STUDY OF MAGNETIC RECONNECTION PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA Yacopo Damizia
Purpose » Tokamak Device » Proto-Sphera Experiment » System Layout Cameras » Implementation optical tomography » Mathematical basis » Algorithm test » Applications » Conclusion STUDY OF MAGNETIC RECONNECTION 25/11/2019 Pagina 2 PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA
Tokamak Device • Magnetic Confinement Machine. • Toroidal shaped. • Realize the magnetic confinement of plasma isolating it from the walls of the toroidal vacuum container thanks to the particular structure of the magnetic field created. • Principal Components: Central transformer Toroidal field coils STUDY OF MAGNETIC RECONNECTION 25/11/2019 Pagina 3 PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA
PROTO-SPHERA • Magnetic Confinement Machine • Class of Compact Toroids • Is dedicated to demonstrating the feasibility of a spherical torus, where the central conductor pole is replaced by a plasma current discharge. • Principal Components: Vacuum vessel in PMMA, Poloidal field coil (INT and EXT) Anode and Cathode • Vacuum Vessel dimensions are 1.7m in height, 2.0m • The plasma arc inside the machine is produced by two electrodes, anode and cathode • The PF coils are located very close to the plasma • The design is as simple as possible, easily assembled, good access. STUDY OF MAGNETIC RECONNECTION 25/11/2019 Pagina 4 PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA
Layout Fast Cameras • The picture on the side shows a 3D representation of the vessel with the cameras positions and their view lines. • Is use six (Basler USB 3.0 600 fps) fast cameras spaced of 60 degree around PROTO-SPHERA. • Two PCs equipped with two dedicated USB3 controllers manage the cameras, three for each of them. • Arduino Nano generates the pulse train for the frames acquisition. By varying the pulses duty cycle allows to control the exposure time for each frame. • The acquisition system was implemented using MARTe2 framework STUDY OF MAGNETIC RECONNECTION 25/11/2019 Pagina 5 PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA
Mathematical basis of Zernike Polynomials • The Zernike polynomials are a complete set of polynomials, that are continuous and orthogonal over a unit circle ( 0 ≤ 𝑠 ≤ 1) . • A large fraction of optical systems in use today employ imaging elements and circular pupils. • Zernike polynomials gives a mathematical description of optical wavefronts propagating through such systems. • There are odd and even Zernike polynomials. Even polynomials are defined as: 𝑛 𝑠, 𝜄 = 𝑆 𝑜 𝑛 𝑠 cos 𝑛𝜄 𝑎 𝑜 −𝑛 𝑠, 𝜄 = 𝑆 𝑜 𝑛 𝑠 sin 𝑛𝜄 𝑎 𝑜 𝑛 𝑠 , is described by: • The radial function 𝑆 𝑜 −1 𝑚 𝑜−𝑚 ! 𝑛 𝑠 = σ 𝑚=0 (𝑜−𝑛)/2 1 2 𝑜−𝑛 −𝑚 ! 𝑠 𝑜−2𝑚 𝑆 𝑜 1 2 𝑜+𝑛 −𝑚 ! Τ 𝑚! Τ STUDY OF MAGNETIC RECONNECTION 25/11/2019 Pagina 6 PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA
Zernike Polynomials application to tomography • These polynomials are a good basis for comparing the point quantities (ρ, η) defined on a unitary circle (in cylindrical coordinate’s (𝜍, 𝜃) ), with their line integrals 𝑔 𝑞, 𝜚 (in azimuth coordinates 𝜚 and impact parameter 𝑞 ) . • Zernike polynomials have a unique property of correspondence between the two sets of Fourier coefficients: ∞ ቄ𝑑 𝑚ቄ𝑑 𝑡 𝜍 = 𝑡 𝑎 𝑛 𝑚 (𝜍) 𝑛 𝑛 + 2𝑚 + 1 𝑏 𝑛 𝑚=0 ∞ ቄ𝑑 𝑚ቄ𝑑 𝑡 p = 𝑡 sin 𝑛 + 2𝑚 + 1 arccos 𝑞 𝑔 𝑏 𝑛 𝑛 𝑚=0 • The highest m-value is about equal to the number of detector arrays. • Maximum l-number depends upon the sampling density of the chords STUDY OF MAGNETIC RECONNECTION 25/11/2019 Pagina 7 PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA
Algoritm test • Test of accuracy of the reconstructions • Phantom distributions (Gaussian) are used in order to check the real potentiality of the cameras configuration. • Tomography 2D. • Adding virtual chords that clamp the boundary of the zone under analysis to zero. • Error of 15 % for simulate real data • Realistic interpretation of the data STUDY OF MAGNETIC RECONNECTION 25/11/2019 Pagina 8 PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA
Tomographic reconstruction 1 1 • Shot number 1618 in Hydrogen. • Mosaic of the six cameras. • 3 Frames at the plasma breakdown. 2 • The red line represents the slice of pixels used in the tomography. • The reconstructed sizes of the slim tori seem quite reasonable (about 20 cm). STUDY OF MAGNETIC RECONNECTION 25/11/2019 Pagina 9 PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA
Tomographic reconstruction 2 • Shot number 1618 in Hydrogen. • Mosaic of the six cameras. • Frames at the plasma shutoff. • The red line represents the slice of pixels used in the tomography. STUDY OF MAGNETIC RECONNECTION 25/11/2019 Pagina 10 PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA
Mosaic shot 1618 • Different frames during the shot 1618: Breakdown Intermediate Shutoff • Mosaic video STUDY OF MAGNETIC RECONNECTION 25/11/2019 Pagina 11 PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA
Conclusions and further developments • New system of fast cameras for see the plasma from all perspective. • Algorithm developed with Zernike provides a realistic interpretation of the data but is under study in which range is reliable. • Camera alignment is accurate to the millimetre, a greater precision is required. • Overexposed images can often be obtained, due to the rapid change in plasma brightness. • It could try another alghoritm for test the recontruction obtained, like using iterative method. • Next step is 3D tomography reconstruction of the plasma. • Now that the geometry is known, could be tried a stereoscopy 3D. STUDY OF MAGNETIC RECONNECTION 25/11/2019 Pagina 12 PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA
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