PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF - - PowerPoint PPT Presentation

Yacopo Damizia

STUDY OF MAGNETIC RECONNECTION PHENOMENA ON THE PROTO-SPHERA EXPERIMENT THROUGH THE ANALYSIS OF FAST CAMERAS DATA

Purpose

» Tokamak Device » Proto-Sphera Experiment » System Layout Cameras » Implementation optical tomography » Mathematical basis » Algorithm test » Applications » Conclusion

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Tokamak Device

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• Magnetic Confinement Machine.
• Toroidal shaped.
• Realize the magnetic confinement
• f plasma isolating it from the walls
• f the toroidal vacuum container

thanks to the particular structure of the magnetic field created.

• Principal Components:

Central transformer Toroidal field coils

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.

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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

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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: 𝑎𝑜

𝑛 𝑠, 𝜄 = 𝑆𝑜 𝑛 𝑠 cos 𝑛𝜄

𝑎𝑜

−𝑛 𝑠, 𝜄 = 𝑆𝑜 𝑛 𝑠 sin 𝑛𝜄

• The radial function 𝑆𝑜

𝑛 𝑠 , is described by:

𝑆𝑜

𝑛 𝑠 = σ𝑚=0 (𝑜−𝑛)/2 −1 𝑚 𝑜−𝑚 ! 𝑚! Τ

1 2 𝑜+𝑛 −𝑚 ! Τ 1 2 𝑜−𝑛 −𝑚 ! 𝑠𝑜−2𝑚

Zernike Polynomials application to tomography

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• 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: 𝑕𝑛

ቄ𝑑 𝑡 𝜍 = ෍ 𝑚=0 ∞

𝑛 + 2𝑚 + 1 𝑏𝑛

𝑚ቄ𝑑 𝑡 𝑎𝑛 𝑚 (𝜍)

𝑔

𝑛 ቄ𝑑 𝑡 p = ෍ 𝑚=0 ∞

𝑏𝑛

𝑚ቄ𝑑 𝑡 sin 𝑛 + 2𝑚 + 1 arccos 𝑞

• The highest m-value is about equal to the number of detector

arrays.

• Maximum l-number depends upon the sampling density of the

chords

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

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Tomographic reconstruction 1

• Shot number 1618 in Hydrogen.
• Mosaic of the six cameras.
• Frames at the plasma breakdown.
• 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).

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1 2 3

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.

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Mosaic shot 1618

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• Different frames

during the shot 1618: Breakdown Intermediate Shutoff

• Mosaic video

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.

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