1 14 th IAEA TM on Energetic Particles, Vienna, Austria, Sep. 1-4, 2015 - Physics of self-heating in burning plasmas - Alfvén Acoustic Channel for Ion Energy in High-Beta Tokamak Plasmas A. Bierwage in collaboration with P. Lauber, N. Aiba, K. Shinohara and M. Yagi Fusion alphas (≦ 3.5 MeV) Bulk ions (≦ 10 keV) Fusion Electrons (≦ 10 keV) Collisional heating Collisional heating Q: Are there other self-heating channels, besides collisions with electrons? Outline Part 1. MHD response in high-beta JT-60U plasma with N-NB Part 2. Local analysis with a linear gyrokinetic model (LIGKA) A: MHD Alfvén acoustic channels with ω≈ωTAE not seen in GK case for Te ≈ Ti . But: Te ≫ Ti regime and EP effects on sound spectra deserve attention. ? Motivation: ▶ Burning plasmas will rely on efficient self-heating. ▶ Reliable predictions for fusion performance requires knowledge of all relevant self-heating channels. I-10
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Alfvén Acoustic Channel for Ion Energyin High-Beta Tokamak Plasmas
A. Bierwage in collaboration with
P. Lauber, N. Aiba, K. Shinohara and M. Yagi
Fusion alphas(≦ 3.5 MeV)
Bulk ions(≦ 10 keV)
Fu
sio
n
Electrons(≦ 10 keV)
Collisionalheating
Collisionalheating
Q: Are there other self-heating channels, besides collisions with electrons?
Outline
Part 1. MHD response in high-beta JT-60U plasma with N-NB
Part 2. Local analysis with a linear gyrokinetic model (LIGKA)
A: MHD Alfvén acoustic channels with ω≈ωTAE not seen in GK case for Te ≈ Ti .
But: Te ≫ Ti regime and EP effects on sound spectra deserve attention.
?
Motivation: ▶ Burning plasmas will rely on efficient self-heating.
▶ Reliable predictions for fusion performance requires knowledge of all relevant self-heating channels.
I-10
I-10 (A. Bierwage) 2
▶ Thanks:
A.B. thanks Yasushi Todo (NIFS, Japan) for providing the code MEGA.
▶ Computational resources:
HELIOS at IFERC-CSC in Japan is provided by the Broader Approach collaboration between Euratom and Japan implemented by Fusion for Energy and JAEA.
▶ Grants:
This work has been supported by Japan Society for Promotion of Science (JSPS) Grant-in-Aid of Scientific Research number 25820443.
This work has been partly 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.
▶ Energetic particle modes (EPM), couple to sound waves via BACMs
Bierwage et al.,Phys. Rev. Lett. 114
(2015) 015002
I-10 (A. Bierwage) 10
−∂∂ t [∇ 1
vA2 ∇⊥ϕ ] + B⋅∇
( ∇×∇×A )||⋅B
B2 + ( b×∇ A || )⋅∇μ0 j0 ||
B
= −∑a
μ0∫d2 v ea ( v̂d⋅∇ J0 f )a + ∑a
b×∇ (βa ⊥
2Ωa)⋅∇ ∇⊥
2ϕ + ∑
a
3βa⊥
8Ωa2
∇⊥
4 ∂∂ t
ϕ + B⋅∇ 1B ∑
a
βa
4∇⊥
2 A||
Current equation / gyrokinetic moment equation (GKM)
Approximations:
▶ No trapped particle effects.
▶ Sound wave coupling up to first order (geodesic).
▶ Zero orbit width and FLR only up to order (k
⊥ρ)4.
▶ Isotropic Maxw. distribution for all species a={e,i,h}.
▶ Deuterium only.
Q: Can we confirm this MHD prediction in a GK world?
→ Part 2: Local analysis with a linear gyrokinetic model
Energy density gradients(“ballooning”)
Diamagnetic current
0 = ∑a
ea na1 = ∑a
ea∫d2 v (J0(ρ ∇⊥) f )a + ∇⊥
min i0
B2 ∇⊥ ϕ(x ) +3P i⊥
4B2Ωi
2 ∇⊥4ϕ(x ) + O ((k⊥ρa )
6 )
Quasi-neutrallity equation (QN)
Charge density gradients FLR polarization terms
Current gradient (“kink”)Inertia Field line bending (FLB)
4th-order FLR inertia High-beta FLB
▶ Code: LIGKA [Ph. Lauber, Max Planck IPP, Germany]
▶ Here: Local eigenvalue analysis → Continuous spectra ω(r),γ(r).
Lauber et al.,J. Comp. Phys. 226
(2007) 447
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▶ For parameter scans, vary the above reference profiles as
→ Te(ρ)= const. x T
e
ref(ρ)
→ Th(ρ)= const. x T
h
ref(ρ)
▶ Focus on toroidal harmonic n = 3.
Profiles for N-NB-driven high-beta JT-60U plasma
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▶ Local growth parameter Г: ▶ Purpose here:
Г = 2πγ/ω = γτ = ln |Ф(t+τ) / Ф(t) | Look for changes in Alfvén continua
e.g.: Г ≶ -2 → Ф(t+τ) / Ф(t) ≶ 10% in association with sound waves.
▶ Observations:
• Sound continua are strongly damped (ГS < -2) and structure of Alfvén continuum damping (ωA,ГA) smooth. → In GK results we find no evidence of Alfvén acoustic channels with ω≈ωA .
• Compressional stabilization of Alfvén waves increases towards ωBAE. (modified by ωж ). → Conversion to KBM, drift-Alfvén-ballooning modes.
Results for Te = T
e
ref, Ti = T
i
ref, βh = 0 → β ≈ βref / 2
zoom
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▶ Observations:
• GK continua near ω≈ωBAAE < 0.1 match MHD continua, and their damping is reduced significantly (Г > -2).
• BAE accumulation pts. now marg. stable (Г > -0.01).
• Sound continua with ω > 0.1 still strongly damped ...
• ... but structure of Alfvén continua (ωA,ГA) has changed. ▶ Expectation for Te ≫ Ti regime:
• Reduced damping of sound branches with ω > 0.1. → Look for increasing changes in Alfvén continua and relation to sound waves.
Results for Te = 2.8 x T
e
ref, Ti = T
i
ref, βh = 0 → β ≈ βref
zoom
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▶ Observation:
“Hot sound” continua ωhS
(ρ) appear → Weakly damped for ω ≦ 0.1, and
correlate with changes in ωA(ρ)≈ωTAE,u.
Results for Te = T
e
ref, Ti = T
i
ref, βh0
= 1.8% → β = βref
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Energeticions
Soundwaves
Alfvénwaves
Resonantdrive
Co
up
lin
gCurrent status:
▶ MHD predicts Alfvén acoustic channels with ωBAE
<ω≈ωTAE
.
→ Try to understand how the MHD picture of such channels translates to the GK world. How can we identify them?
▶ Local GK analysis (ω,γ): Strong damping when Te ≈ T
i.
→ Results draw attention to Te ≫ Ti regime and EP effects: ω
A(ρ) changes and “hot sound” branches ω
hS(ρ) appear.
☞ GTC results suggest moderate damping of nonperturb. global BAAE modes even for Te ≈ Ti. [Z. Lin et al, poster P-19]
Ongoing work and future steps:
▶ Explore Te ≫ T
i regime.
▶ Clarify role of “hot sound” continua ωhS
(ρ).
▶ Include trapped particles, FOW effects, realistic Fh(E,μ).
▶ Global analysis and energy flows at finite amplitudes.
Relevance of this work: (once we progress to the NL regime)
▶ Better understanding of energy flows in high-beta fusion experiments (e.g., JT-60SA) and burning plasmas (DEMO).
▶ “Anomalous bulk heating” and effect on EP confinement:
A) improvement (damping reduces mode amplitudes);
B) deterioration (damping increased probability for bursts and large-amplitude relaxation events).