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.
60