First-Principle Simulations ReproduceMultiple Cycles of Abrupt Large Relaxation Events
in Beam-Driven JT-60U Plasmas
Andreas Bierwage (QST)
in collaboration with K. Shinohara (QST), Y. Todo (NIFS),
N. Aiba, M. Ishikawa, G. Matsunaga, M. Takechi, M. Toma and M.Yagi (QST)
26th IAEA Fusion Energy Conference, 17-22 Oct. 2016, Kyoto, Japan
JT-60 tokamak (1985-2010):
▶ Rich database of important observations.
▶ Some observations still await to be explained. One such phenomenon:
Abrupt Large Events (ALE)
→ Robustly observedduring N-NB injectionwhen 1 < q
0 < 2.
2
ALE observations in JT-60U experiments
ALEs are large δBθ
spikes
seen at 40-60 ms intervals …
… each time causing an abrupt 20% drop in the core neutron emission.
[Shinohara et al., PPCF'04][Ishikawa et al., NF'05]Minor radius
Evidence foravalanche-like transportof energetic particles (EP).
17th IAEA FEC, 1998, Yokohama, Japan: First observation of ALEs in JT-60U.
[Kusama et al., Nucl. Fusion 1999]
3
ALE
EP-driven Alfvén mode activity also observed between ALEs
ALE intervals are filledby low-amplitude bursts of
“fast frequency-sweeping (fast FS)”
n=1 energetic particle modes (EPM)
“Fast FS”n=1 EPMs
[Shinohara et al., NF'02]
ShotE032359
[EPMs predicted by L.Chen PoP'94]
4
Fast FS modes were accurately reproduced in simulations
Extended MEGA sim. with realistic N-NB source & collisions.
→ Qualitative and quantitative validation on multiple time scales.
[Todo et al., PFR'03]▶ 2003: First simulation of a single chirp ofn=1 EPM using hybrid code MEGA.
▶ 2010: Multiple chirps simulated with areduced 1-D “bump-on-tail” model.
▶ 2014:
[Lesur et al., PoP'10]
Enlarged 0.4 ms windowIntermittent bursts(5-10 ms periods)
Chirping(1-3 ms)
Global beating(0.1-0.3 ms)
[Bierwage et al., IAEA FEC 2014; APS-DPP 2016; submitted to NF]
Ext. MEGA simulation results:
5
Successful simulationof Abrupt Large Events
Outline:
1. Simulation model and methods
2. Results and validation against experiments
3. Prospects (ALE trigger physics, prediction)
New milestone 2015-2016
ALE
on supercomputer
6
Simulation setup based on JT-60U experiment
MHD equilibrium: Shaped high-β plasma with normal shear
7
Simulation setup based on JT-60U experiment
EP source: 2 × 2.5 MW co-current N-NBI with E0 = 400 keV
8
Hybrid code for self-consistent long-time simulations Based on MEGA code by Y. Todo (NIFS) + source & collision model from OFMC code
Shear Alfvén, slow and fast waves,resistive, viscous, thermal diffusion.
Guiding center ‖ streaming, ⊥ drifts,gyroaverage, collisions, sources, wall.Wave-
particleinter-actions
(0.01-100 ms)
MHD waves Energetic particle (EP) motion
∂ρb
∂ t=−∇⋅(ρbδ ub) , μ0 J = ∇×B
ρb
∂ub
∂ t=−ρbu b⋅∇ ub − ∇ pb + (J−JEP,eff )×B
∂B∂ t
=−∇×E, E = −ub×B + ηδ J
+ νρb (Γ−1 ) [ (∇ ×ub )2+43
(∇⋅ub )2] + χ ∇ 2pb
− [∇ ×(νρb ∇×ub ) +43
∇ (νρb ∇⋅ub )]
∂pb
∂ t=−∇⋅(pbub)− (Γ−1) [pb ∇⋅ub + η(J−Jh,eff )⋅δ J ]
Bulk plasma: MHD model(t): 4th-order Runge Kutta, Δt
mhd ≈ 1 ns
(R,φ,Z): finite differences, non-slip b.c.
Energetic ions: Kinetic model(t): 4th-order Runge Kutta, Δt
pic ≧ Δt
mhd
(fgc
): PIC, δf or full-f guiding center distribution
JEP,eff
B, E
4-pt.gyro-avg.
m v||
d v ||
d t= v || *⋅(qE− μ ∇ B)
dμ
dt= 0 + O(β ϵδ) with ϵδ∼
ρ⊥
LB∼ ω
ΩL≪1
dR gc
dt= −
μ
qB*∇ B×b̂⏞v B
+v ||
B*(B + ρ||B∇×b̂)⏞
v || *
+E×b̂B*
⏞vE *
≡ Ugc
μ ≡m v⊥
2
2B, ρ|| ≡
v ||ωL, B* ≡B [1+ρ|| b̂⋅(∇×b̂)] , b̂ ≡
BB
v '|| =v ||
v(v+Δ v L )+
v⊥
vΔ vTsinΩ , v '⊥=√ (vL+Δ vL )
2+Δ vT
2−(v ' || )
2
9
Confirmed by validation againstDIII-D and JT-60U experimentsand numerical sensitivity studies.
First-principle model for global large-amp. Alfvén modes
Direct effect of Γ,η,ν,χ is weak for modes in validity regime of MHD:
▶ long wavelength n 〜 O(1)
▶ high frequencies ω 〜 ωA
Effectively no free parameters for global large-amp. Alfvén modes.
∂ρb
∂ t=−∇⋅(ρb δub) , μ0J = ∇×B
ρb
∂ub
∂ t=−ρbub⋅∇ ub − ∇ pb + (J−JEP,eff )×B
∂B∂ t
=−∇ ×E, E =−ub×B + ηδJ
+ νρb(Γ−1 ) [ ( ∇×ub )
2+43
(∇⋅ub )2 ] + χ∇
2pb
− [∇×(νρb ∇×ub ) + 43
∇ ( νρb ∇⋅ub ) ]
∂pb
∂ t=−∇⋅(pbub)− (Γ−1) [pb ∇⋅ub + η(J−Jh,eff )⋅δ J ]
[Todo at al., NF'14; NF'15]
[Bierwage et al., NF'16]
[Bierwage et al., submitted to NF]
“Free” parameters:
▶ Γ= 5/3 controls compressibility (→ “beta-induced low-freq. gap)
▶ η,ν,χ〜 10-6vA0
R0
dissipate small-scale structures arising from radial phase mixing (→ “continuum damping”)
MHD
10
Speed-up by up to factor 5 gives access to long time scalessuch as ALE cycles and steady-state formation (> 50 ms).
Problem: Self-consistent simulation too slow for ALE cycles
ALE
4 ms 1 ms 4 ms 4 ms 4 ms1 ms 1 ms 1 ms
… …Classical Hybrid Classical Classical ClassicalHybrid Hybrid Hybrid
t=0: Start ofbeam injection
[Todo et al., NF'14, NF'15]
Time
βEP Need to simulate of the order 100 ms!
Use “Multi-phase method”:
Interlaced classical and hybrid simulation phases. (no MHD) (with MHD)
11
“Multi-phase method” for long-time simulations
12
Reproduced: Multiple ALE cycles
MEGA multi-phase simulation: ALE-like spikes at t = 80, 130, 175 ms
JT-60U experiment: Large ALEs typically seen at 40-60 ms intervals
13
Reproduced: Energetic particle avalanche (ΔβEP,0
≈ -25%)
Location and magnitudeof simulated relaxationis consistent with experiments.
Demonstrated that multi-phase method can be used to predictEP transport in presence of weak and strong Alfvén mode activity.
MEGA multi-phase simulation:
Velocity-integrated energy density (βEP
)
[Shinohara et al, PPCF'04][Ishikawa et al, NF'05]
JT-60U experiment:
Neutron emission profile
14
ALE
Time
βEP
4 ms 1 ms 4 ms 4 ms 4 ms1 ms 1 ms 1 ms
… …Classical Hybrid Classical Classical ClassicalHybrid Hybrid Hybrid
Restartfrom a stable
“pre-ALE”initial condition Continuous hybrid sim. …
Fluctuations are likely to overshooteach time when MHD is turned onafter a 4 ms break
ALE trigger in multi-phase sim. not fully self-consistent
Method to simulate ALE triggering more self-consistently:
15In principle, sim. data contains all info about trigger physics.
Successfully simulated ALE trigger process self-consistently
MEGA simulation: ALE occurred after “quiet” period of about 4 ms
Chirping n=1 EPMs
16
New finding: Multi-wavelength character of ALEs
MEGA simulation: n=1-3 reach large amplitudes
17
New finding: Multi-wavelength character of ALEs
MEGA simulation: n=1-3 reach large amplitudes
JT-60U experiment: Data mining confirmed simulation result
18
Summary and prospects:
1. Implemented multi-time-scale simulation model
✓ Used fast multi-phase sim. for multiple ALE cycles ✓ Used self-consistent sim. for individual ALEs
2. Reproduced ALEs and validated against experiments
✓ ALE cycles, ✓ EP avalanches, ✓ Multi-n character
Enables us to study theALE trigger process on afirst-principle physics basis &develop predictive capability.
For first insights, see:
▶ Poster TH/4-3 (afternoon),▶ ITPA EP meeting (next week),▶ Additional slides for discussion.
ALE
First-Principle Simulations ReproduceMultiple Cycles of Abrupt Large Relaxation Events
in Beam-Driven JT-60U Plasmas
Andreas Bierwage (QST)
in collaboration with K. Shinohara (QST), Y. Todo (NIFS),
N. Aiba, M. Ishikawa, G. Matsunaga, M. Takechi, M. Toma and M.Yagi (QST)
26th IAEA Fusion Energy Conference, 17-22 Oct. 2016, Kyoto, Japan
Additional slides for discussionconcerning ALE trigger physics
2
Trigger physics: Complicated and under investigation
In NSTX experiments
[Fredrickson et al. NF'06]
multi-n spectra ωn(t)
showed strong correlation between- onset of resonance overlaps, and- onset of an EP avalanche.
n = 1
n = 2
n = 3
Time
Freq. Multiple moddes withdifferent ω and n
Here, the situationlooks different:
▶ Overlaps in ω occur more often than ALEs.
▶ Lin. resonance overlaps were also predicted.
→ ALE trigger mechanism is more obscure and involves dynamics in A
n, r
n,, ω
n, and E
kin.
3Resonant phase space islands pulsate & move w.r.t each other.
Three degrees of freedom per mode (A, ω, r)
The fluctuations do not only have
▶ varying amplitudes (∝ width of resonant phase space islands, → conventional NL resonance overlap)
but also
▶ dynamic frequency spectra (→ varying number and location of▶ dynamic radial structures. active resonances in phase space)
Amplitude An [a.u.]
Frequency fn [kHz]
Minor radius rn / a
[Berk et al., NF'95]
[Zonca et al., NF'05]
4
Evidence for necessity of multi-n fluctuations
Here,a combination of n=2 and n=3produces large fluctuations.
At least two different n are needed.
But: Here we varied only the mode spectrum.EP distribution was already set up for an ALE!
Conventional initial-value sims. (no src., no coll.) starting just before ALE#2 at t = 129 ms.
5
Demonstration of multi-time-scale effects
(a) Sim. with continuousN-NB injection
(b) N-NBs turned offat t = 118 ms
ALE
EP slow-down plays key role for determining ALE period length.
I
[Bierwage et al., NF'14][Bierwage & Shinohara, PoP'14, PoP'16a, PoP'16b]
I: n=1 dies soon after beams turned off
▶ n=1 driven directly by newly born EPs (here 400 keV)
6
Demonstration of multi-time-scale effects
[Bierwage et al., NF'14][Bierwage & Shinohara, PoP'14, PoP'16a, PoP'16b]
(a) Sim. with continuousN-NB injection
I: n=1 dies soon after beams turned off
II: Retarded response of n=2, 3 modes
▶ n=1 driven directly by newly born EPs (here 400 keV)
▶ Coll. slow-down fills n=2,3 resonances in 200-400 keV range
ALE
EP slow-down plays key role for determining ALE period length.
I I I
(b) N-NBs turned offat t = 118 ms
7
Demonstration of multi-time-scale effects
[Bierwage et al., NF'14][Bierwage & Shinohara, PoP'14, PoP'16a, PoP'16b]
(a) Sim. with continuousN-NB injection
I: n=1 dies soon after beams turned off
II: Retarded response of n=2, 3 modes
III: Revival of n=1 mode in inner core
▶ n=1 driven directly by newly born EPs (here 400 keV)
▶ Coll. slow-down fills n=2,3 resonances in 200-400 keV range
▶ n=2, 3 mode activity at r/a>0.5 builds up gradients at r/a<0.5
ALE
EP slow-down plays key role for determining ALE period length.
I I I II I
(b) N-NBs turned offat t = 118 ms
8
Evidence for retarded response due to coll. slow-down
[Bierwage et al., NF'14]
9
Evidence for retarded response due to coll. slow-down
Resonant drive of lin. eigenmodes
Bierwage & Shinohara PoP'14,'16a,'16b
10
Nonlinear mode interactions via resonant particles
Radius
Toroidal
direction
Amplitude Mode A
Mode B
(2) Convective amplification
(1) Particle pumping
Radius
Amplitude
A B
11
Milestone:
0.1-0.3 ms
1-5 ms
Globalprofile build-up
& collisionalslow-down
Within the regime where MHD is valid (long wavelength, high frequency)the hybrid code MEGA has largely succeeded in the simulation ofMHD and EP dynamics, and their interplay on a wide range of t-scales.
10-100 ms
(A) Steady state
Time
βEP
0.1-0.3 ms
Time
βEP
(B) Relaxationevents
Chirping
EPavalanche
12
Prospects:Within the regime where MHD is valid (long wavelength, high frequency)the hybrid code MEGA has largely succeeded in the simulation ofMHD and EP dynamics, and their interplay on a wide range of t-scales.
Apply tostudy & explainALE trigger.
→ In progress Apply toother casesand makepredictions.
→ JT-60SA, ITER
Extend tolow-frequencyregime.
→ Kinetic bulkion modelin preparation
Use the physics insights won to develop effcient reduced modelsthat are needed for integrated simulations and scenario development.
→ E.g., self-consistent and accurate equilibria for burning plasmas.
ALE
13
Abrupt Large Events (ALE) in experiments
Routinely observed in N-NB-driven high-β discharges when 1 < q(0) < 2.
Large separation of time scales: ALE period (〜50 ms) >> ALE duration (〜0.1 ms).
Motivation and goal for this study:
→ Important to clarify underlying physics in order to be able to predict ALEs.
→ For this, reproduce ALEs in simulations and study in “numerical experiments”.
Large fluctuation amplitudes:
- Total neutron emission 10%, locally on axis up to 25%
- Magnetic fluctuations spike 4-8 times above background (chirping modes)
14
Trigger problem - History of simulations of ALE scenarios
Conventional short-time simulationsstarting from unstable initial condition
2005 Todo et al. (MEGA, n=1)
→ Found n=1 Energetic Particle Mode (EPM)→ Shown to be responsible for bursts of chirping modes occuring between ALEs
2007 Briguglio et al. (HMGC, n=1)
→ Demonstrated that even single n=1 EPM can cause ALE-like fast ion transport→ But not clear how one can reach such a strongly unstable state
2013-2015 Bierwage et al. (MEGA, n=1-4)
→ Demonstrated destabilization of n=3 mode and subsequent convective amplification→ Possibility of multi-n interaction via linear or nonlinear resonance overlap
Abrupt transition from weak to strong fluctuations … Known 1-D paradigms:
1995 Berk et al.: Nonlinear resonance overlap between resonant phase space islands
2005 Zonca et al.: Convective amplification of single-n mode (multi-m res. overlap)
Chirping n=1 EPMs
Radialdependenceof resonantfrequencies
Next: Clarify how these physics ingredients act and interact on multiple time scales:
Long-time simulations including 5-D fh, MHD, collisions, sources and sinks