1. Reduction of ELM energy loss by pellet injection for ELM pacing
TH/5-3
Reduction of ELM energy loss by
pellet injection for ELM pacing
Thank you, Mr. Chairman.
I would like to talk about the reduction of ELM energy loss by pellet injection for ELM pacing.
N. Hayashi1, N. Aiba1, T. Takizuka2, N. Oyama1
1 JAEA, 2 Osaka univ.

2. Introduction
2/15
Pellet injection is considered as one possible method to reduce ELM energy loss by increasing ELM frequency (ELM pacing).
ELM pacing by pellet requires,
(1) Significant reduction of ELM energy loss
(2) Small impact on plasma performance
(3) Less particle fueling
Pellet injection is considered as one possible method to reduce ELM energy loss by increasing ELM frequency, so called ELM pacing. ELM pacing by pellet requires reduction of ELM energy loss, small impact on target plasma, ex. we do not want to reduce the pedestal pressure, and less particle fueling, we have to repeat the pellet injection for ELM pacing and thus have to use smallest pellet not to change much density profile produced by other fueling methods. Purpose of this paper is to do integrated simulations by TOPICS-IB with various parameters, pellet injection location, timing, size and speed, to study the reduction of ELM energy loss by a pellet and to examine suitable conditions of pellet injection for ELM pacing.
Purpose of this paper
Integrated simulations by TOPICS-IB with various parameters
(pellet injection location, timing, size and speed)
- Study reduction of ELM energy loss by pellet
- Examine suitable conditions of pellet injection for ELM pacing

3. Pedestal modeling in TOPICS-IB
3/15
Ablated pellet with ExB drift (APLEX) model
Ablation, energy absorption, ExB drift, homogenization
Background
plasma profile
Energy loss
Particle & energy sources
Particle
escaping
from core
Hayashi
NF11
1.5D core transport
( TOPICS )
Core neutrals
(2D Monte-Calro)
Diffusivities enhanced on the basis of eigenfunction profile
Here I explain pedestal modeling in TOPICS-IB. TOPICS-IB is based on 1.5D transport code TOPICS extended to integrated simulation for burning plasmas. TOPICS is coupled with an linear MHD stability code MARG2D. Stability of toroidal mode number n from 1 to 50 modes is checked in this study. This ELM model enhances diffusivities in TOPICS on the basis of eigenfunctions. TOPICS is also coupled with the SOL-divertor model named the dynamics five-point model and based on integral fluid equations. We also integrate neutral code/model in the core and SOL-divertor regions for density dynamics. This ELM version of TOPICS-IB could reproduced experimentally observed dependence of ELM energy loss on collisionality and pressure gradient inside pedestal top. For pellet triggered ELM, we have further coupled ablated pellet with ExB drift (APLEX) model. This model treats with pellet ablation for background plasma profile, energy absorption leading to energy loss in background plasma, ExB drift of detached pellet plasma cloud and its homogenization resulting in particle and energy sources in background plasma. The particle escaping from core region is used as source for SOL-divertor neutral model.
ELM model
Hayashi
NF09
Linear MHD stability
( MARG2D )
SOL-divertor
(D5PM)
SOL-div.
neutral model
n=1-50 modes checked in this study
ELM version of TOPICS-IB could reproduce experimentally observed dependence of ELM energy loss on collisionality & pressure gradient inside pedestal top.

4. Integrated simulation results by TOPICS-IB
4/15
Integrated simulation results by TOPICS-IB
Let me show integrated simulation results by TOPICS-IB

5. Reference natural ELMs for pellet injection
5/15
- Pellet injectors: HFS & LFS
- 3 timings chosen for pellet injection
A: early, B: middle, C: late
- Simulation with JT-60U parameters
Prescribed anomalous diffusivity
Neoclassical diffusivity in given pedestal width
ΔWELM ~ 0.06 MJ
Wped ~ 1 MJ
ΔWELM/Wped ~ 0.06
At first, I show simulation of reference natural ELMs for pellet injection with JT-60U parameters. These figures show time evolution of stored energy in one ELM cycle with time period of 26ms, and profile of total pressure at ELM onset. Here is pedestal top, we apply prescribed anomalous diffusivity inside the pedestal top and neoclassical diffusivity in given pedestal width. These figures show profiles of total pressure at ELM onset and just after ELM, and enhanced diffusivity during each ELM. Intermediate-n, n nearly equal to 20 mode becomes unstable and diffusivity based on square of eigenfunction is enhanced in whole pedestal during 0.2ms. ELM energy loss is about 6% of pedestal stored energy. We use pellet injectors at HFS and LFS, and chose 3 timings for pellet injection, A early , B middle, C late timings. dt is elapsed time from previous natural ELM and the value normalized by cycle period are shown. Pedestal pressure normalized by the maximum value at ELM onset is about 85% for A, 95% for B and 99% for C.
Intermediate-n (n ~ 20)
unstable
Diffusivity enhanced
in whole pedestal

6. ELM triggering by pellet energy absorption
6/15
ELM triggering by pellet energy absorption
Mechanism:
HFS injection at early timing A
(1) Pellet cloud absorbs background plasma energy. ExB drift shifts heated cloud inward for HFS pellet (or outward for LFS pellet) & deposits its energy in other region
Pellet size rp=0.6mm, speed vp=120m/s
Hayashi NF11
n≥31
unstable
(2) Modify background plasma profile & produce a local region with steeper pressure gradient, triggering an ELM
Mode number and eigenfunction depend on pellet injection location, timing, size and speed.
Right case: Narrow eigenfunction compared with natural ELM, leading to small loss
ELM can be triggered by pellet energy absorption as found in previous IAEA, and its mechanism is explained as follows. These figures show profiles of total background pressure, normalized pressure gradient and diffusivity just before HFS pellet injection at early timing A with these pellet size and speed. At first, pellet cloud absorbs background plasma energy, then ExB drift shifts the heated cloud inward for HFS pellet or outward for LFS pellet, and deposits its energy in other region, then modify background plasma profile and produce a local region with steeper pressure gradient, this triggering an ELM. Vertical dotted line denotes pellet position at ELM onset. In this case, mode number is higher than natural ELM and eigenfucntion is narrow compared with natural ELM, leading to small loss. Mode number and eigenfunction depend on pellet injection location, timing, size and speed.

7. Dependence of ELM energy loss on pellet injection timing
7/15
Dependence of ELM energy loss on pellet injection timing
We study dependence of ELM energy loss on pellet injection timing.

8. Middle timing in natural ELM cycle is suitable to pellet injection for ELM pacing.
8/15
Earlier timing → Smaller energy loss
Late timing → Large energy loss (no merit)
- Higher-n modes with localized
eigenfunctions near pedestal top
- Temporal decrease in BS current
→ magnetic shear increase
→ prevent lower-n modes
- BUT, reduction of pedestal pressure
Energy loss vs
elapsed time from previous natural ELM
These figures show stored energy evolution in one natural ELM cycle and normalized ELM energy loss as a function of normalized elapsed time from previous natural ELM. These black triangles denote energy loss of natural ELMs. We obtained energy losses induced by LFS and HFS pellet with fixed size and speed for each injection timing. We will start ELM pacing from each timing as shown here. At late timing, large energy loss comparable to the natural ELM. Early timing, small energy loss because pellet triggers higher-n modes with localized eigenfunctions near the pedestal top. Temporal decrease in bootstrap current leads to magnetic shear increases and this prevents the onset of lower-n modes. But, early timing, however, leads to the reduction of target pedestal pressure. We also obtained pellet induced energy loss for various pellet size and speed. For different size or speed, small energy loss in the middle timing B. As a result, middle timing in natural ELM cycle is suitable to pellet injection for ELM pacing.
Different size or speed
→ Small energy loss in middle timing

9. Pellet size & speed dependence of ELM energy loss
9/15
Pellet size & speed dependence of ELM energy loss
Suitable conditions for ELM pacing by pellet
We found middle injection timing in natural ELM cycle is suitable for ELM pacing. We next study pellet size and speed dependence of ELM energy loss at middle injection timing.
Injection timing in
natural ELM cycle
early middle late

10. Energy loss can be significantly reduced by
LFS small pellet.
10/15
ELM energy loss vs pellet radius
At middle timing,
Size variation with fixed speed
LFS smaller pellet → Smaller energy loss
HFS smaller pellet → Larger energy loss
At middle timing, we vary pellet size with fixed speed. This figure shows the dependence of ELM energy loss on the pellet radius of HFS and LFS pellet, this line denotes the energy loss level of natural ELM. This open symbol denote pellet size not to trigger ELM. LFS small pellet leads to small energy loss. On the other hand, HFS small pellet, large energy loss. This figure shows ELM enhanced diffusivity profiles for LFS and HFS pellet in this size. This vertical dotted line indicates pedestal top position. ExB drift of pellet cloud produces narrow pressure perturbation for LFS small pellet, or wide perturbation for HFS small pellet, resulting in the difference of eigenfunction profile as shown in this figure. As a result, energy loss can be significantly reduced by a LFS small pellet.
ExB drift of pellet cloud produces
Narrow perturbation for LFS small pellet or
Wide perturbation for HFS small pellet
→ Difference of eigenfunction profile

11. Fast LHS pellet approaching pedestal top can significantly reduce ELM energy loss.
11/15
ELM energy loss vs pellet speed
With LFS small pellet at middle timing,
Speed variation with fixed size
Faster pellet → Smaller energy loss
BUT, Faster pellet penetrating deeper into pedestal & Smaller ELM
→ Increase in core particle fueling
→ Only slight increase in core density,
even for fast speed enough to
approach pedestal top
Pellet ablation depth &
Core density increase
With LFS pellet at middle timing, we vary pellet speed with fixed size. This figure shows dependence of ELM energy loss on the pellet speed. Faster pellet leads to smaller energy loss. But, faster pellet penetrating deeper into core and smaller ELM leads to increase in core particle fueling. This figure shows pellet ablation depth, closed circles, and core density increase, open circles, as a function of pellet speed. Here is pedestal top depth. But, as shown in this region, only slight increase in core density even for fast enough to approach pedestal top. As a result, fast LFS pellet reduces ELM energy loss.

12. Requirements for reduction of ELM energy loss
12/15
Requirements for reduction of ELM energy loss
From simulation results with various parameters (pellet injection location, timing, size and speed)
Suitable conditions for ELM pacing by pellet
From simulation results with various parameters, pellet injection location, timing, size and speed, we study requirements for reduction of ELM energy loss. Up to now, we found these suitable conditions for ELM pacing, middle timing, LFS, fast enough speed to approach pedestal top.
Injection timing in
natural ELM cycle
early middle late
Pellet injection location
LFS HFS
fast enough to approach pedestal top
Pellet speed

13. ELM triggering by pellet at deep position results in significant reduction of ELM energy loss.
13/15
ELM energy loss & unstable mode location vs pellet position at ELM onset
Triggering at deep position
→ Small energy loss
High-n ballooning modes with
localized eigenfunctions near
pedestal top
High-n
Triggering at shallow position
→ Large energy loss
Intermediate-n modes with wide
eigenfunctions
Intermediate-n
This figure shows ELM energy loss as a function of pellet position at ELM onset for the suitable conditions, LHS small pellet at middle timing. This horizontal bar is mode location. Vertical dotted line denotes pedestal top position and horizontal line energy loss of natural ELM. ELM triggering at deep position leads to small energy loss because of high-n ballooning modes with localized eigenfunctions near pedestal top. Triggering at shallow position leads to large energy loss because of lower-n modes with wide eigenfunctions. I add the other data for various parameters. We can confirm ELM triggering by pellet deep position results in significant reduction of ELM energy loss. With most suitable conditions, here, we repeat pellet injection.
Repeat pellet !

14. Continuous pellet simulation with most suitable conditions
14/15
fdpump : Pumping fraction of total particle
flux to divertor plate
Core density increase due to particle fueling by pellet can be compensated by reducing gas puff and enhancing divertor pumping.
Collapse profile
at each ELM
triggered by pellet
ΔWELM reduction : 1/4.5
fELM increase : x 3.3
pellet particle fueling ~ gas puff
ELM frequency increase can be mitigated by pedestal neoclassical transport (∝ n/T1/2) with transient density increase by pellet.
These figures show time evolution of stored energy and volume-averaged core density for natural ELMs. Core density increases. In the simulation model, pumping fraction of total particle flux to divertor plate is set to 0.1%. LFS pellet starts from this middle timing of natural ELM cycle with gas puff switched off and enhancing the divertor pumping to 1%. Each pellet triggers almost the same mode and collapse profile at each ELM triggered by pellet is shown in this figure, pressure profiles at pellet injection and just after ELM. Core density increase is comparable to case of natural ELMs. This indicates core density increase due to particle fueling by pellet can be compensated by reducing gas puff and enhancing divertor pumping. ELM energy loss reduction is 1 over 4.5, but ELM frequency increase by 3.3 times and pellet particle fueling is almost the same gas puff switched off at pellet start. The ELM frequency increase estimated by energy reduction is 4.5, but larger than obtained value 3.3. ELM frequency increase can be mitigated by pedestal neoclassical transport, proportional to density and inversely proportional to square root of temperature, with transient density increase by pellet. We successfully demonstrated continuous pellet injection with most suitable conditions.

15. Conclusion Integrated code TOPICS-IB predicts,
15/15
Integrated code TOPICS-IB predicts,
Small pellet significantly reduces ELM energy loss
By penetrating deeply into pedestal and triggering high-n modes with localized eigenfunctions near pedestal top,
With following conditions ;
Injection timing in natural ELM cycle (target Pped/Pped,max)
early middle late
(~ 85% ~ 95% ~ 99%)
Pellet injection location
Finally, I would like to conclude my talk.
LFS HFS
fast enough to approach pedestal top
Pellet speed
The above conditions lead to small impact on plasma performance & less particle fueling, and thus are suitable for ELM pacing by pellet.

16. Future works - ITER simulation
Evaluate pellet size to reduce ELM energy loss
Study ELM pacing consistent with other particle fueling for the target density profile
- Model improvement
Pedestal model (time evolution of width)
- Sensitivity study
Simulations with other sets of parameters and the other triggering mechanism (pellet transport enhancement)
- Comparison with experiments and nonlinear MHD simulations
Trigger timing, energy loss, mode number etc.