## 3 Calculation Results
### ELM Control by Pellet Injection  
It is predicted that the natural (or \"uncontrolled\") pulsed releases of particles from the column edge through the separatrix (edge localized modes, ELMs) in facilities under construction (including ITER) will lead to high pulsed heat loads on the plasma-facing components, which can substantially decrease their lifetime. It was shown [23] that the critical ELM parameters can be determined either by the loads on the divertor components or the first wall components, depending on the plasma configuration. Estimates made for ITER under the assumption that ELMs will affect the plasma \(Z_{\textit{eff}}\) due to transport of impurities (including the first wall and divertor materials) show that the requirements to ELM control needed to maintain the necessary impurity concentration in the plasma are stricter than the requirements to prevent excessive erosion of the divertor and first wall components [23]. For conditions under which uncontrolled ELMs exceed the limits for the erosion of divertor components and the first wall, ELM control is needed. This can be carried out by suppressing type I ELMs by controlled ELM stimulation using the inverse dependence of the energy loss in ELMs (\(\delta W_{ELM}\)) and their frequency (\(f_{ELM}\)) [24],  
\[f_{ELM}=\alpha_{ELM}\frac{P_{\textit{SOL}}}{\delta W_{ELM}} \tag{15}\]  
Figure 6: Variation of total confinement times for (**a**) energy \(\tau_{E}\), (**b**) ions \(\tau_{p}\) and (**c**) ions, without accounting for recycling \(\tau_{tot}\) in the working window of densities <\(n_{e}\)¿ and confinement parameters \(\tau_{p}/\tau_{E}\). where \(P_{SOL}\) is the power flow from the core plasma into SOL and \(\alpha_{ELM}\) is the fraction of the power that is deposited in ELMs. The expected minimum frequency of controlled ELMs will substantially depend on the requirements to the energy deposited in ELMs and the value of \(\alpha_{ELM}\), which, according to experimental measurements, is usually taken to be equal to 0.2-0.4 [25]. The change of the pellet ion source \(S_{pd}\) (i.e., the flow of D + T particles required to fuel the core plasma in the form of pellets injected from the high magnetic field side (HFS)), taking into account convective ELMs (in addition to \"natural\" ELMs) calculated in a manner similar to [8], is shown in Figure 7. It is seen that the increase in fuel flow to compensate for the particle losses in ELMs is 2-3 times, depending on \(\alpha_{ELM}\), which has to be accounted for in requirements for the system of pellet injection. The flows of particles from pellets into the plasma are up to 1.6 times lower than those calculated earlier (in the corresponding working points). The considered range of flows through the pellet injection system corresponds to the chosen requirements to the pellet injection system (PIS) of ITER and it is twice as small even for the maximum values of \(S_{pel}\) and \(\alpha_{ELM}\). From this, one can conclude that, even taking into account the additional flow of particles needed to stimulate ELMs from the low magnetic field side (LFS), the considered requirements for the PIS system are achievable from the engineering standpoint. The frequency of fuel pellet injection (with maximum size for each separate plasma density) \(f_{pel(HFS)}\) is shown in Figure 8 depending on \(\alpha_{ELM}\) for the working window of plasma parameters. The dashed line shows the levels of \(f_{ELM}\) necessary for stimulation of ELMs with \(\delta W_{ELM}\)\(\sim\)0.5 MJ (comparable to the value accepted for ITER) due to pellet injection. In Figure 8, frequencies \(f_{ELM}\) are also marked, necessary to stimulate ELMs with lower values of \(\delta W_{ELM}\). The obtained result differs quantitatively from earlier obtained results [8] but it is the same in principle. It is seen that, in the significant fraction of the working window with \(\tau_{p}\)/\(\tau_{E}\) > 1.7 for \(\alpha_{ELM}\) = 0.2 and with \(\tau_{p}\)/\(\tau_{E}\) > 1.2-1.4 for \(\alpha_{ELM}\) = 0.4, additional stimulation of ELMs is necessary.