Hiroshi Tojo, IAEA TM/ISTW2008, Frascati, Italy, October 2008 Features of High Frequency Mode during Internal Reconnection Events on MAST Graduate School

Hiroshi Tojo, IAEA TM/ISTW2008, Frascati, Italy, October 2008

Features of High Frequency Mode during Internal Reconnection Events on MAST

Graduate School of Frontier Sciences, The University of Tokyo Kashiwa 277-8561, Japana) EURATOM/UKAEA Fusion Association, Culham Science Centre, OX14 3DB, UK

H. Tojo, M. P. Gryaznevich(a, A. Ejiri, Y. Takase, R. Martin(a, A. Sykes(a

The Joint Meeting of 4th IAEA Technical Meeting on Spherical Tori and

14th International Workshop on Spherical Torus ENEA, Frascati, Roma, Italy October, 7-10, 2008


What is an Internal Reconnection Event (IRE)?

1. Plasma deformation

• IRE is a magnetic reconnection between inside and outside magnetic flux

2. During IRE plasma energy is lost along flux lines through fast parallel transport

• Helical deformation, followed by reconnection, is caused by linear and non-linear growth and coupling of pressure-driven modes

• IRE is a very common instability observed in STs• Three-dimensional resistive MHD simulations:

Naoki Mizuguchi, Takaya Hayashi, 　 Phys. Plasmas, 7, 940 (2000)

Plasma deformation Energy flow CCD picture, START


Three different cases have been analyzed by Hayashi and Mizuguchi:

Case 1:

high-β, q(0) < 1

Case 2:

high-β, q(0) > 1

Case 3: note much lower threshold!

low-β, q(0) < 1

linear growth of low-n modes non- linear coupling and fast growth of high-n modes

slow linear growth of high-n modes

non-linear phase

slow linear growth of low-n modes non- linear coupling and fast growth of low-n modes

We compare these simulations with MAST experimental results


Objectives of these studies:

To measure mode numbers and growth rates SXR cameras and Mirnov coils are used to measure mode structure

To perform non-linear mode coupling and growth analysis

Helical filamentary models are employed to find the interaction between the precursor modes including high-m/n numbers

To investigate the drive of this instability (is it pressure driven, as predicted by theory? or not)

Pressure profile evolution studies before the reconnection


Objectives of these studies:

We will show how a toroidally localized increase in the pressure gradient, caused either by phase alignment of two modes*, or by a locked mode, can cause IRE

(*) as predicted by Hayashi

n=1 n=2N. Mizuguchi, T. Hayashi et al., Physics of Plasmas 7,940 (2000)


Experimental setup on MAST

Soft X-ray cameras:

Horizontal (32ch) and Vertical (12ch) chords

Mirnov coils:

Poloidal (up to 59coils) and Toroidal arrays (up to12 coils)

TS (Thomson scattering) system :

for determination of pressure gradient

Possible to compare SXR and TS data by using EFIT


Helical filament model is used for poloidal mode analysis:

m/n=2/1 m/n=5/2

We calculate magnetic fields produced by helical filaments at Mirnov coils position


Trajectories of helical filaments (along magnetic field)

cossin zr

t

BB

B

R

r

d

d

EFIT

φ : toroidal angle, normalized by 2θ : poloidal angle, normalized by 2 r : minor radius of rational surface (from EFIT）R : major radius of rational surface

)(exp 0 lmnl nmiI

))((0

0 lmninmnl eII

(high aspect approximation)

① equally spaced toroidal angles　 ② toroidal offset (initial position)

① ②(currents of helical filaments)

φmn(θ)

Trajectories of helical filaments

H. Tojo et al., Rev. Sci. Inst. in press (2008)


Fitting parameters and identification of the mode numbers

Single mode

Filamentary models

Signal (Mirnov coils)

parameters:

one mode number, I0 , φ0

find suitable mode numbers and try to get its time evolution

assuming single mode

Multi mode

subtract single mode results for lower mode number

from input data

Use single mode method for higher mode numbers

Note:

The fitting are executed for each time slice

Signal from Mirnov coils are integrated and high-passed (>1kHz)


Identification of mode number and example for m/n=2/1 mode

poloidal turn (normalized)0.0 1.0 0.0 1.0

(b) Maximum filament current: I21[A]

growth of 2/1 mode with τ~2 ms

(c) normalized toroidal offset :φ0

toroidal rotation of the mode

(d) residual error:χ2

acceptable when <10

N

iy

iyiy

raw

i

rawfiti

22

222

)(

/)()(

χ2: 1.91

χ2: 2.16

Single mode with m/n=2/1


IRE with m/n=2/1 mode precursor and low-n mode coupling

Recovery after IRE

2/1 precursor

Start of reconnection

SXR chord signals from horizontal SXR camera show penetration of reconnection from the edge to the core

high-n modes


Appearance of n = 2 mode (case 3, Hayashi)

m/n=2/1 mode with 3 - 4 kHz

shot with similar behavior shot 18552

Appearance of a little faster but different mode, suggesting non-linear coupling between the two modes


Alignment of the 2/1 and 5/2 modes: filamentary models

2/1 mode

Peaks of two modes appear at the same position at the same time which results in increase of local flux deformation

5/2 mode


Time evolution of the two modes: coupling and phase alignment

Fourier spectrogram of n=odd and n=even components of outer Mirnov signals shows that two modes start rotating with the same speed from t = 367ms, suggesting phase alignment and non-linear coupling of low-n modes

coupling


IRE with Locked Mode

internal mode (n=1) locked

Major disruption after IRE

high-f (~100kHz) modes start before the collapse due to local increase in pressure gradient caused by LM

SXR chords from the horizontal SXR camera show localization of high-n modes


High toroidal mode numbers: cross spectrum analysis

Mirnov coils signals normalized by the distance from the axis and positions of coils

Cross correlation analysis using OMAHA coils (Outboard Mirnov coil with high-pass filter)

The cross phase suggests n = 5 - 7


The high-frequency mode shows the pressure driven nature

Pressure profile from TS system Time evolution of peaking factor (Pf)

with strong high-f and locked mode

steep pressure gradient

(1.0<R<1.2)

HCAM#5-10 with high-f mode

(R < 1.2 m, calculated by EFIT)

Steep pressure profile (>1.5×104 Pa/m) causes destabilization of ballooning modes and reconnection

Pf (peaking factor)=PMAX/ LFM

PMAX: maximum electron pressure

LFM: Full width at half maximum


Comparison with the predictions (Hayashi results)

IRE with m/n=2/1 precursor and low-n mode coupling

similar to the Case 3: non-linear growth of low-n toroidal components

Strictly, no consideration of tearing mode in modeling, but experimental data suggests toroidal alignment of n=1 and 2 modes.

high-n low-n

IRE with locked mode

similar to the Case 1 and Case 2 in modeling: pressure driven ballooning modes with high-n

n=1 locked mode is not a precursor but changes local pressure profile with the same effect as in previous case

Application of external error field may cause similar effect – experiments on-going


Conclusions and summary

Mode structure and pressure profile evolution preceding Internal reconnection events (IRE) have been studied.

SXR data shows propagation of decrease in SXR from the outside of the plasma to the core

Alignment of low-n modes preceding IRE has been observed, as predicted by modeling

After locking of n=1 mode, pressure driven ballooning modes with high-n are observed caused by local increase in pressure gradient


Future work

Analysis of high βregimesDetailed poloidal mode analysisDetailed measurements of pressure profile

s with TS for identification of the source of the high-n modes

Excitation of IREs with external error fields

Documents

Hiroshi Tojo, IAEA TM/ISTW2008, Frascati, Italy, October 2008 Features of High Frequency Mode during Internal Reconnection Events on MAST Graduate School