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

Supported by Office ofScience

Collaboration with N.C. Luhmann, Jr.,UCD, T. Munsat, U. Colorado, AJH Donne, FOM,

and TEXTOR team

ContentsNew 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, 195003 & 195004, ‘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

Characteristic of the Tokamak PlasmaTEXTOR (Torus-Experiment for Technology Oriented Research)

Bv

Bt

Bp

major radius: 1.75 mminor radius: 0.50 mplasma current: ≤

≤≤

0.5 (0.8) MAtoroidal field: 2.8 Tpulse length: 10 sec

Stability of tokamak plasmas: magnetic helicityMagneto-Hydro-Dynamics (MHD) – “instability of m/n=1/1 mode”

Characteristic emission of magnetically confined plasmasElectron Cyclotron Emission (ECE) – reliable local Temeasurement : behaves as a “blackbody radiation source”

2D 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

Te fluctuation measurementReal time fluctuations can be studied down to ~1% levelFluctuation studies down to 0.1 % level have been performed using long time integration

Conventional 1-D ECE system 2-D ECE imaging system

Characteristics of 2-D ECEI imaging on TEXTOR

ECEI/MIR system on TEXTOR

Adjustable lens

128 channels (16 x 8)Spatial resolution (2 cm x 1 cm)Time resolution = 5 μsec.

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 ΔTe(r,t)/<Te(r,t)>;< > is time average temperature and constant for this study

Time resolution; ~ 5 μsReal time signal at ~1% level of Te fluctuation (~10 eV)Sub ~1% level of fluctuation was studied with integration time

Sawtooth crash via composite 2-D viewsCore 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

Relevant TEXTOR plasma parametersGlobal parameters:

Plasma parameters:

Kadomtsev reconnection time:

cmohm

scmrotV

scmsC

scmtheV

scmpBAV

scmTBAV

⋅−×≈

×≅

×≅

×≅

×≅

×≅

6103.1

/6105.6

/7105.3

/9100.2

/7107.1)(

/108.3)( 8

η

kGapBTTB

6.1)(3.2

≅

=

.sec650*21 μητττ ≈⋅≈ Ak

><Δ

e

e

TT

sec)(μTime

MWnbiPkApI

3400≅

=

4.0%0.1

≅

≈

pT

ββ

Background of the sawtooth oscillationSawtooth 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)<1Y-point reconnection (Sweet-Parker model)Helical symmetry

Quasi-interchange mode model (J. Wesson, ’86)

q(0) ~1 and driven by magnetic instabilityHelical symmetry

Central q value remains at ~ 0.7 (TEXTOR; H. Soltwisch, ’88 &TFTR; F. Levinton, ’94)

ητττ ⋅≈ *21

AkA. Sykes et al. PRL, 36, 140, 1976

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

Magnetic reconnection modelReconnection models

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

2-D visualization through computer animationDirect comparison with measurements

Time evolution of the island and m=1 mode agrees well with the measurement except the crash time

Models based on helically symmetric crash pattern

Helically symmetric crash zone

Full reconnection model –Current driven kink instability leads to reconnectionQuasi-interchange model –Magnetic instability (q-shear) without reconnectionBoth can generate pre-cursor signal similar to the experimental observationMeasured current profiles before and after the crash does not agree with both models

Reconnection zone orfield line opening is

symmetric along the q~1 surface

High-n ballooning mode model (high β)Ballooning modes (“pressure finger”) predominantly at the low field side can lead to disruption (localized reconnection)

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 modelY. Nagayama, et al., (’96), M. Yamada et al. (95)

Y. Nishimura, et al. (’99)

High Field side Low field side

W. Park, et al. (’96)

Comparison with the ballooning mode modelLow 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.

Simulation results from Nishimura et al.Plasma condition (βp ~0.4 and βt ~2 %) is similar to the experimental results

High field sideReconnection at high field side is forbidden in Ballooning mode modelInward indentation of magnetic flux Collective behavior of heat is contrast to the stochastic one from simulation

High field side Low field side

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

Crash pattern at the observation viewCrash 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 cmEffective poloidal view can be larger than the actual one (almost twice)

Helically symmetry of the reconnection zone

Non-trivial with one systemPlasma rotation can effectively increase toroidal window

Arrow is direction of the m=1 mode

during the crash time

Toroidally localized reconnection zoneRotating plasma provides a wide viewing window along the toroidal direction

Vr ~6.5 x106 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 slimThe 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)

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 patternReconnection event has to be not only localized but also random phenomenon

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)

Demonstration of localizationImage sequence from crash phase in rotating plasma

Sequence of images at the laboratory viewInterpolated image sequence of reconnection region in plasma frame Interpolated image sequence of “cold island” evolution in plasma frame

3-D random local reconnection modelLocal 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 sidesReconnection is random occurance

Reconnection zone or field line opening is finite along the q~1 surface and the occurrence is random

SummaryNew 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 modelsFull reconnection, is largely consistent except no heat flow (no reconnection) before the pressure finger develops and the reconnection zone is not helically symmetricQuasi-interchange model – Inconsistent with the measurement (magnetic instability (magnetic shear) is not likely a dominant mechanism) and crash zone is not helically symmetricBallooning 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

Comparison with images from the quasi-interchange 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 crescentThe observed images of the island are vertically elongated shape, not oval shape

This model does not require any type of magnetic field reconnectionNo sign of reconnection at the low field side is consistent with the image of the hot spot during precursor periodReconnection does occur when it has a pressure driven mode in the experiment.