Published Data
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Publication Figures
Publication Date:
0000-00-00
First Author:
C J Ham
Title:
Explosive ballooning flux tubes in tokamaks
Paper Identifier:
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| Figure Reference | Title | Description | Number of Figure Data Items | Identifier | Download Figure Details | ||
|---|---|---|---|---|---|---|---|
| Figure 1 | Explosive ballooning flux tubes in tokamaks – Fig 1 | Profile of safety factor, q, (solid line, left hand axis) and of normalized pressure, ?N = 2?0R0q2p0(r)/B2 0, (dashed line, right hand axis) for the internal transport barrier. | 0 | CF/15/485 | Download | ||
| Figure 2 | Explosive ballooning flux tubes in tokamaks – Fig2 | Elliptical (orange) flux tube with r ? ?2 ? S ? ?1 sliding along (blue) surface S = 0 parting surrounding (black) field lines. Note the tube’s displacement is larger on the large R part of the flux surfaces – the tube balloons. The magnetic shear (s = rq?/q) causes the twist and narrowing of the tube on the inside. | 1 | CF/15/486 | Download | ||
| Figure 3 | Explosive ballooning flux tubes in tokamaks – Fig 3 | s-? diagram illustrating the linear instability boundary. The equilibrium chosen here follows the trajectory of the dash-dotted line as r0 is increased. No surfaces are linearly unstable. | 0 | CF/15/487 | Download | ||
| Figure 4 | Explosive ballooning flux tubes in tokamaks – Fig 4 | The upper plot shows the shape of the field line at different times, r = r(?, r0, t) for r0 = 0.61. The solid lines start with the initial condition just greater than the unstable equilibrium state rcrit and evolve upwards. The dash-dotted lines start with the initial condition just less than the unstable equilibrium state rcrit and evolve downwards. The final state of this evolution is the unperturbed field line. The lower plot shows the time evolution of maximum value along the field line rmax(t) = r(0, r0, t). Again, the solid (dash-dotted) line starts with the initial condition just greater (just less) than the unstable equilibrium state rcrit. | 0 | CF/15/488 | Download | ||
| Figure 5 | Explosive ballooning flux tubes in tokamaks – Fig 5 | Relative energy, E, evaluated from Eq.(6) for three equilibrium solutions, F? ? = 0, of Eq.(4). The dotted line is the unperturbed energy, the dashed line is the unstable displaced equilibrium energy (E(rcrit, r0)) and the solid line is the displaced stable equilibrium energy (E(rsat, r0)). The stable displaced equilibrium is the lowest energy state for 0.593 < r0 < 0.679. | 0 | CF/15/489 | Download | ||
| Figure 6 | Explosive ballooning flux tubes in tokamaks – Fig 6 | A measure of the ballooning displacement = (?N(r0) ? ?N(rmax)/(2?p?0) for the two perturbed equilibrium states (left-hand axis). Field lines in the displaced lower energy equilibrium can cross a substantial fraction of the pressure profile (solid line) – for example the r0 = 0.61 field line balloons across about 73% of the pressure profile. The unstable equilibrium is shown by the dash-dotted line. The rmax for the saturated field lines is shown as the dashed line (righthand axis) and the rmax for the unstable equilibria are shown as the dotted line. Note that for 0.58 < r0 < 0.68 the field lines “overtake” i.e. rmax(r1 0) > rmax(r2 0) if r1 0 < r2 0. | 0 | CF/15/490 | Download | ||
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