M. Coppins

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.

A study of the stability of the Z pinch under fusion conditions using the Hall fluid model

The Hall fluid model (a quasineutral two‐fluid model with Te=0) is used to investigate the effect of the Hall term on the m=0 instability in a pure Z pinch. The problem is treated numerically by a linearized initial value code. Two different equilibria are investigated. The growth rate of the fastest growing magnetohydrodynamic mode is increased for one equilibrium and reduced for the other by the inclusion of the Hall term, and in the second case new modes with high growth rates are found. The possibility of Hall term destabilization of MHD stable equilibria is suggested.

Fluid model of the boundary of a one-dimensional plasma under the influence of an oblique magnetic field for a wide range of collisionality

The effect of a magnetic field on the boundary of a plasma is studied using a one-dimensional fluid model based on the work of K.-U. Riemann [Contrib. Plasma. Phys. 34, 127 (1994)]. The model takes into account the effects of both collisions and ionization. Two limiting regimes are identified: the collisional presheath and the (highly) magnetized presheath. Results from this model demonstrate that a highly magnetized presheath may be treated in terms of two regions: The B-aligned presheath and a Chodura layer [R. Chodura, Phys. Fluids 25, 1628 (1982)]. The properties of this Chodura layer are explored in some detail and it is found that the size of this layer, for example, follows a simple expression in the highly magnetized regime. Finally, an attempt is made to recover the singular behavior of the Chodura layer as the magnetic field becomes very strong and use a pseudo two-scale approach to resolve both scale lengths of the magnetized presheath.

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.

Coaxial discharge with axial magnetic field: Demonstration that the Boltzmann relation for electrons generally does not hold in magnetized plasmas

A one-dimensional two-fluid model is used to describe the quasineutral plasma of a discharge formed between coaxial cylinders under the influence of an axial magnetic field. The geometry treated in this paper is symmetric about the z-axis and is radially varying. The nested cylinders are necessarily different in size, leading to a potential difference between the sheath edges of the discharge plasma. This can be removed by applying a strong enough magnetic field, which also has the effect of flattening the potential profile, i.e., reducing the electric field in the plasma volume. In a previous publication [T. M. G. Zimmermann et al., Phys. Plasmas 16, 043501 (2009)], the authors examined the validity of the Boltzmann relation for electrons when applied to a similar geometry. When the magnetic field becomes strong enough to affect the electron flow in the radial direction, this expression breaks down. It was further discovered that certain situations require a self-consistent treatment of magnetic fields, since significant azimuthal currents can arise in such geometries. This work is applied and extended to offer a complete description of the electron density.

Ideal magnetohydrodynamic linear instabilities in the Z-pinch

The application of ideal magnetohydrodynamic (MHD) linear stability theory to the Z-pinch is discussed. Numerical solutions of the MHD eigenvalue equation are described. Growth rates and the spatial structure of eigenmodes have been obtained and the stabilising effect of a conducting wall on the m=1 mode has been studied. A detailed analysis of experimental results from Imperial College is presented.

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.

Linear stability of the collisionless, large Larmor radius Z-pinch

The Vlasov fluid model is used to study the m=0 and m=1 internal and free boundary modes in a collisionless, large Larmor radius Z pinch. Two methods (initial value and variational) are employed, and give good agreement. The growth rate can be reduced from its zero Larmor radius value by a factor of up to 10 for m=1, and up to 3 for m=0. Stability thresholds and the role of resonant ions are discussed.