Dataset for the published article "ITER relevant multi-emissive sheaths at normal magnetic field inclination"

The data contained in the zip files constitute the main research data of the publication entitled as "ITER relevant multi-emissive sheaths at normal magnetic field inclination" [1]. All the datasets constitute post-processed output from the 2D3V SPICE2 Particle-In-Cell (PIC) code. All the PIC simulations have been performed by M. Komm and A. Podolnik. The input is specified by the plasma density, the electron temperature and the surface temperature. The plasma parameters are relevant to partially mitigated ITER edge-localized modes (ELMs). The output concerns the incident plasma current densities, the emitted electron current densities and their standard deviation, the normal wall electrostatic field, the average electron incident energy, the average electron incident angle with respect to the wall normal and the virtual cathode depth. 

The assumptions below are followed in all simulations: (i) The Bohm pre-sheath structure is unaltered by the escaping emitted electrons, since the ions are injected at the plasma boundary with a speed distribution satisfying the Bohm criterion. (ii) Irrespective of the emission, the wall is biased with respect to the plasma boundary with a magnitude fixed by the ambipolarity of the plasma fluxes. (iii) The sheath is collisionless. (iv) The wall is perfectly planar. (v) A homogeneous quasi-neutral plasma boundary and an infinite emitting wall with a homogeneous prescribed surface temperature are considered.

Sheaths that form between plasma-facing components (PFCs) and standard scrape-off-layer plasmas can be described by the classical model of one-dimensional magnetized multi-positive ion sheaths. There are various conditions that need to be satisfied for this model to be valid such as negligible cross-field drifts, low collisionality and weak electron emission.

In contemporary metallic tokamaks, the weak emission condition is violated in the divertor region during intra-ELM as well as inter-ELM periods; thermionic emission being an effective electron emission mechanism from hot tungsten PFCs. As a result of the localized ELM-wetted area, the incident plasma currents can be assumed to remain nearly ambipolar and thus the non-ambipolar current should be equal to the emitted current that escapes to the Bohm pre-sheath. This escaping current density generates a strong volumetric Lorentz force that drives melt layer motion leading to macroscopic PFC erosion. At very elevated surface temperatures, the nominal thermionic current densities are so large that they become incompatible with the classical Bohm pre-sheath structure. As a consequence, space charge accumulation in the sheath leads to the formation of a virtual cathode that limits the escaping thermionic current to a constant value causing the recapture of a fraction of the thermo-electrons. Thus, there is a transition from a monotonic to a non-monotonic potential profile, with the latter known as the space-charge limited (SCL) regime of the emissive sheath. In the case of oblique magnetic field inclination angles, the SCL transition is still realized, but further complications arise due to the suppression of the nominal thermionic current by recapture during Larmor gyration. In contemporary tokamaks, this transition generally occurs at temperatures below the tungsten melting point, thus particular attention has been paid to the SCL sheaths, since they nearly exclusively surround the molten tungsten PFCs. The thermionic emissive sheath in the SCL regime has been thoroughly investigated in our previous works, where an accurate semi-empirical expression for the limited value of the escaping thermionic current as function of the plasma conditions and magnetic field inclination angle was constructed on the basis of systematic PIC simulations [2-4].

On the other hand, during ITER intra-ELM periods, the predicted elevated electron temperatures and high plasma densities of the pre-sheath edge should have a strong impact on the emissive sheath established above hot tungsten PFCs. In particular, the high plasma electron temperatures could enable significant contributions from electron-induced electron emission (secondary electron emission and electron backscattering), the intense normal surface electrostatic fields indicate that thermionic emission is coupled with field emission (in the Schottky regime) and the strong plasma currents suggest that virtual cathodes are formed at much higher surface temperatures (so that the monotonic potential profile regime is of primary interest for melt motion). In order to explore this novel multi-emissive sheath regime, a a comprehensive tungsten electron emission model has been implemented that features accurate analytical descriptions of the yields, energy and angular distributions for the processes of field-assisted thermionic emission, secondary electron emission and electron backscattering [5]. In the present publication [1], at normal magnetic field inclinations, highly accurate analytical semi-empirical expressions are provided for the secondary electron emission current, electron backscattering current and thermionic current in the monotonic regime as well as for the total escaping current in the SCL regime. These semi-empirical expressions have been benchmarked against comprehensive PIC simulations, whose primary post-processed data are provided herein.

[1] P. Tolias, M. Komm, S. Ratynskaia and A. Podolnik, "ITER relevant multi-emissive sheaths at normal magnetic field inclination", Nucl. Fusion 63 (2023) 026007.
[2] M. Komm, S. Ratynskaia, P. Tolias, J. Cavalier, R. Dejarnac, J. P. Gunn and A. Podolnik, "On thermionic emission from plasma-facing components in tokamak-relevant conditions", Plasma Phys. Control. Fusion 59 (2017) 094002.
[3] M. Komm, P. Tolias, S. Ratynskaia, R. Dejarnac, J. P. Gunn, K. Krieger, A. Podolnik, R. A. Pitts and R. Panek, "Simulations of thermionic suppression during tungsten transient melting experiments", Phys. Scr. T170 (2017) 014069.
[4] M. Komm, S. Ratynskaia, P. Tolias and A. Podolnik, "Space-charge limited thermionic sheaths in magnetized fusion plasmas", Nucl. Fusion 60 (2020) 054002.
[5] P. Tolias, M. Komm, S. Ratynskaia and A. Podolnik, "Origin and nature of the emissive sheath surrounding hot tungsten tokamak surfaces", Nucl. Mater. Energy 25 (2020) 100818.