CHAPTER 3

The Experiment and the Diagnostic

3.1 RFP

The RFP is a toroidal plasma confinement device which that utilizes magnetic fields to

confine the plasma. A unique feature of the RFP is reversal of the toroidal component

of the magnetic field in the edge region of the plasma. The magnitudes of toroidal and

poloidal fields are comparable in an RFP. The radial profile of MST magnetic fields is

shown in figure 1. This also represents a typical radial profile in an RFP.

FIGURE 1. Radial profiles of MST magnetic fields for a 380 kA standard plasma

discharge.

The relatively weak toroidal magnetic field causes the safety factor in the RFP

to be less than 1 over the plasma cross section and has a negative impact on plasma

stability. This also causes magnetic fluctuations to be relatively large [ref]. The RFP

exhibits a dynamo mechanism for plasma sustainment. At the heart of this mechanism

20

is a naturally occurring relaxation phenomenon, which causes the plasma to evolve to a

minimum energy state. The sawtooth phenomenon in the RFP is a discrete dynamo

event that brings the plasma closer to this relaxed state. While sawteeth occur

periodically in RFP’s, the equilibrium after each relaxation, in general, is considered to

be similar in each case. This fact allows for ensemble analysis of data with respect to

sawtooth crash times [ref]. The high level of magnetic fluctuations (~1.5 % of mean

equilibrium fields) [ref], periodic disturbances in magnetic topology (introduced by

sawteeth) and comparable but, less well determined magnetic field components makes

the RFP very different from other magnetic confinement devices investigated by the

HIBP. Magnetic fluctuations in tokamaks are much less than 1% [ref] and are relatively

constant over the discharge, while stellarator fields are very precisely determined [ref].

3.1.1 RFP plasma formation and sustainment

The phenomenon of field reversal in magnetic confinement systems was first

experimentally observed in the ZETA device in 1960 [ref] and spawned a multitude of

experimental investigations on the RFP. However, it was not until 1974 that a

theoretical explanation for field reversal and plasma relaxation was proposed by J.B.

Taylor [ref]. Many features that are observed in RFP experiments are found to agree

with the Taylor model of plasma relaxation [ref]. In this work he established a

connection between the spontaneous field reversal generated in the RFP and the

phenomenon of plasma relaxation in toroidal devices where the confining fields obeyed

certain characteristics. He identified the requirement for reversal to hinge on two

quantities that were inherently related to the total plasma current, size of the minor

21

radius and the magnetic field on axis. In RFP operation these terms are known as “the

pinch parameter theta” and “the field reversal parameter F” and are defined by the

following equations:

(1)

(2)

The details of the RFP relaxation are discussed in a number of references [ref]. The

dynamo mechanism, which is believed to sustain the RFP field reversal is discussed in

detail in the following references [ref]. The following qualitative discussion will be

limited to the startup, formation and sustainment of the MST-RFP. Figure 2 illustrates

the startup and formation of the MST plasma discharge. The individual steps are

explained below.

Figure 2. MST-RFP startup and plasma formation

22

The operation of the MST begins with the charging up of capacitor banks, which are

used for poloidal and toroidal field generation (not indicated in figure 2). The following

steps take place in sequence to produce an MST plasma discharge:

(1) A small amount of gas is puffed into the system and ionized.

(2) Current is driven in the shell in the poloidal direction.

(3) The surface current produces a toroidal magnetic field inside the vacuum vessel

in accordance with Ampere’s law.

(4) At this point a larger capacitor bank is discharged and a change of poloidal flux

is activated by transformer action. The change in flux produces an inductive

electric field in the toroidal direction.

(5) Further gas is injected into the vacuum vessel. The gas that was ionized in (1)

now follows the field lines and starts to ionize the neutral fuel species just

injected. Once ionized, the particles are confined to their lowest order Larmor

radius excursions about the field lines and cause further ionization. The density

of the plasma begins to increase at this point.

(6) The consequence of the action mentioned in step (5) causes the plasma current

to be formed.

(7) In accordance with Ampere’s law the toroidal plasma current gives rise to a

poloidal component of the magnetic field.

Beyond this startup and formation step of the MST plasma is the phenomenon of

field reversal and plasma sustainment. The reversal of the toroidal field takes place

almost immediately after the formation of the plasma. As explained above, owing

23

to the relative magnitudes of the field components, once the pinch parameter, ‘theta’

reaches a critical value, the reversal criterion becomes satisfied and the plasma

begins to spontaneously reverse. The time trace of the average toroidal magnetic

field and the magnetic field at the wall for a typical 380 kA MST discharge is shown

in figure 3. The field at the wall begins to undergo the reversal process at ~2 ms. A

time trace of the pinch parameter is also plotted in figure 3, which shows that no

reversal occurs below the critical theta value, which is ~1.54 for MST. The

sustainment of the plasma is provided by a pulse-forming network that drives the

inductive electric field for a period of ~60-70ms [ref]. In general the plasma is

sustained for a time period of almost 70ms in a 380 kA discharge.

24

Figure 3 Plots of average toroidal field <Bt>, toroidal field at the wall Bt(wall) and pinch parameter – theta in a high current standard discharge

3.1.2 The sawtooth cycle

An RFP is accompanied characterized by the generation of toroidal flux due to

redistribution of current in the core. This dynamics process is called the sawtooth crash

and has been described in numerous references [ref]. Sawtooth Sawteeth occur

frequently in MST with no specified periodicity. The basic phenomenon of a sawtooth

crash is described below.

The inductive electric field, E, and the mainly toroidal magnetic field drive

parallel current in the core. Quantitatively this is given by the following equation:

(3)

25

The term is higher in the core because both the inductive electric field and majority

of the magnetic field there are in the toroidal direction. At the reversal surface this

product is zero. At the edge this value is small and negative. The variation in the

product of across the minor radius causes the current profile to be peaked in the

core1. Additionally, because the electron temperature in the core of the plasma is higher

than at the edge, the resistivity in the core is lower than at the edge (assuming Spitzer

resistivity ). The lowering of core resistivity also causes the current profile in

the core to become peaked. Consequently as the current gradient starts to increase as a

result of this resistivity profile, it acts a source of free energy to drive the tearing

instability. These tearing instabilities then bring the plasma closer to a relaxed state in a

discrete event or “sawtooth”. The dynamo mechanism that is associated with a

sawtooth crash generates toroidal flux in the plasma. The increase of the average

toroidal field at the sawtooth crash is indicative of this phenomenon (figure 3)

1 In general the core in an RFP is defined to be the region inside the reversal surface (r~43 cm)

26

In MST, the sawtooth cycle is defined to be the time period ranging from the

beginning of one sawtooth crash to the beginning of the next. It is characterized by a

rather quick crash phase on the order of a 100 microseconds followed by a relatively

slow rise phase on the order of a few milliseconds. The period in between can be

described as one in which the plasma is in a quasi-equilibrium phase. The global

parameters such as plasma current and density do not change dramatically during this

time period. This time period is also seen to be an opportune moment for HIBP

measurements because of the rather slow variation in the magnetic topology compared

to the fast changes during the sawtooth cycle. The HIBP experiments discussed in this

thesis focus on results obtained at times that are at least 1.5 ms away from the sawtooth

crash.

3.2 MST

The maximum machine parameters of MST are summarized in table 1.

MST parameter Value

480 kA

2 x

0.48 T

1100 eV

500 eV

9 %

9 ms

Pulse length 70 ms

Table 3-1. Optimum MST plasma parameters achieved.

27

Of the presently operating RFPs, MST is large in size and has a record of

impressive achievements. Also, what sets this machine apart from other RFP’s or other

toroidal devices is the machine design itself. MST has no external field coils and

utilizes a one-turn iron core transformer, a thick aluminum vacuum shell and an array of

pulse forming networks to achieve plasma confinement [ref]. A schematic diagram of

the device is given in figure 4 below.

Figure 3.4. Schematic of the MST-RFP [ref]

The MST operational procedure is remarkably simple considering the

engineering complexity of this device. The operator needs only to be mindful of a

handful of items for successful operation such as main bank voltages (that determine the

toroidal field & the plasma current) and gas fueling. Waveforms of the primary current

in the transformer and the plasma current are monitored once the discharge takes place.

In addition, the density, radiation levels, field reversal parameter and termination of the

plasma current are important parameters that determine the overall characteristic of a

plasma discharge. The cycle time of operation depends on how much capacitor bank

28

voltage is required to produce the plasma, the time needed for cooling of the vacuum

vessel and the time needed for data acquired to be stored and readying digitizers for

acquiring data for the subsequent shot. Typical cycle times for operation ranges from

2.5 to 4 minutes depending on the plasma current. In a typical day, it is not uncommon

to take over 200 shots. MST is capable of operating in a multitude of modes that

produce a variety of discharges. A number of these discharges were utilized in the

experiments discussed in this thesis and are described below.

3.2.3 MST parameters

The plasmas produced in MST are monitored on a shot-to-shot basis. There are a

number of parameters that are monitored immediately after a discharge takes place and

there are other parameters that need significant signal processing before they are known

to any appreciable extent. In general, 7 different types of discharges can be produced in

MST. This thesis deals with three of the variants. The important plasma parameters

(both operator controlled and machine determined) and the nature of these discharges

will be described below.

29

3.2.3.1. Plasma current

The plasma current in MST ranges from 140-450 kA. Typically 250-280 kA is

categorized as low current and 350-450 kA as high current. Time trace of the plasma

current in a typical 380 kA standard plasma discharge is shown in figure 5.

Figure 5. Plasma current in a typical 380 kA plasma discharge.

30

The total plasma current is measured using a Rogowski coil [ref] and is

reproduced rather well on a shot-to-shot basis. However, it has been often observed that

the flat-top in MST is not always re-producible. In some cases, the current flat tops

after reaching a peak value (before a sawtooth crash). While in others the plasma

current starts to decay rather rapidly after it peaks. This decay can be up to 3% of the

peak value. The main causes for this irregularity in the plasma current is due toare

mechanisms which that control the way in which the capacitor banks fire in the pulse-

forming network (PFN). This irregularity is use of concern from an HIBP perspective.

Since the HIBP particle trajectories are sensitive to the magnetic field, any deviation by

more than a few percent in the current can cause significant changes (~3cm) in the

measurement location (discussed in chapter 5). Hence, reliable HIBP measurements are

made over a time period when the changes are limited to less than a few percent.

3.3.2 Density

The typical densities in MST are summarized in table 2. When the machine is

relatively clean, stable operations at any given plasma current are easily achieved

over a large number of shots. The plasma density then tends to be quite

reproducible even over several sawtooth intervals. The electron density in MST is

measured using a CO2 interferometer diagnostic. The central cord averaged

measurement is used to characterize the peak density during the discharge. A time

trace from a typical 380 kA standard discharge is shown in figure 6.

High current Low Current Locked Biased

n_e 0.5 –1.6 0.5-1.2 0.5-1 0.7-1.2

31

Table 2. Density range in four different MST plasma discharges. All values are multiplied by

Figure 6. Time trace of line averaged central density in a 383 kA standard discharge.

The density in a standard discharge changes at the sawtooth crash. The drop in

the magnitude signals a loss of electrons (and ions) from the plasma at this time. The

control of plasma density is inherently related to machine wall cleanliness because

fueling from the vacuum vessel wall can be a significant component of the total fuel

used to produce the plasma.

3.2.3.3 Field reversal parameter

The field reversal parameter (F) characterizes changes in the magnetic field in an RFP.

More specifically, F is mathematically defined as:

(4)

Wherewhere, is the toroidal magnetic field at the wall of the machine and

is the average toroidal field. A time trace of F in a typical standard 380 kA

standard discharge is shown in figure 7.

32

Figure 7. Time trace of the field reversal parameter in a typical 380 kA standard discharge.

Typically, F decreases very rapidly in magnitude 1-1.5 ms after the crash and

remains fairly constant until the next crash. The changes in F are associated with

changes in the average magnetic field as well as at the wall as defined by equation (1).

At the onset of a sawtooth crash, the magnitude of F increases sharply. This behavior is

consistent with the RFP dynamo theory. The increase in F at the crash signals a

reduction in toroidal flux.

3.2.3.4 Sawtooth crash

The sawteeth sawtooth oscillations are characteristic of all standard MST discharges.

While they are essential for the plasma to be sustained, they also introduce abrupt

changes in the magnetic topology. Such crashes typically occur at multiple times

during a shot with no specific periodicity. Furthermore, neither the time event of a

sawtooth crash, nor the interval between two successive crashes is identical in any two

discharges. However, in discharges that are “similar”, sawtooth crashes occur at

approximately the same time during the shot. It is important to note that the physics of

the sawtooth crash may or may not be similar from one crash to the next, much less

33

from one discharge to another. The dominant n=6 toroidal mode rotation is one such

parameter that can change dramatically from one sawtooth cycle to the next and plays

an important role in the HIBP potential profile measurement. Physics issues

surrounding a sawtooth crash have been ongoing subject of investigation in MST [ref].

In 380 kA discharges, there are usually 3-4 sawtooth crashes during the flat-top

phase. The time period between each successive crash ranges from 7-9 ms. Sawteeth

are more prevalent in a low current discharge with the time between two successive

crashes lessening to around 5-6 ms. There is no major change in sawtooth activity in

biased discharges compared to the low current standard case. However, the locked

discharge has no sawtooth crashes.

3.2.3.5 Mode Velocity

Like the sawtooth crash, the magnetic mode rotation velocity is also determined solely

by the dynamics of the plasma. The m=1,n=6 magnetic mode is the dominant mode in

MST (as inferred from MHD theory [ref] . From an HIBP perspective, the n=6 mode

velocity has been found to be an important parameter in determining shot-to-shot

reproducibility since it has been found to correlates remarkably well with the magnitude

of the plasma potential. The magnitude of the phase velocity of the n=6 mode is

experimentally observed to be similar to the toroidal impurity flow in low current

standard discharges [ref]. Hence any relationship between toroidal plasma flow and the

radial electric field can also be related to the phase velocity of this mode. Thus, it is

important to group only discharges that have similar mode velocities for the purpose of

measuring the radial electric field. This topic will be discussed in detail in chapters 4

34

and 6. A typical time trace of the n=6 mode phase velocity is given in figure 8. The

n=6 mode is typically observed to slow down rapidly to a zero speed during a sawtooth

crash and then re-accelerate to a peak value on a slower time scale (~1-2 ms) after it.

Figure 8. Time trace of n=6 mode velocity

The correlation between mode speed and plasma rotation has not been

established in the core in high current discharges since carbon impurity species inside

the hot core (r/a <0.7) rendering it very difficult to obtain a reliable measurement of the

plasma flow. But it is expected that the close correlation observed at low currents

should also prevail at higher currents. Such comparisons will be made in the short-term

future with the CHERS diagnostic measurement of the core toroidal flow.

3.2.4. MST Discharges

There are basically 3 different types of plasmas produced in MST, namely (a) standard,

(b) pulsed poloidal current drive (PPCD) and (c) spontaneous enhanced confinement

[ref]. There are various permutations on a standard discharge with the plasma produced

in each found to be unique in some characteristic. While changing the plasma current

and density alone can produce differences in plasma discharges, the permutations

35

described here result from changes brought about by more complicated mechanisms.

Three such discharges are: locked, edge biased and f=0 discharges [ref]. Locked and

edge biased discharges are interesting from an HIBP perspective because the measured

plasma potential and radial electric field are both different from the standard discharge.

Only HIBP measurements associated with the variations in the standard discharge will

be discussed in this thesis. Typical time traces of the various parameters in these

discharges will be presented and discussed in connection with the experiments in

chapter 4.

3.2.4.1 Standard discharge

The word “standard”standard in this context refers to the most basic type of plasma

produced in MST. In these discharges, no extra effort is required to clean the vacuum

vessel walls, to monitor fuel injected into the plasma (enhanced confinement discharge

[ref]), or to apply external electric fields to modify plasma currents (pulsed poloidal

current drive discharges). The current in the standard discharge ranges from 120 kA to

500 kA. Low current discharges range from 200-280 kA and high currents range from

380-450 kA. Certain minimum conditions are required to produce this discharge,

namely a relatively good vacuum (> 2 e-62x10-6 Torr) and a relatively clean MST

chamber for plasma breakdown to occur (plasma cleanliness is not easily quantitatively

explained). The standard discharges, for the most part, are rather reproducible and

allow for averaging of data collected over different sawtooth events (discussed below).

On a shot-to-shot basis, the main variations in the standard discharge are the rotation

velocity of the n=6 mode, the electron density and the times at which sawteeth occur

36

during the discharge. The plasma parameters in a high current standard discharge are

given in table 3. Changes in these parameters over the time period associated with

HIBP measurements will be discussed in chapter 4.

MST parameter Value

380 kA

1.0 x

0.358 T

15 V

325 eV

300 eV

6 %

1-2 ms

Pulse length 70 ms

Table 3. MST parameters in a 383 kA standard discharge

3.2.4.2. Locked discharge

A locked discharge is produced when a rotating magnetic structure phase locks relative

to the vacuum vessel, or simply ceases to rotate in the lab frame. In MST, such a

magnetic structure is the n=6 toroidal number mode. Mode locking occurs when the

mode’s angular velocity is made to match that of some other entity such as an externally

applied field error though an electromagnetic torque. Typically in a standard discharge,

the phenomenon of locking occurs immediately following a sawtooth crash. Prior to the

sawtooth crash, the phase velocity of the n=6 mode reaches up to 40 km/s, although

37

values in the range of 20-30 km/s are more typical. In the time period of ~100 s near

the crash there is a rapid deceleration of the mode, a phenomenon described as

temporary locking. Immediately following the sawtooth crash the modes are observed

to re-accelerate on a slower time scale of a few ms. In some instances, due to the

electromagnetic interaction between a field error and the magnetic mode, the

acceleration is retarded and the mode remains permanently locked for the remainder of

the discharge [ref]. Figure 6 shows the time trace of the n=6 mode phase velocity in a

typical locked discharge.

Figure 6. n=6 mode velocity in a locked discharge. Locking occurs at 13.5ms.

While the mechanisms underlying the phenomenon of mode locking are

identified, detailed information about the relationship between plasma parameters or

equilibrium quantities and locking is not quite clear. In particular, the relationship

between the radial electric field and mode locking is an interesting study because of the

close physics ties of both with plasma rotation.

Characteristically, the plasma conditions in locked discharges tends to be rather

degraded. The plasma confinement time rapidly decreases, while the line average

density can increase or remain constant. In general, the electron temperature decreases

as well [ref]. The plasma potential in the core is also observed to decrease in locked

38

shots by about 500-600V compared to a standard discharge at approximately the same

plasma density. Locked discharges can be produced at almost any plasma current,

though it is more prevalentthey are more common in high current discharges, where the

modes can lock spontaneously during the discharge. The occurrence of locking is also

observed to increase with plasma density at fixed plasma currents. In discharges where

locking does not spontaneously occur, the plasma can be induced into locking by

application of externally applied field errors [ref]. This method is often used to produce

locking in low current discharges.

Locking is also dependent to an extent on the fueling species. Natural locking

tends to be less prevalent in standard 250-380 kA plasmas, which use deuterium as the

main fuel species. Hydrogen plasmas tend to naturally lock even at low plasma currents

[ref]. 01191425428782

39

3.4.2.3 Edge Biased discharge

In low plasma currents (less than 280 kA), insertion of biased electrodes in standard

rotating plasmas has been found to impact the edge and core rotation [ref]. In particular

the rotation at the edge is observed to increase substantially while that at the core is seen

to slow down considerably. Thus, there has been considerable interest in investigating

the radial electric field in response to these dramatic changes in rotation. While the

edge electric field has been measured with probes in such discharges, in the core had

remained uninvestigated until now. measurements in the edge have been shown to

exhibit strong flow shear behavior, and results are consistent with the reduction in

electrostatic turbulence induced particle transport due to enhanced flow shear [ref-

terry]. On the other hand, biasing does not reduce the magnetic fluctuations that plague

the standard discharge in MST, hence no reduction in magnetic fluctuation induced

particle transport is observed in these discharges.

The procedure of bringing about a biased discharge is illustrated in figure 8

[ref]. Typically a couple of electrodes or current injectors are inserted 8-10cm into the

plasma and turned on for a period of 10 ms during the middle of a discharge. Current is

driven along the magnetic field by applying an electrostatic voltage between electrode

that intercept the field lines and the vacuum vesell vessel wall. Electrons are injected

along the field lines and an electron current equal to the injected current is

simultaneously driven across magnetic field lines to the wall [ref].

40

Figure 8. Set up for producing a biased discharge. The probe is biased negative with respect to the MST vacuum chamber.

The mode and plasma rotation at the edge are affected in the following way.

The forces created by the injected current exerts a torque on the plasma causing a

strong toroidal flow. At the edge, the magnetic field is mostly in the poloidal direction

and the injected current is radial thus causing a net toroidal force. Naturally, the overall

dynamics of mode rotation is are determined by a torque balance between the forces due

to viscosity, other drag forces and that due to the J x B forces caused by current

injection. The forces that affect the rotation act in the toroidal direction, hence it is also

assumed that flow at the edge is expected to contribute to the total flow there.

While the changes in the edge flow can be explained by the changes brought about

injecting edge radial current, the changes in the core flow profile are due to other

mechanisms. One such mechanism is viscous coupling between the edge and the core

plasma that brings about a change in the core rotation in response to the changes at the

edge. The exact dynamics are more complicated and described in [ref]. Experimental

measurements of core flow in these discharges show that the overall magnitude of the

41

toroidal impurity flow is reduced by over 75% over the duration of biasing. Typically

toroidal flow changes from ~23 km/s to about 7.5 km/s. On the other hand the poloidal

impurity flow is not observed to change much at all (~5-7 km/s). The impact of the

change in rotation will be discussed further in chapter 6 in connection with the radial

electric field measurements in the core region. One of the main reasons biased

discharges are limited to low currents is because of probe survival issues. High plasma

temperatures (~325 eV) are characteristic of higher plasma currents (380 kA) and

provide virtually no chance for probe tip survival.

Besides changes in rotation, a dramatic increase in the plasma density also

occurs during the time of biasing. This increase is primarily due to the emission of

particles from the probes and also due to a particle sourcing as a result of enhanced

confinement. High level of UV radiation also takes place in a biased discharge and is

primarily due to the increase in the impurity species from probe contamination. The

UV level can increase by more than a factor of 4-5 compared to a standard discharge.

This poses significant challenges for HIBP measurements because of UV loading of

HIBP ion beam deflection system [ref].

3.2.5 Diagnostics

The plasma parameters measured by each MST diagnostic and the experimental

conditions under which each is able to operate are given in table 4 below. The actual

range of plasma coverage is not indicated in the table.

DIAGNOSTIC PARAMETER OPERATIONAL RANGE

Thomson Scattering Electron temperature

42

Ion dynamics spectrometer Limited to plasma edge in high Ip

CHERS Ion density & temperature profile >250 kA

Rutherford Scattering Ion temperatureImpurity line monitors UV RadiationCo2 interferometer Density profile All IpFIR interferometer Central density All IpPolarimeter Current profile High IpCoil array/ Rogowski coils Magnetic fluctuations All IpMotional Stark Effect Mean B on axis All Ip

HIBPPlasma PotentialElectric fieldPhi/ n fluctuations

>250 kAUV loading affects sweeps in f=0

Langmuir probe

Plasma PotentialElectric fieldPotential/density fluctuations

Limited to edge in low and high Ip

Table 4. List of diagnostics on MST.

3.2 HIBP

The HIBP is a charged particle diagnostic which is capable of making unperturbing

nonperturbing measurements of the plasma potential profile in high temperature

plasmas. In this section, the principles of HIBP measurement of plasma potential will

be described. The HIBP system applied on MST-RFP will also be discussed.

3.2.1 Technique of Heavy Ion Beam Probing

The technique of Heavy ion beam probing is illustrated in figure 9. The MST-HIBP

operation is based on the injection of Sodium sodium or Potassium potassium ions into

the MST plasma. These singly charged ions, called the primary beam, become further

ionized in the plasma, primarily due to collisions with the plasma electrons. This

ionization occurs along the length of the entire primary beam and the resultant doubly

charged ions become separated from the primary by virtue of the Lorentz force acting

on the particles as shown in figure 9.

43

Figure 9. Principles of Heavy Ion Beam Probing

While this spray of secondary ions emanates along the primary beam, only a

portion of it actually exits from the machine vessel and enters the region of the HIBP

called the secondary beamline. There the secondary beam is no longer acted upon by

the magnetic fields in the plasma and drifts towards the entrance of the electrostatic

energy analyzer. The MST-HIBP system is equipped with electrostatic deflection plates

in the secondary beamline to alter the ion beam trajectory. The beam then enters the

analyzer through a 10 cm by 0.6cm opening called the entrance aperture. There are

three such apertures in the MST HIBP analyzer and their opening sizes can be

individually controlled. The HIBP analyzer utilizes an electrostatic field to deflect the

incoming ion beam onto a detector (also shown in figure 9). This detector consists of

four electrically isolated plates. The energy of the secondary beam is computed using

experimentally determined calibration constants, the relative amounts of signal on the

four detector plates and knowledge of the angles of the analyzer orientation with respect

to the beamline axis.

44

3.2.2 Principles of potential measurement

The HIBP measurement of plasma potential is based on the principle of conservation of energy. An illustration of potential measurement is shown in figure 10.

Figure 10. Principle of potential measurement. The injection location, the point of ionization and the point of detection are numerically labeled.

The measurement of the potential requires the beam energy of the injected and detected

species to be known. At point 1, the beam energy of the primary beam is entirely

kinetic. Once this beam enters the plasma, it begins to experience the potential energy

due to presence of a charge distribution in the plasma. Depending on whether the

potential of the plasma is positive or negative, the primary beam either moves up a hill

or down a valley. In MST, where the potential is measured to be positive, the ion beam

slows down as it moves up the potential hill. In doing so, it loses kinetic energy and

gains an equivalent amount of potential energy (assuming that collisions have not

caused the particles to loose any energy). At point 2, the ion that has moved up the hill

loses an electron and becomes doubly charged2. The beam energy of this “new” 2 There is nothing special about location 2. Ionization occurs along the entire path of the primary beam. Point 2 here simply illustrates a point where the emerging secondary beam can follow a trajectory which will allow it to safely exit the MST chamber and be detected.

45

speciessecondary ion is now different because of the loss of an electron. The kinetic

energy of the new beam is not different from the kinetic energy of the primary beam

because the momentum transfer that takes place during the electron loss process is

negligible. However, the potential energy of the primary beam is different from that of

the secondary because of difference in the electronic charge of the two species. The

doubly charged beam makes its way down the potential hill, gaining kinetic energy in

the process. Once it exits the plasma, its energy is entirely kinetic. The general

expression for the plasma potential can be obtained in the following way:

The total energy of the primary beam at points 1 and 2 is given by:

(5)

(6)

where, T and U refer to the kinetic and potential energy respectively. The subscript

“primary “ primary refers to the primary beam. The numerical subscript refers to the

location in the system as shown in Figure 10 9.

Since the total energy is conserved, we can equate (5) and (6):

or rearranging:

(7)

The total energy of the secondary beam at point 2 and 3 is:

(8)

(9)

Similarly equating the total energy of the secondary beam at points 2 and 3 we get:

46

(10)

Since the kinetic energy of the primary and the secondary beams at point 2 are not very

different (difference being equal to the kinetic energy of the electron), these two

quantities can be equated to one another:

Equation 10 then becomes:

(11)

Substituting the expression for from equation 7 in equation 11 we get:

Re-arranging this we get

(12)

The potential energies in the above equation can be expressed in terms of the plasma

potential ( ) of the measurement location.

The terms on the right can be expressed in terms of measurable HIBP primary beam (

) and secondary beam ( ) energies. The primary beam energy is

simply the charge of the primary beam times the accelerating voltage.

The charged species in the MST-HIBP experiments are simply singly and doubly

ionized.

47

Finally expressing equation 8 in terms of the above quantities and re-arranging we get:

(13)

The secondary ion beam energy is given by the following formula [ref]:

The quantities featured in this equation are: The accelerator and analyzer voltages,

calibration constants of the analyzer, namely the “gain (G)” and “offline processing

term (F)” and the detected signals on each of the four detector plates and an angle

which defines the angle made by the secondary beam in the plane of the analyzer with

reference to the axis of the secondary beamline (figure 13).

In terms of the measured secondary beam energy equation 9 can be expressed as:

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(14)

This equation shows that the accuracy of the measurement of plasma potential depends

on the how well the energy analyzer is calibrated. The offline processing term is

directly proportional to the change in the potential measured at each point in the plasma

and is thus most relevant for electric field measurement. Theta and alpha are illustrated

in figure 11 and measured with respect to the beamline and analyzer. The impact of the

uncertainty in these angles will be discussed in the appendices.

Figure 11. Illustration of angles and made by the secondary beam. The figure on the top is a view from above and the lower FIGURE below is a side view of the system

3.2.3 MST-HIBP system

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The MST-HIBP system [ref] was custom designed for the Madison Symmetric Torus.

However, a large percentage of the system requirements were adapted from previous

Rensselaer HIBP systems. A great deal of the system is documented in [ref].

The MST -HIBP [ref] system consists of the following: A (200 kV) ion

accelerator, two beamlines- -- one for the primary beam and one for the secondary

beam, multiple sets of sweep or deflection plates- -- needed for steering the primary and

secondary beam, high voltage power supplies, an electrostatic energy analyzer and high

voltage measurement equipment. An outline of the system is illustrated in figure 12.

The energy analyzer will be discussed in appendix B.

Figure 12. Major components of the MST-HIBP system

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3.2.3.1 MST-HIBP design work

While the HIBP had to be custom designed, the specific problems facing the initial

design work focused on two main items: the beam energy requirement and the location

of the primary and the secondary beamline. These two items were addressed in a

preliminary design study where it was determined that the MST-HIBP had a good deal

of flexibility in the ion species to be used for probing. Because of relatively weaker

magnetic fields in MST (0.4 T) compared to tokamaks (2T), lithium, sodium and

potassium ions were viable options for choice of probing species. In addition, it was

determined that a highly three dimensional beamline positioning would be required for

successful detection of the secondary ion beam because of the highly three dimensional

HIBP ion beam trajectories [ref]. The primary and secondary beamlines were toroidally

separated by 10 degrees and poloidally separated by 86 degrees. In addition, the

primary beamline was tilted at an angle of 3 degrees towards the exit port [ref].

Secondly, real-estate requirements also played an important role in the design work. In

this regard, several different schemes for positioning the primary and secondary

beamlines at various toroidal and poloidal locations on MST were investigated to ensure

that the HIBP would fit with existing diagnostics and other machine hardware. Thirdly,

the incorporation of previously existing components from the ATF, ISX-B and TEXT

HIBPs has been an important part of the design work of the MST-HIBP diagnostic.

Finally, a number of other important issues ranging from overcoming challenges

provided by small ports and large level of UV during the plasma discharge played an

equally important role in the final shaping of the MST-HIBP design. [ref]

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3.2.3.2 Beam energy requirement

The beam energy requirement is addressed by examining the equation for the Larmor

radius of the HIBP beam in a given magnetic field.

(15)

Rearranging the above equation and setting the condition that (minor radius) we

obtain the following relation:

(16)

Where refers to the beam energy of the HIBP ion beam, and m is the mass of the

beam species, B is the peak magnetic field, and a is the minor radius.

The inequality arises because of the need for the HIBP ion beam to escape any possible

confinement in the plasma. What is important to observe in the above equation is that

the beam energy varies as the square of the magnetic field, which in MST is

significantly less than those of other beam probe systems.

The maximum magnetic field in MST is on the order of 0.48 T. This is a rather

modest magnetic field for the HIBP considering that former devices include a 2T

magnetic field in the TEXT -tokamak. The relatively weak magnetic field and the

relatively large minor radii, compared to other RPI-HIBP’s, limited the beam energy

requirement to low values. Initial calculations of the beam energy indicated that a 40-

90 keV Na beam was adequate for HIBP operations on MST. Given the low magnetic

fields and the voltage capability of the HIBP accelerator, even Li ions were considered

feasible for HIBP experiments. The beam energy requirements for Lithium would push

the ion accelerator to its operational limits of 200 keV. Early trajectory calculations

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also showed that a very low energy Li beam (7 keV) could also be used to probe the

extreme edge region of MST [ref]. Given the choice of ions and the range of beam

energy, the MST-HIBP system can be viewed to be a very versatile system from the

perspective of heavy ion beam probing.

3.2.3.3 Trajectory modeling and port pair determination

Simulation of HIBP primary and secondary ion beam trajectories were

conducted to determine the location of the entrance port and the overall plasma

coverage. Because of complicated three dimensional ion beam trajectories and the

requirement to scan as much of the plasma minor radii as possible, the existing

combinations of ports on MST were inadequate for HIBP purposes. Ultimately the

design was based on selecting the largest available port for the secondary beam and

locating (through simulations) a new port for the primary beamline. [ref]].

Preliminary information about the magnetic field for ion orbit simulations was

provided by the MST group. This magnetic field information was obtained using a

toroidal equilibrium code for a circular cross section RFP (MSTEQ) [ref] and was used

to determine sample volume coverage in MST as well as to determine port pairs. Since

HIBP ion orbits are sensitive to the magnetic field, the accuracy of the trajectory study

is determined to a large extent by just how well established the magnetic equilibrium

is In this sense a comparison is provided (figure 13) between the field generated from

MSTEQ used in the design work of MST-HIBP and that obtained from MSTFit [ref]

used to determine sample volume locations for experiments described in this thesis

(discussed in chapter 5). Some of the quantities that show demonstrate the differences

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between the two models are also shown. Plot (a), Magnetic magnetic field strength: the

magnitude of the toroidal and poloidal fields vary by 20% and 15% respectively

between the two models. Plot (b), Sample sample locations computed using a ion beam

injection conditions and energy show that they vary by ~7 cm. Plot (c), A a view from

above of the ion beam trajectories in the ssecondary secondary beamline region shows

that the HIBP secondary beam (as computed using the old model lands approximately

30cm away from the detector). [ref].

__________________________________________________Figure 13. HIBP ion trajectories used to demonstrate the difference between the MSTEQ model and equilibrium generated from MSTFit. (a) Magnitudes of fields (b) Difference in HIBP measurement locations (c) HIBP ion orbits.

The HIBP ion orbits in MST are fully three dimensional. Typical primary and

secondary ion beam trajectories in the MST are illustrated in figure 14. These

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trajectories are much like those in a Stellarator [ref]. Three-dimensional trajectories in

MST arise because of the relatively equal magnitudes of the poloidal and toroidal

components of the confining magnetic field. In MST, the toroidal field component

dominates in the core region while the poloidal component starts to become larger at

r/a~0.4. Hence, the toroidal deflection of the primary and secondary beam is

significant.

Figure 14. HIBP ion beam trajectories in poloidal plane and view from above.

3.2.3.4 Sweep system design

As discussed in the section above, the result of the simulation study was also used to

design the ion beam deflection system. This system is significantly more complicated

than that installed on any previous RPI-HIBP system. The layout of the primary

beamline deflection system is shown in figure 15. The type of arrangement of plates

shown in this figure is called a cross over sweep design [ref]. The name cross over

stems from the fact that the primary beam is deflected by two sets of radial/toroidal

sweep plates with each set deflecting the beam in completely opposite directions. The

requirement for the cross over system stems from its ability to accomplish large angle

steering of the primary ion beam by circumventing the need for a large port. In MST

this entrance port is 4.5” in diameter.

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Figure 154. Cross over sweep system used to deflect the primary beam ions in the MST-HIBP

The goal of the primary beamline sweeps was to deflect ion beams with energies

of up to 200 keV by as much as +/-20 degrees in the radial direction and +/-5 degrees

in the toroidal direction. The basic components of this system consist ofare four sets of

stainless steel parallel plates. Two sets of plates are aligned in the toroidal direction and

the other two sets are aligned to produce a deflection of the injected ion beam in the

radial direction.

A second sweep system was also incorporated in the secondary beamline of the

MST HIBP. This is the first application of such a deflection system on an RPI HIBP.

Its inclusion was to accommodate the wide spread of angles made by secondary beam

fan that exits the MST vacuum vessel. There is one set of plates capable of steering the

fan in a vertical direction and two sets of sweeps that deflect the beam in the lateral or

toroidal direction. The layout of this system is shown in figure 165.

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Figure 165. MST-HIBP primary and secondary sweep systems

2.3.7 Other design work

Like cross over sweeps, magnetic suppression structures in the primary and secondary

beamlines are among some of the newer components in the MST-HIBP. Numerous

tests were conducted pre-installation, to characterize the loading suffered experienced

by the HIBP deflection plates due to the plasma particles and UV escaping from the

ports [ref]. The experimental setup involved using a pair of parallel plates separated by

1” with plate dimensions ~2” wide by 3” long (with one plate connected to the high

voltage output of a power supply and the other grounded). These plates were exposed

to ~200 kA, 0.5 x density MST plasma through a 4.5” port. The plates were

located approximately 4.5” “ away from the MST vacuum vessel wall. Tests revealed

that the level of UV and plasma (mostly electrons) was too large for any positive or

negative voltage to be held on the plates. Total radiated power in standard MST

plasmas can be as large as 2 MW [ref]. Calculations show that for the two processes

UV and plasma leakage effects, the total electron saturation current was on the order of

8A, and 1 A respectively [ref]. Calculations assume 80mA/cm^2 and ~10 mA/cm^2 of

electron saturation current due to plasma and UV. Further tests with a 1cm diameter

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aperture and a wire mesh (transparency unknown) and magnets (~2 kG at the center of

the aperture) allowed both positive and negative voltages of up to +/- 5kV to be held,

indicating that magnetic suppression scheme could help reduce prevent the unconfined

ions and electrons from entering the HIBP sweep plate region.

The final magnetic suppression structures designed for the primary and

secondary beamlines are described in detail in [ref]. A photograph of this structure is

given in figure. Given the already small exit port, the size of the aperture used in the

secondary beamline was 8 cm by 11 cm wide and 1 cm deep (midlplane) and its outer

diameter was 4.5”. The peak magnetic field was 1.7 kG at the midplane of the

structure. The value of the magnetic field was estimated using calculations of the fields

required to trap 200 eV electrons.

3.2.3.6 Summary

MST falls into a class of magnetic confinement devices known as a reversed field

pinches. The comparable magnitudes of the poloidal and toroidal magnetic field,

periodic sawteeth in magnetic energy and relatively large magnetic fluctuation levels

(~1.5%) characterize the MST –RFP’s plasma behaviour. In the context of other RFP

configurations, MST is a device with a relatively large cross section, and operates at

medium densities (~1.2x ) and plasma current (<450 kA). MST is also

relatively easy to operate and can produce a variety of difference different plasma

discharges with some small changes in operational procedures. Plasma current, density,

field reversal parameter and gas fueling are important parameters that characterize an

MST discharge and are among the important parameters monitored during operation.

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All of these quantities undergo periodic changes brought about by relaxation of the RFP

plasma to a near minimum energy state as a result of a sawtooth crash. The periodic

sawtooth crash (recurring on ~6-9 ms time scale) is a robust feature of MST and is

prevalent in almost all of the different types of discharges3. Sawtooth Sawteeth changes

magnetic equilibrium equilibria by ~50%, density by ~20% and plasma current by ~4%

in time scales of ~0.1 ms. Standard, locked and electrode electrode-biased discharges

are some examples of MST plasmas which are characterized by dramatic changes in

density (biased), flow velocity (biased, locked) and confinement (biased). These

discharges have been investigated using the HIBP. Of these, the standard discharge is

also the most reproducible in terms of sawteeth sawtooth occurrence, plasma current

and density. The MST plasma is often simultaneously diagnosed for temperature, flow,

density and magnetic behavior. In this connection, the application of the heavy ion

beam probe diagnostic for the first time in an RFP [ref] has provided the first ever

results of plasma potential measurements in the core of a hot RFP [ref] along with

simultaneous measurements of the above mentioned parameters.

The heavy ion beam probe (HIBP) is a charged particle diagnostic which that

possesses an unique ability to make unperturbing nonperturbing measurements of

plasma potential profiles. The measurement of the difference between the injected and

the detected beams allows for a direct and localized measurement of the plasma

potential to be made in the plasma. For its application on MST, the design of the MST-

HIBP system has incorporated information from extensive simulation results to

determine port pair combinations, and sweep plate loading tests to determine plasma

3 Sawtooth oscillations are suppressed completely in pulsed poloidal current drive discharges and its magnitude is weakened significantly in enhanced confinement discharges

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and UV suppression structures for operation of its cross over sweep deflection system.

The latter two characterize some of the novel but essential components of the MST-

HIBP system [ref]. The MST-HIBP is also one of the most versatile systems designed

by the RPI group because of its ability to use Sodiumsodium, Potassium potassium and

lithium ions as probing species. This is due to a lower confining magnetic field (<0.48

T) on MST compared to tokamaks. In experiments, typical probing energies range from

40 to 75 keV (Sodiumsodium) to investigate low and high current discharges,

respectively.

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