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