study, only the studied parameter is varied while all other parameters are kept fixed. Divertor gas puffing is always considered as the reference case for the midplane gas puffing cases.

Scan of gas puff rate
A scan of gas puff rate is studied. This is to understand the amount of gas needed to achieve a significant increase of ICRF power coupling, and to find the best strategy to distribute the gas puff rate between the two midplane GPOs. The studied cases are shown in table 1. Since the planned maximum total gas puff rate for midplane gas puffing is about 4.55 × 10 22 el s −1 [21], thus only cases with a gas puff rate equal or smaller than this value are considered. The first case is the lower divertor gas puffing (Case 1), in which the total gas puff rate is 4.55 × 10 22 el s −1 and the injected gas is equally distributed among the four GPOs. As long as the total gas puff rate is kept the same, adding more toroidal divertor valves will not change the SOL density, since the divertor gas puffing always leads to a homogenous SOL density due to the particular field line structures near the divertor. The other five cases (Cases 2-6) are midplane gas puffing. The injected gas puff rate for each GPO is shown in table 1, in which Cases 2-4 are a scan of gas puff rate and Cases 5-6 are used to investigate different gas puff rate between the two midplane GPOs.
It should be noted that in steady state plasma, the main particle source (more than 90%) comes from the recycling flux at the divertor, while only a few percent of the total particle flux are generated by gas puffing. This is indicated by various experiments and simulations, e.g. in AUG and JET. However, in the plasma ramp up phase, the particle source mainly comes externally, for example from divertor gas puffing. In the simulations, only steady state plasma is considered.
To best utilize the gas injected from the midplane, the poloidal distribution of the injected gas should have the same extent as the height of the antenna. This is achieved by radially retracting the GPOs from the plasma, such that the gas has the space to spread poloidally while penetrating radially inward. Note that in reality, the GPO is located radially behind the wall, and the gas has to penetrate the gaps between the blanket modules to reach the plasma, making the distribution of the injected gas more complicated. Nevertheless, the poloidal and toroidal spreading of gas inside the vacuum vessel is expected reasonably approximated in the simulations.
Upon reaching the plasma with a temperature comparable or higher than ionization potential, the injected gas gets ionized, and the SOL density is modified. As described in section 2, the field line connections to the gas cloud in front of the GPO play an important role. An example of 3D density distributions in the presence of divertor gas puffing (Case 1) and midplane gas puffing (Case 4) is shown in figure 4. The results clearly show that midplane gas puffing significantly increases the SOL density in front of both antennas. This density increase is localized on flux tubes which are connected to the region of high density (density cloud) close to the midplane GPOs. In the SOL, magnetic field lines are open and end at the divertor plates or first wall. A density higher than the background can exist on some flux tubes. In the core, a local density increase on a flux tube usually leads to a global density increase on the whole flux surface.
The calculated 3D density by EMC3-EIRENE is then projected into 1D by averaging before it can be used in the ANTI-TER II code. In the density averaging method, the density values on the same flux surface and spatially within the antenna range are averaged into one density value. The radial coordinate R is selected toroidally at the center of the antenna and poloidally in the midplane (Z = 0.6 m). Thus, a scan of flux surfaces at different radial positions in the SOL allows us to obtain a radial density profile. In fact, this density averaging method is the same as the one which was used for AUG [3] and JET [8], where the antenna codes also use 1D density profile as input. Recent development of the RAPLICASOL code by including a 3D realistic ITER antenna makes it possible to use the full 3D density profiles for coupling resistance calculations. These works will be developed elsewhere.
The averaged density profiles for Cases 1-6 are given in figure 5. The results clearly show that all midplane gas puffing cases increases the SOL density in front of the two antennas and shift the cut-off density position toward the wall, i.e. reduce the evanescent distance. A higher total gas puff rate (Cases 2-4) leads to a higher density increase. When the gas puff rate is the same for both antennas, the density increase in front of the ICRFA antenna is slightly larger than the ICRFB antenna since part of field lines from the GPO near Port 15 are    connected to the ICRFA antenna. When using different gas puff rate between the two GPOs, the density increase in front of the two antennas becomes quite different. In Case 5, only the GPO near Port 13 is switched on. As a result, the density increase in front of the ICRFA antenna is the largest among the studied cases while the density increase in front of the ICRFB antenna is much smaller. In Case 6, the gas puff rate of the GPO near Port 13 is half as the one near Port 15, so that the density increase in front of the ICRFB antenna is obviously larger than in front of the ICRFA antenna. With the given density profiles, the power spectrum and coupling resistance are then calculated by ANTITER II. For each short strap, the input strap resistance is equal to the strap length (l str = 0.25 m) times its radiation resistance per unit length, which depends on the toroidal phasing of the antenna. For each toroidal phasing, the total coupling resistance R c of the antenna array is then the sum of 24 such contributions. The maximum total radiated power is derived from this quantity, for its maximum allowed design voltage [18]. It represents the antenna power capability for a given strap current amplitude. An example for divertor gas puffing (Case 1) and midplane gas puffing (Case 4) is given in figure 6, showing that midplane gas puffing significantly increases the amplitude of the coupling resistance spectrum.
The coupled ICRF power and coupling resistance can be derived from the integration of power spectrum. The results in figure 6 indicate that midplane gas puffing (Case 5) increases the coupling resistance significantly (by about a factor of two) for all antenna phasings. A comparison of coupling resistance for all cases is shown in figure 7. Cases 2-4 have equal shares of gas puff rate between the two GPOs. They show that the coupling resistance increases as the gas puff rate increases within the studied range of [0, 4.55 × 10 22 el s −1 ]. In Case 5, the total gas puff rate is the same as in Case 4, but only the GPO near Port 13 is switched on. Although the density increase in front of the ICRFA antenna in Case 5 is more significantly than in Case 4, the calculated coupling resistance of the ICRFA antenna in Case 5 is even a bit smaller than in Case 4. This is because the density gradient also plays an important role in determining the coupling resistance. The increase of density and coupling resistance for the ICRFB antenna for Case 5 is only modest. In Case 6, although the gas puff rate of the GPO near Port 15 is higher than that near Port 13, the resulting density increase is not very different from Case 4 for both antennas. As a result, the coupling resistance increase in Case 6 is of the same order as in Case 4. The results shown in figure 7 also indicate that for different cases, the increase of coupling resistance is almost independent of antenna phasing.

Scan of poloidal GPO location
For all midplane gas puffing cases discussed in the previous section, the midplane GPO is poloidally located at the center of the antenna (Z = 0.62 m). However, in this standard plasma scenario, the outmost plasma flux surface is closer to the lower part of the antenna than the upper part. Consequently, more injected neutral gas is ionized in front of the lower part of the antenna, making the density increase in the lower half of the antenna larger than the upper half. One effective method to equalize the density increase in the lower and upper half of the antenna is to poloidally shift the GPO upward. A scan of upward shift distance for the GPO is performed, as shown in table 2. In the studied cases, Case 4 has no upward shift of GPO and is considered as the reference case. Cases 7-9 have an upward shift of 20 cm, 30 cm and 40 cm, respectively.
A comparison of 3D density between Case 4 and Case 9 is shown in figure 8. As soon as the midplane GPOs are shifted upward, the high density regions, or the 'density filaments' along flux tubes, are shifted upward. To have a more quantitative understanding of the density modifications, the averaged 1D density profiles in front of the upper half and of lower half      the same. For midplane gas puffing without the GPO shift (Case 4), the coupling resistance of the upper half of the antenna is smaller than that of the lower half of the antenna, especially for ICRFB antenna. As the GPO is moving upward, the difference of coupling resistance between the lower half and upper half of the antenna becomes smaller. They are roughly equal to each other when the GPO is shifted by 30 cm.
Thus, for this particular baseline plasma equilibrium, an upward shift of 30 cm of the midplane GPOs is necessary to obtain an equalized increase of density and coupling resistance for the upper half and lower half of the antenna. However, it should be noted that this poloidal density asymmetry depends on the magnetic equilibrium used. For other plasma scenarios, the magnetic equilibrium can be very different. In addition, the magnetic equilibrium itself can also fluctuate due to plasma instabilities, leading to different poloidal density asymmetries. Moreover, due to engineering considerations, the other possible poloidal location of midplane GPO is 1 m higher, which is excessive and could be detrimental to the lower antenna halves. Thus, no attempt was made to modify the poloidal Table 3. Scan of separatrix density (cases 10-15).  location of the midplane GPOs (Z = 0.62 m). The impact of the inhomogeneity of the density repartition should be however analyzed more in depth, for example on the impedance matching.

Scan of separatrix density
Various plasma scenarios in ITER can result in very different SOL densities. In order to test whether midplane gas puffing will still increase the ICRF power coupling significantly in different plasma scenarios in a broad range of SOL density, a scan of the separatrix density is performed, as shown in table 3.
In this parameter scan, the separatrix density is the only variable, while all other plasma parameters are kept constant. Note the separatrix density we mentioned in all tables is the initial density we set at the separatrix position in EMC3-EIRENE before running the code. It will change when the EMC3-EIRENE simulation reaches convergence. In the EMC3-EIRENE runs of interest, the final stationary separatrix density will decrease by 5%-15% compared to its initial value. This difference clearly appears on figure 11. The averaged density profiles of the studied cases are shown in figure 11. In the case with a small separatrix density, such as 3.5 × 10 19 m −3 , the density in the far SOL is rather low and the fast wave evanescent distance can very large. For instance, it is 12 cm in Case 10. In cases like this, a midplane gas puffing is particularly needed to improve the SOL density. For the same gas puffing method, when the separatrix density becomes higher, the SOL density becomes higher and the fast wave evanescent distance becomes smaller. Midplane    gas puffing increases the SOL density significantly for all studied separatrix densities. The coupling resistance is then calculated and shown as a function of separatrix density. The results (figure 12) indicate that for divertor gas puffing, the coupling resistance is increased by ∼60% when the separatrix density increases from 3.5 × 10 19 m −3 to 4.5 × 10 19 m −3 . It keeps roughly unchanged as the separatrix density further increases. This increase trend is different to midplane gas puffing, in which the coupling resistance is increased significantly when the density increases in the range of [3.5 × 10 19 , 4.5 × 10 19 m −3 ] and in the range of [5.5 × 10 19 , 6.5 × 10 19 m −3 ]. Most important, the midplane gas puffing increases the coupling resistance by a factor of two compared to the divertor gas puffing for all studied separatrix densities.

Scan of transport (diffusion) parameter
Besides the scan of the separatrix density, a scan of the particle transport parameter (i.e. diffusion coefficient D ⊥ ) is further performed. The studied cases are shown in table 4, in which D ⊥ varies from 0.5 m 2 s −1 to 1.25 m 2 s −1 , chosen to represent a variation of the SOL plasma based on the previous experience with EMC3-EIRENE, while all other parameters are kept the same. The calculated SOL density (figure 13) shows that a larger D ⊥ leads to a larger SOL density and a smaller evanescent distance. For all investigated cases with different D ⊥ values, midplane gas puffing increases the SOL density significantly compared to divertor gas puffing.
The coupling resistance is then calculated and expressed as a function of particle diffusion coefficient, as shown in figure 14. Overall, the coupling resistance increases as D ⊥ increases. Compared to divertor gas puffing, midplane gas puffing increases the coupling resistance significantly (by a factor of two) for all antenna phasing and for all D ⊥ values.
From the scan of the separatrix density and the scan of the transport parameter, it is clear that the midplane gas puffing increases the local density and the coupling resistance significantly in all studied plasma scenarios. These plasma scenarios include cases with very low SOL density and cases with very high SOL density.

Scan of radial distance between plasma and antenna
For all ANTITER II simulations shown in the previous sections, the ICRF antenna is set at a radial position of Figure 13. Averaged density profiles for cases with different particle transport parameters in EMC3 EIRENE.   Firstly, a scan of R ant is done for midplane gas puffing at different gas puff rates but with the same initial value of the separatrix density (4.5 × 10 19 m −3 ), as shown in figure 15. Again, the divertor gas puffing is used as a reference here. Then, a scan of R ant is performed for cases with different initial separatrix densities but the same gas puff rate, as shown in figure 16. As expected, the coupling resistance shows a rather strong dependence on R ant . Overall, the midplane gas puffing increases the coupling resistance significantly (by a factor of two) compared to divertor gas puffing for all studied cases with different R ant values.

Discussion
To have a more detailed understanding of the influence of the parameter scan on the coupled ICRF power, the distance between the antenna and position of cut-off density (i.e. the fast wave evanescent distance d co ) as a function of the studied  parameter, and the coupled ICRF power per antenna (P rad,41V ) as a function of d co are calculated and shown in figures 17-20. In the calculations, the ICRFA antenna with a phasing of [0 π 0 π] and a strap voltage of 41 kV peak are considered. Please note that the computed coupled powers here are figures of merit obtained for a given system maximum voltage (hence they do not consider the available source power and may exceed the latter). The divertor gas puffing is considered as the reference case. As expected, when the gas puff rate or the separatrix density or the perpendicular particle diffusion coefficient increases, d co decreases and the coupled ICRF power increases. Since the coupled ICRF power depends exponentially on d co , (see for example [22]), and as shown in our results, a small decrease of d co would lead to a significant increase of coupled ICRF power. For instance, when d co decreases from 16 cm to 12 cm (as shown in figure 17), the coupled ICRF power increases from 12.6 MW to 34.5 MW. The scan of poloidal upward shift of GPO indicates that an upward shift of 30 cm would make d co (and thus the coupled ICRF power) of the lower and upper half of the antenna roughly equal to each other. These conclusions are consistent with the ones made in the previous sections.
Although midplane gas puffing close to the antenna is beneficial for improving ICRF coupling, a too large gas puff rate may increase the risk of antenna arcing. Previous experiments and simulations show that the minimum of the modified Paschen curve for D 2 is ∼1 mbar cm [23]. Assuming the distance between two potential arcing conductors of the antenna is 100 cm, a neutral gas pressure of ∼10 −2 mbar is required to have an effective arcing. Considering additional RF and surface processes assisting the gas breakdown, as well as an assistance by the ionized plasma injected into the antenna,  one realistically needs to be below 10 −3 mbar in order to be on the safe side of the breakdown.
Previously, high gas puff rates very close to, or even inside the antenna were tested experimentally. On AUG, arcing is only seen when a gas puff rate is larger than 1 × 10 22 el s −1 locally inside the antenna with the optically closed Faraday screen (i.e. antenna with bad pumping) [2]. This should exceed the possible conditions for ITER when a gas with a puff rate of 2.5 × 10 22 el s −1 is injected significantly further away from antenna, where gas will spread in a large volume or be ionized before reaching the antenna. On JET, the gas pressure in front of the antenna is ∼10 −5 mbar during divertor gas puffing, and this value increases to ∼10 −4 mbar during midplane gas puffing. Pressures below 10 −4 mbar should be safe from the point of view of the gas breakdown inside the antenna [24]. In ITER, the neutral density in front of the antenna is in the level of ∼1 × 10 19 m −3 , namely the gas pressure is in the level of ∼4 × 10 10−4 mbar during midplane gas puffing (with a maximum puff rate of 2.5 × 10 22 el s −1 per GPO). Thus, to avoid potential arcing on the ITER antenna, the maximum amount of injected gas should be used with care.

Conclusions
Previous ITER simulations show that with the same amount of injected gas, the local midplane gas puffing close to the ICRF antennas increases considerably more the ICRF power coupling than the divertor or even top gas puffing [18]. In order to characterize the improvement of the ICRF power coupling by the midplane gas puffing in various plasma scenarios in ITER, a comprehensive parametric study has been carried out. As with the previous simulations, here again the ANTITER II code was used to calculate the antenna coupling resistance, with the EMC3-EIRENE code supplying the density profiles in front of the antennas. In particular, parameter scans have been performed for the gas puff rate, the poloidal location of the GPOs, the separatrix density, the transport parameter (diffusion coefficient) and the radial distance between plasma and antenna, as well as the antenna phasing.
From the scan of gas puff rate, it is shown that compared to the divertor gas puffing, the midplane gas puffing increases the coupling resistance very significantly (by a factor of two or more) for all antenna phasings. For the gas puff rate in the range of [0, 4.55 × 10 22 el s −1 ], a higher gas puff rate leads to a larger increase of local SOL density and coupling resistance. When puffing the same amount of gas from the two midplane GPOs, the density in front of the ICRFA antenna (near Port 13) is slightly higher than the ICRFB antenna (near Port 15) due to field line connections from the GPO near Port 15 to the top of the ICRFA antenna. Moreover, puffing all the gas at one GPO does not necessary lead to a higher coupling resistance for the adjacent antenna since density gradient also plays a role in determining the coupling resistance.
From the scan of poloidal location of GPO, it is shown that when puffing the gas from the geometrical poloidal center of the antenna (Z = 0.62 m), the density increase in front of the lower half of the antenna is slightly higher than that in front of the upper half. This is because for the studied baseline equilibrium, the separatrix is closer to the lower part of the antenna than to the upper part, leading to a stronger ionization in front of the lower half of the antenna. An upward shift of the GPO by ∼30 cm can lead to the same density and coupling resistance increase for the upper half and for the lower half of the antenna. However, this poloidal density inhomogeneity in front of the antenna during midplane gas puffing strongly depends on the plasma equilibrium and scenario. Due to engineering constraints, the only possibility would have been a 1 m upward shift of the midplane GPO, which would not have been advantageous and was not pursued further. The possibility of accommodating plasma equilibria with a more symmetric gap pattern in front of the antennas should be investigated.
From the scan of the separatrix density and scan of the transport parameter (diffusion coefficient), it can be seen that a higher separatrix density or a higher transport parameter will lead to a higher SOL density and a higher coupling resistance. Most important of all, it is shown that the midplane gas puffing increases the antenna density and the coupling resistance significantly (by about a factor of two or even more) for all the antenna phasings in all the studied plasma scenarios. These plasma scenarios include cases with a very low SOL density and cases with a very high SOL density as well as different antenna to plasma distances.
It is worth mentioning that efforts have been spent on characterizing the improvement of ICRF power coupling by local gas puffing with full-wave modelling with the TOPICA and RAPLICASOL codes. Also, preliminary RAPLICASOL modelling shows that local gas puffing can reduce the excitation of surface and coaxial modes, together with the near fields in low density baseline plasmas. These works will be reported elsewhere.
In conclusion, based on the comprehensive parametric studies of the midplane gas puffing for ITER in this paper, we are confident to reiterate the strong recommendation to ITER to use the proposed midplane gas puffing to maximize the ICRF power coupling. This midplane gas puffing method is quite robust in improving ICRF power coupling for a broad range of plasma parameters and assumptions on the SOL density. In particular, it will become extremely important when the SOL plasma density is very low.