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Edge stability in tokamak plasmas

S. Saarelma, C. Gimblett, T. Hender, A. Kirk, H. Meyer and MAST Team, UKAEA Fusion, UK

H. Wilson, University of York, UKS. Günter, L. Horton, IPP Garching, Germany

Y. Andrew, M. Kempenaars, A. Korotkov, A. Loarte, E. de la Luna, P. Monier-Garbet,V. Parail and Contributors to EFDA-JET work programme

O.J. Kwon, Daegu University, Gyungbuk, South Korea

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Outline

• “Standard” ELM-model• JET, ASDEX Upgrade• MAST, difference to other machines• Detailed analysis of MAST edge stability• Peeling-model for ELMs

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JETMAST

ELMs• Short bursts of edge plasma+ Remove impurities and help controlling plasma density, but- Can cause unacceptable erosion on divertors• From experiments we know, what the ELMs look like:

– D-signal,

– Changes in profiles,

– Camera pictures,

– etc.

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• The stability analysis tries to answer to two questions:

Purpose of the edge stability analysis

1.What triggers the ELMs ?

2. Is there a way to control the ELMs ?

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“Standard” ELM-modelE

dg

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ensi

ty

Edge pressure gradientB

allo

on

ing

lim

it

Peeling limit

1

Stable

2

Bootstrap currentbuilds up

34

(Connor, Hastie, Wilson, Miller, PoP, 1998)

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MHD stability analysis method

• Using experimental data construct an equilibrium with self-consistent bootstrap current.

• Investigate the stability of the equilibrium using MHD stability codes such as – GATO , only low-n

– MISHKA, low- to intermediate-n

– ELITE, intermediate- to high-n

• Vary the edge pressure gradient () and current density (j~1/shear) to find stability boundaries near the experimental point.

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ASDEX Upgrade & JET

• The standard ELM model is tested on experimental AUG and JET plasmas.

• The model is tested for Type I, II and III ELMs.

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JET ELMsJET #55937, Type I ELMs, MISHKA n=10 mode amplitude

Fourier decomposition of the mode

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JET gas scan

Type III ELM

Type I ELMs

=0.98, the most unstable mode number plotted = high-n ballooning unstable

•Type I ELMs: At the intermediate-n peeling-ballooning stability boundary.•Type III ELMs: Below the first ballooning stability boundary•Power scan, similar results for Type I and Type III ELMs.

The result reproduced using ELITE by O.J. Kwon !

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AUG, Type II ELMs

• Type II ELMs:– High triangularity (), high q95, close to double null configuration.

– Edge pressure gradient comparable to Type I ELMy plasmas.

Type II conditions cause the unstable mode to become more localised to the edge

Smaller ELMs

GATO (n=3):

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MAST ELMs

• MAST parameters :– R=0.85m, a=0.65, Bt=0.52 T

– Ip=1.35 MA (achieved), 2MA (design)

– PNBI=3.3 MW (achieved), 5 MW (design)

– Small aspect ratio– A lot of NBI power for a small volume:

• Fast rotation

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MAST ELM Stability analysis

• MAST has very good diagnostics for Te and ne profiles.

• Current is assumed to be a combination of inductive and bootstrap current.

#8901 high resolution Thomson scattering density and temperature profiles 15 ms before an ELM

Density

Temperature

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MAST edge instabilities (1)

• The MAST equilibria can have two types of instabilities

– If = mqedge-n is very small, peeling modes can become unstable.

– The peeling modes have very narrow width and its stability is very sensitive to the edge value of q.

– Unlikely a trigger for ELMs.

n=7

Mode localised near the x-points.ELITE:

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n=6

MAST edge instabilities (2)

• With increased pressure, a more robust peeling-ballooning mode becomes unstable. – It is not sensitive to the edge value of q.– It has wider radial extent, across the whole pedestal.

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Edge stability and pressure

=0.1

=0.5

• With experimental profiles, only very narrow peeling modes with small growth rate are unstable.• Increasing edge pressure gradient drives wider peeling-ballooning modes with larger growth rate unstable.

=m-nqsurf

Peeling-ballooning modes are the likely triggers of ELMs in MAST

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MAST edge stability diagram

MAST #8209, =0.99

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Sensitivity to the pedestal position

steepest gradient=0.987 steepest gradient=0.991

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Pedestal position scan• If instead of the pedestal height, the pedestal position is varied,

the wide peeling-ballooning modes become destabilised within the error margin of the pedestal position.

Peeling modes: Small-n (n=1-3) modes are the most unstable.

Peeling-ballooning modes:n of the most unstable mode increases with pedestal position: n=6 most unstable at =0.996 and n=25 at =0.999.

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Single null vs. double null (1)

• Experiment: no ELMs in single-null discharges.• Is the shape reason for the change in stability boundaries ?• Stability analysis, same profiles, varying plasma shape:

No stability difference due to the boundary shape

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Single null vs. double null (2)

• But using the profiles from a single-null discharge (#7508), the wide peeling-ballooning modes with large growth rate are stable when the pedestal position is varied.

• Also increasing the pedestal height by 100 % does not change the stability.

• The different temperature and density profiles responsible for the change in stability and ELM-free behaviour.

Still unknown:Why are the profiles different in single-null discharges ?

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Stabilisation through velocity shear• Before an ELM, the edge toroidal velocity changes from 25 km/s to

0 km/s within less than 1 cm.

• During an ELM, the velocity shear flattens.

• What is the effect of velocity shear on the stability ?

The rotation shear has a stabilising effect. However, the rotation shear required for the complete stabilisation is slightly higher than the experimental value

Growth rate (peeling-ballooning mode) vs. vped

Experimental toroidal rotation profile

Experimental level

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MAST ELM model

1. The edge pressure gradient exceeds the stability limit for a static plasma.2. Plasma reaches the stability limit for a rotating plasma and the instability starts to grow. Low-n modes become unstable first because they are the least affected by the sheared rotation stabilisation.3. The growing instability ties the adjacent flux surfaces together and flattens the rotation profile. High-n modes become dominant.4. The growth of the mode becomes even faster as the rotation shear disappears.

ELM crash

Velocity profile

Pressure profile with stability limits

Flux surfaces near the plasma edge

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Aspect ratio and rotation• Does the same ELM model work with conventional tokamaks?

• No, ELMy JET plasma is not affected by edge rotation shear.

• The reason: The stabilising effect of rotation shear becomes weaker as the aspect ratio increases.

• Even in spherical tokamaks, relatively fast edge rotation (~20% of sound speed) is needed for the stabilisation The rotation has little effect on conventional tokamak ELMs. The standard ELM model still works for conventional tokamaks or with spherical

tokamaks with no or weak beams.

n=10

ELITE: circular plasma with an edge mode

=a/R

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ELM model for Type III ELMs

• Let us assume that Type III ELMs are current-driven peeling modes (in any case they are well below the ballooning stability boundary)

• During an ELM crash, the current starts relaxing in outer annular region.

• The relaxation produces a negative surface skin current which has a stabilising effect on the peeling modes. All peeling modes at certain radial width become stable.

Pre-ELM current profile

Post-ELM current profile

Post-ELM skin currents

j(r)

r

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•Use the toroidal peeling criterion + width prediction to compute WELM/WPED from the model:

More in: C.G. Gimblett, R.J Hastie, P. Helander31th EPS, Tarragona, 2005

(MAST parameters, no trapped particles, parabolic pressure profile)

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Conclusions

• Standard ELM model agrees with experimental observations in conventional tokamaks– Edge plasmas are unstable to peeling-ballooning modes.

• Before an ELM, MAST edge plasma is– unstable against narrow peeling modes with low growth rate

– close to the stability limit for wider peeling-ballooning modes

• The high-n modes are stabilised at experimental edge rotation profiles suggesting a modification to the ELM model for STs.

• An analytical model for peeling modes and skin currents can explain destabilisation and stabilisation of the edge during the ELM cycle.

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Future challenges

• X-point effects on the stability

• Near x-point, the magnetic field becomes ergodised– No flux surfaces– A limit for current MHD stability codes– New tools needed for modelling

n=10