Dr. Robert C. Wolf Dr. Fred Levinton

TOKAMAK PLASMA DIAGNOSTICS

Hinds Instruments photoelastic modulators (PEMs) have played an im-portant role in nuclear fusion energy research. A Stokes polarimeter usinga special dual PEM system is used with “tokamak” plasma fusion reactorsfor determining characteristics of the magnetic field and the plasma.This technique is called “Motional Stark Effect Polarimetry” or the“MSE Diagnostic.”

A “tokamak” is a device for containing a plasma (ionized gas) using a strongmagnetic field. Originally conceived by Soviet scientists Igor Tamm andAndrei Sakharov, it is today the most promising of several such magneticcontainment devices. The tokamak is the focus of an intense worldwideeffort to control nuclear fusion for electric power generation.

The plasma (an ionized gas of the heavy hydrogen isotopes deuterium,H , and, on rare occasions, tritium, H ) is enclosed in a vacuum chamber inthe shape of a torus (donut). The idea is to “contain” the plasma at the veryhigh temperatures required for nuclear fusion (about 100 million degreesC) using magnetic fields. One of these magnetic fields, the “toroidal” field,is produced by large current-carrying coils around the torus. The magneticflux from these coils is also toroidal in shape, and the field lines “fill” thetorus cavity (Figure 1a).

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H INDS I N S TR U ME N TS , I N C .

PEMTM

APPLICATIONSNEWS FOR USERSOF PHOTOELASTICMODULATORS

SUMMER 2002

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PEM-based Stokes PolarimeterDual PEM SystemsHINDS Teams With SEMATECH

A B O U T T H E S C I E N T I S T S

Dr. Fred Levinton

Dr. Robert C. Wolf

Nova Photonics, Inc.

Max-Planck Institut für Plasmaphysik

by Dr. Theodore C. Oakberg, Senior Applications Scientist

I N S I D E P E M

Dr. Fred Levinton received his B.Sc. Degree inphysics from McGill University, Canada, and hisPh.D. in physics from Columbia University. Hedeveloped the motional Stark effect (MSE)diagnostic for measuring the magnetic field inhigh temperature plasmas which was imple-mented at the Princeton Plasma Physics Lab.Dr. Levinton received the American PhysicalSociety’s

for the concept and develop-ment of the MSE diagnostic. He is currently withNova Photonics, Inc.

Robert C. Wolf received his Diploma from theUniversity of Aachen and his Ph.D. from theUniversity of Düsseldorf in 1993. In 1996 hebecame associated with the ASDEX Upgradetokamak, one of the magnetic confinementfusion devices of the Max-Planck-Institut fürPlasmaphysik in Garching, Germany, and theredeveloped the Motional Stark Effect polarimeter.At present he is working at the Joint EuropeanTorus tokamak, the world’s largest facility of itskind, as task force leader responsible for theprogram concerning improved confinementregimes. In September 2002 he will move toForschungszentrum Jülich to become one of thedirectors of the Institut für Plasmaphysik.

1997 Award For Excellence In PlasmaPhysics Research

To respond to this issue, Hinds has extended its corecompetency in low-level visible birefringence measurements todevelop a system to characterize birefringence in any opticalmaterial transparent at 193 nm or 157 nm. We were awarded acontract with SEMATECH to expedite the development of theDUV birefringence measurement system. They have taskedHinds to provide the semiconductor industry with measurementmetrology for QC, as well as lab R&D use, for characterizing theinteraction between DUV light and CaF in lithography imagingsystems.

Data from a prototype DUV birefringence measurementsystem was reported at International SEMATECH’s 157nmTechnical Data Review this May in Dallas, TX. One of our seniorapplication scientists, Dr. Bob Wang, showed 2-D images as well

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as contour maps which vividly displayed both the magnitudeand corresponding fast axis angle of residual and the recentlydiscovered intrinsic form of birefringence in CaF at 157 nm.An example is shown in Figure 5. This data represents the firstmultidimensional characterization of CaF ’s birefringence at157 nm resulting from our collaboration with SEMATECH.Dr. Wang’s preliminary findings, measured at different crystalorientations, confirmed high levels of intrinsic birefringence.Furthermore, the 2-D birefringence maps of the entire surfacesof CaF cubic samples measured at the (110) orientationdemonstrated significant variation in birefringence, possiblydue to residual birefringence in those samples. Lower levels ofbirefringence, with significant variation in magnitude andangle, were also observed for the (001) orientation.

One design solution that has been proposed to reducethe intrinsic birefringence at 157 nm is to couple lenses inthe imaging system at offsetting orientations. Dr. Wangdemonstrated the validity of this approach. He presented datafrom two stacked cubes that had the same orientation (110)with a resulting total mean birefringence of 54 nm. When oneof the cubes was rotated by 90°, the total birefringence wasdrastically reduced to below 1 nm/cm.

Hinds is aggressively pursuing the development of a DUVbirefringence measurement system and has an engineeringmodel in development. A commercial system capable ofmeasuring samples as large as 400 mm diameter x 270 mm thickis scheduled to be available during the second half of 2002.

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Photoelastic modulators have historically been used in polarimetry. Whenthe PEM is used as a polarization analyzer, it is generally useful to use a dualPEM system. A dual PEM system can characterize any polarization state byobtaining all four Stokes vectors simultaneously. By using a dual PEMsystem, the unparalleled high sensitivity, spectral range and stability ofphotoelastic modulators (PEMs) can be applied to study polarization.

One of the first uses for the PEM was astronomical polarimetry.Applications can also be found in Stokes polarimetry and Optical Rotation.Other polarization analysis PEM applications include laser lightcharacterization and magnetic field diagnostics in tokamaks throughoutthe world. (continued on page 5)

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HINDS INSTRUMENTS, INC.

SUMMER 2002 5

The II/ZS37-50

Polarization Analysis and Stokes Polarimetry

Astronomical Polarimetry

Tokamak

has ZnSe as the optical material. Thisprovides a transmission range from 514nm to 18µm. ThisPEM has applications in the infrared region of the lightspectrum. It is used to analyze both broadband light sourcesand infrared lasers, such as the CO laser.

Like all Hinds PEMs, these systems provide the uniquebenefit of a wide acceptance angle (> ± 20 degrees), a goodtransmission for a wide wavelength range, high powerhandling capabilities and a high polarization sensitivity. Thetable below compares the technical specifications for all ofthe dual PEM systems.

The most common use for a dual PEM system is to analyzethe polarization state of a light source. There are differentways to represent light polarization. One of these is to useStokes vectors or parameters (I, Q, U and V). Using the 1f and2f reference signals from each of the controllers, a dual PEMsystem is able to provide all four of the Stokes para-meterssimultaneously. Any light polarization can be charac-terizedby using these four parameters. For more informa-tion,please see the Stokes Polarimetry application note on ourwebsite.

One of the first uses of the photoelastic modulator wasastronomical polarimetry. Dr. James Kemp, late Professor ofPhysics at the University of Oregon, used PEMs to study thepolarization of light from nearby stars and features on thesun, such as sunspots. The four Stokes parameters (I, Q, U, V)give a complete description of the polarization state of thesestellar light sources. For more information on this applica-tion, please refer to Hinds Instruments’ PEM Newsletter #1on our website.

Hinds Instruments manufactures a dual PEM system specifi-cally designed for Motional Stark Effect (MSE) diagnosticpolarimeters associated with tokamaks. A detailed descrip-tion of this application is the feature article of this newsletter.

Dual PEM systems provide the capability to make realtime polarization analysis measurements. These systems areavailable in a wide variety of materials and configurations tosupport many diverse applications. A Hinds sales engineer orapplication scientist will be glad to explain any of theseoptions. Please contact us with any questions or comments.

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Applications for Dual PEM Systems

Dual PEM ModelsHinds Instruments has five standard dual PEM systems forapplications that require different useful apertures andmeasurements in different spectral regions. The dual PEMmodels are:

systems use the series IPEM with fused silica as the optical material. The series l PEMhas a rectangular shaped optic that has a useful aperturethat is limited by the height of the optic. These small systemsare useful when the light source has a small beam diameter.

Most of the dual PEM systems utilize the series II PEMs,which contain octagonal shaped optical elements. Theseries II PEMs meet higher requirements for magnitude ofmodulation and offer symmetrical distribution of PEMretardation over a larger aperture range.

systems also employhigh quality fused silica as the optical material and have atransmission range of 170nm to 2.6µm. Both models areuseful for quarter and half wave retardation in the UV,visible and near IR light spectral regions. Of the two models,the II/FS20-23 system has the benefit of a larger aperture.This is especially useful if the light source has a large beamdiameter or more than one light source is to beimaged through the optic. The II/FS42-47, on the other hand,provides a more compact optical head configuration.

• I/FS50-55 • II/FS42-47• I/FS47-50 • II/ZS37-50 • II/FS20-23

The I/FS50-55 and the I/FS47-50

The II/FS20-23 and the II/FS42-47

A PEM-based Stokes Polarimeter forTokamak Plasma Diagnostics

Tokamak Plasma Fusion Reactors

Dual PEM Systems for Polarimetry

A Most research tokamaks use only deuterium,a stable isotope of hydrogen. Future power-producing fusionreactors will likely use tritium as well as deuterium. As ofthe date of this article, the use of tritium has been testedonly at the TFTR tokamak at Princeton and the JET facility inCulham, U.K. .

Dual PEM Systems for Polarimetry(continued from page 1)

Model Optical Nominal Spectral Range Range of Range of Useful

Material frequencies /4 Retardation /2 Retardation apertureλ λ

II/ZS37-50 *II/FS20-23 *II/FS42-47 *I/FS50-55I/FS47-50

ZnSe 37 - 50kHz 550nm - 18µm 550nm - 18µm 550nm - 10µm 13mmFused Silica 20 - 23kHz 170nm - 2.6µm 170nm - 2.6µm 170nm - 2.5µm 45mmFused Silica 42 - 47kHz 170nm - 2.6µm 170nm - 2.6µm 170nm - 2.6µm 23mmFused Silica 50 - 55kHz 170nm - 2.6µm 170nm - 2µm 170nm - 1µm 16mmFused Silica 47 - 50kHz 170nm - 2.6µm 170nm - 2µm 170nm - 1µm 16mm

Technical Specifications for Dual PEM-90 Systems

*Useful aperture is defined as the area for which the average retardation is 90% of the retardation at the center. For more information, please contact Hinds Instruments.

Figure 5.IntrinsicBirefringenceof CaF at157nm

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HINDSTeams WithSEMATECH

Development of the PEM Stokes polarimeter for tokamakplasma diagnostics

The ASDEX Upgrade tokamak, details of the Stokespolarimeter installation

The PEM Stokes polarimeter that is used with tokamaks wasinvented by Dr. Fred Levinton with the assistance of the lateDr. James Kemp of the University of Oregon. A beam ofneutral deuterium atoms is injected into the tokamak

plasma. The atoms become excited and emit the red“Balmer alpha” light at about 656 nm. The light of

interest is polarized perpendicular to the magneticfield in the vicinity of the light emitting atoms. The

polarimeter measures the direction of polarization ofthe light and thus may be used to determine the direction

of the magnetic field.Modern versions of the dual PEM feature a 20 kHz PEM

and a 23 kHz PEM mounted in a single optical head enclosurewith their retardation axes at 45 degrees with each other.The optical head material is frequently plastic, since theforces induced on metal enclosures by a rapidly changingmagnetic field can be very strong.

A typical PEM Stokes polarimeter installation is at the ASDEX(Axially Symmetric Divertor Experiment) Upgrade tokamak atthe Max Planck Institute for Plasma Physics at Garching insouthern Germany. Dr. Robert Wolf was the scientist respon-sible for the installation of this polarimeter system.

The ASDEX Upgrade tokamak is designed specifically forexperiments on magnetic divertors. Divertors are devices forremoving unwanted (impurity) ions from the plasma. Thetoroidal chamber has a major radius of 1.65 meters and aminor radius of 0.5 meters. Toroidal field strengths aretypically 2 to 3 Tesla and the plasma current is typically amillion amperes.

An important component of all tokamaks is a coil lo-cated at the center of the torus. A tokamak “run” begins withthe chamber being filled with H gas at very low pressure. Arapidly changing current in the coil at the center of the torusprovides a strong induced electromotive force inside thetorus. Any existing free electrons are sufficient to ionize therest of the gas and produce a plasma. The plasma thenbecomes the “secondary winding” of a transformer with theplasma current being determined by the rate of change ofthe current in the center coil (primary) and the resistivity ofthe plasma. Electrical resistance heating provides the initialheating of the plasma.

Additional heating of the plasma is required to achievethe high temperatures required for nuclear fusion. Onemethod is by injecting neutral deuterium atoms into theplasma at high speeds (i.e. high kinetic energies). Electricallyneutral atoms must be injected, since ions would be repelledby the magnetic field. The neutral atoms eventually becomeionized and become part of the plasma.

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SUMMER 2002HINDS INSTRUMENTS, INC. 32

The second field, called the “poloidal” magnetic field, isproduced by a strong current in the plasma. This field has theunique property that it is weakest at the center of the currentdistribution and strongest at the periphery of the currentdistribution. The direction of the poloidal field is shown inFigure 1b.

The strength of this poloidal magnetic field vs. positionis of great interest to plasma scientists, since it can shed lighton the stability of the plasma and the distribution of thecurrent density inside the plasma. The PEM-based Stokespolarimeter offers a means of determining the magnitude ofthe poloidal field vs. position in the plasma. This has led toimproved understanding and performance of tokamakplasmas.

In a power-producing tokamak reactor, the plasma willconsist of ionized H , H and free electrons. Since all theparticles in the plasma are electrically charged, the magneticfield is able to contain them. The kinetic energies of the Hand H ions must be high enough that during somecollisions, the electrostatic forces of repulsion can beovercome and the two colliding particles can get closeenough for a fusion reaction to take place. A typical fusionreaction is:

The energy released (as kinetic energy of the particles) fromeach “successful” collision is about 17.6 MeV.

B

2-4

5

2 3

2

3

H + H He + n + energy2 3 4 1→

A top view showing the torus vacuum chamber, theneutral deuterium beam and the dual PEM is shown inFigure 2.

The light from the deuterium beam is reflected by amirror into the polarimeter optics. The light is focused usingtwo lenses through the dual PEM and the polarizer to a fiberoptics array. There are 10 lines-of-sight, each with a line of 6fiber optic bundles for measuring the light polarizationdirection at 10 points along the H beam. The array patternof the ends of the fiber bundles is also shown in Figure 2.

In the mid-plane of the torus, the toroidal magneticfield component at each point lies in the mid-plane andthe poloidal magnetic field component is perpendicularto the mid-plane (Figure 3). The toroidal field is producedprimarily by the large electromagnets and is thereforeknown. (Subtle perturbations of this field occur due to themotion of the electrons and ions in the plasma, but thesecan be calculated.) If the tilt angle of the net magneticfield ( + ) can be determined, the magnitude of thepoloidal field component may be calculated according tothe following equation:

2

BB

B BB

= tan

T

P

T P

γ

γ

p

P

P-1( )B

BP

T

Not all of the H spectral line can be used. The deuteriumatom experiences a strong electric field due to its motion inthe magnetic field ( ). This splits the line into differentcomponents according to the Stark effect. (This phenomenonis called the “Motional Stark Effect”.) Only the componentsare used; these are perpendicular to the net magnetic fieldand their central wavelength is independent of the fieldstrength. If the light is viewed perpendicular to the directionof the induced electric field, the light is linearly polarized. Thespectral bandwidth of the filter/detector must be limited to0.2 to 0.3 nanometers to accept only the components of theH spectral line.

It is also necessary to view the beam line at some angleother than perpendicular to the beam. A Doppler shift of thespectrum line is needed to separate the highest energycomponent of the injected atoms from lower velocitycomponents as well as H radiation from the plasma edge andradiation from charge-exchange reactions. Each channel(line-of-sight) therefore requires measurement of a narrowspectral band at a different central wavelength.

Typical toroidal and poloidal field strengths are shown inFigure 4. The intersection of the beam line and each line-of-sight defines a particular point on the mid-plane inside theplasma where the magnetic field is measured. Since thetoroidal field strength is known, measuring the direction of

α

E = v X B

σ

σα

αC

SUMMER 2002 4

There are a number of unique design features associatedwith this and other tokamak PEM polarimeter systems.

The PEM electronic heads are susceptible to strongmagnetic fields. It is therefore necessary to locate theelectronic heads some distance away from the dual opticalhead, or magnetically shield the electronic heads or both.The coaxial head-to-head cables are 15 meters long for theASDEX Upgrade tokamak installation.

Optical fiber bundles are used to conduct the lightfrom the PEM assembly to the individual detectors(photomultiplier tubes or PMTs). The intensity modulatedlight signals are carried to the control room where thedetectors and associated electronics are located. The polari-zation of the light is lost in the fibers, but this is an advan-tage, since the type of PMTs being used are polarizationsensitive.

An aspheric lens collimates the light coming from theend of the fiber bundle which passes through an interferencefilter and another lens to the photomultiplier tube. Eachinterference filter has a spectral bandwidth of about 0.2 to0.3 nm. The center wavelength of each filter is “tuned” byvarying the filter temperature and/or tilting the filter. Eachchannel has a single PMT which is connected to a pre-amplifier with a gain of 10 volt/amp. Each pre-amplifier isthen connected to two lock-in amplifiers, one at 40 kHz andthe other at 46 kHz (twice the oscillation frequencies of thePEMs).

The output of each lock-in amplifier goes to an A-D con-verter. Data is sampled at a rate of 1 kHz. At the present,ASDEX Upgrade data is reduced at the end of the run. Itwould be possible to perform real-time data analysis and usethe information in a feedback loop to control the reactor.This may be tried with the ASDEX Upgrade in the future.

Novel system design details

Protecting the PEM electronic heads from strongmagnetic fields.

Optical signal transmission via optical fibers

Fine tuning of wavelength selection

Real-time data analysis

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SummaryStokes polarimeters using a dual PEM are an important partof the diagnostics of tokamak plasmas in installationsaround the world. Hinds Instruments employees are proudof the role our product plays in nuclear fusion research. Weat Hinds Instruments are very grateful to Dr. Fred Levinton ofFusion Physics for developing this application of thephotoelastic modulator and for his assistance with thisarticle. I am personally grateful to Dr. Robert Wolf for hisassistance in helping me understand the operation of thetokamak and the details of the Motional Stark Effectpolarimeter and for his assistance in preparing this article.

In recent years, optical lithography has continued itstransition to shorter wavelengths in order to produce moreadvanced microchips. The next generation of optical litho-graphy systems will use F Excimer lasers operating at157 nm. Due to its unique optical properties and readinessfor large-scale production, calcium fluoride (CaF ) is the onlypractical optical material available for use in stepper andscanner lenses at this wavelength. Consequently, linear bire-fringence in CaF components has emerged as an importantquality parameter for the optical lithography industry.

In May 2001, as part of a project with InternationalSEMATECH, researchers at the National Institute ofStandards and Technology (NIST) reported intrinsicbirefringence in CaF that affects lens design and images atthe wafer level in 157 nm microlithography systems. Thisnews came as an unwelcome surprise to the opticallithography industry. Prior to this discovery it was commonlyassumed, incorrectly, that CaF , belonging to the cubiccrystal group, was an “isotropic” material.

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B T B P

Z Z

a) Toroidal magnetic field b) Poloidal magnetic field

Figure 1. Magnetic fields in a tokamak

...PEM-based Stokes Polarimeterfor Tokamak Plasma Diagnostics

B Both the toroidal and poloidal magnetic fields serve to “contain” the plasma.This containment is a consequence of the laws of electromagnetism, which predictthat a charged particle when moving at right angles to a uniform magnetic field willfollow a circular path, returning to its original position. If the particle has a velocitycomponent parallel to the field, the path of the particle will be a helix, with thecenter of the helix being parallel to the magnetic field. Even non-uniform magneticfields can “contain” charged particles if the proper conditions of particle speed,mass, electric charge and magnetic field strength are met.

C The magnitude of the Doppler shift in wavelength is proportional to the compo-nent of the particle velocity along the direction of the line of sight.

Hinds Instruments recommends that the electronic heads be located in a magneticfield no stronger than 100 Gauss or 0.01 Tesla.

DFigure 2. Neutral deuterium beam, details of the ASDEXStokes polarimeter.Upgrade

2 aspheric lenses

interferencefilter

Polarizer

2 Photoelasticmodulators (PEM)

Q4

Q5

Opticalfibers

Mirror

Mirrorprotectionwindow

Observationoptics

Neutral beams

PhotomultiplierLock-in

ADCS2 2

Lock-inADCS2 1

2ω2

2ω1

1

2

Figure 3. Geometric relationship between thetoroidal field, poloidal field and pitch angle γp.

Bp

γp

BT

B

Figure 4. Relative intensities of toroidal and poloidalmagnetic fields, vs radial position.

Insidewall

torusvacuumchamber toroidal

fieldstrength

poloidalfieldstrength

Outsidewall

0 r

B

3

4

Bibliography1. Herman, Robin, “Fusion: The Search for Endless Energy”, Cambridge

University Press, 1990.2. F.M. Levinton, et.al., “Magnetic field pitch angle diagnostic using the

motional Stark effect”, (invited), Rev. Sci. Instrum. 2914 (1990).3. F.M. Levinton, “The multichannel motional Stark effect diagnostic on

TFTR,” Rev. Sci. Inst. 5157 (1992).4. D. Wroblewski and L.L. Lao, “Polarimetry of motional Stark effect and

determination of current profiles in DIII-D”, (invited) Rev. Sci. Instrum.5140 (1992).

5. F.M. Levinton, et.al., “Improved Confinement with Reversed MagneticShear in TFTR”, Phys. Rev. Lett 4417 (1995).

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the polarization of the componentof the light determines the strength ofthe poloidal field component. Fromthe distribution of the poloidal fieldvs. position inside the plasma, it ispossible to calculate the currentdensity distribution inside the plasma.This is very important information tothe scientists who are studying thetokamak plasma.

σ

Hinds Instruments Teams with InternationalSEMATECH to Develop an Instrument thatCharacterizes Birefringence in Calcium Fluoridefor 157 nm Microlithography

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Documents

Dr. Robert C. Wolf Dr. Fred Levinton