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 : 1 H + 1 H → 2 H + 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 : 1 H + 1 H → 2 H + ν + e + Deuterium-tritium (D-T) fusion: 2 H + 3 H → 4 He + 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 : 1 H + 1 H → 2 H + ν + e + Deuterium-tritium (D-T) fusion: 2 H + 3 H → 4 He + 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 10 6 K (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 10 6 K (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 10 6 K (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 10 6 K (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 10 6 K (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 10 6 K (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 10 6 K (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 100 kHz . 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 100 kHz . 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 100 kHz . At the edge, the plasma is colder and electrons and ions can recombine. Recombination and later desexcitation induce visible light emission. Example: electron H α 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 100 kHz . At the edge, the plasma is colder and electrons and ions can recombine. Recombination and later desexcitation induce visible light emission. Example: electron H α 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 100 kHz . At the edge, the plasma is colder and electrons and ions can recombine. Recombination and later desexcitation induce visible light emission. Example: electron H α 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 : S 0 (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 = I 0 + W = KS 0 + 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 = I 0 + W = KS 0 + 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 = I 0 + W = KS 0 + W where W is a Gaussian noise. A classical approach for regulization of inverse problems is the singular value decomposition (SVD): find u i ( 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 = I 0 + W = KS 0 + W where W is a Gaussian noise. A classical approach for regulization of inverse problems is the singular value decomposition (SVD): find u i ( x , y ) in the camera plane, v i ( 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 = I 0 + W = KS 0 + W where W is a Gaussian noise. A classical approach for regulization of inverse problems is the singular value decomposition (SVD): find u i ( x , y ) in the camera plane, v i ( r , θ ) in the poloidal plane, η i positive real numbers, such that K ∗ u i = η i v i Kv i = η i u i R. Nguyen van yen (FU Berlin) Boundary layers and dissipation September 20, 2012 8 / 16