Global electromagnetic gyrokinetic simulations of TAEs in ITER · Global electromagnetic...
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Max-Planck-Institut f¨ ur Plasmaphysik Global electromagnetic gyrokinetic simulations of TAEs in ITER T. Hayward-Schneider 1 *, Ph. Lauber 1 , A. Bottino 1 1 Max Planck Institute for Plasma Physics, 85748 Garching, Germany Motivation ITER will present a challenge in terms of dealing with significant quantities of fu- sion alpha particles for the first time. Their interaction with Alfv´ enic instabilities presents a challenge for modelling future scenarios. While the ITER 15MA scenario [1] has received plenty of attention in the past [2-9], the models used to address the problem vary, and have not all agreed. In this work, we present the application of an initial value global electromagnetic gyrokinetic model, using the ORB5 particle-in-cell code [10, 11], to the problem of Toroidal Alfv´ en Eigenmodes (TAEs) in the ITER 15MA scenario. ITER 15MA Scenario 0 1 2 3 4 0 0.5 1 Safety factor (q) s 0.9 1 1.1 1.2 0 0.2 0.4 0.6 temperature [keV] density [10 19 m -3 ] 0 8x10 17 1.6x10 18 0 0.5 1 density [m -3 ] Radial position double 1.5% n e s=0 ~ nominal Compared to the nominal scenario (above), we make the following changes: I Remove steep gradients at the plasma edge (around s>0.9) I Neglect the trace impurities (He & Be) I Treat the alpha particles as 900 keV Maxwellian species I Replace 50:50 D:T mix with 2.5 H isotope I Consider double (and nominal) alpha density Numerical tool: ORB5 “ORB5: a global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry” [11] I Originally developed at SPC (Switzerland) I now at SPC, IPP (Germany) and Univ. of Warwick (UK) I Filter applied in toroidal and poloidal mode numbers I m(r )= nq (r ) ± Δm I Effectively mitigates with the so-called cancellation problem using the pullback scheme [12] (leads to an order of magn. increase of time step) I Drift-kinetic, fluid, hybrid, and adiabatic electron models present: I These results all with kinetic (reduced mass ratio) electrons I Gyrokinetic or drift-kinetic ions (here: bulk gyro-, EPs drift- kinetic) I Previously used for turbulence studies as well as EP physics: I ITPA-TAE benchmark [13], DIII-D RSAE/TAE benchmark [14] Numerical parameters: all presented simulations were performed using {32, 128, 32}· 10 6 markers for the bulk ions, electrons, and EPs respectively. Full radius simulations used a grid of (1024, 512, 128) in the radial, poloidal, and toroidal directions, (512, 256, 128) for reduced annulus (0.2 – 0.7). For large n (> 30), the poloidal and toroidal grids were increased, for some cases with small n, reduced. Unless otherwise stated, the timestep was 1.875 ω -1 ci . ω ci /ω A ∼ 187, ω A ∼ 1.05 × 10 6 rad s -1 . Annular simulations have a cost of ∼ 0.5 core-hr per step, full radius ∼ 0.9. Results: Radiative damping If we look at the the subdominant harmonics either side of the mode, shortly after initialization, we see radially propagating waves, indicative of KAW (here m=25/28, TAE is m=26/27) Conclusions I Global, electromagnetic gyrokinetic code ORB5 applied to TAEs in ITER 15MA scenario I Robust scenario, only minor modifications to profiles made I Systematic linear studies for both reduced annulus and full domain simulations I Nonlinear, multimode studies begun [1] A. Polevoi et al. JFR (2002) [2] N. Gorelenkov et al. PPPL Rep. (2008) [3] R. Waltz et al. NF (2014) [4] S. Pinches et al. POP (2015) [5] Ph. Lauber PPCF (2015) [6] M. Schneller et al. PPCF (2015) [7] P. Rodrigues et al. NF (2015) [8] M. Fitzgerald et al. NF (2016) [9] M. Isaev et al. PPR (2017) [10] S. Jolliet et al. CPC (2007) [11] E. Lanti et al. CPC (sub.) [12] A. Mishchenko et al. CPC (2019) [13] R. Hatzky et al. NF (2018) [14] S. Taimourzadeh et al. NF (2019) Simulations were performed under the project ORBFAST on the EUROfusion Marconi supercom- puter operated by CINECA and on the Cobra supercomputer of the Max Planck Society, operated by the MPCDF. Results: TAE modes Example mode structures: Here we show two global simulation domain examples, run on the full radius (0 ≤ s ≤ 1). Fig. 1: Snapshots of the electrostatic potential for TAEs with n = 12 (left) and n = 30 (right). R / Z are in units of ρ s . Examples of mode evolution: For low/medium mode numbers, such as n = 12, we see global structures, and the presence of multiple coexisting modes. For higher mode numbers, such as n = 30, we see localized structures. Fig. 2 (Upper): n = 12: Evolution of the harmonics of the electrostatic potential (left), spectrogram (middle). We compare these to eigenfunctions obtained from LIGKA (right). Fig. 3 (Lower): n = 30: Evolution of the harmonics of the electrostatic potential (left), spectrogram (middle), obtained from ORB5. (Right), we show a multi-mode nonlinear simulation with 20 ≤ n ≤ 30 allowed in the filter. This simulation was run with 10x the number of markers, and on an annular domain (note that the legend here refers to n). Effect of the electron mass: We expect a dependence of the electron mass on the electron Landau damping. Also a numerical dependence on the permitted timestep as the electrons become lighter (faster). −0.01 −0.005 0 0.005 0.01 0.015 0.02 1000 γ [ω A ] Δt * m i /m e 8000 4557 3200 1600 800 400 200 100 0.477 0.478 0.479 0.48 0.481 0.482 0.483 0.484 0.485 1000 ω [ω A ] Δt * m i /m e 8000 4557 3200 1600 800 400 200 100 -7 -6 -5 -4 -3 -2 -1 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Damping [%] Mass ratio Analytical Numerical Fig. 4: Convergence with the time step of the growth rate (left) and frequency (middle) of the n = 26 TAE (annular domain, 0.2 ≤ s ≤=0.7) for different m i /m e (legends). We see a systematic offset towards an increase in damping for the cases with heavy electrons. (Right) the damping rates from LIGKA (background plasma only) for heavy electrons. TAE linear spectrum: Putting this together, we perform simulations with both full radius and annular (0.2 ≤ s ≤ 0.7) toroidal mode numbers ranging from n = 10 to n = 40. The case of n = 26, annular is as included above in the electron mass/dt study. For that case, we include on the figures also the case with n = 26 with the nominal EP density. For lower n (< 18), we see multiple unstable modes, or the most unstable mode is not the one most strongly initialized, therefore the error on a simple fit for the growth rate is considerable (grey background). * Corresponding author: [email protected] IAEA TM on Energetic Particles (EPPI), Shizuoka City, September 2019 This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement number 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
Transcript of Global electromagnetic gyrokinetic simulations of TAEs in ITER · Global electromagnetic...
Max-Planck-Institut fur Plasmaphysik
Global electromagnetic gyrokinetic simulations of TAEs in ITERT. Hayward-Schneider1*, Ph. Lauber1, A. Bottino1 1Max Planck Institute for Plasma Physics, 85748 Garching, Germany
Motivation
ITER will present a challenge in terms of dealing with significant quantities of fu-sion alpha particles for the first time. Their interaction with Alfvenic instabilitiespresents a challenge for modelling future scenarios.
While the ITER 15MA scenario [1] has received plenty of attention in the past[2-9], the models used to address the problem vary, and have not all agreed.
In this work, we present the application of an initial value global electromagneticgyrokinetic model, using the ORB5 particle-in-cell code [10, 11], to the problemof Toroidal Alfven Eigenmodes (TAEs) in the ITER 15MA scenario.
ITER 15MA Scenario
0
1
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3
4
0 0.5 1
Safe
ty f
act
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(q)
s
0.9
1
1.1
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0 0.2 0.4 0.6
tem
pera
ture
[ke
V]
densi
ty [
10
19m
-3]
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8x1017
1.6x1018
0 0.5 1
dens
ity [m
-3]
Radial position
double
1.5% ne
s=0
~
nominal
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4
Z [m
]
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5.5
6.0
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B [T]Compared to the nominal scenario (above), we makethe following changes:
I Remove steep gradients at the plasma edge(around s>0.9)
I Neglect the trace impurities (He & Be)
I Treat the alpha particles as 900 keV Maxwellianspecies
I Replace 50:50 D:T mix with 2.5H isotope
I Consider double (and nominal) alpha density
Numerical tool: ORB5
“ORB5: a global electromagnetic gyrokinetic code using the PIC approach intoroidal geometry” [11]
I Originally developed at SPC (Switzerland)I now at SPC, IPP (Germany) and Univ. of Warwick (UK)
I Filter applied in toroidal and poloidal mode numbersI m(r) = nq(r)±∆m
I Effectively mitigates with the so-called cancellation problem using thepullback scheme [12] (leads to an order of magn. increase of time step)
I Drift-kinetic, fluid, hybrid, and adiabatic electron models present:I These results all with kinetic (reduced mass ratio) electrons
I Gyrokinetic or drift-kinetic ions (here: bulk gyro-, EPs drift- kinetic)I Previously used for turbulence studies as well as EP physics:
I ITPA-TAE benchmark [13], DIII-D RSAE/TAE benchmark [14]
Numerical parameters:all presented simulations were performed using {32, 128, 32} · 106 markersfor the bulk ions, electrons, and EPs respectively.Full radius simulations used a grid of (1024, 512, 128) in the radial, poloidal,and toroidal directions, (512, 256, 128) for reduced annulus (0.2 – 0.7).For large n (> 30), the poloidal and toroidal grids were increased, for somecases with small n, reduced.Unless otherwise stated, the timestep was 1.875 ω−1
ci . ωci/ωA ∼ 187,ωA ∼ 1.05 × 106 rad s−1.Annular simulations have a cost of ∼ 0.5 core-hr per step, full radius ∼ 0.9.
Results: Radiative damping
If we look at the the subdominant harmonics either side of the mode, shortlyafter initialization, we see radially propagating waves, indicative of KAW (herem=25/28, TAE is m=26/27)
ConclusionsI Global, electromagnetic gyrokinetic code ORB5 applied to TAEs in ITER
15MA scenarioI Robust scenario, only minor modifications to profiles made
I Systematic linear studies for both reduced annulus and full domainsimulations
I Nonlinear, multimode studies begun
[1] A. Polevoi et al. JFR (2002)
[2] N. Gorelenkov et al. PPPL Rep.
(2008)
[3] R. Waltz et al. NF (2014)
[4] S. Pinches et al. POP (2015)
[5] Ph. Lauber PPCF (2015)
[6] M. Schneller et al. PPCF (2015)
[7] P. Rodrigues et al. NF (2015)
[8] M. Fitzgerald et al. NF (2016)
[9] M. Isaev et al. PPR (2017)
[10] S. Jolliet et al. CPC (2007)
[11] E. Lanti et al. CPC (sub.)
[12] A. Mishchenko et al. CPC
(2019)
[13] R. Hatzky et al. NF (2018)
[14] S. Taimourzadeh et al. NF
(2019)
Simulations were performed under the project ORBFAST on the EUROfusion Marconi supercom-puter operated by CINECA and on the Cobra supercomputer of the Max Planck Society, operatedby the MPCDF.
Results: TAE modesExample mode structures: Here we show two global simulation domain examples, run on the full radius (0 ≤ s ≤ 1).
Fig. 1: Snapshots of the electrostatic potential for TAEs with n = 12 (left) and n = 30 (right). R / Z are in units of ρs.
Examples of mode evolution: For low/medium mode numbers, such as n = 12, we see global structures, and thepresence of multiple coexisting modes. For higher mode numbers, such as n = 30, we see localized structures.
0 20000 40000 60000 80000
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0 10000 20000 30000 40000 50000 60000 70000 8000010 8
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n=3028293031
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0 20000 40000 60000 80000 100000 120000 140000
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202122232425
2627282930
Fig. 2 (Upper): n = 12: Evolution of the harmonics of the electrostatic potential (left), spectrogram (middle). We comparethese to eigenfunctions obtained from LIGKA (right).Fig. 3 (Lower): n = 30: Evolution of the harmonics of the electrostatic potential (left), spectrogram (middle), obtainedfrom ORB5. (Right), we show a multi-mode nonlinear simulation with 20 ≤ n ≤ 30 allowed in the filter. This simulationwas run with 10x the number of markers, and on an annular domain (note that the legend here refers to n).
Effect of the electron mass: We expect a dependence of the electron mass on the electron Landau damping. Also anumerical dependence on the permitted timestep as the electrons become lighter (faster).
−0.01
−0.005
0
0.005
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A]
Δt * mi/me
8000455732001600800400200100
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A]
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Dam
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AnalyticalNumerical
Fig. 4: Convergence with the time step of the growth rate (left) and frequency (middle) of the n = 26 TAE (annulardomain, 0.2 ≤ s ≤= 0.7) for different mi/me (legends). We see a systematic offset towards an increase in damping forthe cases with heavy electrons. (Right) the damping rates from LIGKA (background plasma only) for heavy electrons.
TAE linear spectrum:
10 15 20 25 30 35 40n
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[A]
full radiusannulus
10 15 20 25 30 35 40n
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[A]
full radiusannulus
Putting this together, we perform simulations with both full radius and annular (0.2 ≤ s ≤ 0.7) toroidal mode numbersranging from n = 10 to n = 40. The case of n = 26, annular is as included above in the electron mass/dt study. Forthat case, we include on the figures also the case with n = 26 with the nominal EP density. For lower n (< 18), we seemultiple unstable modes, or the most unstable mode is not the one most strongly initialized, therefore the error on a simplefit for the growth rate is considerable (grey background).
* Corresponding author:[email protected]
IAEA TM on Energetic Particles (EPPI),Shizuoka City, September 2019
This work has been carried out within the framework of the EUROfusion Consortium and has received funding fromthe Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement number 633053.The views and opinions expressed herein do not necessarily reflect those of the European Commission.
