TH/3-1Ra TH/3-1Ra Nonperturbative Effects of Nonperturbative Effects of Energetic Ions on Alfvén EigenmodesEnergetic Ions on Alfvén Eigenmodesby Y. Todo et al. by Y. Todo et al.

EX/5-4RbEX/5-4RbConfiguration Dependence of Energetic Configuration Dependence of Energetic Ion Driven Alfven Eigenmodes in the LIon Driven Alfven Eigenmodes in the Large Helical Devicearge Helical Deviceby S. Yamamoto et al.by S. Yamamoto et al.

Nonperturbative Effects of Nonperturbative Effects of Energetic Ions on Alfvén EigenmodesEnergetic Ions on Alfvén Eigenmodes

Y. Todo, N. Nakajima (NIFS)Y. Todo, N. Nakajima (NIFS)

K. Shinohara, M. Takechi, M. Ishikawa (JAERI)K. Shinohara, M. Takechi, M. Ishikawa (JAERI)

S. Yamamoto (Inst. Adv. Energy, Kyoto Univ.)S. Yamamoto (Inst. Adv. Energy, Kyoto Univ.)

November 1-6, 2004November 1-6, 2004

20th IAEA Fusion Energy Conference20th IAEA Fusion Energy Conference

Vilamoura, PortugalVilamoura, Portugal

TH/3-1Ra

OutlineOutline

Linear properties of an unstable mode in a JT-Linear properties of an unstable mode in a JT-60U plasma were investigated. The unstable 60U plasma were investigated. The unstable mode is a nonlocal energetic particle mode mode is a nonlocal energetic particle mode (EPM). (EPM).

Nonlinear simulation of the frequency Nonlinear simulation of the frequency sweeping of the nonlocal EPM. sweeping of the nonlocal EPM.

Extension of the MEGA code to the helical Extension of the MEGA code to the helical coordinate system. coordinate system.

Fast Frequency Sweeping Mode observed in Fast Frequency Sweeping Mode observed in the JT-60U plasma with NNB injectionthe JT-60U plasma with NNB injection

K. Shinohara et al., Nucl. Fusion 41, 603 (2001).

Frequency sweeping takes place both upward and downward by 10-20kHz in 1-5 ms.

Investigations of the spatial profile and the nonlinear evolution of the unstable mode are needed.

MEGA: a simulation code for MHD and eneMEGA: a simulation code for MHD and energetic particlesrgetic particles

[Y. Todo and T. Sato, [Y. Todo and T. Sato, Phys. Plasmas Phys. Plasmas 55, 1321 (1998), 1321 (1998)]]

1.1. Plasma is divided into “energetic ions” + “MHD fluiPlasma is divided into “energetic ions” + “MHD fluid”.d”.

2.2. Electromagnetic fields are given by MHD equations.Electromagnetic fields are given by MHD equations.

3.3. Energetic ions are described by the drift-kinetic equatiEnergetic ions are described by the drift-kinetic equation.on.

4.4. MHD equilibria consistent with energetic ion distributMHD equilibria consistent with energetic ion distributions are constructed using an extended Grad-Shafranoions are constructed using an extended Grad-Shafranov equation [E.V. Belova et al. Phys. Plasmas 10, 3240 v equation [E.V. Belova et al. Phys. Plasmas 10, 3240 (2003)].(2003)].

Frequency and location of the unstable modeFrequency and location of the unstable mode

Toroidal mode

number n=1

q(0)=1.64

q=2.5 at r/a=0.8

The unstable mode is not located at the TAE gap at r/a=0.8.

This indicates that the unstable mode is not a TAE.

0

0.1

0.2

0.3

0.4

0.5

0.6

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1

ω/ω

A q

/r a

Alfven continuum

q

unstable mode

Energetic ion orbit width broadens the Energetic ion orbit width broadens the spatial width of the unstable modespatial width of the unstable mode

€

ρh /a = 0.08

€

ρh /a = 0.0333

-1 10-4

0 100

1 10-4

2 10-4

3 10-4

0 0.2 0.4 0.6 0.8 1

vr,cos

[a.u.]

r/a

m=2

m=1 m=3

-1 10-4

0 100

1 10-4

2 10-4

3 10-4

0 0.2 0.4 0.6 0.8 1

vr,sin

[a.u.]

r/a

m=2

m=1

m=3

-1 10-6

-5 10-7

0 100

5 10-7

1 10-6

1.5 10-6

2 10-6

2.5 10-6

0 0.2 0.4 0.6 0.8 1

vr,cos

[a.u.]

r/a

m=2

m=1

m=3

-1 10-6

-5 10-7

0 100

5 10-7

1 10-6

1.5 10-6

2 10-6

2.5 10-6

0 0.2 0.4 0.6 0.8 1

vr,sin

[a.u.]

r/a

m=1 m=2

m=3

Effects of the energetic ion orbit widthEffects of the energetic ion orbit width

Peak location and radial width of the unstable mode spatial profile versus energetic ion orbit width.

Growth rate and real frequency of the unstable mode versus energetic ion orbit width.

0

0.05

0.1

0.15

0.2

0.25

0.3

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.02 0.04 0.06 0.08 0.1

rpeak

/a Δr

w/a

ρh/a

0 100

1 10-2

2 10-2

3 10-2

4 10-2

5 10-2

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.02 0.04 0.06 0.08 0.1

γ/ωA

ω/ω

A

ρh/a

Nonlocal Energetic Particle ModeNonlocal Energetic Particle Mode

1. The spatial width of the unstable mode with the smallest orbit width gives an upper limit of the spatial width which the MHD effects alone can induce.

2. For the experimental condition of the JT-60U plasma, the energetic ions broadens the spatial profile of the unstable mode by a factor of 3.

3. The major part of the spatial profile of the unstable mode is induced by the energetic ions.

4. It is concluded that the unstable mode is primarily induced by the energetic ions and the name “nonlocal EPM” can be justified.

Frequency sweeping of the nonlocal EPMFrequency sweeping of the nonlocal EPM(The initial energetic ion beta value is 2/5 of (The initial energetic ion beta value is 2/5 of

the classical distribution.)the classical distribution.)

Left: Time evolution of the cosine part of radial magnetic field. Br, average/B~510-4

Right: Frequency shifts both upward and downward by 9% (~5kHz) in 400 Alfvén time (~0.3ms). Close to the experiment.

-1 10-3

-5 10-4

0 100

5 10-4

1 10-3

0 400 800 1200 1600

B,r cos

/B

ωAt

1.05

1.00

0.95

0.90

ω/ω

140012001000800ωAt

0.9 0.8

0.7

0.7

0.6 0.6

0.6 0.5

0.5

Comparison with the hole-clump pair creation Comparison with the hole-clump pair creation II

ForFor γd/ωA=0.027, γL/ωA=0.040, the hole-clump pair creation theory [H. L. Berk et al., Phys. Lett. A 234, 213 (1997); 2[H. L. Berk et al., Phys. Lett. A 234, 213 (1997); 238, 408(E) (1998)]38, 408(E) (1998)] predicts frequency shift ω=0.44 γL(γdt)1/2=0.018 ωA in 400 Alfvén time. This corresponds to 7% of the real frequency and 4kHz. This is consistent with the simulation results.

This suggests that the hole-clump pair creation causes the fast frequency sweeping in the JT-60U plasma.

Extension of the MEGA Code for Extension of the MEGA Code for Helical Plasmas Helical Plasmas

The interesting experimental results of Alfvén eigenmodes in thThe interesting experimental results of Alfvén eigenmodes in the LHD and CHS plasmas motivate us to extend the MEGA code e LHD and CHS plasmas motivate us to extend the MEGA code for helical plasmas. for helical plasmas.

The MEGA code has been extended to the helical coordinate sysThe MEGA code has been extended to the helical coordinate system (utem (u11,u,u22,u,u33) which is used in the MHD equilibrium code, HIN) which is used in the MHD equilibrium code, HINT. T.

€

h = −1/2

M = 10

R = R0 + u1 cos(hMu 3) + u2sin(hMu3)

z = −[u1sin(hMu3) − u2cos(hMu 3)]

ϕ = −u3

Relation between the Relation between the helical coordinates and helical coordinates and the cylindrical the cylindrical coordinates (R, coordinates (R, , z): , z):

Investigation of a TAE in an LHD-like Investigation of a TAE in an LHD-like plasmaplasma

・ h0=1.3%

・ The initial equilibrium is calculated using the HINT code.

・ TAE with the toroidal mode number n=2

・ω /ωA~0.31, γ/ωA~0.028

-5 10-6

0 100

5 10-6

1 10-5

1.5 10-5

2 10-5

2.5 10-5

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.2 0.4 0.6 0.8 1

iota

r/a

vr/vA

m=5

m=4

m=3

-3 10-5

-2 10-5

-1 10-5

0 100

1 10-5

2 10-5

3 10-5

4 10-5

0 50 100 150

vr,cos

/vA

ωAt

10-7

10-6

10-5

10-4

0 50 100 150

vr/vA

ωAt

SummarySummary TH/3-1RaTH/3-1Ra

A nonlocal EPM exists near the plasma center in the JT-60U plasmA nonlocal EPM exists near the plasma center in the JT-60U plasma. a.

The nonlinear simulation demonstrated that the frequency shifts of The nonlinear simulation demonstrated that the frequency shifts of the nonlocal EPM are close to the experimental results. the nonlocal EPM are close to the experimental results.

The MEGA code has been successfully extended to the helical cooThe MEGA code has been successfully extended to the helical coordinate system. rdinate system.

EX/5-4RbEX/5-4Rb The Alfvén eigenmodes observed in the LHD plasmas were compaThe Alfvén eigenmodes observed in the LHD plasmas were compa

red with the CAS3D3 calculation results.red with the CAS3D3 calculation results. The magnetic shear is the key to control the Alfvén eigenmodesThe magnetic shear is the key to control the Alfvén eigenmodes in in

the LHD plasma. the LHD plasma. This suggests that the continuum damping is the most important daThis suggests that the continuum damping is the most important da

mping mechanism in the LHD plasma. mping mechanism in the LHD plasma. The upper envelope of the fluctuation amplitude scales as <The upper envelope of the fluctuation amplitude scales as <b//b//>>22. .

Configuration Dependence of Energetic Ion Driven AlfvéConfiguration Dependence of Energetic Ion Driven Alfvén Eigenmodes in the Large Helical Devicen Eigenmodes in the Large Helical Device

S. YamamotoS. Yamamoto11, K. Toi, K. Toi22, , N. NakajimaN. Nakajima22, S. Ohdachi, S. Ohdachi22, S. Sakakibara, S. Sakakibara22,,C. NührenbergC. Nührenberg33, K.Y. Watanabe, K.Y. Watanabe22, S. Murakami, S. Murakami44, M. Osakabe, M. Osakabe22, N. Ohyabu, N. Ohyabu22,,

K. KawahataK. Kawahata22, M. Goto, M. Goto22, Y. Takeiri, Y. Takeiri22, K. Tanaka, K. Tanaka22, T. Tokuzawa, T. Tokuzawa22,,K. NariharaK. Narihara22, Y. Narushima, Y. Narushima22, S. Masuzaki, S. Masuzaki22, S. Morita, S. Morita22, I. Yamada, I. Yamada22,,

H. YamadaH. Yamada22, LHD experimental group, LHD experimental group

1) Institute of Advanced Energy, Kyoto University, Uji, Japan2) National Institute for Fusion Science, Toki, Japan3) Max-Planck-Institute für Plasmaphysik, IPP-Euratom Association, Greifswald, Germany4) Graduate School of Engineering, Kyoto University, Kyoto, Japan

20th IAEA Fusion Energy ConferenceNovember 1 ~ 6, 2004Vilamoura, Portugal

EX/5-4Rb

ObjectiveObjective

The energetic ion driven Alfvén eigenmodes such as thThe energetic ion driven Alfvén eigenmodes such as the toroidicity-induced Alfvén eigenmmodes (TAE) and te toroidicity-induced Alfvén eigenmmodes (TAE) and the helicity-induced Alfvén eigenmodes (HAE) are obsehe helicity-induced Alfvén eigenmodes (HAE) are observed in the NBI-heated LHD plasmas. rved in the NBI-heated LHD plasmas.

Clarify the magnetic configuration dependence of AlfvClarify the magnetic configuration dependence of Alfvén eigenmodes. The magnetic configuration is controlleén eigenmodes. The magnetic configuration is controlled by the vacuum magnetic axis position and the plasma d by the vacuum magnetic axis position and the plasma beta value. beta value.

Compare the observed Alfvén eigenmodes with the CACompare the observed Alfvén eigenmodes with the CAS3D3 calculation results. S3D3 calculation results.

Profiles of rotational transform and magnetic shear

Configuration 1:

high magnetic shear

Configuration 2:

middle magnetic shear

Configuration 3:

low magnetic shear

Alfvén eigenmodes in high magnetic shear (configuration 1)

Two bursting Alfvén eigenmodes are observed after t=0.8s.

Dotted and dashed curves denote fTAE(m/n=2,3/1) and fTAE(m/n=3,4/2)

Comparison of the observed frequencies with the eigenmodes calculated using the CAS3D3 code

The n=1 and 2 modes are identified with the core-localized TAE and the global TAE, respectively.

Nf=1

C-TAE

m=2,3

G-TAE

m=3,4,5

Nf=2

Alfvén eigenmodes in middle magnetic shear (configuration 2)

A number of bursting global TAEs with n=2-5 are observed.

An ellipticity-induced Alfvén eigenmode with n=5 (f=125kHz at t=1.5s) is observed.

Comparison of the observed frequencies with the eigenmodes calculated using the CAS3D3 code

The global TAE is localized around the TAE gap: “gap localized TAE”.

Nf=2 Nf=5

Alfvén eigenmodes in low magnetic shear (configuration 3)

A number of bursting global TAEs with n=1-5 are observed.

Appreciable energetic ion transport [EX/P4-44].

Helicity-induced Alfvén eigenmode (f~200kHz at t=1.5s).

Comparison of the observed frequencies with the eigenmode calculated using the CAS3D3 code

The TAE gaps are well aligned due to the low magnetic shear and the large Shafranov shift.

The TAE with n=2 extends from the core to the edge.

Nf=2(n=±2, ±8,.., ± 52)

HAEgap

AE gap frequency: = 1, = 0: (1,0) - TAE = 2, = 1: (2,1) - HAE21

Magnetic fluctuation amplitude versus <b//>

Threshold value in the beam ion beta is lower for the low magnetic shear (right figure) than the high magnetic shear.

The upper envelope of the magnetic fluctuation amplitude scales as <b//> 2 in the left figure. This suggests the wave-particle trapping.

Rax=3.6 m (high magnetic shear) Rax=3.9 m (low magnetic shear)

Threshold <b//> for each toroidal mode number

The threshold <b//> in the low magnetic shear plasma is lower than that in the middle and high magnetic shear plasmas.

The most unstable mode number is n=2.

SummarySummary TH/3-1RaTH/3-1Ra

A nonlocal EPM exists near the plasma center in the JT-60U plasmA nonlocal EPM exists near the plasma center in the JT-60U plasma. a.

The nonlinear simulation demonstrated that the frequency shifts of The nonlinear simulation demonstrated that the frequency shifts of the nonlocal EPM are close to the experimental results. the nonlocal EPM are close to the experimental results.

The MEGA code has been successfully extended to the helical cooThe MEGA code has been successfully extended to the helical coordinate system. rdinate system.

EX/5-4RbEX/5-4Rb The Alfvén eigenmodes observed in the LHD plasmas were compaThe Alfvén eigenmodes observed in the LHD plasmas were compa

red with the CAS3D3 calculation results.red with the CAS3D3 calculation results. The magnetic shear is the key to control the Alfvén eigenmodes in The magnetic shear is the key to control the Alfvén eigenmodes in

the LHD plasma. the LHD plasma. This suggests that the continuum damping is the most important daThis suggests that the continuum damping is the most important da

mping mechanism in the LHD plasma. mping mechanism in the LHD plasma. The upper envelope of the fluctuation amplitude scales as <The upper envelope of the fluctuation amplitude scales as <b//b//>>22. .