A wide-angle view of the MAST plasma at one instant in time during the evolution of a type-I ELM (Courtesy of A. Kirk, Culham Laboratory, UK). Here, the bright emission bands, referred to as ELM filaments, wrap around the outer surface of the plasma in helical patterns that connect the upper and lower divertors. The pitch of these filaments is aligned with the local magnetic field, which typically has a rather steep angle with respect to the equatorial plane of the plasma due to the relative strength of the poloidal field compared to that of the toroidal field in spherical tokamaks such as MAST. Note that the intensity of the emission in these filaments is not uniform along their helical axis and that these structures are seen to protrude from the surface as they approach the upper hyperbolic point where they become much more toroidally aligned. These protrusions are consistent with the type of structure predicted by the topology of homoclinic and heteroclinic tangles invoked in the ELM model presented below. Here, the protrusions correspond to the lobes of the tangle, which become narrower in the poloidal direction and more extended in the radial direction as they approach a hyperbolic point (Fig. 5 shows the 

A wide-angle view of the MAST plasma at one instant in time during the evolution of a type-I ELM (Courtesy of A. Kirk, Culham Laboratory, UK). Here, the bright emission bands, referred to as ELM filaments, wrap around the outer surface of the plasma in helical patterns that connect the upper and lower divertors. The pitch of these filaments is aligned with the local magnetic field, which typically has a rather steep angle with respect to the equatorial plane of the plasma due to the relative strength of the poloidal field compared to that of the toroidal field in spherical tokamaks such as MAST. Note that the intensity of the emission in these filaments is not uniform along their helical axis and that these structures are seen to protrude from the surface as they approach the upper hyperbolic point where they become much more toroidally aligned. These protrusions are consistent with the type of structure predicted by the topology of homoclinic and heteroclinic tangles invoked in the ELM model presented below. Here, the protrusions correspond to the lobes of the tangle, which become narrower in the poloidal direction and more extended in the radial direction as they approach a hyperbolic point (Fig. 5 shows the 

Source publication
A series of type-I ELM impulses seen in the lower (primary) divertor deuterium (D α ) recycling emissions during DIII-D discharge 126006 where f ELM = 50 → 75 Hz is correlated to
Time evolution of the plasma current measured by a pair of lower divertor Langmuir probes located 28 mm apart in major radius ( R ) during an ELM DIII-D discharge 138229. Type-II ELMs are...
A wide-angle view of the MAST plasma at one instant in time during the evolution of a type-I ELM (Courtesy of A. Kirk, Culham Laboratory, UK). Here, the bright emission bands, referred to as ELM...
(a) Full poloidal cross sectional view of a separatrix homoclinic tangle formed by an applied external n =1 magnetic perturbation due to the DIII-D field-error correction coil with a current of 8...
Lower divertor (a) magnetic footprint formed on HFS vertical wall by an externally applied n =1 perturbation (no plasma response) from the DIII-D field-error correction coil with a current of 8...
Poincaré plots of (a) the calculated structure of the stable and unstable invariant manifolds in the primary divertor with a current of 100 A in flux tube number 1 (not clearly visible) and (b)...
Poincaré plots of (a) the formation of flux tube number 3 in the secondary divertor as the current in flux tube 1 is increased to 130 A, (b) flux tube number 2 is not completely formed at 150 A.
Poincaré plots of (a) the formation of flux tube number 2 in the secondary divertor at 200 A in flux tube number 1 and the appearance of a new partially formed flux tube (number 4) while (b) at...
Context 1
... spherical tokamaks such as MAST ( Kirk et al., 2004;Kirk et al., 2007) and NSTX ( Maingi et al., 2005) are equipped with visible light fast framing cameras that can capture images of type-I ELMs. Figure 4 provides a full view of the plasmas captured during a type-I ELM in MAST. Here, the bright emission bands, referred to as ELM filaments, wrap around the outer surface of the plasma in helical patterns that connect the upper and lower divertors. ...
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Context 2
... structure as prescribed by the Hamiltonian nature of the tangle in the model as it approaches a region of weak poloidal magnetic field near the hyperbolic points. These protruding lobes form a spiraling magnetic footprint that converges to the unperturbed intersection of the separatrix with the divertor target plate similar to the one shown in Fig. 4 of Roeder et al., (2003) for an n=1 homoclinic tangle in DIII-D. These magnetic footprints are essential elements of the nonlinear ELM model presented ...
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Context 3
... topology are consistent with the heat flux patterns measured in the DIII-D divertor during a type-I ELM ( Wingen et al., 2009a). A key question studied during these simulations addresses how the topological evolution prescribed by the model conforms to experimental measurements of type-I ELM dynamics. In particular, data such as that shown in Fig. 4 suggest that the peak in the toroidal mode spectrum of an ELM increases in mode number during the nonlinear growth phase. As discussed below, a bifurcation in the separatrix topology has been identified during the early growth phase of the instability. This bifurcation involves the appearance of heteroclinic invariant manifolds ...
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Citations

  • ... A model based on the topological changes in the magnetic structure is used in the following. A conceptual electromagnetic model, which interprets the dynamics of the edge plasma and the evolution of the pedestal magnetic topology following the linear growth phase of a peeling–ballooning instability, was proposed [14, 15] and numerically implemented [16]. The model assumes that thermoelectric currents are driven in the plasma edge by the heat delivered to the target plates during the plasma pedestal collapse. ...
    ... In discharge 133908, the secondary X-point is very close to the primary separatrix, about 10.5 cm, so that the connection to the upper targets is established easily. Only about 150 A initial current is necessary to form the first large tube [15, 20]. For other discharges the necessary current can be much larger, resulting in a different scenario of flux tube formation. ...
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