simulation study of kinetic effects on plasma coherent ... · simulation study of kinetic effects...

Simulation Study of Kinetic Effectson Plasma Coherent Structures

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November 23, 2013

Hiroki Hasegawa1, 2 and Seiji Ishiguro1, 2

1Fundamental Physics Simulation Research Division, Department of Helical Plasma Research, National Institute for Fusion Science (NIFS)

2Department of Fusion Science, The Graduate University for Advanced Studies (Sokendai)

JIFT Workshop 2013- New Aspects of Plasma Kinetic Simulation -

- Aim at Holistic Simulation of Fusion Peripheral Plasma -

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Presentation Outline

1. Introduction> Holistic Simulation (Macro-Micro Interlocked (MMI) Algorithm)> Aim at Application to Fusion Peripheral Plasma Research> Plasma Blob

2. Simulation Model

3. Simulation Results> Effect of Larmor radius> Particle Flows in a Blob

4. Summary and Future Works

1. Introduction

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Also, if we would like to study drastic phenomena (ex. shock waves, phase transformation, burst, etc.)by macroscopic simulations, the assumption of some models or the parameterization are needed.

In macro layer simulations, control or adjustable parameters(which are mostly empirical) are generally included.

On the other hand, the whole system simulations based on the first principles without empirical assumptions is impossible.

How do we realize an integrated predictive modeling?

1-1. Holistic Simulation

Macro layer

Micro layer


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T. Sato, J. Phys.: Conf. Ser. 16, 310 (2005).

Macro-Micro Interlocked (MMI) Algorithm [1]

Macro layer

Micro layer


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T. Sato, J. Phys.: Conf. Ser. 16, 310 (2005).

Active domain

Macro-Micro Interlocked (MMI) Algorithm [1]

Applications

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Adaptive Mesh Refinement(AMR) Method

MHD simulation+ PIC simulation

Friction Dynamics

Holistic Climate Model

http://www-nsrp.nifs.ac.jp/activity/activity08.html

K. Watanabe et al., JAMSTEC Rep. Res. Dev. 9(1), 75 (2009).

http://www.jamstec.go.jp/esc/projects/fy2008/17-kusano.pdfK. Watanabe et al., JAMSTEC Rep. Res. Dev. 9(1), 75 (2009).


Condensed Matter Physics

http://locs.bw.nitech.ac.jp/mediawiki/index.php

Application to Auroral Arc Formation

Downward electrons are strongly energized to produce excitation of ionospheric molecules. The ionospheric density is also strongly modulated by the local enhancement of ionization, which in turn changes the evolution of the magnetosphere-ionosphere current system.

The twin plasma convection flow generated in the vicinity of the magnetosphericequator by the solar wind is expected to induce the region 1 current system [2].

[2] T. Iijima and T. A. Potemra, J. Geophys. Res., 81, 2165, 1976.

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These pictures are reprinted from“http://www.jamstec.go.jp/less/space_earth/ja/research-introduction/auroral.html”.


Simulation Model

T. Sato, H. Hasegawa, and N. Ohno, Comput. Sci. Disc. 2, 015007 (2009).H. Hasegawa, N. Ohno, and T. Sato, Plasma Fusion Res. 6, 2401128 (2011).H. Hasegawa, N. Ohno, and T. Sato, NAGARE (J. Jpn. Soc. Fluid Mech.) 30(5), 401 (2011) (in Japanese). 7


> Using the MMI code, we have been enabled to obtain the 3D-distribution dataof the auroral emission intensity.

> Visualize the auroral lights by the special volume rendering methodfor large-scale.

Sight from the ground. Sight from the high altitude.

N. Ohno, H. Hasegawa, and T. Sato, IEEE Trans. Plasma Sci. 39, 2708 (2011).


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Auroral Emission

1-2. Aim at Application to Fusion Peripheral Plasma Research

Which of regions in fusion plasma needs a holistic simulations?

Peripheral region in fusion plasma needs a holistic simulationbecause the peripheral plasma dynamics consists of multi-physics;physics described by fluid equations, sheath formation, atomic and molecular processes between ionized and neutral particles, and PWI, etc...

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Many theoretical and numerical studies of blobs have been performed on the basis of two-dimensional reduced fluid models.

However, closures for 𝐽∥ and kinetic effects, such as sheath formation between a SOL plasma and a divertor plate and velocity difference between ions and electronsare treated under some assumptions and parameterization in such a kind of macroscopic model.

With a three dimensional electrostatic plasma particle code, we study blob dynamics including self-consistent kinetic effects.

First Step toward Our Aim

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As first step toward our aim, we focus on blob dynamics in the peripheral plasma.And then, before developing the holistic model of blob simulation, we study the blob dynamics with the particle simulation model.

Because...

Plasma Transport in Scrape-Off Layer （SOL）

CorePlasma

SOL

Divertor

Divertor

X pointSeparatrix

Private Region

First Wall

In SOL, it was believed that the parallel diffusive plasma transport becomes more important than the radial transport.

Assuming that the radial transport is diffusive, the radial density distribution is given by

Thus,

where

−d

d𝑟𝐷⊥

d𝑛

d𝑟=𝑛𝑐s𝐿∥

.

𝑛 𝑟 = 𝑛 0 exp −𝑟

𝜆,

𝜆 =𝐷⊥𝐿∥𝑐s

1/2

In a typical tokamak device, l is a few centimeter.

𝑐s =𝑘B𝑇

𝑚i

1/2

1-3. Plasma Blob

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But it is reported that the density profile in the far SOL is flatter than the exponential distributionin recent experiments.M.V. Umansky et al., “Comments on particle and energy balance in the edge plasma of Alcator C-Mod”, Phys. Plasmas 5, 3373 (1998).

1-3. Plasma Blob

Such a density profile is not explained by only a diffusive mechanism.A study by a fluid simulation suggested that the radial transport in the SOL is more convective.A. Yu. Pigarov et al., “Tokamak edge plasma simulation including anomalous cross-field convective transport”,

Phys. Plasma 9, 1287 (2002).

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A theory of plasma blob dynamics was suggested as the mechanism of the convective radial transport.S. Krasheninnikov, “On scrape off layer plasma transport”, Phys. Lett. A 283, 368 (2001).

・Plasma filaments along the magnetic field line

・The curvature drift or grad-B drift induce a vertical charge polarization in such a coherent structure.

・The electric field induced by the charge polarization results in an outwards ExB drift.

S. I. Krasheninnikov, D. A. D’Ippolito, and J. R. Myra, “Recent theoretical progress in understanding coherent structures in edge and SOL turbulence”,

J. Plasma Phys., 74 (5), 679–717 (2008).

＋＋＋

－－－

First Wall

Blob

Magnetic Field

ElectricField

Plasma Blob

1-3. Plasma Blob

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zAt the boundary x = 0, particles are absorbed.

y B ∇B

Lz0

x

Periodic boundary condition is applied in the y and z directions.

x : the radial direction, x = 0 : the first wally : the poloidal directionz : the toroidal direction

𝐵 =2𝐿𝑥

3𝐿𝑥 − 𝑥𝐵0

Periodic Boundary Case

2. Simulation Model

We have developed the three-dimensional electrostatic particle simulation code with particle absorbing boundaries.

[6] S. Ishiguro and H. Hasegawa, “Three-dimensional particle-in-cell simulation of scrape-off-layer plasmas”, J. Plasma Phys. 72, 1233 (2006).

Blob

First Wall

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zAt the boundary x = 0 and z = 0, Lz , particles are absorbed.

y B ∇B

Lz0

x

Periodic boundary condition is applied in the y direction.

x : the radial direction, x = 0 : the first wally : the poloidal directionz : the toroidal direction, both ends correspond to divertor plates.

𝐵 =2𝐿𝑥

3𝐿𝑥 − 𝑥𝐵0

Absorbing Boundary Case

Blob

End PlateEnd Plate

First Wall

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2. Simulation Model

We have developed the three-dimensional electrostatic particle simulation code with particle absorbing boundaries.

[6] S. Ishiguro and H. Hasegawa, “Three-dimensional particle-in-cell simulation of scrape-off-layer plasmas”, J. Plasma Phys. 72, 1233 (2006).

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Electron density distribution in the x-y plane (Periodic Boundary Case):

3-1. Effect of Larmor Radius

|We|/ wpe = 10

|We|/ wpe = 1

3. Simulation Results

Ti/ Te = 0.25

Ti/ Te = 1

Ti/ Te = 4

Ti/ Te = 0.25

|We|/ wpe = 10

|We|/ wpe = 10

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|We|/ wpe = 10

|We|/ wpe = 1

Ti/ Te = 0.25

Ti/ Te = 1

Ti/ Te = 4

Ti/ Te = 0.25

|We|/ wpe = 10

|We|/ wpe = 10

Electric potential distribution in the x-y plane (Periodic Boundary Case):

3-1. Effect of Larmor Radius

3. Simulation Results

The y component of the electric currentat z / lDe = 128.

The z component of the electric current

Schematic diagram of the current system in a blob

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We have found the spontaneous electric current system in a blob.

J||

J||

J⊥∇B3-2. Particle Flows in a Blob

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3-2. Particle Flows in a Blob

The y component of the electric currentat z / lDe = 128.

The z component of the electric current

J||

J||

J⊥∇B

We have found the spontaneous electric current system in a blob.

The maximum value of observed parallel (toroidal) current density is 𝐽∥ ≈ 0.7 𝑛0𝑒𝑐s.

Stream lines of the current in a blob

Velocity Distributions of Electron flows

vez/vTe

z

y

B

∇B

Lz

0 xLx

Ly

z/le = 248 ~ 256

z/le = 124 ~ 132

z/le = 0 ~ 83-2. Particle Flows in a Blob

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Velocity Distributions of Ion flows

z

y

B

∇B

Lz

0 xLx

Ly

wpet = 600

wpet = 100

3-2. Particle Flows in a Blob

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We have developed a three dimensional electrostatic particle code to study blob dynamics including kinetic effects.

We then showed results of simulations.

When the end plates which correspond to divertor plates are placed in both ends in the toroidal direction, the spontaneous electric current system in a blob has been found.

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Future works

Optimize the code to apply it to a huge system size. Develop the code including the collision process.

> study the effect of the drift wave instability.

Develop a multi-scale and multi-physics simulation code for the blob dynamics with the macro-micro interlocked (MMI) algorithm.

Investigate the effect of kinetic dynamics:> Shear flow by a non-uniform sheath profile, etc...

J. R. Angus, M. V. Umansky, and S. I. Krasheninnikov, Phys. Rev. Lett. 108, 215002 (2012).etc.

S. I. Krasheninnikov et al., Phys. Plasmas 4, 1638 (1997).O. V. Batishchev et al., Phys. Plasmas 4, 1672 (1997).S. Nakazawa et al., Plasma Phys. Control. Fusion 42, 401 (2000).B. L. Stansfield et al., J. Nucl. Mater. 241–243, 739 (1997). N. Ohno et al., J. Plasma Fusion Res. 80, 275 (2004).H. Tanaka et al., Phys. Plasmas 17, 102509 (2010).etc.

The end plate short-circuits the vertical charge polarization in a blob.

However, the sheath potential sustains the potential difference in a blob.

Study the effect of kinetic dynamics on detached plasma process.

The detached divertor plasma disturbs short circuit.

simulation study of kinetic effects on plasma coherent ... · simulation study of kinetic effects...

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