M. Bacharis

Dust in tokamaks: An overview of the physical model of the dust in tokamaks code

The dynamical behavior of dust produced in tokamaks is an important issue for fusion. In this work, the current status of the dust in tokamaks (DTOKS) [J. D. Martin et al., Europhys Lett. 83, 65001 (2008)] dust transport code will be presented. A detailed description of the various elements of its underlying physical model will be given together with representative simulation results for the mega amp spherical tokamak (MAST) [A. Sykes et al., Nucl. Fusion 41, 1423 (2001)]. Furthermore, a brief description of the various components of the dust transport (DUSTT) [R. D. Smirnov et al., Plasma Phys. Controlled Fusion 49, 347 (2007)] code will also be presented in comparison with DTOKS.

Modelling dust transport in tokamaks

The DTOKS code, which models dust transport through tokamak plasmas, is described. The floating potential and charge of a dust grain in a plasma and the fluxes of energy to and from it are calculated. From this model, the temperature of the dust grain can be estimated. A plasma background is supplied by a standard tokamak edge modelling code (B2SOLPS5.0), and dust transport through MAST (the MegaAmp Spherical Tokamak) and ITER plasmas is presented. We conclude that micron-radius tungsten dust can reach the separatrix in ITER.

Electron emission in a source-collector sheath system: A kinetic study

The classical source-collector sheath system describes a plasma that forms between a Maxwellian source and an absorbing wall. The plasma is assumed to be collisionless and without ionization. Two distinct areas are being formed: the collector sheath, an ion-rich region in contact with the absorbing boundary, and the source sheath, which is an electron-rich area near the Maxwellian source. In this work, we study a modified version of the classical source-collector sheath system, where the wall is no longer absorbing but emits electrons. As a result, we have two different types of collector sheath, one where a potential well is formed and one without a potential well. We examine the effect of electron emission for a range of conditions for the plasma and the emitted electrons. In the first part of this work, we study the problem analytically, and in the second, using our kinetic Vlasov code, Yggdrasil. The simulation results are in very good agreement with the predictions of our theoretical model.

The effect of dust grain size on the floating potential of dust in a collisionless plasma

Dust immersed in plasma quickly charges to a potential where the ion and electron currents to it balance; this is the floating potential. In order to determine dust behaviour the floating potential must be known. The most used theory for determining this is orbital motion limited (OML). The OML floating potential depends on the ion to electron temperature ratio (β) and the plasma ion species (A). In reality the floating potential also depends strongly on the size of the dust grain (ρ = a/λD, where a is the radius of the grain and λD is the Debye length). Using a particle-in-cell code, dust is simulated in a collisionless plasma, the floating potential is investigated and the expressions provided allowing fast and accurate prediction of the floating potential as a function of β, A and ρ.

Modelling of tungsten and beryllium dust in ITER

Production of dust particles during tokamak operation is a critical issue for magnetic confinement fusion. Their introduction into the reactor can have serious consequence on its performance and can constitute a safety issue. For these reasons the study of dust particles in tokamaks is crucial. Direct experimental observations of such particles that would give insight into their behaviour are quite challenging. In this context, numerical modelling of the relevant phenomena, plays a key role for better understanding the transport mechanisms of dust in tokamaks. In this work the dust transport code, Dust in tokamaks (DTOKS), is used to investigate how far tungsten and beryllium dust grains can penetrate into the ITER plasma. We simulate W and Be dust grains, with radii rd = 1–100 µm, and injection velocities, vinj = 1–100 ms−1, ejected from three different locations of the ITER vessel. It was found that particles with radius larger than 10 µm, with vinj = 10 m s−1, can survive long enough to reach the separatrix. Furthermore, the important roles of the initial injection velocity and injection location have been highlighted.

Dust grain charging in RF discharges

In this work modifications of the orbital motion limited approach are used to investigate the impact of time varying phenomena on the floating potential of a dust grain. The main interest is focused on different regimes relevant for RF discharges. Three cases are considered. First, the case of the RF sheath. Second, the case of charging in the bulk plasma with a time varying electric field and third, the case when the time varying current in the bulk plasma is carried only by a fraction of the electron population. This last case is relevant to low pressure discharges when stochastic heating is important.

Floating potential of large dust grains with electron emission

Electron emission from the surface of solid particles plays an important role in many dusty plasma phenomena and applications. Examples of such cases include fusion plasmas and dusty plasma systems in our solar system. Electron emission complicates the physics of the plasma-dust interaction. One of the most important aspects of the physics of the dust plasma interaction is the calculation of the particles floating potential. This is the potential a dust particle acquires when it is in contact with a plasma and it plays a very important role for determining its dynamical behaviour. The orbital motion limited (OML) approach is used in most cases in the literature to model the dust charging physics. However, this approach has severe limitations when the size of the particles is larger than the electron Debye length λDe . Addressing this shortcoming for cases without electron emission, a modified version of OML (MOML) was developed for modelling the charging physics of dust grains larger than the electron Debye length. In this work, we will focus on extending MOML in cases where the particles emit electrons. Furthermore, a general method for calculating the floating potential of dust particles with electron emission will be presented for a range of grain sizes.

Diffusion and stochastic heating of a dust cloud in tokamak edge plasmas

The diffusion due to collisions with ions of a cloud of nano-meter dust particles in the region of the scrape-off-layer (SOL) of a tokamak is considered and it is shown that for the conditions in the Frascati tokamak upgrade, the cloud can expand to reach the SOL limit in very short times without ablating. The conditions for stochastic heating of the cloud and acceleration of a larger particle to hyper-velocities, taking into account the effect of decreasing dust density in the cloud, are established.

A kinetic study of the source–collector sheath system in a drifting plasma

The source–collector sheath system describes a plasma that forms between a Maxwellian source and an absorbing wall. The plasma is assumed to be collisionless and without ionization. Two distinct areas are being formed: the collector sheath, an ion-rich region in contact with the absorbing boundary, and the source sheath, which is an electron-rich area near the Maxwellian source. Our work examines the effect that shifted Maxwellian distributions at the plasma source have on the characteristics of such a system. This is studied for a range of drift velocities and ratios of ion and electron temperatures. We study the problem both analytically and using our kinetic Vlasov code, Yggdrasil. The simulation results are in very good agreement with the predictions of our theoretical model.