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Chapter 7
Summary and further work
7.1 Main results
A heavy ion beam probe has been successfully implemented on an RFP for the first
time [ref]. Numerous design and operational challenges have been overcome to obtain
the first ever measurements of space potential and potential profiles in the core of a hot
(>300 eV) reversed field pinch magnetic confinement device [ref]. Although the core
potential had been believed to be positive (as inferred from edge measurements), its
magnitude of ~1800V in high current plasmas has now been established[ref].
Confirmed also is the existence of a radially outward directed electric field with a
magnitude of approximately 2300-2600 V/m in these discharges. While electric field
and rotation have been linked in toroidal confinement devices [ref], this hypothesis has
also been confirmed in an RFP by investigating plasmas with a variety of rotational
properties. It has been found that the radial electric field is large ~2 kV/m and
outwardly directed in a low current standard plasma where toroidal rotation speed is on
the order of 22.5 km/s. Additionally, the electric field as inferred from HIBP potential
profile measurements is small or even zero when the toroidal rotation speeds reduce to
7.5 km/s. The poloidal rotation velocity was measured to range from 4-7.5 km/s in all
three discharges.
The results obtained in this thesis are divided into two main sections. The first
deals with establishing the ability of the HIBP to make quality measurements of the
plasma potential profile in high current standard discharges (discussed in chapters 4 and
5). Though plagued by high levels of magnetic turbulence induced particle losses
2
[ref]and by sawtooth crashes that periodically destroy the magnetic topology[ref], the
standard discharge in MST was also the most robust, easily reproduced and the simplest
to investigate. The scatter in the potential data from shots that were similar required
scrutinizing MST parameters which were most important for determining shot to shot
reproducibility. In this connection the variation of plasma potential with density and
n=6 mode phase velocity were identified and studied. The plasma potential was found
to vary inversely with plasma density in high current standard discharges at mid-way
through the minor radius of the plasma [ref]. Typical plasma potential ranged from
1200 to 2300V in densities of 1.6 to 0.5 x 1013 / cm 3 . The connection between plasma
potential and phase rotation of the core resonant dominant tearing mode (m=1, n=6
mode) at a similar location revealed a linear relationship between the two quantities.
Typically, higher plasma potentials (2200 V in a 383 kA plasma) corresponded to an
n=6 mode phase velocity of ~40 km/s1.
Periodic disturbances in the magnetic topology introduced by sawtooth crashes
in MST limited useful data taking time to about 6 ms in high current standard
discharges and to approximately 3 ms in low current standard discharges. For
consistency, each realization of the potential profile was referenced to a sawtooth crash
and grouped according to their relative proximity to a crash. This method allowed a
time average potential profile to be obtained at three time periods during a sawtooth
cycle in high current standard discharges. These results showed that the plasma
potential remained positive (1750-2000V) during the time period spanning from 1.5 ms
after a sawtooth crash to ~1 ms before a the next crash. The time evolution of the
1
Typical maximum value in discharges investigated
3
electric fields over the same time period showed that the peak electric field evolved
from 2300 to ~ 2700V/m. While the HIBP was able to measure the evolution of plasma
potential near the sawtooth crash, the interpretation of these results requires further
work which will require additional information on the fields. However, the positive
potential measured near the vicinity of the sawtooth crash suggests that the core remains
stochastic over the entire discharge [ref].
The development of an equilibrium magnetic field reconstruction routine played
a key role in allowing a confident measurement of the radial electric field to be made in
a device where most of the magnetic field is generated by the plasma itself (discussed in
chapter 5). The time resolved electric field measurements reported in this thesis relied
on the ability of MSTFit to generate a 0.1 ms time-averaged equilibrium specified at an
arbitrary time during plasma discharges in which electric fields were measured. The
versatility of MSTFit and the sensitivity of the HIBP were exploited to generate
equilibria which were consistent with HIBP experimental results.
The second part of the thesis discussed the relationship between plasma rotation
and the radial electric field (chapter 6). Simultaneous measurements of core rotation
and pressure gradient revealed that the measured electric field magnitude of 1600-2000
 
V/m correlated predominantly with v  B rotation over the radial range of 17< r < 25
cm. Outside this range, pressure gradient terms were important contributors to the
radial force balance. The electric fields in biased and locked discharges were found to
be small and correlate with dramatically reduced levels (7.5km/s) of toroidal plasma
rotation compared to standard discharges (22.5 km/s). However a conclusive test of the
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radial force balance awaits measurement of core ion temperature and electron density in
these discharges2.
 
In regions of relatively weak pressure gradients, E  B rotation tended to be the
dominant source of perpendicular flow in the core in standard discharges. The peak
magnitude of this drift was on the order of ~9 km/s in low current standard discharges.
The significance of the diamagnetic drift was greater for r > 25 cm. Inside this radius it
represented roughly 25% (~2.5 km/s) of the total perpendicular flow ( ~12 km/s) as
computed from measurements of total plasma flow in MST. Additionally, the fact that
 
the measured poloidal rotation was in a direction opposite to the poloidal E  B drift
was quantitatively analyzed and attributed to a large poloidal component of the parallel
flow in MST [ref].
Finally these results have also helped answer some long standing questions on
the nature of the ambipolar electric field in stochastic magnetic fields (chapter 6). HIBP
results suggest that currently existing theories on transport in stochastic fields need to
include effects of plasma rotation in order to present a self consistent picture of
transport in MST-RFP. The theoretically predicted value of the electric field in the core
is smaller by a factor of 5-10 compared to HIBP measured results.
7.2 Further extensions of this work
Areas of HIBP developmental work which require future attention are:

Development of a magnetic bending system in the secondary beamline to obtain
a greater degree of radial coverage.
2
Electron density profile was measured in a biased discharge.
5

Development of a computer controlled ion beam trajectory deflection system:
Utilization of Labview software and a computer with GPIB capablilty will allow
programming of the sweep plate voltages required to enhance coverage of the
plasma cross section [ref]. The existing database of sweep values can be
incorporated [ref]. Implementation of this system will allow for efficient
detection of secondary beam when investigating novel discharge conditions.

Increasing confidence in equilibrium reconstruction:
As knowledge of secondary beam exit vectors is an important element of
generating an equilibrium that is compatible with diagnostic results, the
confidence in selecting this vector in simulation work needs to be improved. An
aperture placed at the exit port can be used to pin-point the location of the
secondary beam at the exit port [ref]. This combined with information about the
landing point of the beam on the detector will help narrow the available choices
for the secondary beam exit vector.
Summary of possible physics investigation:

Developing the confidence level of the HIBP measurement of plasma potential is
by far the most important item. The sign of the plasma potential indicates the nature
of the confined species. Hence, the potential in discharges that possess very good
confinement properties would be in direct contradiction with the direction of the
radial electric field if the offset in the plasma potential was large and positive.
However probing the edge region, both inside and outside the reversal surface can
provide an opportunity to compare the two values. The HIBP measurements can be
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compared with probe measurements to determine if there is any substantial offset in
HIBP potential measurements.

Further investigation of biased plasmas in the core will help understand relationship
between electric field and flow. While the experiments described in this thesis
were conducted in experiments where core toroidal flow was small but finite, the
impact of zero plasma rotation has not yet been investigated. It is expected that if
the radial electric field is still inherently related to bulk toroidal flow, then the
impact of such an experiment would be to establish the existence of a negative
electric field. However, whether the plasma potential changes sign is an open
question. The flow in the core can also be reversed to further investigate the radial
electric field in this region [ref]. On the other hand, the electric field in positively
edge biased plasmas which speed up rotation has not been measured. Simultaneous
measurements of the pressure profile are important for relating electric field with
flows, especially if the contribution from pressure gradient is large.

Locked plasmas should be investigated in situations where locking is spontaneous
and caused by non-linear interaction of internal torques in the plasma [ref]. In the
experiments described here the n=6 mode was locked by applying external field
errors. By determining the radial electric field before and after locking, and
comparing it with standard discharges, its impact on the observed phenomenon of
locking can be investigated.

Investigation of the radial electric field in hydrogen plasmas should also be
investigated. The difference in plasma rotation due to different species has been
identified in MST [ref]. Because hydrogen plasmas tend to rotate faster than
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deuterium [ref], whether the radial electric field will change in these plasmas is an
open question.

Enhanced confinement is a major thrust of the RFP experimental program. In this
connection, spontaneous enhanced confinement (EC) and pulsed poloidal current
drive plasmas in MST should continue to be investigated. The investigation in EC
plasmas has shown that mode rotation of up to 65 km/s is not uncommon.
However, the reduction of magnetic fluctuation induced transport and the impact of
increased rotation on the magnitude and the sign of the plasma potential will be
 
useful to investigate in the core region. In the edge, the effects of strong E  B
induced flow shear and its impact on turbulent transport in both plasmas have been
investigated at low currents. The investigation of the transition from standard to
enhanced confinement in high current discharges, will be of great importance to the
physics study of MST.
In conclusion, all of these measurements and improvements in the HIBP system
will make this diagnostic an even more valuable tool for potential and electric field
related studies on MST.