Sudden loss of stored energy in tokamaks and stellarators 1/2...tokamak stellarator ... Event frequency vs. released energy Validated understanding of scaling of mechanisms: e.g. rad

This work has been carried out within the framework of the

EUROfusion Consortium and has received funding from the

European Union‘s Horizon 2020 research and innovation

programme under grant agreement number 633053.

The views and opinions expressed herein do not

necessarily reflect those of the European Commission.

Sudden loss of stored energy in tokamaks and stellarators

6TH IAEA DEMO WORKSHOP

ROSATOM TECHNICAL ACADEMY

Moscow, Russian Federation (Oct. 1, 2019)

A. DINKLAGE1 , S. ÄKÄSLOMPOLO1, M. BERNERT1, C. BIEDERMANN1, H.S. BOSCH1, S. BREZINSEK2, C.P. DHARD1, G. FUCHERT1, D. GATES3, L. GIANNONE1, S. OHDACHI4, R. LUNSFORD3,D. MAIER5, J. MIYAZAWA3, D. NAUJOKS1, B. PETERSON4, M. SICCINIO6,1, C. SUZUKI4, T. SZEPESI6, N. TAMURA4, T. WEGENER1, M. WIRTZ2, R.C. WOLF1, H. YAMADA4, M. ZANINI1 the W7-X Team, the LHD Experiment Team, the ASDEX Upgrade Team.

1Max-Planck-Institut für Plasmaphysik, Garching/Greifswald, Germany2Forschungszentrum Jülich, Jülich, Germany3Princeton Plasma Physics Laboratory, Princeton, NJ, USA4National Institute for Fusion Science, Toki, Japan5Greifswald University, Germany6EUROfusion PMU, Garching, Germany7Wigner RCP, Budapest, Hungary

Outline

Andreas DINKLAGE | Sudden energy loss in tokamaks and stellarators | DPSW-6, Moscow (Russia) | 01 Oct 19 | Page 2

Sudden loss of energy from

fusion-power-plant scale devices

impact of confinement concepts on plasma quenches:

similarities and differences in tokamaks & stellarators

• Generic aspects, figures and conceptual differences

• Sudden loss events at operation limits

Density limits & transients induced

by radiative processes

MHD related transients

Response to high-Z impurities

• Approaches to assess operational exceptions

• Summary and a workshop-style outlook

Runaways in ToreSupra, © A. Loarte

Excessive impurity injection into W7-X

© Th. Wegener, D. Maier et al.

Sudden loss of energy from fusion devices

Proximity

to limits

Operational

exceptions

radiative mechanisms MHD-related

first wall divertor

adapted/modified from T.C. Hender et al., Nucl. Fusion 47 (2007) S128

𝑤 𝜃, 𝜙 Δ𝑡 Γ 𝜃, 𝜙 Δ𝑡

induce sudden

release

Wthermal WmagneticWfast-ions

materials

design

performance targets

RAMI

plasma

instabilitiesconfinement concept

operation and control

scenarios exception handling

Knock-on effects e.g. Τ𝑑𝐼 𝑑𝑡

DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 3


Tokamaks and stellarators

Aspects affecting fast, transient loads

Confinement: 2D tokamaks need plasma current, 3D stellarators not

𝛻𝑝 = Ԧ𝑗 × 𝐵

𝛻 × 𝐵 = 𝜇0Ԧ𝑗 𝛻 ∙ 𝐵 = 0

tokamak

stellarator

H. Wobig, F. Wagner: Magnetic Confinement, in Springer LNP 670 (2005)

𝑃𝑓𝑢𝑠𝑖𝑜𝑛 ∝ 𝑝2 𝑉 ∝ 𝛽2 𝐵4 𝑉

𝜄 =𝑅𝐵𝜃𝑟𝐵𝜑

magnetic confinement

equilibrium

performance

Above a critical heat impact 𝑭𝒄∗

• roughening, cracking, melting,

erruptive evaporation

→ operational risk: mechanical

integrity of plasma facing

components

→ impact on safety, availability and

reactor economy

modified from J. Linke et al., JNM 367-370, 1422 (2007)

The sudden loss of energy W in td on wetted area zS …

Potential effect of transient loads𝑭𝒄=𝐏

𝝉𝒅(𝑴

𝑾𝒎

−𝟐𝒔𝟎.𝟓)

… is a generic issue for all fusion power plant scale devices.DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 5

Safe times td

for sudden loss:

𝜏𝑑 > 𝑾/𝜻𝑺𝑭𝒄∗ 2𝝉𝒅 (𝒔)

10-5 10-3 10-1 101100

101

102

103

104

105

106

10-7

𝑭𝒄∗

~ 𝒪 𝑚𝑠 /𝜻2

𝐸𝑈 − 𝐷𝐸𝑀𝑂 18 𝐻𝐸𝐿𝐼𝐴𝑆 𝑂𝑝𝑡. 𝐶∗

𝑉𝑜𝑙𝑢𝑚𝑒 2519 𝑚3 1407 𝑚3

𝑆𝐿𝐶𝐹𝑆 1563 𝑚21439 𝑚2

𝑃𝑓𝑢𝑠𝑖𝑜𝑛 2𝐺𝑊 1.1𝐺𝑊

F. Schauer et al., FED 88, 1619 (2013)

*F. Warmer et al., PPCF 58, 074006 (2016)

Basic figures for DEMO scale devices

(𝑞𝑛𝑒𝑢𝑡𝑟𝑜𝑛𝑠 ~1.2 𝑀𝑊𝑚−2~0.65 𝑀𝑊𝑚−2)

+H-mode

𝑄 ~40 ~20

DEMO concept Burning plasma deviceCharacter

Van-Mises-stresses (MPa) in one HELIAS 5-B coil module

Pol. cross section of EU- DEMO (baseline 2018) (not a 1:1 comparison)

M. Siccinio et al, FED (submitted, 2019)

𝑊𝑡ℎ𝑒𝑟𝑚𝑎𝑙 ~1.2𝐺𝐽+

~0.5𝐺𝐽

𝑊𝑚𝑎𝑔 ~1.1𝐺𝐽 ~𝒪 10𝑀𝐽 ?

𝑊𝐹𝐼 ~0.2𝐺𝐽 ~𝒪 0.1𝐺𝐽 ?


tokamak stellarator

𝑊𝑐𝑜𝑖𝑙𝑠 ~192𝐺𝐽 ~110𝐺𝐽

Sudden loss of energy close to

operation limits

operational limits leading to sudden losses

tokamaksstellarators

Troyon-limit

low order rationals

𝑛𝑐 < 𝑐𝑃0.6

𝑓𝑖𝑚𝑝0.4

𝑛𝑆𝑢𝑑𝑜 < 0.25𝑃𝐵

𝑎2𝑅𝑛𝐺𝑊 <𝐼𝑝

𝜋𝑎2

Greenwald-limit

𝛽𝑁 = 𝛽𝐼𝑝

𝑎𝐵< 3.5%

𝑀𝐴

𝑇𝑚

𝑞95 > ~2

+ RWM, VDE, …

Sudo-(like)-limits

A. Weller et al., PPCF 45 A285 (2003)

Limits affect fusion performance: underlying mechanisms set time-scales


beta-limit

Greenwald, PPCF 44 R27 (2002)

Zanca et a., Nucl. Fusion 57 056010 (2017)

Fuchert et al., to be publishedl

Complication: large parameter variations may involve several mechanisms.

Tearing modes

Example ASDEX-Upgrade:H-mode density limit in tokamaks

M. Bernert et al. PPCF 57, 014038 (2015)

Evolution of tokamak H-mode with density

• Constant gas puff from 1.5s

• Wkin decreases

• Prad constant

• Full detachment of outer divertor

(as for C density limit)

immediately before disruption 5.8s

• MARFE at X-point moving upward

• tearing mode triggered

• causes disruption in L-mode (~nGW)

• Sequence of mechanisms involves MHD,

transport, radiative processes

Soft and hard limits: when do we get to the

point of no return (i.e. mitigation required)?

State-space control for active control to

avoid the final termination


Example W7-X: energy loss in ECCD experiments

Collapse in with `strong´ ECCD

Sawtooth-like activities when iotaprofile is distorted by ECCD (~15kA co)

No complete loss in MHD phase

1 – Precursors start2 – Crash; density increase3 – ECE cut-off – high density(wall fluxes?) 4 – ECE signal restored, but parameters continue to decay. 5 – Temperature spike. Power not absorbed anymore

Energy decay ~ 0.2 tEMinor asymmetries in divertor loads

DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 10M. Zanini et al., to be published

Where does the power go in radiative collapses?


B. Peterson et al., PPCF 45 1167 (2003)

H.R. Koslowski, et al., Fusion Sci. Technol. 49:2T, 147 (2006)

LHDW7-X

TEXTOR

Poloidal asymmetriesD. Naujoks, et al., SFP Workshop 2019

450ms

W7-X

550ms 580ms

Exceptional in limiter discharges (debris?)

toroidal localization in 3D

U. Wenzel et al., Nucl. Fusion 58, 096025 (2018)Toroidally symmetric

Edge collapse

MARFE

Tomographic e reconstructions © Y. Liu

Poloidally symmetricPol. & tor. symmetric

MHD related instabilities in tokamaks

Timescale set by instability mechanism

Pathways involve radiation and MHD

leading to disruptions (see next papers)

Thermal quench

Radiation – cold plasma into core

Radiating layer, contraction of temperature profile

Uncontrolled profile shrinkage

Current profile affected

Destruction of MHD equilibrium

Heat flows to wall

Cools quickly – plasma cannot carry current

Current induced into wall & runaways (CQ)

Complicated in detail with multiple pathways

td < ms ~ f(a)


JET

V. Riccardo, A. Loarte et al., Nucl. Fusion 45, 1427 (2005)

• in IDB plasmas:

pellet fuelled plasmas

… 1021m-3, 600 eV, b~4%

steep density gradient

• In the course of density profile

steepening

shrinking begins at edge

fast collapse of core

High-n balloning/reconnection

Fast energy loss in LHD

Core density collapes (CDC) at high b/density in LHD

Energy loss up to 50%

in dt < ms with pol. asymmetries

Miyazawa et al., Plasma Fusion Res. 3, S1047 (2008)

Ohdachi et al.Contrib. Plasma Phys. 50, 552 (2010)

Andreas DINKLAGE | Transient energy loss in tokamaks and stellarators | IAEA TM DEMO, Moscow (Russia) | 01 Oct 19 | Page

13

Fast energy loss in W7-AS/W7-Xfast plasma termination

in current ramps - NTMs

Stellarators are not immune against MHD-type instabilities:

Scenarios with avoidance of low order rational i values: (small) ECCD DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 14

W7-AS

A. Weller PPCF 2003

𝜏𝑑 ~ 20𝑚𝑠

Δ𝑡𝑐 ~ 1.7𝑚𝑠

ൗ𝑑𝐼 𝑑𝑡 ~1.1𝑀𝐴𝑠−1

Worst-case total collapse in W7-X

D. Naujoks, SFP 2019

High-Z response: hollow Te

R. Neu et al., JNM 438 S34 (2013)

V. Arunasalm et al., Proc. 8th EPS (1977) , p.13

High-Z: Prad in centre→ cooling→ loss of T’ → accumulation

Current profile affectedDouble tearing modes → internal disruptions


Early observations

Hollow Te profile due to centralW radiation in PLT (IP = 0.36MA, ne = 2.6x10

19m-3)

m=3 and2 instab. lead to collapse𝜏𝑑 < 0.1 × 𝜏𝐸

Andreas DINKLAGE | W7-X Results | QST, Naka (Japan) | 02 Aug 19 | Page 16

Approaches to assess

operational exceptions

𝜏𝐝 (ms) 𝜏𝐼𝑆𝑆04 (ms)

1st LBO-killer 66.3 ± 0.3 / 58.8 ± 0.3 201.0 ± 0.6

2nd LBO-killer (heating off) 20.6 ± 0.3 / 22.9 ± 0.3 166.3 ± 0.3

High-Z time response: iron injection into W7-X

(6.3 ± 2.2) x 1017 particles of Fe: Prad, Fe = (1.8 ± 0.8) MW →

additional cooling effects (co-injected material) / confinement degradation


D. Maier, M.Sc. Thesis, U Greifswald (2019)

Th. Wegener et al., Rev. Sci. Instrum. 2019

loca

l e

lectr

on

co

olin

g tim

e (

ms)

plasma radius (m)

𝝉𝒅w/ heating

w/o heating

𝝉𝒅

Spatial distribution of loads

No indication for poloidal asymmetry but for toroidal localization of Prad.


D. Maier, M.Sc. Thesis, U Greifswald (2019)

No toroidal variations of divertor loads Toroidal variations of visible light

How much powder kills W7-X and AUG?

radiated power

line density

temperatures

plasma energy

plasma current

• Increasing amount of B4C granules

• ~80 mg leads to radiative collapse

• poloidally symmetric radiation

• td ~ 120ms ~ tE

R. Lunsford et al., to be published

Ti

Te


W7-X

How much powder kills W7-X and AUG?

• powder injection from t>3.4s

• 120 mg/s @ 3.8s: Prad > Pheat(specific mass unknown)

• plasma termination ~ 4.0s (killergas)

• Where does Prad go?

• td < 20 ms

R. Lunsford et al., Nucl. Fusion 2019

PRADPNBI

ne – corene – edge

H98 WMHD


4.00 4.02 4.044.03.83.63.4time (s)

3.4s 3.8s 3.995s 4.054s

ASDEX-Upgrade Dropper

Vacuum confinement: recovery in stellarators

A. Dinklage et al., Nucl. Fusion 59, 076010 (2019)M. Zanini et al., to be published


W7-X LHD

• Open questions:

Fast ions? Where does WFI go in 2D and 3D?

Physics of core impurity accumulation

Localization of loss channels:

wetted area – how large and where?

Event frequency vs. released energy

Validated understanding of scaling of mechanisms:

e.g. rad. release on entire wall

at 0.1 x tE ~ f(V) may resolve issues

Impact on system studies → RAMI

Gaps, ideas and synergies


• Plans – induced termination:

Core impurity injection

on LHD

Pellet-fueling triggered

instabilities TESPEL (N. Tamura)

Loads w/ ASCOT/CAD & wall probe

CP. Dhard et al., submitted 2019

Leading differences relevant to sudden energy loss events:

Wmag, R/a, working point (n, b), different onset & interaction of loss mechanisms

Basic differences tokamaks & stellarators

Schauer et al.,

FED 88, 1619 (2013) Federici et al., FED 136, 729 (2018)

FFHR-d1HELIAS-5BEU-DEMO


Significant part of the magnetic field

generated by a plasma current

• Good confinement properties

• Concept further developed

• Pulsed operation

• Current driven instabilities/disruptions

Magnetic field essentially by external coils

• Requires elaborate optimization to achieve

necessary confinement

• Is ~1½ device generations behind

• Intrinsically steady state

• Soft operational boundaries

tokamakstellarators

Yanagi et al.,

J Fusion Energy 38, 147 (2019)

The confinement concept matters: occurrence, time-scales and spatial distribution

• Concepts share plasma physics (radiation, MHD), engineering aspects (Fc, B, ... – defines mitigation requirements) and performance targets

• Conceptual differences: Ip → Wmag: runaways in tokamaks

W th: disruptions (TQ) on tMHD – no disruptions in stellarators but fast MHD events

Effective density limit higher/lacking in stellarators: lower pa, higher b

3D transport – higher R - lower aspect ratio

Fast ion confinement and impurity transport: are 3D more malign?

• Confinement concept affects nature of instabilities – role of 1/q and shear Tokamaks: tMHD ↔ Prad (tE) – active control

Stellarators: tE ↔ Prad (tMHD) – find appropriate operation point

• Intentional excessive impurity injection and fueling pellets appear to offer systematic methodologies for more detailed insight – value of comparative studies.

• Differences in maturity of confinement concept developments stellarators ~ 30m3, no broad databases, reactor scale scenarios to be developed and validated,

3D engineering

tokamaks: ~860m3 ante portas, specific scenarios, control schemes progressed, specific engineering underway

Stellarators apparently more benign in terms of impacts from sudden energy loss – but for reactor scale devices no conclusive claim if generic challenges for fusion reactors resolved

Summary: impact of confinement concepton sudden energy loss


• Appendix


Transient radiative power loss

𝑃𝑟𝑎𝑑 =

𝑍𝑖

න𝑛𝑖𝑛𝑒𝐿𝑍𝑖 𝑇𝑒 𝑑𝑉

T. Pütterich et al., Nucl. Fusion 59 056013 (2019)

Stability is set by specific shape of cooling curve and electron temperature

𝑇𝑒 ↘

𝜕𝐿/𝜕𝑇𝑒 < 0

𝑃𝑟𝑎𝑑 ↗

Radiative cooling

𝑃𝑟𝑎𝑑 > 𝑃ℎ𝑒𝑎𝑡

Collapse, MARFE

𝜏𝑑 < 𝒪 𝜏𝐸


Documents

Sudden loss of stored energy in tokamaks and stellarators 1/2...tokamak stellarator ... Event frequency vs. released energy Validated understanding of scaling of mechanisms: e.g. rad