Snakes and similar coherent structures in tokamaks A. Y. Aydemir 1, K. C. Shaing 2, and F. W. Waelbroeck 1 1 Institute for Fusion Studies, The University of Texas at Austin, Austin, TX 78712 2 Plasma and Space Science Center, and Department of Physics, National Cheng Kung University, Tainan, Taiwan 70101, Republic of China Plasma Instabilities 1
Localized coherent structures in tokamak plasmas Improved confinement has been the holy grail of fusion research since the beginning. Nonlinear coherent structures that form, in most instances, accidentally present examples where confinement is unreasonably good. Thus, we may learn a great deal by studying how they form, how they interact with the rest of the plasma column, and why confinement is so unreasonably good within them. Here we present some very preliminary work addressing some of these issues. 2
Experimental observations JET (1) Density snake at q=1 surface in JET Snakes are observed as regions of enhanced soft X-ray emissions at q=1, 3/2 surfaces after D 2 pellet injection. Weller (JET) PRL (1987) 9/5/11 5th IAEA Technical Meeting--The Theory of Immediate effect is that the density profile becomes hollow and temperature drops, leading to lower X-ray emissions. On this symmetric change, a nonsymmetric snake-like region of enhanced emissions is superimposed in space-time plots of soft X-ray emissions. Δn e ~ n e ; density can be higher by a factor of two in the snake. ΔT e < 100eV (negative). Disappears in about 100ms. 3
Experimental observations JET (2) A q=2 snake in an OS discharge in JET Forms spontaneously in optimized shear (OS) discharges near an ITB. Spatially localized feature(width~10cm) with a double-helix structure seen on SXR and ECE diagnostics. Associated with a local extremum in q- profile at the q=2 surface; seems like it should be rather fragile. ΔT e can be +/-; similarly current perturbation can be +/-. Not quite like a q=1 snake it may not be an island!? Alper et al. 26 th EPS (1999). It has a deleterious effect on confinement; it eats away the ITB. 9/5/11 5th IAEA Technical Meeting--The Theory of 4
Experimental observations Tore Supra Snake geometry in Tore Supra As in JET, Tore Supra snakes form after pellet injection. Δn e /n e ~ 25-140%, ΔT e < 0. Also impurity (C) accumulation inside good confinement, as in JET. But they are localized not on the q=1 surface but well inside: r snake /r q=1 ~0.5! A second q=1 surface inside? But it survives sawtooth crashes, so a third q=1 surface? Pecquet et al., NF (1997) 9/5/11 5th IAEA Technical Meeting--The Theory of 5
Experimental observations Impurity snakes (1) Impurity (W) snake in ASDEX In ASDEX, tungsten injection into the core through laser ablation leads to an m=1, n=1 snake in the SXR signal in NBI-heated discharges nothing in ohmic discharges. It is attributed to W-accumulation within an island at the q=1 surface. It disappears with a sawtooth crash but reforms afterwards, unlike the JET snakes. Electron density is ~20% higher in the snake. Naujoks (ASDEX) NF (1996) Decay times are long sometimes hardly any decrease of W could be observed during time intervals of about 2s. 9/5/11 5th IAEA Technical Meeting--The Theory of 6
Experimental observations Impurity snakes (2) Impurity (Mo) snake in C-Mod In C-Mod, inadvertent injection of molybdenum leads to accumulation of the impurity in a snake-like structure at the q=1 surface. It has many of the characteristics of the JET snakes. It is not believed to be associated with a displaced hot core but with an actual m=1 island. Delgado-Aparicio EPS (2011) 9/5/11 5th IAEA Technical Meeting--The Theory of 7
Experimental observations Current ribbon in JET Impurity (Mo) snake in C-Mod In JET, a current ribbon is observed on the Mirnov signals. It is described as a kink in the flux surfaces, not an island. Solano et al., PRL (2010) It is a localized structure (width~ 2mm) located at the q=4 surface near the top of the pedestal that survives ~ 1-2 s! 9/5/11 5th IAEA Technical Meeting--The Theory of 8
What are these coherent structures? Snake phenomenology (Wesson 1995) Since the field lines close on themselves at rational surfaces, the ablation cloud from a pellet remains localized to those field lines that intersect the pellet path. Thus the local cooling effect is much stronger than on normal flux surfaces. Lower local temperature leads to enhanced resistivity and reduced current density. The current perturbation leads to the formation of a magnetic island, which traps the ablated material. This process is especially effective at the q=1 surface, since a field line closes on itself after a single transit around the torus; in other words, the q=1 surface spreads the ablation cloud the least. Once formed, snakes survive forever ; they exhibit extraordinary confinement and stability properties. 9
Confinement in snakes is neoclassical (or better?) The initial temperature depression disappears in ~100 ms, but the density enhancement in the snake, by as much as a factor of two, may last 2 s (JET). Thus, the snake survival time can be much longer than expected from neoclassical losses. In fact, the snake density may increase in time. Coupled with observations of impurity accumulation within snakes, increasing n e implies the existence of an inward pinch (Wesson, PPCF (1995)). Islands break the toroidal symmetry of the ambient magnetic field. Resulting momentum transport induced by this symmetry-breaking can lead to enhanced confinement within the island due to a combination of turbulence suppression and orbit squeezing (Shaing, PoP (2005)). Bootstrap current driven by enhanced density in the island (due to pellet injection) can be stabilizing (Shaing et al. PoP (2007)). 10
Are these coherent structures saturated ideal modes? (1) 11
Are these coherent structures saturated ideal modes? (2) 12
Are these coherent structures saturated ideal modes? (3) Ideal internal kink can be unstable even with q 0 > 1. Displaced core forms a crescent near q=1 surface. But C-Mod analysis seems to rule this out in favor of an m=1 island! 13
Snakes in the presence of non-ideal effects Snakes at the q=1 surface can remain as coherent structures with enhanced confinement through many sawtooth crashes. Where does this stability come from? A linear m=1 mode can be stabilized by kinetic effects (diamagnetic drifts, energetic particles, etc.). However, a nonlinear m=1 island that remains stable as a coherent structure for very long times is difficult to explain. Here we present preliminary results on the stabilizing effects of bootstrap currents driven by enhanced density gradients within the island separatrix after pellet injection. Theory of this nonlinear stabilization mechanism was developed in an earlier work by Shaing, Houlberg, and Peng, PoP (2007). 14
Bootstrap current and the nonlinear stability of an m=1 island 15
Nonlinear calculations with the Four-field model Hazeltine, Hsu, and Morrison, PF (1987). 16
Bootstrap current model 17
Stable snakes at the q=1 surface Island width, w/a = 0.15. Because of the ad hoc bootstrap model, for large islands, slowly decaying nonlinear oscillations are set up. 18
Snake and m=1 island comparison Snake m=1 island A nonlinearly growing m=1 island looks quite different from a stable snake. 9/5/11 5th IAEA Technical Meeting--The Theory of 19
Snake and m=1 island comparison: Current and potential are also quite different J Z φ Snake m=1 island 20
Summary Snakes and similar coherent structures were designed by nature to confound the theorists. However, understanding their origins, their extraordinary stability, and long survival times may help us understand tokamak confinement and transport better. Of course they are extraordinarily interesting objects in their own right. Density and impurity snakes at the q=1 surface may be partially understood in terms of an m=1, n=1 island stabilized by the bootstrap current driven by an enhanced density gradient in the island. Shear-flow generated self-consistently in these stable islands may be responsible for reduced transport and very long particle confinement times. 21