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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
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 4
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 ?
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 6
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
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 8
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
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 9
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?
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 11
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)
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 12
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
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 15
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
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 17
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.
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 18
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
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 19
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
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 20
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
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 21
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
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 22
• 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
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 23
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
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 24
• Appendix
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 25
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
DINKLAGE | Sudden energy losses in tokamaks and stellarators| 01 Oct 19 | Page 26