Abstract

This thesis describes the design and implementation of a variety of magnetic diagnostic devices on the Helicity Injected Tokamak II (HIT-II) experiment. A method is developed to determine the calibration factors for the three major types of magnetic diagnostic devices on the experiment: flux loops, rogowski segments, and surface magnetic field probes. All of these are calibrated by comparing the measured data with the values obtained from a Green Function calculation utilizing the available data of the currents in the poloidal or toroidal field coil power-supplies. The Green Functions for normal and poloidal signals are calculated from a filament-based model of the PFC, the magnetic vector potential, and complete elliptic integrals. The toroidal Green Functions are calculated from Ampere's Law. Data on the currents in the coil power supplies is gathered using slightly modified, commercially available current transducers. The pickup of poloidal magnetic field components in the toroidal windings of the magnetic surface probes is investigated, and found to be insignificant. All diagnostic devices are successfully calibrated and the data used for the calibration, together with additional data to confirm the calibration accuracy is presented.

Table of Contents

1. Introduction
   • The HIT-II Experiment
   • Magnetic Diagnostic Devices
2. Theory
   • Flux Loops
   • Rogowski Loops
   • Magnetic Probes
   • Green Function
3. Description of Experimental Equipment
   • PFC Power Supply Current Transducers
   • Toroidal Field Current Transducer
   • Flux Loops
   • Plasma Current Rogowski
   • Magnetic Probes
   • Data Acquisition System
4. Experimental Procedure
   • Verification of Green Function Calculation
   • Determination of Center Column Sheet Location
   • Calibration of Normal and Poloidal Diagnostics
   • Calibration of Toroidal Diagnostics
5. Presentation of Results
6. Summary and Conclusion

Introduction

In order to harness the energy released during a fusion reaction for the purpose of electricity production, the hot fusion plasma must be contained at sufficient density and over a long enough period of time for the constituents to react with each other. One possible way to achieve this is by confining the plasma utilizing magnetic fields. A variety of magnetic confinement geometries have been developed in recent years, but the most extensively researched concept is that of the Tokamak. The basic geometry of a Tokamak is shown schematically in Figure 1.

Running currents through the toroidal field coils (shown in dark red) generates a strong toroidal magnetic field. By driving a current through the plasma itself, an additional poloidal field is created, so that by superposition the magnetic field-lines acquire a helical form. The vertical field coils (shown in blue) generate an additional vertical (or poloidal) field, which interacts with the toroidal current to provide an inward radial force, balancing the hoop-stress on the plasma.

The HIT-II Experiment

The Helicity Injected Tokamak II is a plasma confinement experiment with the geometry of a low aspect ratio Tokamak. It investigates the use of Coaxial Helicity Injection (CHI) to generate a steady-state plasma current, which is preferable over pulsed methods to avoid cyclic fatigue of the reactor materials. CHI tends to drive the bulk of the electron thermal distribution. It therefore promises to have a number of additional advantages over other steady-state current drive methods, such as neutral beam injection or radio frequency (RF) current drive. HIT-II is a pulsed experiment, with one discharge (referred to as a 'shot') lasting for up to 40 milliseconds. In HIT-II the copper shells of the earlier HIT experiment are replaced with thin, stainless steel shells. In addition, a flux based feedback control system for the poloidal field coils is added allowing transformer as well as CHI current drive. Previous results from the HIT experiment indicate that CHI tends to generate a hollow current profile. Since transformer current drive produces a peaked profile, the combination of both allows for current profile control. Figure 2 shows a schematic of the HIT-II experiment.

The experiments main chamber is formed from two thin stainless steel shells penetrated by the center column. The entire assembly is seated in a cylindrical stainless steel tank. Due to limitations in ceiling space the experiment is designed with its center column parallel to the floor. There are three main coil sets on the experiment: the toroidal field (TF) coil, the poloidal or vertical field coils (PFCs), and the ohmic drive center-column coil stack (CC). The TF coil is formed by a segmented cable wound over the TF coil frame and through an epoxy reinforced G10 matrix inside the center column. The PFCs are mounted in a phenolic assembly on the outside of the two shells, and the ohmic coils are positioned inside the center column, enveloping the epoxy matrix. The entire machine sits on a stand constructed from aluminum and wood. In order to reduce vibrations the stand sits on air springs.

Figure 3 shows a photograph of the HIT-II experiment before external diagnostic equipment has been mounted onto the machine. To inject helicity, DC voltage is applied between a graphite electrode on the outside surface of the center column, and the inner surface of the outer shell, which is coated with tungsten to prevent material degradation. Coaxial, ceramic insulators mounted on the ends of the central column electrically separate the two electrodes.

The TF coil is powered by a 24 x 0.55 mF capacitor bank. The PFC set is powered by up to 28 individual power supplies, which are feedback controlled via various flux-loops installed on the machine. This allows for precise control of the poloidal magnetic field components during operation of the experiment. Initial breakdown of the plasma is achieved either with the help of a plasma gun , or by utilizing the first row of the sustainment bank, which powers the DC helicity injector. The entire sustainment bank consists of a total of 20 rows. Two parallel groups consisting of two trays in series each make up a row, providing a total capacitance of 36mF. Each tray carries 24 1.5 mF capacitors.

Magnetic Diagnostic Devices

A large number of diagnostic devices on the HIT-II experiment collect their data through interaction with magnetic fields. These devices are either intended to directly measure magnetic properties (e.g. flux-loops, magnetic probes), or to obtain current data, based on the magnetic effects generated by the current under investigation (e.g. Rogowski loops). The data obtained from these shell mounted magnetic diagnostic devices is used to reconstruct the plasma Equilibrium State inside the experiment, as well as to determine the plasma and shell currents during the experiment. The implementation and calibration of these devices is the topic of this thesis.

Theory

There are three basic kinds of magnetic diagnostic devices installed on the HIT-II experiment: magnetic probes, flux loops, and Rogowski loops. This chapter describes the physics that is involved in their design and operation. Next, the derivation is presented which is used in calculating the expected diagnostic values, based on the current data measured for the magnetic field coils. The values thus derived are used to calibrate the various diagnostic devices.

Flux Loops

This is the simplest device that can be used to measure the magnetic field over a given spatial cross-section. It consists of a loop of wire connected to an integrating circuit. The loop can have multiple turns to increase the device's sensitivity. Figure 4 shows a basic illustration. In order to give the flux loop a clearly defined area, and to avoid magnetic interference between neighboring devices, the leads need to be twisted when leaving the loop. In a uniform, time-varying magnetic field B(t) the voltage measured is related to the magnetic field by Faraday's Law , leading to the following expression:

N is the number of turns, A is the cross-sectional area of the flux loop, and V the voltage measured at the end of the leads. For non-uniform magnetic fields, the quantity of interest is generally the total, instantaneous magnetic flux inside the flux loop F = BA. This requires that the signal be passed through an analog integrating circuit as shown below.

The resulting relation between the observed voltage V and the magnetic flux present in the experiment is as follows:

Here RC is the time constant of the integrator. In the most general case, the resistance of the flux loop wire itself must also be accounted for. In addition, it might be necessary to use an attenuator between the flux loop and the integrator circuit to avoid saturation of the electronic components.

Rogowski Loops

A Rogowski loop is a solenoidal coil whose ends are brought together to create a shape approximating a torus. Figure 5 shows a schematic of the basic layout. Note that it is not necessary for the loop to be circular. Any shape is permissible, as long as it forms a closed loop. The purpose of the Rogowski loop is to provide a measurement of the current flowing through the large cross-sectional area of the toroid.

As long as the small cross sectional area of the winding (A) is constant, and the magnetic field varies only a small amount between two consecutive turns and the area A, the total flux in the loop can be written as follows:

Here l denotes the circumferential length of the loop along the solenoidal axis, n is the number of turns per unit length, and B the magnetic field strength. In order to eliminate contributions from flux through the major cross-sectional area, the coil's return lead needs to be passed through the center of the solenoid. Using Ampere's law, the above expression can be simplified to get a linear relationship between the voltage at the Rogowski loop's leads and the rate of change of the current flowing through its cross-section. Integration of the voltage signal then leads to the desired result of current data versus time.

Thus the Rogowski loop provides a direct measurement of the current flowing through its center, independently of the distribution of that current within the major cross-sectional area. This makes it ideally suited for the purpose of measuring the toroidal plasma current in the HIT-II experiment, since no physical contact with the plasma is required.

To obtain more localized data on the structure of the current within the Rogowski loop, the coil can be subdivided into several segments. Care must be taken in this case to return all segment leads inside the windings of the entire toroid. The total current is then readily calculated by summing the individual contributions, while the individual segment data provides insight into the current density distribution.

Magnetic Probes

Magnetic probes are in principle identical to magnetic flux loops, and operate on the same physical principles. The main difference is in the geometry of the device. A single magnetic probe may consist of up to three separate coil windings to gather data on all three spatial components of the magnetic field. The cross-sectional area of the windings is significantly smaller than that of a flux loop in order to improves spatial resolution, while the number of turns per winding is increased to maintain signal strength. Figure 6 shows the basic geometry of a magnetic probe and its approximate dimensions.

The relationship between the observed voltage signal and the measured B-field strength is given by the following equations:

Where RC is the time constant of the integrator again, N the number of turns for the particular winding under consideration, and A the cross-sectional area of the winding. As with the flux loop, the resistance of the wire itself must be accounted for, and it might be necessary to use an attenuator between the probe and the integrator circuit to avoid saturation of the electronic components.

Green Function

In order to calibrate the various diagnostic devices, an absolute reference is required which provides reliable data for a given test setup inside the experiment. One way to obtain this reference data is to run a test case in the experiment, for which the magnetic flux and field strength values can easily be calculated once the currents in all active coils are known. The function that indicates the flux or B-field present in a particular diagnostic per ampere of current applied to a given coil is referred to as a Green Function. For the case of a coil set of circular cross-section the Green Functions can be calculated utilizing a filament based model of the coils together with elliptic integrals in the computation. Since the resulting relations are linear, they can be summed over all active coils, yielding a steady state solution for each diagnostic device under investigation.

Poloidal and Normal Green Function

The PFC current data is gathered using the PFC current transducers and the resulting Green Functions are calculated with the help of a program written in the Interactive Data Language (IDL). Once the Green Functions are known the total fluxes or B-fields expected for all applicable diagnostic devices are easily determined and then compared with the values actually measured for a given shot number. The data resulting from the Green Function calculation represents the magnetic state of the experiment after all magnetic flux has completely soaked through the surrounding materials (or the equivalent instantaneous state if no flux limiting material was present at all). To approximate the theoretical model, the PFC flux-feedback demand wave-form is set to a constant value and held for as long as possible (approximately 30 ms), providing enough time for the measured data to asymptotically approach the values given by the Green Function calculations. The source codes are listed in APPENDIX A: Computational Resources. Next a short derivation of the complete elliptic integral solutions is presented. These are used to calculate the B-field and flux values for a given circular coil filament, centered on the machine axis.

Since it is known from Maxwell's Equations that the divergence of the magnetic field is zero everywhere, a magnetic vector potential can be defined:

If the Coulomb gauge transformation is now employed ( ), then the relation between the magnetic vector potential A and the current density J is given as follows:

This is of course Poisson's equation, and the general solution in unbounded space is then given by the following expression:

Here r indicates the position of the point where the field is evaluated and r' is the position vector of the current element. Consider now a circular coil filament of radius a, lying in the x/y plane, centered a distance b from the origin and carrying a current I. Figure 7 shows the geometry under discussion. The current density J has only a single component in the F direction. Expressed in cylindrical coordinates, it can be written as follows:

The delta functions restrict current flow to the region of the coil filament in the r and z directions. The current density can now be written in vector format.

Since the problem exhibits cylindrical symmetry, one can freely choose the azimuthal coordinate where the final expression is to be evaluated. Choosing fi=0 results in the azimuthal integration producing no net contribution for the x-component. Therefore only the y component of J needs to be considered in the actual integration. Inserting the obtained expression for the current density into the integration formula for the magnetic vector potential leads to this:

Substituting for the term in the denominator and changing the general volume element to one for cylindrical coordinates the final form is obtained.

Next the integration of the delta functions is performed:

This result can now be expressed in terms of the complete elliptical integrals K and E.

By substituting and utilizing the symmetry of the cosine function together with a trigonometric identity, the following algebraic manipulation leads to the desired result.

Now the elliptic integral parameter k can be defined and the magnetic vector potential is obtained in its final form.

From this expression of the magnetic vector potential the magnetic field values are easily obtained. As defined earlier the magnetic field is the curl of A:

Calculating the derivatives the following expressions for the B-fields are obtained:

The magnetic flux can also easily be calculated from the magnetic vector potential:

Given these relations, the magnetic field strength and flux for a given magnetic diagnostic device of known position can be calculated from the observed current data in a coil-set of circular coils.

Toroidal Green Function

A toroidal coil consists of a circular ring around which a long wire is wrapped. Using the Biot-Savart law, it can be shown that the generated field inside the torus is purely circumferential and independent of the cross-sectional shape of the coil, as long as the shape does not vary over the circumference of the torus.12 The magnitude of the magnetic field is then easily determined by applying Ampere's Law to a circle of radius r about the major axis of the torus, inside the cross-sectional area.

Here I is the current in the coil leads and n the number of turns in the coil. Knowing the position of the toroidal surface magnetic probes and the current in the TF coil thus allows an absolute calibration of the probes using the above relation.

Description of Experimental Equipment

This section describes the physical construction of all the diagnostic devices, their installation on the experiment, and the data acquisition system.

PFC Power Supply Current Transducers

Unlike in the HIT experiment, the poloidal field coils (PFC) of the HIT-II experiment are feedback controlled. Any given subset of the 28 PFCs can be associated with any one of the flux-loops on the experiment. For each coil-subset, a flux-shape (wave form) indicating the desired magnetic flux value vs. time is programmed into the data acquisition system. During a shot, the current output of the PFC power-supplies is then continually adjusted by the feedback mechanism, so that the flux observed at the specified location matches the desired wave form previously stored in the database.
The poloidal field coil power supply current transducers are not installed on the HIT-II experiment itself, but are mounted on a patch panel which allows for flexibility in assigning a particular PFC power supply to a given coil subset. Their main purpose is to monitor the current output of the power supply, thereby providing information on the response of the power supply to its feedback control mechanism. In addition, they provide a reference for magnetic diagnostic calibration. By utilizing the obtained current data to calculate the magnetic values that should be measured by a diagnostic at a given location, and comparing this value with the actually measured data, the device can be calibrated within the accuracy of the current transducers, which is approximately one percent.

Physical Description

The measuring devices are slightly modified model HTA-1000S current transducers, manufactured by LEM America. Figure 9 shows the physical dimensions of the device. Due to the close proximity of the sensors to each other in combination with the strong currents in the PFC power supply leads, additional noise-reduction measures are necessary. Figure 10 shows a schematic drawing of the shielded assembly.

In order to minimize magnetic cross talk, the transducers are mounted with a minimum distance of five inches between neighboring elements. In addition, the entire transducer housing is coated with RF/ES shielding paint, leaving only a small gap for the magnetic flux to penetrate to the measuring element. The conductive coating is then grounded through the shield in the data connection. The technically relevant data is summarized in Table 1.

Table 1: Technical specifications for PFC current transducers

Parameter	Value
Accuracy at +25 deg C	±1%
Supply Voltage	+ and - 15 V (±5%)
Zero Offset at +25 deg C	± 10 mV max
Zero Offset Drift	± 1 mV / deg C max
Temperature Gain Variation	± 0.05% of reading per deg C
Response Time	3 msec max
Frequency Range	RMS current x frequency > 400,000
Output	0-4 V (0-1000 Amps measured current)
Connector	Molex 5045-04 AG

Since the manufacturer calibrates the current transducers prior to shipping, no further calibration of the device is necessary.

Toroidal Field Current Transducer

The toroidal field (TF) is generated by a single 40 turn TF coil, passing through the center column of the experiment and separated into 10 individual return-bundles azimuthally evenly spaced on the outside of the vacuum vessel. The current in the TF coil is measured with two Rogowski coils attached to one of the return bundles. They are constructed of insulated wire wrapped (0.8 turns / mm) around nylon reinforced plastic tubing with a 5 cm2 cross-sectional area. To increase frequency response, the Rogowski loops are connected through a 1 kW series resistor and are terminated with 50 W in the control room. Only one Rogowski loop is actively integrated, while the second is passively integrated. Neither one is electrostaticly shielded.

Flux Loops

As outlined above, flux loop / integrator combinations serve the purpose of providing a voltage signal proportional to the magnetic flux in the area inside the loop. There are a total of 53 flux loops on the HIT-II experiment, wound on the outside casing of the ohmic transformer coils, along the central column, and distributed over the outer shell. In addition to providing information of the plasma's behavior on the surface, the obtained data is also used to yield boundary conditions when reconstructing the plasma's internal equilibrium state.

Location Figure 11 shows a schematic of the flux loop locations on the HIT-II experiment. There are fourteen flux loops of equal area on the transformer coils (Transformer Coil Flux Loops). Another set of fourteen flux loops is wound onto a layer of silicon rubber, held against the inner wall of the central column by a thin stainless steel sheet (Center Column Flux Loops). The third set consists of an additional twenty-five flux loops, wound directly onto the outer shells of the experiment (Outer Shell Flux Loops).

Physical Description

The flux loops on the center column and transformer coil stack consist of ten turn windings of No. 32, high temperature magnet wire. To provide electrostatic shielding, they are wound between layers of conductive adhesive copper tape, which are then grounded. Additional, high temperature insulation between the layers is provided through the use of Kapton tape.

There are two different versions of flux loops mounted on the outer shell of the experiment. The first is wound directly onto the stainless steel shell of the vacuum-vessel and held in place with small stainless steel clips spot-welded onto the shell. Each of these has ten turns, and in this case, electrostatic shielding is provided through the use of coaxial cable. The center wire serves as the actual flux loop, while the coaxial braid is used as the electrostatic shielding. Any loop voltage induced into the flux loop by a changing magnetic field is also present inside the braid, thereby minimizing capacitive coupling between the flux loop and its shielding. However, any electrostatic interference generated in the surrounding space is shielded by the coaxial braid, which is connected to ground on one side only to avoid a ground loop. Figure 12 shows a schematic of the electrical connections (for simplicity only a single turn flux loop is shown).

The second type is similar to the flux loops on the center column and uses the same copper/Kapton-tape setup as electrostatic shielding. It also has ten turns for each flux loop.

Calibration

Calibration of the flux loops requires the determination of the proportionality factor, which relates the measured voltage signal to the observed flux. The following quantities affect this scale-factor:

• the resistance of the flux loop and its leads, RFL [W]
• the value for the attenuator in the signal chain, Fatt [dB]
• the input (terminator) resistance into the integrating circuit, Rterm [W]
• the number of turns in the flux loop, N

The scale factor is then given by the following relationship:

After determining the scale factor from the measured resistance data, an additional flux value can be obtained from PFC current data for comparison. By calculating the Green Functions for each PFC and flux loop, a steady state value for the flux measured in a given loop per ampere of current in a given coil is generated. By multiplying with the observed current data and summing over all coils, a total flux value for each flux loop is obtained. The Green Function for each individual coil/flux loop is calculated using Maxwell's Equations together with the help of elliptic integrals. Between the two methods of the Green Function calculation, and measurement of the resistances in the circuitry, a very good calibration can be achieved, where the data agrees with the calculated values within approximately one percent. For a description of the data acquisition system closing the rest of the signal chain behind the integrator see the separate section below.

Plasma Current Rogowski

The plasma current rogowski is a segmented rogowski loop mounted through the inside of the center column and along the outside shell. Its purpose is to measure the total toroidal plasma current. Since it also picks up contributions from currents running through the walls of the vacuum vessel, these contributions are measured separately and then subtracted from the total value attributed to the plasma current.

Location

The plasma rogowski consist of 22 elements: 11 inside the center column and 11 along the outside shell. The center column segments are mounted on the same stainless steel sheet that supports the magnetic probes and flux loops. The segments along the outer shell are taped directly onto the vacuum vessel using high temperature Kapton tape. Figure 14 shows a cross-section of the experiment indicating the locations of the individual segments' center-points.

Physical Description

The segments of the rogowski are constructed from hollow 1/4-inch diameter Teflon tubing, onto which No. 32, high temperature magnet wire has been wound with the help of a powered drill. The segments are then arrayed inside a layer of Teflon shrink tubing to form three larger groupings: one for the center column and two for the injector and absorber halves of the outer shell. The contributions from all these segments are then individually digitized and added inside the database to obtain the total plasma current and its distribution along the walls of the confinement region on the experiment.

Calibration

In order to calibrate the individual rogowski segments the raw voltage signal is multiplied by a scale-factor and then compared to the B-field values calculated with the help of the current data and the Green Functions. Since the B-field varies over the expanse of the rogowski segment, the values calculated by the Green Function routine are averaged over the volume occupied by the segment. For each segment, three coordinates are measured of the CAD drawings used for the construction of the experiment. A grid of points is then interpolated for a total of 15 points per segment. Comparing the calculated and measured field traces the scale factor is then adjusted until an agreement between both is achieved.

Magnetic Probes

There are 74 magnetic probes mounted on the experiment. Their purpose is to perform surface magnetic measurements, which can then be used to reconstruct the internal Equilibrium State of the plasma. Thirty-two probes are attached to the outer shell of the vacuum vessel, and another 42 are located inside the center column.

Location

Figure 15 shows the location of the magnetic probe's axial arrays on the experiment. There are two axial arrays along the outside shell of the confinement region and extending into the injector, opposing each other at 0 and 180 degrees. Each of these arrays consists of 12 probes, two of them in the injector region. A third axial array of 21 probes is located inside the center column. In addition, there are 4-probe azimuthal arrays in the absorber and injector regions, each probe 90 degrees offset from its neighbor, and the entire ring rotated 30 degrees relative to the axial arrays.

Each outer shell probe is mounted inside a small stainless steel cup, which is then attached to the shell by a port in the vacuum vessel. The magnetic probes on the center column are fastened to a rolled stainless steel sheet, spring loaded against the inner wall of the main structural tube of the center column. The probes are attached to the sheet by small stainless steel clips gripping the probes' Teflon center-body and spot-welded onto the sheet. An additional coating of a silicone based high-temperature adhesive prevents the probe from small movements within its mount. There is an axial array consisting of 21 probes along the column, and 5 azimuthal arrays, two consisting of 8 probes, and three more made of 4 probes each. Note that each of the azimuthal arrays share one probe with the axial array, thereby arriving at a total of 42 center column probes.

Physical Description

The 32 shell probes have three individual windings to measure the magnetic field in all three axis, while the 42 center column probes have only two windings to measure the radial and the poloidal field components, generating a total of 180 twisted pair leads. Figure 17 shows the physical dimensions of the center-body for the probes located on the shell.

The center-body is made of KEL-F, a non-conducting, non-magnetic material with very small temperature dependent expansion. It is precision machined from ˝ inch diameter rod to tolerances of ±0.002 inches. Each of the windings consists of approximately sixty turns of No. 32, high temperature magnet wire. The entire probe assembly is then mounted into a small stainless steel cup, and aligned in such a way that the toroidal winding generates no signal in a purely poloidal field.
The center column probes' center body is machined from Teflon, since the tolerance requirements are not as stringent due to its larger size. The two windings are also made of No. 32, high temperature magnet wire. Alignment is achieved with the help of a notch on both ends of the center-body, in which the stainless steel clip snaps in when the probe is correctly aligned. Figure 18 shows the dimensions of the probe's center-body.Careful measurement and adjustments during the spot-welding process achieve alignment of the clips.

Calibration The calibration procedure for the normal, and poloidal windings of the outer shell probes is identical to that of the rogowski segments. The toroidal winding of the outer shell probes is calibrated using current data from the TF current transducers and the TF coil model developed in the section: Toroidal Green Functions.

Data Acquisition System

The data from all diagnostic devices is read and stored with LeCroy 6810 and 8210 digitizers mounted in CAMAC crates. All signals are integrated using a 50 ohm input active integration circuit, designed and assembled within the experiment group by Dan Lotz. The CAMAC crates are linked to a Kinetic Systems 2000 Serial Highway Driver, controlled by a CTR VAX mainframe. The CAMAC crates are mounted in four racks: three inside the control room and one electrically floating rack in the experiment room. Once the data is stored inside the digitizers, the MIT developed Model Data System (MDS) software is used to retrieve the data through the serial highway connection and store it to a hard disk. For safety reasons, the data is then periodically backed up onto 1.2-GB capacity Digital Audio Tape (DAT).

The floating rack is grounded to the center electrode, and acquires data from the magnetic probes, rogowski segments and flux loops located within the center column of the experiment. Twisted pair leads from the various diagnostics are soldered to Lemo connectors within a shielded junction box suspended from the ceiling above the experiment. RG174/U coax cables running inside a tinned copper-braid shield connect the junction box to the floating rack. Within the floating rack, all cables are threaded through ferrite cores to inhibit common mode transients. A Tygon tube and another copper braid, connected to ground and a copper screen room within which the floating rack is kept, encase the copper braid shielding. Fiber optic U-port adapters allow the floating rack to be electrically isolated from the rest of the data acquisition system. The crates inside the floating rack are powered through a low feed-through capacitance isolation transformer.

All other diagnostic device data is fed to the control room racks through a BNC bulkhead above the absorber side of the machine. RG58/U coax cables are used for the connection between the bulkhead and the control room. To minimize interference problems, all cables are laid inside a grounded aluminum channel and threaded through ferrite cores.

Experimental Procedure

The chapter describes the procedures to verify the chosen methodology and achieve the final calibration results.

Verification of Green Function Calculation

Upon completion of the HIT-II experiment assembly, the placement of the center column relative to the outside shell was found to be within 1 mm of the nominal values specified in the CAD drawings, thereby establishing the coordinate system used in the following calibration procedure with equal accuracy. This provides precise values for the locations of all poloidal field coils. In addition, the transformer stack flux loops were wound directly onto the outside surface of the transformer coils, so that their precise position and radius is also known. This makes the transformer flux loops an ideal diagnostic to verify the validity and accuracy of the Green Function calculation procedure.

In order to minimize the effects of integrator drift in the circuitry, a 'no power base-line' (NPB) shot is taken at the beginning of each calibration procedure. During this shot, the data acquisition system is triggered without any power being fed to the various power supplies of the experiment. The results are then subtracted from the data used for the actual calibration. The data is smoothed over 50 points, using a boxcar-averaging algorithm to further increase the accuracy of the calibration mechanism. The total number of sample-points taken during a shot is 32768, corresponding to a sampling frequency of 1 MHz.

First, the scale-factors for the transformer flux loops are determined by measuring the resistances in the various components of the circuitry (compare Chapter 2:Flux Loops). Next, a time-independent magnetic geometry is created in the experiment for a duration of 25 msec or longer. The data gathered by the PFC current transducers is then passed to the calibration routine to determine the scale-factor based on the Green Function calculation. Comparing the flux data scaled by the factor obtained from resistance measurements, with the flux trace resulting from the calculation provides a direct indication of the validity and accuracy of the Green Functions calculation method. This is repeated several times using varying magnetic geometries.

The results obtained show the two methods to agree within one percent of the observed flux values. This sufficiently establishes the validity and accuracy of the Green Functions calculation method derived in CHAPTER 1: Theory.

Determination of Center Column Sheet Location

The magnetic diagnostics located on the center column (flux loops, rogowski segments, and magnetic probes) are mounted on a stainless steel sheet, rolled up and spring-loaded inside the outer wall of the center column. Due to unforeseen difficulties, this stainless steel sheet might have shifted laterally by up to 3 centimeters in either direction during the assembly of the HIT-II experiment. While the relative location of the diagnostics to each other remains unchanged, the absolute location within the coordinate system of the experiment is no longer known. It is therefore necessary to determine the precise amount of this shift in order to obtain the accurate location of the attached diagnostics.

To determine the shift of the sheet, a procedure similar to the one used to validate the Green Function calculation is used. Again, the scale factor of the center column flux loops is determined by measuring the resistances in the circuit elements. Then a second scale-factor is obtained by the Green Function calculation, using a first guess estimate for the shift to provide locations for the flux loops. After comparing the two values, the estimate for the shift is adjusted to further minimize the deviation. This process is then iteratively repeated until the two scale-factors converge and a final value for the shift is obtained.

Calibration of Normal and Poloidal Diagnostics

To calibrate the various poloidal and normal magnetic diagnostics on the experiment, a suitable magnetic field is generated using only the poloidal field coils. The field geometry is chosen to provide good signal strength at the various positions of the diagnostic devices. The field is held constant for approximately 25 milliseconds via flux-feedback control. The calibration factors can then be determined by achieving a match between the values measured with the diagnostic, and the calculated values based on the current data for the same shot. After the calibration data is obtained, and the desired scale-factors are determined and entered into the database, a second shot is taken to verify the results.

Calibration of Toroidal Diagnostics

Since the PFC do not generate any toroidal field components, the toroidal windings of the outer shell surface magnetic probes are calibrated using the TF coil and current transducer. The soak through time of the vacuum vessel (stainless steel skin time) is significantly less than the fall off time of the TF coil power supplies (RC time). This makes it possible to use a simple TF model as outlined Chapter 1 to determine the Green Functions for the various toroidal probes on the outer shell. The Green Functions can now be used in conjunction with data from the TF current transducers and magnetic signals observed by the probes to determine the scale-factors required for a match of the two traces.

A second issue of concern is the alignment of the outer shell probes in respect to the poloidal and toroidal directions. To minimize pickup of poloidal field components in the toroidal windings and vice versa, the following procedure is implemented during probe installation: An AC field is generated with a single poloidal field coil, and the probe is then rotated until no field is observed on the toroidal winding. Once the pickup has been zeroed out, the probe is fastened in its final position by tightening the con flat holding the probe-cup. Subtracting a multiple of the signal observed on the poloidal winding of a given probe from its toroidal signal can compensate any residual poloidal pickup. The correct factor is determined by zeroing the measured toroidal signal when a purely poloidal field is present. It turns out however, that the initial alignment of the probes during installation was sufficiently accurate to make additional compensation for poloidal pickup unnecessary.

Presentation of Results

This section presents the data used for the calibration of the individual diagnostic devices, and data from the various diagnostic types observed during a typical plasma shot. Depending on the diagnostic to be calibrated a largely poloidal or mostly radial magnetic field geometry is chosen and implemented by the use of flux feedback control. Once the calibration data is obtained, and the desired scale-factors are determined and updated in the database, a second shot is taken to verify the results. In the case of poloidal and normal magnetic field calibrations, the setup of the PFC patch panel and the wave forms utilized are stored in the database.

Since the data in this section consists of a large number of plots, it is omitted in this online version to conserve resources.

Summary and Conclusion

This thesis describes the design and implementation of a variety of magnetic diagnostic devices on the Helicity Injected Tokamak II (HIT-II) experiment. A method is developed to determine the calibration factors for the three major types of magnetic diagnostic devices on the experiment: flux loops, rogowski segments, and magnetic field probes. All of these can be calibrated by comparing the measured data with the values obtained from a Green Function calculation utilizing the available data of the currents in the poloidal field coil (PFC) or toroidal field (TF) power-supplies. The poloidal and normal Green Functions are determined by use of a filament-based model of the PFC, the magnetic vector potential, and complete elliptic integrals. Data on the currents in the PFC power supplies is gathered using slightly modified, commercially available current transducers. All diagnostic devices are successfully calibrated and the data used for the calibration, as well as additional data to confirm the calibration's accuracy is presented. Table 4 shows the repeat accuracy for the various diagnostic devices averaged over all devices in a given category.

Table 4: Overview of repeat accuracy for all diagnostics

Category	Device	Averaged Repeat Deviation
Flux Loops	Transformer Center Column Outer Shell	0.1 % 1.7 % 0.4 %
Plasma Rogowski	Center Column Shell	0.7 % 1.0 %
Magnetic Probe	Center Column Normal Center Column Poloidal Shell Normal Shell Poloidal Shell Toroidal	0.04 % 0.4 % 0.3 % 0.8 % 0.3 %

The relatively poor performance of the center-column flux loops is attributed to the possibility of deformation of the flux loop windings during the assembly of the experiment. This may have lead to the flux loops not lying inside a plane normal to the machine axis as was originally intended. The repeat accuracy of all calibrations lies well within the useful range of signal to noise ratio observed during typical operation of the experiment.

A relatively large number of individual windings on the shell magnetic probes were damaged during assembly, most noticeably in the azimuthal array located in the injector. This is due to the method used in fixating the PFC CS1 at the injector. During the installation the coil scraped over the probe-leads, which lead to the damage. Although in some cases only some of the three windings were severed for a given probe, the remaining windings show unusually high scale-factors and data gathered by these devices should be subjected to additional scrutiny. The pickup of poloidal magnetic field components in the toroidal windings of the outer shell magnetic probes was also investigated and found to be below noise level.

Spot-checks of some of the calibration factors for each class of diagnostic device were performed using varying magnetic field geometries, and found to be within expected tolerances. However, it is still recommended to re-calibrated magnetic diagnostic devices in regular intervals, especially whenever large changes in the vacuum magnetic field geometry are implemented. The software and procedures developed in this thesis allow for convenient calibration of all magnetic diagnostics on the experiment whenever the need arises. A strong emphasis has been placed on making the interface as user friendly and intuitive as possible.