## 3 Calculation Results
### ELM Control by Pellet Injection
This can be performed by injecting pellets from the LFS and/or decreasing the size of fuel pellets [8]. The specific solution should be chosen based on detailed simulations and determination of the size of the pellets injected from different directions. Figure 7: Dependence of the size of the pellet source \(S_{pel}\) on \(\alpha_{ELM}\) for the cases with natural and convective ELMs in the working window of densities <\(\tau_{e}\)> and confinement parameters \(\tau_{p}\)/\(\tau_{E}\). The scale on the right shows the agreement between color and values of \(S_{pel}\). Estimates of the size of LFS pellets required for reliable initiation of ELMs (for example, [26]) by the method described in [23] give the value of \(\sim\)1.0 mm\({}^{3}\). This agrees with modern experimental data from JET, DIII-D, and ASDEX Upgrade [23]. Since the fuel injection flows weakly depend on the LFS injection parameters (see [8]), we left the analysis of the minimum pellet size for ELM stimulation to the future. Control of ELM frequency \(f_{ELM}\) and energy losses in ELMs \(\delta W_{ELM}\) by pellet injection is considered as the main scheme of ELM control for ITER and other facilities under construction. Experiments carried out at DIII-D showed the high efficiency of this method in decreasing the ELM energy released in the divertor [27]. It was shown experimentally that the energy of ELMs released in the divertor decreased 10 times for ELMs controlled by pellet injection compared with uncontrolled ELMs under the same discharge conditions [27]. To apply this method in constructed facilities including ITER and determine the requirements to the PIS, one needs to additionally study:  
1. the size of the pellets required for reliable stimulation of ELMs and changes in the flows of fuel components in the FC caused by it;
2. the geometry of pellet injection for fueling the plasma and stimulating ELMs;
3. the effect of this control method on the parameters of density pedestal of the core plasma and, consequently, its confinement and the characteristics of the neutron source. Figure 9 shows the density profiles of the main components of the plasma core provided by different ion sources: NBI, pellets, and neutrals through the separatrix. It is seen that the latter forms a relatively uniform profile despite the source having a peak at the plasma periphery (see Figure 9c,d). At the same time, the sources of pellets and the beam have maximums close to the system axis, which provide the characteristic density profiles. It was noted in [28] that the radial profile of the source of neutrals from the beam is calculated by the NUBEAM code [29] that is incorporated into the ASTRA transport code. The high boundary density of ions that are supplied in the form of atoms from the divertor zone is generated as a result of the decrease of the scrape-off layer (SOL) thickness \(\lambda_{q}\) due to the high magnetic field (see, e.g., [30]). Of the experimental data accessible in open literature, only the results from Alcator C-Mod [31; 32] can be compared with the DEMO-FNS and ITER facilities. Figure 8: Frequency of fuel pellet injection (HFS) that contain 10% of the amount of particles \(N_{core}\) and the required frequency of pellet injection for stimulation of ELMs with \(\delta W_{ELM}\sim 0.5\) MJ (and below) at (**a**) \(\alpha_{ELM}=0.2\) and (**b**) \(\alpha_{ELM}=0.4\) in the working window of densities \(<\)\(n_{e}\)\(>\) and confinement parameters \(\tau_{p}/\tau_{E}\). The scales on the right show the agreement between color and values of \(f_{pel}\). In an accurate approach, it is necessary to simulate the profiles created in plasma (with given properties) during ablation of pellets with the given composition, size, velocity, frequency, and injection direction. Approach [33] allows one to calculate the evaporation rate of the pellet material, yet to obtain the source profile it is necessary to take into consideration the drift of the evaporated material after ablation.