Nuclear fusion Light nuclei can react together and form heavier - - PowerPoint PPT Presentation

Nuclear fusion

Light nuclei can react together and form heavier nuclei, for example:

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 2 / 16

Nuclear fusion

Light nuclei can react together and form heavier nuclei, for example:

Proton-proton (H-H) fusion : 1H + 1H → 2H + ν + e+

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 2 / 16

Nuclear fusion

Light nuclei can react together and form heavier nuclei, for example:

Proton-proton (H-H) fusion : 1H + 1H → 2H + ν + e+ Deuterium-tritium (D-T) fusion: 2H + 3H → 4He + n

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 2 / 16

Nuclear fusion

Light nuclei can react together and form heavier nuclei, for example:

Proton-proton (H-H) fusion : 1H + 1H → 2H + ν + e+ Deuterium-tritium (D-T) fusion: 2H + 3H → 4He + n

The nuclei must initially have a lot of kinetic energy to overcome electrostatic repulsion.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 2 / 16

Magnetic confinement

The necessary kinetic energy can be provided by heating to temperatures of order 106K (more than in the center of the Sun).

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 3 / 16

Magnetic confinement

The necessary kinetic energy can be provided by heating to temperatures of order 106K (more than in the center of the Sun). At these temperatures, the matter is a fully ionized plasma.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 3 / 16

Magnetic confinement

The necessary kinetic energy can be provided by heating to temperatures of order 106K (more than in the center of the Sun). At these temperatures, the matter is a fully ionized plasma. To maintain the temperature over a long time, the plasma must be confined.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 3 / 16

Magnetic confinement

The necessary kinetic energy can be provided by heating to temperatures of order 106K (more than in the center of the Sun). At these temperatures, the matter is a fully ionized plasma. To maintain the temperature over a long time, the plasma must be confined. One way to confine it is to use a magnetic fields.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 3 / 16

Magnetic confinement

The necessary kinetic energy can be provided by heating to temperatures of order 106K (more than in the center of the Sun). At these temperatures, the matter is a fully ionized plasma. To maintain the temperature over a long time, the plasma must be confined. One way to confine it is to use a magnetic fields.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 3 / 16

Magnetic confinement

The necessary kinetic energy can be provided by heating to temperatures of order 106K (more than in the center of the Sun). At these temperatures, the matter is a fully ionized plasma. To maintain the temperature over a long time, the plasma must be confined. One way to confine it is to use a magnetic fields.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 3 / 16

Magnetic confinement

The necessary kinetic energy can be provided by heating to temperatures of order 106K (more than in the center of the Sun). At these temperatures, the matter is a fully ionized plasma. To maintain the temperature over a long time, the plasma must be confined. One way to confine it is to use a magnetic fields.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 3 / 16

Edge turbulence and light emission

At the edge of the plasma, there are huge temperature and density gradients.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 5 / 16

Edge turbulence and light emission

At the edge of the plasma, there are huge temperature and density gradients. These gradients drive intense fluctuations in the plasma, which are called edge turbulence. They have frequencies of up to 100kHz.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 5 / 16

Edge turbulence and light emission

At the edge of the plasma, there are huge temperature and density gradients. These gradients drive intense fluctuations in the plasma, which are called edge turbulence. They have frequencies of up to 100kHz. At the edge, the plasma is colder and electrons and ions can recombine.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 5 / 16

Edge turbulence and light emission

At the edge of the plasma, there are huge temperature and density gradients. These gradients drive intense fluctuations in the plasma, which are called edge turbulence. They have frequencies of up to 100kHz. At the edge, the plasma is colder and electrons and ions can recombine. Recombination and later desexcitation induce visible light emission. Example: electron Hα line with λ = 656.3nm.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 5 / 16

Edge turbulence and light emission

At the edge of the plasma, there are huge temperature and density gradients. These gradients drive intense fluctuations in the plasma, which are called edge turbulence. They have frequencies of up to 100kHz. At the edge, the plasma is colder and electrons and ions can recombine. Recombination and later desexcitation induce visible light emission. Example: electron Hα line with λ = 656.3nm. This emitted light can be recorded by a fast camera and analyzed.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 5 / 16

Edge turbulence and light emission

At the edge of the plasma, there are huge temperature and density gradients. These gradients drive intense fluctuations in the plasma, which are called edge turbulence. They have frequencies of up to 100kHz. At the edge, the plasma is colder and electrons and ions can recombine. Recombination and later desexcitation induce visible light emission. Example: electron Hα line with λ = 656.3nm. This emitted light can be recorded by a fast camera and analyzed. Play movie

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 5 / 16

Geometric configuration

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 6 / 16

Geometric configuration

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 6 / 16

Geometric configuration

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 6 / 16

Geometric configuration

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 6 / 16

Geometric configuration

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 6 / 16

Geometric configuration

We have thus defined an integral transformation K : S0(Ψ, θ) → I(x, y).

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 6 / 16

Illustration of the inverse problem

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 7 / 16

Illustration of the inverse problem

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 7 / 16

Illustration of the inverse problem

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 7 / 16

Illustration of the inverse problem

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 7 / 16

Regularization by SVD

Assume that the observed intensity is I = I0 + W = KS0 + W where W is a Gaussian noise.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 8 / 16

Regularization by SVD

Assume that the observed intensity is I = I0 + W = KS0 + W where W is a Gaussian noise. A classical approach for regulization of inverse problems is the singular value decomposition (SVD): find

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 8 / 16

Regularization by SVD

Assume that the observed intensity is I = I0 + W = KS0 + W where W is a Gaussian noise. A classical approach for regulization of inverse problems is the singular value decomposition (SVD): find

ui(x, y) in the camera plane,

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 8 / 16

Regularization by SVD

Assume that the observed intensity is I = I0 + W = KS0 + W where W is a Gaussian noise. A classical approach for regulization of inverse problems is the singular value decomposition (SVD): find

ui(x, y) in the camera plane, vi(r, θ) in the poloidal plane,

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 8 / 16

Regularization by SVD

Assume that the observed intensity is I = I0 + W = KS0 + W where W is a Gaussian noise. A classical approach for regulization of inverse problems is the singular value decomposition (SVD): find

ui(x, y) in the camera plane, vi(r, θ) in the poloidal plane, ηi positive real numbers,

such that K ∗ui = ηivi Kvi = ηiui

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 8 / 16

Regularization by SVD

This implies the reconstruction formula: S =

N0

• i=1

η−1

i

I | uivi

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 9 / 16

Regularization by SVD

This implies the reconstruction formula: S =

N0

• i=1

η−1

i

I | uivi

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 9 / 16

Regularization by SVD

This implies the reconstruction formula: S =

N0

• i=1

η−1

i

I | uivi N0 = 10

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 9 / 16

Regularization by SVD

This implies the reconstruction formula: S =

N0

• i=1

η−1

i

I | uivi N0 = 10

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 9 / 16

Regularization by SVD

This implies the reconstruction formula: S =

N0

• i=1

η−1

i

I | uivi N0 = 160

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 9 / 16

Regularization by SVD

This implies the reconstruction formula: S =

N0

• i=1

η−1

i

I | uivi N0 = 640

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 9 / 16

Regularization by SVD

This implies the reconstruction formula: S =

N0

• i=1

η−1

i

I | uivi N0 = 1089

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 9 / 16

Regularization by SVD

This implies the reconstruction formula: S =

N0

• i=1

η−1

i

I | uivi Problems of SVD :

it is inefficient (computing the decomposition is very expensive), there is no automatic criterion to find the optimal number of modes, the denoised solution is usually too smooth : localized features are lost.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 9 / 16

Wavelet-vaguelette decomposition

Alternative method1 : wavelet-vaguelette decomposition (WVD) K ∗ξλ = κλψλ Kψλ = κλχλ where (ψλ) is an orthogonal wavelet basis in the poloidal plane.

1Tchamitchian ’87, Donoho ’92

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 10 / 16

Wavelet-vaguelette decomposition

Alternative method1 : wavelet-vaguelette decomposition (WVD) K ∗ξλ = κλψλ Kψλ = κλχλ where (ψλ) is an orthogonal wavelet basis in the poloidal plane.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 10 / 16

Wavelet-vaguelette decomposition

Alternative method1 : wavelet-vaguelette decomposition (WVD) K ∗ξλ = κλψλ Kψλ = κλχλ where (ψλ) is an orthogonal wavelet basis in the poloidal plane. This leads to the reconstruction formula: S =

• λ∈Λ

κ−1

λ I | ξλψλ

Denoising can be achieved by thresholding of wavelet coefficients: SWVD =

• λ∈Λ

ρΘ(|I | ξλ|)κ−1

λ I | ξλψλ

1Tchamitchian ’87, Donoho ’92

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 10 / 16

Threshold selection procedure

Since W is a Gaussian white noise, its vaguelette coefficients are Gaussian and identically distributed.

2Azzalini,Farge,Schneider ’04

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 11 / 16

Threshold selection procedure

Since W is a Gaussian white noise, its vaguelette coefficients are Gaussian and identically distributed. Apply wavelet denoising philosophy: the vaguelette coefficients of the noise are close to zero, while the vaguelette coefficients of the signal are large.

2Azzalini,Farge,Schneider ’04

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 11 / 16

Threshold selection procedure

Since W is a Gaussian white noise, its vaguelette coefficients are Gaussian and identically distributed. Apply wavelet denoising philosophy: the vaguelette coefficients of the noise are close to zero, while the vaguelette coefficients of the signal are large. The threshold can be determined by the criterion2: Θ = cσI(Θ), where σI(Θ) is the standard deviation of the vaguelette coefficients which are in [−Θ, Θ].

2Azzalini,Farge,Schneider ’04

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 11 / 16

Results

Let us apply WVD to our academic example.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 12 / 16

Results

Let us apply WVD to our academic example.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 12 / 16

Results

Let us apply WVD to our academic example.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 12 / 16

Results

Let us apply WVD to our academic example.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 12 / 16

Results

Let us apply WVD to our academic example. We obtain good denoising and preserve the sharp features of the image.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 12 / 16

Application to Tore Supra movie

First the geometry of the camera is determined: this is done by detecting keypoints of the vessel on the full movie.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 13 / 16

Application to Tore Supra movie

First the geometry of the camera is determined: this is done by detecting keypoints of the vessel on the full movie. Then the magnetic field geometry is reconstructed from the parameters of the experiment using specific software.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 13 / 16

Application to Tore Supra movie

First the geometry of the camera is determined: this is done by detecting keypoints of the vessel on the full movie. Then the magnetic field geometry is reconstructed from the parameters of the experiment using specific software. The matrix of the operator K can then be constructed, and then the vaguelettes.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 13 / 16

Application to Tore Supra movie

First the geometry of the camera is determined: this is done by detecting keypoints of the vessel on the full movie. Then the magnetic field geometry is reconstructed from the parameters of the experiment using specific software. The matrix of the operator K can then be constructed, and then the vaguelettes. Finally, the WVD inversion procedure is applied to all frames of the movie.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 13 / 16

Application to Tore Supra movie

First the geometry of the camera is determined: this is done by detecting keypoints of the vessel on the full movie. Then the magnetic field geometry is reconstructed from the parameters of the experiment using specific software. The matrix of the operator K can then be constructed, and then the vaguelettes. Finally, the WVD inversion procedure is applied to all frames of the movie. Play movie

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 13 / 16

Results

Let us apply WVD to our academic example.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 14 / 16

Results

Let us apply WVD to our academic example.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 14 / 16

Results

Let us apply WVD to our academic example.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 14 / 16

Results

Let us apply WVD to our academic example.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 14 / 16

Results

Let us apply WVD to our academic example. We obtain good denoising and preserve the sharp features of the image.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 14 / 16

Summary and conclusion

We have demonstrated a new method to reconstruct light emissivity in the edge of turbulent tokamak plasmas,

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 15 / 16

Summary and conclusion

We have demonstrated a new method to reconstruct light emissivity in the edge of turbulent tokamak plasmas, This could be an important diagnostic in the future for controlling long discharges.

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 15 / 16

Summary and conclusion

We have demonstrated a new method to reconstruct light emissivity in the edge of turbulent tokamak plasmas, This could be an important diagnostic in the future for controlling long discharges. The C++ code is open source and available on demand (rnguyen@math.fu-berlin.de).

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 15 / 16

Summary and conclusion

We have demonstrated a new method to reconstruct light emissivity in the edge of turbulent tokamak plasmas, This could be an important diagnostic in the future for controlling long discharges. The C++ code is open source and available on demand (rnguyen@math.fu-berlin.de). The method still needs to be validated against independent diagnostics,

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 15 / 16

Summary and conclusion

We have demonstrated a new method to reconstruct light emissivity in the edge of turbulent tokamak plasmas, This could be an important diagnostic in the future for controlling long discharges. The C++ code is open source and available on demand (rnguyen@math.fu-berlin.de). The method still needs to be validated against independent diagnostics, Reference: RNVY, N. Fedorczak, F. Brochard, K. Schneider, M. Farge and P. Monier-Garbet, Nuclear Fusion, 52, 013005 (2011)

• R. Nguyen van yen (FU Berlin)

Boundary layers and dissipation September 20, 2012 15 / 16