Alessandro Pau, Ph.DElectrical and Electronic Eng. Department, DIEE - Univ. of Cagliari

Piazza D'Armi, 09123 Cagliari, ItalyTEL: +39 070-6755898

Email: alessandro.pau@diee.unica.it

Tokamaks: magnetic confinement

•Resulting helical magnetic field

• The equilibrium of plasmas embedded in a magnetic field can be described by the magneto-hydro-dynamic (MHD) theory. MHD instabilities have the effect to strongly restrict fusion performance in magnetic confined plasmas (operational limits).

Ideal MHD

Prof. Gnesotto (RFX Padova) – Basic Engineering Course PhD in Fusion Science and Engineering 2011

Equilibrium equations

Prof. Gnesotto (RFX Padova) – Basic Engineering Course PhD in Fusion Science and Engineering 2011

Coordinate system in a toroidal geometry

a) axisymmetric coordinatesfor toroidal geometry

b) poloidal cross sectioncoordinates

GRAD-SHAFRANOV EQUATION f(ψ)

ITER

NESTED FLUX SURFACES

• Elongation• Triangularity

EQUILIBRIUM: vertical magnetic field (along Z) JxB inwards

Stability parameters

•Safety factor q

•Ampere’s law

•Internal inductance

•beta

ratio between kinetic plasma pressure, averaged over the plasma volume, and the corresponding magnetic pressure.

•Magnetic shear

variation of the magnetic field windingangle moving radially through subsequentmagnetic surfaces.

MHD Stability

Prof. Pautasso (IPP Garching)– Introduzione alla fisica e alla tecnologia della fusione nucleare 2012

MHD Stability: the energy principle

Prof. Pautasso (IPP Garching) – Introduzione alla fisica e alla tecnologia della fusione nucleare 2012

Current drivenPressure driven

Kink modes

Interchange instabilityBallooning modes

MHDinstabilities: basic distinction 1

Current driven instabilities Pressure driven instabilities(kink mode) (interchange mode)

• Instabilities driven by the gradient of plasma current;

• Kink of the plasma fluxtubes on macroscopic scale;

• plasma column distorsion

• Instabilities driven by the gradient of plasma pressure;

• They develop on local scale and internally;• The interchange perturbation can lead to

instability, depending on the relative sign of the magnetic feld line curvature and the pressure gradient.

In a confined plasma, an instability is driven by the free energy contained in the equilibrium configuration

MHD instabilities: basic distinction 2

MHD instabilities: basic distinction 3

Radial perturbation

ResonanceTotal magnetic field

MHD instabilities: ideal and resistive

Prof. Pautasso (IPP Garching) – Introduzione alla fisica e alla tecnologia della fusione nucleare 2012

MHD instabilities

Prof. Pautasso (IPP Garching) – Introduzione alla fisica e alla tecnologia della fusione nucleare 2012

MHD instabilities

Prof. Pautasso (IPP Garching) – Introduzione alla fisica e alla tecnologia della fusione nucleare 2012

Operational limits

• Ideally in a DT plasma, when particular conditions are provided, α particlesheating is sufficient to sustain plasma temperature against energy losses:

IGNITION (nuclear fusion reaction becomes self-sustaining)

FUEL DENSITY

TEMPERATUREENERGY CONFINEMENT TIME

• Three main basic quantities have to be maximized:- energy confinement time- fuel density- normalized pressure beta

• The optimization process is very often limited by MHD instabilities, which canbe either pressure driven or current driven and can lead to the termination of the plasma confinement:

- hard limit: disruptions- soft limit: degradation of the plasma confinement

(derived by Lawson criterion)

Figure of merit for fusion performance nTtE

H. Zohm (IPP Garching), Joint European Research Doctoral Network in Fusion Science and Engineering, 2011

Plasma discharge characterised by

• external control param.: Bt, R0, a, k, d, Pheat, FD…

• integral plasma param.: b = 2m0<p>/B2, Ip …

• plasma profiles: pressure p(r), current density j(r)

Aim is to generate power, so

• Pfusion/Pheat (power needed to sustain plasma)should be high• tE = Wplasma/Pheat (energy confinement time)

In present day experiments, Pheat comesfrom external heating systems• Q = Pfus/Pext Pfus/Pheat ~ nTtE

In a reactor, Pheat mainly by a-(self)heating:• Q = Pfus/Pext (ignited plasma)

The aim is to generate and sustain a plasma of• T ~ several 10 keV, • tE ~ several seconds and • n ~ 1020 particles / m3

Optimisation of nTtE: ideal pressure limit

H. Zohm (IPP Garching), Joint European Research Doctoral Network in Fusion Science and Engineering, 2011

Optimising nT means high pressure and, for given B:

high b = 2m0 <p> / B2

This quantity is limited by (MHD) instabilities

‘Ideal’ MHD limit (ultimate limit, plasma unstable on Alfvén time scale ~ 10 ms,only limited by inertia)

• ‘Troyon’ limit bmax ~ Ip/(aB), leads to definition of bN = b/(Ip/(aB))

b

[%]

‘Resistive’ MHD limit (on local current redistribution time scale ~ 100 ms)

• ‘Neoclassical Tearing Mode’ (NTM)driven by loss of bootstrap currentwithin magnetic island

bN=b/(Ip/aB)=3.5

b limit

Operational limits: Hugill Diagram

Since T has an optimum value at ~ 20 keV,n should be as high as possible

• density is limited by disruptions due to excessive edge cooling

• empirical ‘Greenwald’ limit, nGr ~ Ip/(pa2) high Ip helps to obtain high n

295 qLimit to safety factor q ~ (r/R) (Btor/Bpol)

• for q < 1, tokamak unconditionally unstable central ‘sawtooth’ instability

• for qedge 2, plasma tends to disrupt (external kink) – limits value of Ip

Density limit

Current limit

H. Zohm (IPP Garching), Joint European Research Doctoral Network in Fusion Science and Engineering, 2011

Radiation limit

H R Koslowski (Julich) - 531. WE Heraeus-Seminar, Bad Honnef, Germany, 2013

H R Koslowski (Julich) - 531. WE Heraeus-Seminar, Bad Honnef, Germany, 2013

Radiation limit

H R Koslowski (Julich) - 531. WE Heraeus-Seminar, Bad Honnef, Germany, 2013

Radiation limit

Radiation limit

Radiation cooling of the plasma edge where impurity ions are not fully ionized: as the density increases at the edge, the temperature decreases and the line radiation from low-Z impurities is strongly enhanced (peak at low temperatures in the radiationefficiency. This produces a poloidally symmetric radiation at the plasma edge, whereas more the temperature is reduced due to strong radiation losses, the more the plasma radiation losses are enhanced and this gives rise to further decreases of the temperature feeding the instability process.When the density limit is reached, or in other words, when radiation losses exceedsthe heating power the temperature collapse and the contraction of the plasma current profile by cooling edge makes the plasma unstable to MHD modes, leadingeventually to disruption. This is the basic mechanism at the base of a radiative collapse. Critical density scales with heating power and low effective charge state Zeff, therefore increasing the heating power and reducing the impurity content in the plasma it is possible to achieve higher values of density before to get into the densitylimit. In this conditions there can be the onset of another radiation limit, the MARFE (Multifaceted Asymmetric Radiation From Edge), a poloidally asymmetric radiationinstability which develops usually on the High Field Side (HFS) or near the X-point.

Radiation limit

The conditions for the onset of a MARFE depend on plasma-wall interaction, flux of recycling neutrals of the working gas and the heat flow from the plasma centre to the edge. In this case the maximum achievable density does not depend on the input heating power as we have for a poloidally symmetric radiative collapse, butdepends directly on the average current density, as well as it is clearly expressed by the Greenwald limit. The linear dependency between density and plasma currentdensity is clearly shown in the Hugill diagram.Another important cause of instability related to radiation is by impurityaccumulation. High-Z impurity accumulation in the plasma centre give rise to strong radiation due to the fact that atoms are not fully ionized. This in turn give rise to flattening or even an hollowing of the temperature profiles with a consequentdecreasing of the current density in the centre due to raising of plasma resistivity. This picture is also characterized by hollow q profiles, with values of the safety factoron axis greater than one, and thus no sawthooth crashes, When this mechanism isamplified beyond a certain level the central temperature collapses giving causinginternal disruptions due to the onset of MHD activity.

Locked modes & Error fields

• Stationary MHD perturbation of 2 types:1) locking of inherent MHD instabilities (unstable rotating modes) 2) error field (EF) source (island driven by and EF)

• Slowing down of mode rotation due to friction-forces -> Mode locks to wall (rotationstops)

• Error Field: magnetic field perturbation of the 2D plasma equilibrium originatedoutside of the plasma. (mixture of harmonics n and m)

• Currents and perturbed normal field result in a torque that opposes plasma rotation

• Plasma rotation: stabilizing effect (momentum transfer and sheared rotationcounteract mode locking)

• Non-axisymmetric error fields originate from non-ideal coil alignments and currentfeeders

• Locked modes (2,1) are excited above a critical field threshold

• Threshold depends on density, toroidal field, configuration, plasma rotation, beta, etc

• Critical error fields are in the order Br/Bt ≈ 10-5 .. 10-4

• External error field correction coils are needed to cancel the intrinsic error field

From seminars by G.Pautasso (IPP) and H.R.Koslowski (Julich), 2013

What is a disruption?

A.Pau | EPFL Seminar| 27/06/2016 | Page 25

Precursor phase: growth of MHD instability;

Fast phase: release of the plasma thermal energy on a very fast time scale, known as thermal quench (TQ)• characteristic current spike• drop of the internal inductance• transient in the loop voltage (opposite

sign wrt plasma current;

Quench phase: loss of the whole plasma current • typically associated with the loss of

vertical stability (VDE)• sometimes (especially in mitigated

disruptions) generation of Runaway Electrons (RE).

What is a disruption?

A.Pau | EPFL Seminar| 27/06/2016 | Page 26

CONSEQUENCES

• Thermal loads on structures and PFCs;

• Large vertical and sideways forces:

- Eddy currents (movement of the plasma column and variation of plasma current values);- Halo currents (flow mostly poloidally, with a toroidal symmetric component and an symmetric component (~n=1))

- Relativistic Runaway Electrons (even 70% of the initial Iplasma(tD) ).

H R Koslowski (Julich) - 531. WE Heraeus-Seminar, Bad Honnef, Germany, 2013

Disruptions: avoidance, mitigation & control

• Goal: reduce forces on the vessel and prevent damage to first wall

• Avoidance of disruptions by

Real-time detection of disruption precursor and appropriate action

Detection of locked mode and controlled shutdown of the discharge

Operation in safe regime far from operational limits

• Mitigation of disruptions by

Detection of oncoming disruption with e.g. neural networks etc, and

initialisation of soft stop (reduce plasma shaping, heating power, etc)

Heating to soften the current quench

Massive gas injection (He ... Ar) or pellet/dust injection to mitigate heat

loads and forces, and to prevent runaway generation

Disruptions => Loss of plasma control!

Disruptions: avoidance, mitigation & control

H R Koslowski (Julich) - 531. WE Heraeus-Seminar, Bad Honnef, Germany, 2013

Disruptions: avoidance, mitigation & controlDisruptions: avoidance, mitigation & control

DIEE - CIRCUITS AND

SYSTEM ACTIVITIES

IN FUSION

DEFINITION:MACHINE LEARNING IS THE USE OF ALGORITHMS TO

CREATE AND EXTRACT KNOWLEDGE FROM DATA

Machine Learning workflow for disruption prediction & classification

A.Pau | 21st MHD Stability Control Workshop, San Diego – USA | 07/11/2016

Machine Learning workflow for disruption prediction & classification

A.Pau | 21st MHD Stability Control Workshop, San Diego – USA | 07/11/2016

FEATURE EXTRACTION AND/OR TRANSFORMATION FEATURE SELECTION

STATISTICAL ANALYSIS

CLASSIFICATION

HIGH-DIM. DATA PROCESSING

CLUSTERING

CHOOSE DISTANCE

EVALUATION CRITERIA

UNSUPERVISED LEARNING

FIT/TRAIN THE

MODEL

VALIDATE THE MODEL

TEST THE MODEL

SUPERVISED LEARNING

REGRESSION

CHOOSE ALGORITHM

SIMILARITY MEASURES

NORMALIZATION, OFFSET & OUTLIERS REMOVAL

PREDICTIVEEXPLORATORY

DATA-REDUCTION

COMPONENT PLANES

JET-C70 X 70 NODES

10D INPUT SPACE

A.Pau | 21st MHD Stability Control Workshop, San Diego – USA | 07/11/2016 | Page 31

79,95%

10,28%9,77%

• Relative component distributions of the input data on the 2D map. The dependencies among different variables or similar patterns can be identified by comparing the corresponding component planes

EmptyDisr

Safe

Mixed

GTM 2D MAP

REF: Automatic disruption classification based on manifold learning for real-time applications on JET,Nuclear Fusion 53 093023, 2013

Disruption prediction and classification at JET & ASDEX

A.Pau | 21st MHD Stability Control Workshop, San Diego – USA | 07/11/2016

• By projecting onto the map the temporal evolution of a discharge each sample results to be associated with a node.

• For each sample and each class, a class membership can be defined.

• It is possible to detect sudden transitions in the mapped parameter space.

IMC

NC

Disruption prediction and classification at JET & ASDEX

Machine Learning

IDENTIFICATION OF DIMENSIONLESS

PARAMETERS AND INDICATORS BASED

ON SIGNALS AVAILABLE IN REAL-TIME

SIGNAL

PROCESSIN

G

FEATURE

EXTRACTION

PHYSICS

KNOWLEDGE

MACHINE-INDEPENDENT PHYSICS BASED

MODELS & EMPIRICAL SCALING LAWS

LEARN FROM DATA!LOCKED MODE INDICATOR - JET #82393

Disruption prediction and classification at JET & ASDEX

Image Processing at Wendelstein 7-X (W7-X)

• W7-X, Greifswald, Germania, Max Planck Institute of Plasma Physics

• Scopo: investigare la fattibilità di questotipo di impianto per la produzione di energia.

• Attività: acquisizione, elaborazione, monitoraggio e archiviazione di un grandevolume di immagini digitali e video.Stellarator W7-X

FLIR (IR camera) DIAS (IR camera) PROSILICA (visibile)

Caratterizzazione di eventi termici(strike line) sul

limiter