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When the wavelength of the radiation being studied is comparable to the

size of optical components, the diffraction effect cannot be ignored.

Gaussian beam tracing (GBT) can be used by treating the propagation of

the light as a beam with certain size rather than a ray used in geometrical

optics when analyzing the optics of millimeter-wave diagnostics. Gaussian

optics is an effective way to represent diffraction effect because of its

ability to show the beam size and the intensity that could be altered from

diffraction. GBT has been used in two millimeter-wave diagnostics suited

to ITER geometry. The first is in a design of a Gaussian telescope for

correction of transmission line misalignment in the ITER LFS

reflectometer due to motion of the vessel during heating to operating

temperature from room temperature. The second is a new concept of using

spherical mirrors for electron cyclotron emission imaging (ECEI) and

assessing its promise of a more realistic method of ECEI in ITER than

previous idea of using a cylindrical mirror that requires large access ports

that can be exposed to intense neutron radiation. The spherical mirror

promises a smaller aperture on the first wall of ITER. In this poster, the

simulations of GBT of the two applications are analyzed and discussed.

Abstract

Background

- The arrangement of the optical components was set up on software

Code V.

Analysis I

- Electron Cyclotron Emission Imaging (ECEI) diagnostics is desired for

ITER to detect electron density for studying disruption mitigation,

instability, and MHD phenomena.

- In the future, feedback system could be installed to prevent disruption.

Motivation II

Reference

[1] J. Liu, et al. “Alternative Optical Concept for Electron Cyclotron

Emission Imaging” Rev. Sci. Instrum. 85, 11D802 (2014)

[2] M. Bitter, et al. “Imaging with Spherically Bent Crystals or Reflectors”

J. Phys. B: At. Mol.Opt. Phys. 43, 144011 (2010)

[3] P. Goldsmith ‘Quasioptical Systems: Gaussian Beam Quasioptial

Propagation and Applications’ IEEE Press (1998)

Acknowledgement

- This work was made possible by funding from the Department of

Energy for the Summer Undergraduate Laboratory Internship (SULI)

program. This work is supported by the US DOE Contract No. DE-

AC02-09CH11466.

- Diffraction is not negligible when the wavelength is comparable to the

optical components, and this is the case for several diagnostics ITER

that interact with microwaves.

- Geometrical optics is a useful technique for the alignment of the optical

components, but it does not represent the beam width and shape that

result from diffraction effects.

- Gaussian optics can be used to analyze resulting diffraction effects by

using size of the beam and intensity that initially propagates in Gaussian

distribution.

- Gaussian optics analysis is applied to two diagnostics for ITER: Low

Field Side Reflectometer and Electron Cyclotron Emission Imaging

Diagnostic

1Department of Physics, University of Virginia; 2Princeton Plasma Physics Laboratory; 3Ulsan National Institute of Science and Technology

H. Joo1, M. Bitter2, B. Tobias2, H. Park3, A. Zolfaghari2

Use of Gaussian Beam Tracing in the Design of Millimeter-Wave Diagnostics on ITER

Fig. 1: Comparison of geometrical optics and Gaussian optics

Motivation I

- ITER chamber heats up during its operation, which puts thermal stress

on the diagnostics, misaligning the mirrors.

- The purpose of the apparatus is to keep symmetry of beam size for

outgoing and incoming beams by mechanically retaining the spherical

mirrors to be parallel despite the temperature change.

- Mirror diameter = 100 mm

- Mirror radius = 350 mm

- Focal length, f = 175 mm

- The distances between each

component must stay the same

in order to maintain the

symmetry.

f

f

2f

Fig. 3: 3D configuration of reflectometer

- The width of input Gaussian beam was compared to the width of

resulting Gaussian beam on the image surface in varying wavelengths

and beam widths.

Fig. 2: Parallel waveguides in Gaussian Telescope

- Previous design that uses

cylindrical mirror is not practical

due to its large access port.

- Design using a single spherical

mirror requires much smaller

access port, but the diagnostic is

not compact to be suited for

ITER [1][2].

Fig. 6: ECEI system with cylindrical mirror

Fig. 7: ECEI system with spherical mirror

Future Work

- Double spherical mirror system

with concentric mirrors gives

more linearize and compact

design for ITER.

- The rotational symmetry of the

system gives 2D spatial

resolution.

- Varying angles θ1, θ2, and α can

alter the magnification

𝑀 =cos(2𝜃2 + 𝛼)

cos(2𝜃1 + 𝛼)

Fig. 8: Proposed ECEI system with two

concentric spherical mirror

- The horn is rectangular, which

means that the beam waist of

Gaussian beam emitted is 30% of

the half-width of the aperture. [3]

Analysis II- The arrangement of the optical components was set up on software

Code V.

Fig. 4: Gaussian beam propagation of the

reflectometer

- Smaller the wavelength, smaller half-width has a uniform Gaussian

beam shape

- As the wavelengths and beam size difference gets larger, irregularities in

the beam patterns occur.

- The width of beam waist is

dependent on wavelength of light

and beam width.

- The operation wavelength is

between 1.5 mm – 3 mm.

1 mm 2 mm 5 mm 10 mm

5 mm

20 mm

50 mm

150 mm

Fig. 5: Gaussian beam propagations and beam shape based on wavelengths and

initial beam half-widths

Half-

widths

Wavelengths

Fig. 9: Geometrical tracing of the ECEI

diagnostic

- Based on the geometry of the

microwave horn antenna used

in single mirror system, the

half-widths of the initial

Gaussian beam is X = 0.268 cm

and Y = 0.351 cm.

- The mirrors were 15 cm in

diameter, and the slit size was 3

cm in diameter.

- Same frequency used in single

mirror system was used: 125

GHz.

- The Meridional focus is the

point at which the rays almost

converge in a plane, and where

the access port will be.

- The Sagittal focus is the point at

which the rays focus in the

other plane, and where the

plasma will be.

Fig. 10: Gaussian beam propagation of

the ECEI diagnostic

- Ensure the simulations with exact parameters

- Experimentally verify the results with the simulations for both Gaussian

telescope and double mirror ECEI diagnostics.

- Recreate the experimental result of single mirror ECEI system with

simulation.

- Examine the unexpected shape of Gaussian propagation at Meridional

focus for double mirror system.

- Minimize the height of beam propagation at sagittal focus.

- Vary the angle orientation of double ECEI system and test the

symmetry.

- Optimize the slit shape and size for more focused image with minimized

diffraction effect

Conclusion

- The simulation of the Gaussian telescope illustrates the relationship

between the wavelength and the initial beam size.

- The Gaussian beam retains its size and shape in various angles of

the mirrors, which is required due to thermal heating of ITER.

- The two spherical mirrors’ ability to focus in different planes at different

distances is verified, but why beam shape of Meridional focus so wide is

yet inconclusive.

- The mirrors in concentric arrangement retains the property of a

single mirror system, and makes the design more compact.

Fig. 11: Gaussian beam at the Sagittal Focus

Fig. 12 Gaussian beam at the Meridional

Focus

- Sagittal focus width: 8 cm

- Sagittal focus height: 87 cm

- In order for optimal focusing, the

width and the height of the

Sagittal focus needs to be

minimized

- Meridional focus width: 16 cm

- Meridional focus height: 10 cm

- It is expected that the Meridional

focus will create a flat Gaussian

beam like the Sagittal focus.

- Since Meridional focus is where

the slit will be, the beam size

needs to be minimized to prevent

diffraction and to generate

undisturbed image.