3-D Random Reconnection Model of the Sawtooth Crash

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1 3-D Random Reconnection Model of the Sawtooth Crash Hyeon K. Park Princeton Plasma PhysicsN Laboratory Princeton University at IPELS, 2007 Cairns, Australia August 5-9, 2007 Collaboration with N.C. Luhmann, Jr.,UCD, T. Munsat, U. Colorado, AJH Donne, FOM, and TEXTOR team Supported by Office of Science

2 Contents New approach in physics study of tokamak plasma (Ex. sawtooth oscillation ) Model based on helically symmetric crash zone (reconnection zone) Full reconnection model (Kadomtsev) Quasi-interchange model (Wesson) 3-D local reconnection model Ballooning mode model (W. Park & Nishimura) New technological approach (H. Park et al.,rsi. 75, 3875 (2004), and 74, 4239 (2003)) Microwave video camera New findings of the physics of sawtooth oscillation (H. Park, et al., PRLs 96, & , 06 and PoP, 13,55907, 06) 3-D randomly localized reconnection process driven by a ballooning like pressure driven instability accompanied by the kink instability

3 Characteristic of the Tokamak Plasma TEXTOR (Torus-Experiment for Technology Oriented Research) B v B t B p major radius: 1.75 m minor radius: 0.50 m plasma current: 0.5 (0.8) MA toroidal field: 2.8 T pulse length: 10 sec Stability of tokamak plasmas: magnetic helicity Magneto-Hydro-Dynamics (MHD) instability of m/n=1/1 mode Characteristic emission of magnetically confined plasmas Electron Cyclotron Emission (ECE) reliable local T e measurement : behaves as a blackbody radiation source

4 2D ECE imaging system Conventional 1-D ECE system 2-D ECE imaging system ECE measurement is an established tool for electron temperature measurement in high temperature plasmas Sensitive 1-D array detector, imaging optics, and wide-band mm wave antenna, and IF electronics are required for 2-D imaging system T e fluctuation measurement Real time fluctuations can be studied down to ~1% level Fluctuation studies down to 0.1 % level have been performed using long time integration

5 Characteristics of 2-D ECEI imaging on TEXTOR 128 channels (16 x 8) Spatial resolution (2 cm x 1 cm) Time resolution = 5 μsec. Adjustable lens Radial image size is limited by the bandwidth of the system (8 channels (~8 cm)) LO frequency and/or B field change can extend the radial coverage Poloidal image size is limited by front end optics designed for MIR (16 channels (~16 cm)) Relatively calibrated for fluctuation study ΔT e (r,t)/<t e (r,t)>;< > is time average temperature and constant for this study Time resolution; ~ 5 μs Real time signal at ~1% level of T e fluctuation (~10 ev) Sub ~1% level of fluctuation was studied with integration time ECEI/MIR system on TEXTOR

6 Sawtooth crash via composite 2-D views Core electron temperature (within the inversion radius) flattens after crash Frame 1: Hot spot (m/n=1/1 mode) is in the core before crash Frame 2: Cold flat area (Island) forms inside the inversion radius as reconnection starts Frame 3: Transported heat from the core builds up at the mixing zone (~10 cm layer surrounding the inversion radius) Accumulated heat in the mixing zone will symmetrically diffuse out in radial direction Zeroth order MHD physics is well established

7 Relevant TEXTOR plasma parameters Global parameters: B = 2.3T T B p ( a) 1.6kG Plasma parameters: V B ) cm/ s A T V ( B p ) cm s A 7 / V cm s the 9 / C s cm/ s V rot cm/ s η ohm cm ( 8 I p = 400kA P 3MW nbi β 1.0% T β p 0.4 < ΔT T e e > Kadomtsev reconnection time: τ k 1 τ * τ 650μ sec. 2 η A Time(μ sec)

8 Background of the sawtooth oscillation Sawtooth oscillation: a periodic growth (long) and decay (sudden) of the core pressure of the toroidal plasma (S. von Goeler, 74): Full reconnection model (B. Kadomtsev, 76) q(0)<1 Y-point reconnection (Sweet-Parker model) Helical symmetry Quasi-interchange mode model (J. Wesson, 86) q(0) ~1 and driven by magnetic instability Helical symmetry Central q value remains at ~ 0.7 (TEXTOR; H. Soltwisch, 88 &TFTR; F. Levinton, 94) τ k 1 2 τ * τ A η A. Sykes et al. PRL, 36, 140, 1976

9 Comparison with images from the full reconnection model Remarkable resemblance between 2-D images of the hot spot/island and images from the mature stage of the simulation result of the full reconnection model (tearing type) (Sykes et al.) Magnetic topology change (reconnection) occurred as the island is formed (slow reconnection) No clear heat flow during precursor phase until a sharp temperature point is developed Quasi-interchange mode model does not agree with the measurement

10 Reconnection models Magnetic reconnection model Sweet-Parker model Slow crash time (based on Classical Spitzer resistivity: collision dominated regime) Petschek model Enhanced diffusion at the X region and slow shocks to satisfy jump conditions

11 2-D visualization through computer animation Direct comparison with measurements Time evolution of the island and m=1 mode agrees well with the measurement except the crash time

12 Models based on helically symmetric crash pattern Helically symmetric crash zone Full reconnection model Current driven kink instability leads to reconnection Quasi-interchange model Magnetic instability (q-shear) without reconnection Both can generate pre-cursor signal similar to the experimental observation Measured current profiles before and after the crash does not agree with both models Reconnection zone or field line opening is symmetric along the q~1 surface

13 High-n ballooning mode model (high β) Ballooning modes ( pressure finger ) predominantly at the low field side can lead to disruption (localized reconnection) High Field side Low field side Global stochastic field lines may explain the difference in transport of the current density and pressure (q(0)<1 during the crash) Leads to 3-D local reconnection model Y. Nagayama, et al., ( 96), M. Yamada et al. (95) W. Park, et al. ( 96) Y. Nishimura, et al. ( 99)

14 Comparison with the ballooning mode model Low field side Similarity: Pressure finger of the simulation at low field side (middle figure) is similar to those from 2-D images ( a sharp temperature point ) Difference: Heat flow is highly collective in experiment while stochastic process of the heat diffusion is clear in simulation. High field side Reconnection at high field side is forbidden in Ballooning mode model Inward indentation of magnetic flux Collective behavior of heat is contrast to the stochastic one from simulation High field side Low field side Simulation results from Nishimura et al. Plasma condition (β p ~0.4 and β t ~2 %) is similar to the experimental results

15 3-D local reconnection model Reconnection zone is finite on poloidal and toroidal plane Ballooning mode model: pressure driven Ballooning modes leads to the reconnection at the low magnetic field side only (high field side crash is inhibited) Combination of the full reconnection model (before the crash) and crash pattern at the lower field side with the local field line stochasticity is better approach Reconnection zone or field line opening is finite along q~1 surface and confined to the low magnetic field side

16 Crash pattern at the observation view Crash direction has been observed everywhere in both high and low field sides Often m=1 mode moves toward the core (crash may have occurred elsewhere (inward arrows) Viewing window is 16 cm x 8 cm and the dimension of the poloidal hole is ~15 cm Effective poloidal view can be larger than the actual one (almost twice) Helically symmetry of the reconnection zone Non-trivial with one system Plasma rotation can effectively increase toroidal window Arrow is direction of the m=1 mode during the crash time

17 Toroidally localized reconnection zone Rotating plasma provides a wide viewing window along the toroidal direction V r ~6.5 x10 6 cm/sec gives the toroidal window of ~520 cm for the crash time (~80 μsec) This is comparable to half of the toroidal circumference If the toroidal opening is helically symmetric, Chance of no reconnection zone in the view window is slim The hot spot initially moving toward the opposite side (core side) of the view should be captured due to extended toroidal view due to the plasma rotation 3-D randomly localized reconnection process!!! (Worst case)

18 Low field side crash (fast rotating plasmas) Off-mid plane crash is also observed (right side) at the low field side (moving to the top) Crash pattern runs away from low field side (indication of the crash other than at the low field side left side): no trace of reconnection zone during whole crash time scale 1/4 of ~40 frames has similar crash pattern Reconnection event has to be not only localized but also random phenomenon

19 Interpolation scheme Sawtooth waveform of the repeating growth/crash cycle (a), zoom of single crash event (b), and sequence of 2-D ECEI images corresponding to indicated time-points (c-j)

20 Demonstration of localization Image sequence from crash phase in rotating plasma Sequence of images at the laboratory view Interpolated image sequence of reconnection region in plasma frame Interpolated image sequence of cold island evolution in plasma frame

21 3-D random local reconnection model Local reconnection Reconnection zone is finite along the q~1 surface Local reconnection along q~1 surface is not limited to low field side. Observation of the reconnection at both the high and low field sides Reconnection is random occurance Reconnection zone or field line opening is finite along the q~1 surface and the occurrence is random

22 Summary New paradigm of the reconnection physics by 2-D visualization m/n=1/1 instability is a random 3-D localized magnetic reconnection process Reconnection process is predominantly driven by a pressure driven mode (not Ballooning mode but ballooning like ) Heat transfer is highly collective not stochastic Evolution of theoretical models Full reconnection, is largely consistent except no heat flow (no reconnection) before the pressure finger develops and the reconnection zone is not helically symmetric Quasi-interchange model Inconsistent with the measurement (magnetic instability (magnetic shear) is not likely a dominant mechanism) and crash zone is not helically symmetric Ballooning mode model only finite pressure effect and pressure finger at the LFS is consistent. global stochasticity of field lines may not be the dominant mechanism for heat transfer

23 Comparison with images from the quasiinterchange model No clear resemblance between 2-D images of hot spot/island and projected images from the quasi-interchange model The observed images of the hot spot are part of a circle not part of the crescent The observed images of the island are vertically elongated shape, not oval shape This model does not require any type of magnetic field reconnection No sign of reconnection at the low field side is consistent with the image of the hot spot during precursor period Reconnection does occur when it has a pressure driven mode in the experiment.