Published Data
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Publication Figures
Publication Date:
2020-10-12
First Author:
O. Bardsley
Title:
On the axisymmetric stability of tokamaks with ferromagnetic walls
Paper Identifier:
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| Figure Reference | Title | Description | Number of Figure Data Items | Identifier | Download Figure Details | ||
|---|---|---|---|---|---|---|---|
| Derivations within paper based on these notes | Mathematical derivations | A set of notes taken during the derivation of the mathematics for the above paper. Some are incomplete. Errors may be present. There is no logical ordering. | 0 | CF/20/127 | Download | ||
| Referenced in text | Cylindrical schematic | Schematic of the cylindrical model problem, showing geometry, parameters and co-ordinates. | 0 | CF/20/128 | Download | ||
| Referenced in text | Cylindrical equilibria | Example equilibrium configurations in the cylindrical problem with a ferromagnetic wall and divertor coils. The divertor current varies between the panes and the effective relative permeability varies between the quadrants, increasing clockwise from top-left. Flux surfaces (at the same levels in all plots) are shown in blue, and the LCFS in red. | 0 | CF/20/129 | Download | ||
| Referenced in text | Cylindrical elongation vs destabilising force | Elongation of the last closed flux surface as a function of the destabilising force gradient due to divertor coils for a scan of wall location, wall thickness, magnetic permeability, and divertor current over the ranges indicated. The divertor coils are at r_c = 1.2. Wall-limited cases are shown in red and X-point cases in blue. | 0 | CF/20/130 | Download | ||
| Referenced in text | Cylindrical stabilising wall force vs growth rate | Force due to the wall as a function of the instability growth rate for different murel. Dashed lines show the `thick-wall' (large gamma) limit and dotted lines the `thin-wall' (small gamma) limit. | 0 | CF/20/131 | Download | ||
| Referenced in text | Cylindrical growth rate | Vertical instability growth rate as a function of the destabilising force acting on the plasma, either (a) due to the external coils alone, or (b) including the ferromagnetic force as well. The former collapse in the limit of a thick wall, gammatwogg 1 (note the vertical axis is scaled by murel) whereas the latter collapse for a thin wall, gammatwoll 1. The coil current varies between 0 and Ip. | 0 | CF/20/132 | Download | ||
| Referenced in text | Cylindrical growth rate vs nonmagnetic | (a) Relative change in vertical instability growth rate as a function of its value in the absence of any ferromagnetic effects, keeping the externally-applied destabilising force gradient (and thus plasma elongation) constant. Solid lines show the exact result, and dashed lines the limiting forms for gammatwoll 1 and gammatwogg 1. (b) Exact result again, but normalised by murel. | 0 | CF/20/133 | Download | ||
| Referenced in text | Spherical schematic | Schematic of the spherical model problem, showing geometry, parameters and co-ordinates. | 0 | CF/20/134 | Download | ||
| Referenced in text | Spherical equilibrium plasma wire | Equilibrium magnetic flux surfaces due to a plasma wire. (a) Comparison between ferromagnetic (murel = 3, blue) and non-ferromagnetic (murel = 1, red) cases. (b) Difference between the two, i.e. the field `due to the wall'. Geometry is ri=0.9re, Rp = 0.4re and zp=0; the black cross represents the plasma wire. | 0 | CF/20/135 | Download | ||
| Referenced in text | Radial force balance | The net radial force on the plasma as a function of major radius at various values of external coil current Ic. The parameters are ri=0.9re, Rc = 1.2re, zc = pm0.6re, murel = 3 and we use Lambda = 0.25, Rp/ap = 2. Solid blue lines show the ferromagnetic case, with dashed orange lines the murel=1 equivalent for comparison. Triangles denote equilibria: downward-pointing for stable, upward for unstable. The black cross is the maximum stable equilibrium. Labels `outward' and `inward' indicate the direction of the net force. | 0 | CF/20/136 | Download | ||
| Referenced in text | Spherical equilibria | Equilibrium poloidal magnetic flux surfaces for various divertor currents. The wall, shown in grey, has ri=0.9re and murel = 3. Coils are plotted as orange squares; the vertical field coil current is adjusted in order to keep Rp = 0.6re constant. Red curves show the LCFS, defined either by the X-point or the inboard limiter at R = 0.15re (grey dot). | 0 | CF/20/137 | Download | ||
| Referenced in text | Spherical growth rate | Vertical instability growth rate as a function of the destabilising force acting on the plasma, either (a) due to the equilibrium field line curvature, or (b) including the ferromagnetic force as well. The former collapse in the limit of a thick wall, gammatwogg 1 (note the vertical axis is scaled by murel) whereas the latter collapse for a thin wall, gammatwoll 1. The divertor coil current varies between 0 and 3.5Ip whilst the vertical field coil current is adjusted such that radial force balance is maintained. | 0 | CF/20/138 | Download | ||
| Referenced in text | Spherical current distribution | Induced field at VDE onset. Solid colour shows the toroidal current density distribution within the conducting wall (orange positive, purple negative with respect to Ip) normalised to its maximum absolute value. Contour lines show poloidal magnetic flux surfaces in the vacuum regions associated with this current distribution. | 1 | CF/20/139 | Download | ||
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