Speaker
Description
The electron density ($n_e$) required to unconditionally suppress the runaway electrons (REs), generated during the disruption of a reactor-relevant tokamak plasma, is 2-3 orders of magnitude larger than the $n_e$ of the target plasma. An estimate for a worst case ITER plasma disruption at full current and magnetic field can be found in [1].
The density needed to reduce the RE seed and the final RE current to an acceptable level (e.g. $< $ 1 MA) is smaller, i.e. O(10 - 100)$\times n_e $, and it was calculated by R. Martin-Solis for ITER [2] and for DEMO plasmas [3]. Shattered pellet injectors (SPIs)[4] are being considered for disruption mitigation and particularly for RE suppression in ITER. Whether SPIs can fulfill the mitigation requirements or not needs to be debated more clearly.
In modelling the RE generation, the density increase can be imposed with a Heaviside function. Nevertheless, in the reality, the matter must be injected into the plasma in the form of pellets from the edge and must cross the plasma to reach its center.
The ablation of cryogenic deuterium pellets and the deposition of matter in a plasma is determined by pellet (material, radius, velocity and number) and plasma (dimension, electron density and temperature) parameters.
Most of these parameters are either fixed or constrained. For a given device, the plasma dimension, the density, the plasma current - and therefore the density increase required for RE suppression - are fixed.
Since the deposited matter cools the plasma, induces the fast growth of tearing modes and causes the thermal quench, it must be delivered in the plasma within the so called pre-thermal quench time interval, which lasts a few milliseconds.
The maximum pellet velocity is limited by the injector technology and the minimum by the pre-thermal quench duration; reasonable velocities for reactor relevant plasmas are in the range 1-1.5 km/s since they translate into a pellet transit time from edge to plasma center of 2-3 ms.
According to the Neutral Gas Shielding (NGS) [5] model, one single deuterium pellet, able to increase the electron density by a factor of circa 20, must be launched at a velocity higher than 10 km/s in order to reach the plasma center ($T_e (0)$ = 40 keV). This upper velocity is extremely large if compared to the velocity of the present cryogenic pellets (300-1200 m/s), and it is probably not realizable.
Increasing only $r_p$ at a realistic velocity, e.g. 1200 m/s, does not foster the deposition of the ablated material beyond $\rho \sim 0.5$ (calculation not shown). Therefore, these results suggest to investigate the injection of multiple pellets.
Essentially, only the pellet radius and the number of pellets can and must be varied to obtain the required density increase. If the maximum amount of impurity injected is limited by safety or other reasons, this constrain should also be taken into account.
This contribution presents a discussion of what is required, in terms of number of frozen deuterium pellet, of pellet radius and pellet velocity, to increase the plasma density of a factor of (let's say) 20 within a few milliseconds over the whole plasma cross section of a ITER and of a DEMO-like plasma.
The spatial distribution of the material deposited in the plasma is determined by mostly-known physics mechanisms. The NGS and derived ablation models will be used for parametric studies of the ablation of deuterium (see e.g figure 1) and impurity pellets of different dimensions.
More detailed simulations of the ablation of one single deuterium pellet have been carried out with the HPI2 code [6].
Figure 2 shows the evolution of the density profile for three different pellets launched in a DEMO-like plasma.
If the calculation of the plasmoid drift is suppressed, the largest pellet generates a $\Delta n_e (0) \sim 27 \times 10^{20}$ close to the plasma center.
Nevertheless, the strong outward drift, due to the high $T_e$ (40 keV) of the target plasma, prevents the penetration of the ablated material.
The NGS model predicts a penetration of the largest pellet up to $\rho = 0.65$.
Some results are already certain: The previous benchmark shows that the NGS model is not adequate enough for the calculation of the density increase. In addition, the NGS model indicates a strong dependence of the ablation rate on the plasma temperature. Since the temperature of the target plasma - to be shut-down by the disruption mitigation system - can vary considerably (e.g. by a factor of 20 in ITER and 40 in DEMO, and $r_p(a)$ must vary proportionally) the injection system must be extremely (unrealistically?) flexible.
References
[1] T C Hender et al. Progress in the ITER Physics Basis Chapter 3: MHD stability, operational limits and disruptions 2007 Nucl. Fusion 47 S128-S202
[2] J.R. Martin-Solis et al., Nuclear Fusion (2017) 57 066025
[3] R. Martin Solis et al., DEMO report (2018)
[4] L. Baylor et al., 27th IAEA Fusion Energy Conference FIP/P1-1 (Gandhinagar, 2018)
[5] P.B. Parks et al., Phys. Fluids \bf 21 \rm 10 (1978) 1735
[6] F. Koechel et al., \it Modelling of Pellet Particle Ablation and Deposition: The Hydrogen Pellet Injection code HPI2, \rm Report EFDA-JET-PR(12)57
%E-mail contact of main author: Gabriella.Pautasso@ipp.mpg.de
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| Country or International Organization | Germany |
|---|---|
| Affiliation | IPP Garching |
