# 3.1 MHD

*3.1.1 Optimizing Macroscopic Stability in the Spherical Torus*

Plasma stability at high plasma pressure is required for economically
attractive operation of a thermonuclear fusion reactor based on magnetic
confinement. For nearly all magnetic confinement concepts, engineering
constraints limit the maximum magnetic field that can be applied to
contain the plasma, so an important figure of merit for magnetic fusion
devices is the plasma beta * * 2*~0~ p*/*B*^2^ where *p* is the plasma
pressure and *B* is the magnetic field within the plasma. For tokamak
plasmas, the plasma pressure can vary significantly across the plasma
cross-section and the applied toroidal field dominates the total field
and varies comparatively little within the plasma. Thus, a commonly used
tokamak figure of merit is the toroidal beta *~T~  2~0~p/B~T0~^2^* where
*p* is the volume-averaged pressure and *B~T0~* is the vacuum toroidal
field at the plasma geometric center. Experiments to date have shown
that ideal magnetohydrodynamic (MHD) stability theory provides an
accurate description of the maximum stable beta for tokamak plasmas. It
is expected that this should also be true for spherical torus \[1\] (ST)
plasmas. However, the high beta and low aspect ratio geometry of the ST
can lead to significant alteration of stability physics in several
important respects. For instance, the elevated safety factor and large
edge magnetic shear, high core rotation and rotational shear, and
comparatively low Alfvén speed and associated enhanced drive for
fast-ion instabilities are each unique characteristics of the ST, which
must be independently evaluated for their impact on stability. It is
also expected this evaluation will benefit significantly from proposed
"similarity" experiments with standard aspect ratio tokamaks (DIII-D)
and other ST devices (MAST), which will attempt to determine the role of
aspect ratio in the physics of several MHD modes, including resistive
wall modes, neoclassical tearing modes, and Alfvén eigenmodes.

For the advanced tokamak (AT) and ST concepts to lead to efficient
steady-state reactors, high beta alone is insufficient. In particular,
most reactor design studies have shown that it is important to have a
large fraction of the plasma current be self-generated through the
neoclassical bootstrap effect to minimize power requirements for
auxiliary systems. Plasma current profiles in largely bootstrap current
driven equilibria are generally broad with low plasma internal
inductance, *l~i~*. Tokamak experience has shown that another important
beta parameter, the normalized beta *~N~  ~T~(%)aB~0~ / I~P~(MA)* may
decrease with decreasing *l~i\ ~*\[2,3,4\] in the absence of wall
stabilization. Since *~T~ ~N~ ^2^* when the bootstrap fraction is held
fixed, it is critical to test such scaling in both the AT and ST.

The potential incompatibility between high and efficient
self-sustainment has motivated several theoretical investigations of the
stabilization of highly bootstrapped AT \[5,6\] and ST \[7\] plasmas.
Significant experimental progress has already been made in removing this
incompatibility in advanced tokamak plasmas by combining conducting
structure (wall stabilization) with plasma rotation \[8,9\] and feedback
systems \[10\] to achieve values of *~T~* significantly above the level
possible without stabilizing systems \[11\]. Applying this experience
and understanding to the ST is particularly important, since design
studies \[12\] indicate that a self-sustained ST reactor would
simultaneously require *~N~* values well above and *l~i~* values well
below those achieved in present advanced tokamaks.

The programmatic focus of MHD studies in NSTX in the coming five years
will be to optimize ST plasma stability in discharges lasting
significantly longer than a current diffusion time with beta values
significantly above the no-wall stability limit with a large fraction of
the plasma current being self-generated. In the near term, optimization
of plasma shape and profiles, error-field correction, and feedback
suppression of the resistive wall mode are viewed as capabilities most
likely to aid in the achievement of the above goals. Neoclassical
tearing modes, fast-ion-driven MHD, and edge-localized modes (ELMs) have
already been observed to often have a deleterious impact on performance.
It is also expected that significant progress in the understanding and
control of these modes will be made as improved diagnostics and
additional heating and current profile control tools become available.

# *3.1.2 Overview of Research Plans for FY2004-2008*

Much of NSTX research over the next five to ten years is tightly linked
to the IPPA ST ten-year goal of achieving long-pulse operation at high
performance. Sub-sections of the IPPA five and ten-year ST operational
goals and the IPPA science goal are listed below for reference. The
underlined and italicized segments of the goals pertain most directly to
MHD research on NSTX.

> **IPPA** --- **ST Five-year goal**: Make a preliminary assessment of
> the attractiveness of the ST regarding confinement, *[stability, and
> high-beta operations]{.underline}*, and non-inductive operations (to
> be achieved early in the 2004-2008 time frame).
>
> **IPPA** --- **ST Ten-year goal**: Assess the attractiveness of
> extrapolable, *[long-pulse operation]{.underline}* of the spherical
> torus for time scales much greater than the current penetration time
> scales (to be achieved in the 2009 timeframe).
>
> **IPPA science goal 1**: Advance the *[fundamental understanding of
> plasmas]{.underline}*\... and enhance predictive capabilities through
> *[comparison of experiments, theory, and simulation]{.underline}***.**
>
> ![](media/image1.wmf){width="3.130708661417323in"
> height="4.161023622047244in"}

The IPPA five-year ST goal as it relates to MHD effectively calls for a
preliminary assessment of the MHD stability limits of NSTX and a further
assessment as to whether these achieved limits are attractive.
Ultimately, this attractiveness must be judged by whether or not the
beta values obtainable in long-pulse and with high bootstrap fraction
are relevant to future reactor-scale devices such as a volume neutron
source, a component test facility, or even a demonstration reactor.

The rapid progress of the NSTX team toward making such assessments
becomes more obvious when one considers that the

MHD group is already beginning to study stability physics related to the
IPPA ST ten-year goal -- extrapolative long-pulse operation. In
particular, recent experiments within the MHD and Integrated Scenario
Development (ISD) experimental task groups have obtained discharges with
total pulse length just over 1 second, 700ms *I~P~* = 800kA flat-top
duration, and =6 and =16% held in near steady-state for at least one
current relaxation time (*~CR~* = 200-250ms). The MHD modes present in
this discharge and other parameters of interest are shown in Figure
3.1.1. Of particular interest in these long-pulse high- shots are the
largely internal disruptions in stored energy whose cause is not yet
fully understood. The most likely explanations given the present
understanding are: 1) that the *q*-profile is evolving to an unstable
state, possibly a reverse-shear *q* profile, which destabilizes double
tearing modes at large minor radius, or 2) the plasma is reaching the
ideal with-wall beta limit and is undergoing a disruption with very weak
external component. Without MSE, it is not yet possible to infer if
double tearing modes are the cause of these disruptions. It is
noteworthy that these long-pulse discharges can be run quiescently with
*~N~* up to 5.8, while attempting to push to higher *~N~* \> 6 often
leads to internal disruptions with a prompt loss of 5-20% of the total
stored energy at high *B~T~* \> 4.5kG. Rapidly growing (=200-500s) *n*=1
precursors are observed just prior to these collapses at frequencies
(15-25kHz) well above the edge-rotation frequency, so it is likely that
these modes are either ideally driven or are driven by fast particles
rather than by near-edge tearing modes, although strongly driven core
tearing modes cannot be definitively ruled out.

Previous theoretical calculations have shown that ideal-wall beta limits
with *~N~* \> 8 are possible in NSTX with optimized profiles. In
particular, a broad total pressure peaking factor \< 2.5 is highly
advantageous for strong coupling to the stabilizing passive plates. For
reference, the thermal pressure peaking factor in NSTX H-modes is
typically near 2. In addition, a *q* profile with *q(0) \> 2* with
either monotonic or weakly reversed shear has been shown to improve low
toroidal mode number stability by eliminating low-order mode rational
surfaces while simultaneously aligning the total current profile with
the off-axis bootstrap current resulting from the broad thermal pressure
profile. Important elements in achieving very high limits in
self-sustaining operation are strongly linked to the transport
properties of NSTX plasmas. Just a few examples of this transport/MHD
synergy include: 1) understanding the role of plasma shape and divertor
geometry in thermal confinement, particle confinement, impurity control,
and pressure peaking, 2) understanding the role of saturated NTMs in
confinement degradation, and 3) understanding the role of fast-ion MHD
in the diffusion and loss of NBI fast-ions and its associated impact on
the pressure, rotation, heating, and current-drive profiles from NBI.

*3.1.3 Macroscopic Stability Results and Plans by Topical Area*

The issues discussed above in the MHD programmatic overview highlight
the need for improved diagnostics and control tools in NSTX to
accurately assess the attractiveness of the ST concept in the near-term
and in the five to ten-year time frame. The following subsections
provide a list of topical areas and a fiscal year timeline for achieving
the required physics, diagnostic, and control tools in each area.

## Recent macroscopic stability improvements

![](media/image2.wmf){width="2.6251968503937007in"
height="2.0744094488188978in"}NSTX has made significant progress during
the past year in reaching high beta under a wide range of operating
conditions. As seen in Figure 3.1.2, normalized beta values of *~N~ \>
6* were achieved during the FY2002 run (shown in red) for normalized
currents in the range of 2.5 to 5MA/mT. By operating at high normalized
current *I~P~ /aB~T0~ \> 6* with *I~P~*=1.2MA and *B~T0~*=0.3 Tesla,
toroidal beta values as high as *~T~* =35% with *~N~ \> 5* were
achieved. As seen in the figure, both *~T~* and *~N~* values have
increased by as much as a factor of 2 relative to operation in FY2001.

Future steady-state ST devices will need to rely heavily on the
neoclassical bootstrap current to generate much of the toroidal plasma
current, so achieving high values of poloidal beta is essential to the
ST concept. Figure 3.1.3 shows that NSTX has more than doubled its
poloidal beta values in the last year and has achieved *~P~* 0.8--1 for
cylindrical kink safety factor *q\** = 2.5--3.5 where *q*\* *20~P~/~N~*.
For reference, NSTX target equilibria with *~T~* =40%, *~N~* \> 8, and
*f~BS~* = 50--80% are indicated by the green region in Figure 3.1.3 and
have ~*P*~ values similar to those achieved experimentally. As seen in
the same figure, a roughly 35% increase in experimental *~N~* would be
needed to access *~N~* values \> 8 typical of a fully self-sustaining
ST-based reactor or a high-bootstrap-fraction steady-state component
test facility (CTF).

Several operational and facility improvements aided in achieving the
high stability parameters shown above. These improvements include more
optimal plasma profiles from reliable H-mode access, improved plasma
shaping, error-field reduction, and elevated plasma safety factor. The
influence of these improvements is discussed below.

### 

### Influence of profiles and shape on global stability -- Results

### 

### ![](media/image4.wmf){width="2.6244094488188976in" height="1.702755905511811in"}Plasma profile effects

![](media/image5.wmf){width="2.456299212598425in"
height="2.645275590551181in"}At the beginning of the FY2002 run
campaign, NSTX gained the capability of high-temperature (350C) bake-out
of its graphite plasma facing components. This led to comparatively easy
access to the H-mode and significantly broader pressure profiles that
are predicted to improve stability in various NSTX operating regimes.
These improvements are synergistic, as H-mode operation prior to
error-field reduction (discussed later in this section) was often
degraded by the excitation of 2/1 tearing modes, which often slowed,
locked, and disrupted the plasma \[13\]. Consistent with theoretical
expectations discussed above, Figure 3.1.4 shows a clear trend of
increasing ~N~ with decreasing pressure peaking factor *p(0)/p* in NSTX.
In this figure, the pressure peaking is determined as a best fit to
external poloidal magnetic signals, the measured diamagnetic flux, and a
scaled electron pressure profile as a loose fitting constraint. This
peaking factor is typically well correlated to the peaking factor of the
thermal pressure component of NSTX plasmas.

Broad current profiles from the large off-axis bootstrap current density
resulting from these broad pressure profiles are also predicted to
improve wall stabilized beta limits by removing low-order mode-rational
surfaces. Given the research goal of accessing very low *l~i~* regimes
at high *~N~*, an important question in NSTX stability research is the
beta limit scaling with internal inductance. As stated above, some
higher aspect ratio experiments have shown that the no-wall normalized
beta limit obeys *~N~ 4 l~i~* \[4\]. Figure 3.1.5 shows that this
empirical limit has been exceeded by a factor of 2.5 at intermediate
values of *l~i~ =* 0.6, and shows that even *~N~* *aB~T0~/I~P~* where
* * 2*~0~* *p* / *B*^2^ exceeds 4*l~i~* by as much as a factor of 1.7.
Perhaps more important than the high *~N~ / l~i~* ratio is the trend of
increasing *~N~* with decreasing *l~i~* evident in the figures. Testing
this trend at lower *l~i~* and assessing the influence of wall
stabilization are important research topics, and future experiments will
develop lower *l~i~* discharges to investigate beta limits at *l~i~*
values approaching those of the NSTX design target.

### Influence of plasma shape

![](media/image6.wmf){width="2.7437007874015746in"
height="2.0515748031496064in"}

Increased plasma shaping is well known to improve tokamak ideal MHD
stability, and NSTX is now able to routinely access significantly higher
elongation and triangularity. As seen by the black symbols in Figure
3.1.6, there was previously little advantage to operating with
elongation much above 1.8 in most discharges. Stability analysis for
L-mode discharges obtained prior to machine improvements found that
*n*=1 internal pressure-driven kink mode stability is degraded for
elongation values above 1.8 when the pressure profile is sufficiently
peaked **---** consistent with the data shown in Figure 3.1.6. For the
data following machine improvements shown in red, the broader pressure
profile reduces the internal kink drive and excites a more global *n*=1
mode, which is more sensitive to boundary shaping and the influence of
wall stabilization. Importantly, NSTX data now shows a trend of
increasing *~N~* with increasing elongation up to at least = 2.1. The
NSTX vertical control system is presently being upgraded to allow more
routine access to even higher elongation to further test this trend.

![](media/image7.wmf){width="2.8173228346456693in"
height="2.95748031496063in"}As seen in Figure 3.1.7, NSTX also now more
routinely operates at higher triangularity up to = 0.8. Figure 3.1.7a
shows that there is a relatively weak dependence of *~N~* on
triangularity for \> 0.4, but as seen in Figure 3.1.7b, the highest
*~T~* values have been achieved at the highest triangularity. Thus, the
increase in *~T~* is a result of the ability to operate at higher
normalized current presumably due to the increased edge safety factor
and shear at high . Figure 3.1.7a also shows that *~N~* values have
increased for all triangularity **---** consistent with the finding that
much of the improved stability in NSTX has come from decreased pressure
profile peaking.

### 

### Influence of profiles and shape on global stability - Plans

> *Goal: Measure and control the discharge shape and profiles to
> optimize stability and maximize the pulse duration at high
> performance.*

FY2003-04 Utilize isoflux control algorithm of real-time EFIT (rtEFIT)
to improve boundary shape control during shot. Increase elongation and
triangularity of lower single null discharges and/or elongation of
highly triangular double null discharges to assess changes in normalized
stability limits. Find optimum shape for highest global stability limit
compatible with long-pulse requirement of tolerable ELMs in H-mode
phase. Perform ramp-rate scans to determine fastest ramp-rate compatible
with long-pulse. Assess confinement and pressure peaking as a function
of discharge shape. Generate time evolving ideal stability analysis
between shots to have immediate knowledge of the beta margin reached
above the no-wall limit, and to generate significant statistics of such
results.

FY2004-05 Utilizing MSE constrained reconstructions early during
discharge ramp-up, use early heating and/or current drive from HHFW
and/or NBI to slow current penetration. Optimize heating programming to
elevate *q* profile above 2 with MHD-stable profile if present operating
scenarios are not already doing this. Assess which MHD instabilities
ameliorate the benefits of early heating and correlate with *q* profile
dynamics. Assess normalized beta limits as a function of controllably
low internal inductance. Experimentally access the second stability
region to high-*n* ballooning modes in the ST by exploiting the
synergistic stabilizing effects of low aspect ratio and high central
safety factor. Determine the effect of finite Larmor radius (FLR),
toroidal shear-flow, and other potential stabilization mechanisms of
high-*n* modes in ST geometry by attempting to significantly violate the
Mercier and high-*n* limits.

FY2004-06 Characterize dynamic evolution of equilibrium and compare to
Tokamak Simulation Code (TSC) predictions to benchmark TSC resistivity,
transport, heating, and current-drive models. Use physics knowledge
gained to improve TSC as needed and to design controllers for heating
and current-drive actuators, and to predict performance in future ST
devices. Assess computationally MHD stability properties of promising
scenarios identified with TSC.

FY2006-08 Utilize split PF1A coils to increase elongation up to 2.5 in
low internal inductance plasmas. Utilize MSE-constrained rtEFITs to
measure current profile in real-time. Use Plasma Control System (PCS)
control of EBW and HHFW to heat and drive current to achieve desired
current profile for optimized stability. Combine high operation with
optimized NBI and RF current drive and investigate -limiting
instabilities in equilibria approaching the NSTX design target of ~T~ =
40% with f~BS~ = 50-80%.

FY03-future Work to develop real-time predictive capability for
stability. Consider neural network and other methods such as MHD
spectroscopy. Implement PCS control of NBI, HHFW, and EBW to allow
real-time feedback control of plasma beta. Use in conjunction with
real-time stability information to operate just below relevant MHD
stability limits.

### Error fields and locked modes --- Results and Status

![](media/image8.wmf){width="3.1251968503937007in"
height="4.611811023622047in"}

Resonant error fields resulting from loss of axi-symmetry due to coil
misalignments and other construction imperfections are well known to
potentially lead to tokamak performance degradation \[14,15,16\]. This
process appears to be particularly important near and above the ideal
no-wall limit \[11\] where error-field amplification can lead to strong
rotation damping and possible destabilization of the resistive wall mode
(RWM) in advanced operating regimes. Early in the commissioning and
calibration of the NSTX locked-mode detectors it became apparent that a
3--4cm effective shift of the lower PF5 vertical field coil was
generating predominantly *n*=1 error-field over much of the NSTX plasma
volume. The coil was subsequently shifted and re-shaped to minimize the
*n*=1 error-field component. Measurements of the corrected coil shape
indicate that the *n*=1 radial error-­­­field strength from the PF5 coil
has been reduced by at least an order of magnitude from roughly 12 Gauss
at the outboard mid-plane to less than 1 Gauss. With regard to the
resonant error field, the corresponding *m/n* = 2/1 vacuum island widths
are computed to have been reduced from approximately 4cm to 0.7cm. This
error-field reduction led immediately to improved performance --- most
noticeably in the locking behavior of ohmic discharges and beam-heated
H-mode discharges. Figure 3.1.8 illustrates that prior to error field
reduction (black curves) ohmic discharges routinely exhibited minor
disruptions in plasma current and major disruptions in plasma density
during the *I~P~* flattop phase. In contrast, the red curves in Figure
3.1.8 show that following error-field reduction there is no locking
behavior evident until the solenoid current limit is reached (near
t=290ms) and strong negative loop voltage is applied that disrupts the
plasma.

While significant error-field reduction was achieved through re-shaping
of the PF5 coil, other sources of error field may still be present in
NSTX. Such sources include asymmetric mounting of the passive plates and
all other PF coils on NSTX whose detailed shapes have not been measured
due to access restrictions. As mentioned above, error fields can lead to
error-field amplification of the resistive wall mode, rotation decay,
and mode locking. Indeed, at sufficiently low density in NSTX, ohmic
locked modes are still observed to lock at preferred toroidal locations
--- albeit with significantly smaller amplitude than measured previously
and with more variability in the locking position. Further, at the
present time, no in-vessel measurements of the error field have been
performed. In order to better diagnose the helical structure of error
fields, locked modes, and resistive wall modes in NSTX, internal
toroidal arrays of radial and vertical field sensors placed above and
below the mid-plane have been installed and are presently being
commissioned. Accurate relative position measurement and calibration of
these sensors should allow the eventual inference of PF coil and other
structural asymmetries. Importantly, these sensors are located much
closer to the plasma surface to better detect the reduced amplitude
locked modes and resistive wall modes. These sensors will ultimately be
used by the plasma control system to generate real-time mode amplitudes
and phases for use in active feedback algorithms.

Assessing the sources, amplitudes, and operational impact of static and
time-varying error fields in tokamak devices can be very challenging --
especially for those error fields due to vessel/coil motion. For
instance, the present locked-mode detector set on NSTX routinely
measures a 3-6 Gauss *n*=1 radial error field which is proportional to
the polarity-dependent product of the TF and OH coil currents. Given
these difficulties and the potential benefits of further reducing the
error field, the error-field reduction techniques planned for the next
five-year period will include both structural improvements/alignments
where possible *and* active error-field correction/suppression. The
active coils of this correction system will be comprised of six (1 meter
tall and 55-60 toroidal extent) ex-vessel picture frame coils much like
the DIII-D error-field correction "C-coils." These coils will be placed
symmetrically around the outboard mid-plane of NSTX, centered vertically
between the primary passive plates, and close to the vessel wall. These
coils and their associated power supplies will be capable of generating
at least 40 Gauss of *n*=1 radial field at the plasma surface. This
capability provides a significant safety margin in the event that large
previously undiagnosed error fields are discovered. It also allows a
significant non-resonant *n*=3 field to be generated which may prove
useful for toroidal rotation control. Finally, sufficiently fast power
supplies will allow fast feedback of the RWM in low-rotation plasmas as
described in later sections.

### Error fields and locked modes --- Plans

> *Goal: Measure, then correct non-axisymmetric error fields through
> engineering improvements and externally applied and controlled n=1
> radial fields.*

FY2003-04 Perform experiments using low-density locked modes and beam
pulses to determine locking threshold as a function of density,
rotation, magnetic field, and current. Use locking position to aid
inference of error-field sources. Commission internal RWM/EF sensor
array electronics. Gather engineering data on primary passive plate
misalignment and sensor positions and calibrate signals including
effects of position. Begin assessment of sources of error field such as
PF coils or passive plates.

FY2004 [Install active coil set]{.underline}. Commission TFTR Transrex
and/or new Robicon Switching Power Amplifiers (SPAs). Interface supply
controls to PCS. After utilizing internal sensor measurements to infer
sources of error field, correct error fields directly where possible
through re-alignment. Determine estimated correction coil currents for
canceling residual error fields without active feedback. Perform
experiments varying applied error-field to minimize rotation damping
near and above no-wall limit. Compare predicted currents for optimal
error-field suppression to those that minimize rotation damping. Develop
PCS control algorithms to use optimal pre-programmed correction coil
currents.

FY2004-05 Purchase and install data acquisition for PCS to acquire
needed magnetic sensor signals in real-time for fast feedback control.
Implement calibration algorithms for in-vessel RWM/EF sensor signals.

FY2005-06 Utilize real-time internal sensor measurements during plasma
operations and develop dynamic error-field correction algorithms.
Supplement or replace pre-programmed error-field correction with dynamic
error-field correction.

FY06-future Study possibility of generating stochastic divertor boundary
with non-axisymmetric coils. If promising, attempt to modify/improve
edge confinement, ELMs, and power flux.

## Beta limiting modes

Pressure-driven kink-ballooning modes and resistive wall modes have been
previously shown to be beta limiting in NBI-heated NSTX discharges
\[17\]. Neoclassical tearing modes have also recently been shown to be a
concern for any ST operating regime that relies upon high poloidal beta
and bootstrap fraction \[18\]. The following subsections discuss the
modes typically observed to limit performance at the highest *~T~* and
*~P~* values achieved following recent machine improvements.

### Limiting modes in highest ~T~ discharges

![](media/image9.wmf){width="2.850787401574803in"
height="4.788976377952756in"}

Figure 3.1.3 shows that the present operating limit of *~N~* 6 restricts
the accessible ~P~ and bootstrap fraction for the highest *~T~*
discharges at low *q\** \< 2. Such discharges also often have low
central safety factor near 1 at high . In such discharges, *n*=1
pressure-driven internal kink modes are computed to be ideally unstable
and are observed to grow on 5 to 20ms time-scales and often exhibit
saturation followed by slow amplitude decay. These large internal *m/n*
= 1*/*1 modes can also lead to saturation in , degradation in plasma
rotation, and sometimes rapid disruption. An example of such behavior
for two 1MA discharges with *B~T0~* = 3kG which reach *~T~* =25% and 31%
is shown in Figure 3.1.9. As seen in the figure, *~T~* exhibits
saturation from t=225ms to 260ms in both discharges despite the previous
increase in NBI heating power by a factor of 3. The highest *~T~*
discharge in Figure 3.1.9 is unique in that the limiting mode amplitude
decreases after t=260ms, allowing the stored energy to increase and
ultimately reach *~P~* = 0.7 and *~N~* = 6.2 prior to undergoing an
uncommonly rapid 400MA/s plasma current disruption. Insight into the
structure of this limiting 1/1 has been gained by correlating the plasma
rotation profiles to fluctuation spectra from the NSTX ultra-soft X-ray
(USXR) array. These studies confirm that the 1/1 mode can exist at very
large minor radius (up to *r/a* 0.6) which likely contributes to the
rapidity of the discharge termination.

### 

![](media/image10.wmf){width="3.2881889763779526in"
height="5.081102362204724in"}

### Limiting modes in high ~P~ long-pulse discharges

In contrast to the lower *~P~* achievable at high *~T~*, Figure 3.1.10
shows time-traces of a typical high *~P~*=1.2 discharge with
*I~P~*=800kA, *B~T0~*=4.5kG, and bootstrap current fraction of 35 to
40%. Figure 3.1.10a shows that during the first 400ms of this discharge,
an *n*=2 mode is measured to initiate near 300ms coincident with a short
burst (amplitude spike) of *n*=1 activity. At t=430ms, Figure 3.1.10c
shows that another burst of *n*=1 activity causes a drop in *~P~*
followed by a subsequent re-heat of the plasma. After this burst at
430ms, Figure 3.1.10d shows that a longer-lived lower-frequency *n*=1
mode initiates which may be a neoclassical tearing mode (NTM). Figure
3.1.10e shows that each continuous mode and *n*=1 burst event decreases
the central rotation speed, and following the second collapse of*~P~* at
t=500ms, the rotation decay is accelerated. Finally, Figure 3.1.10f
shows that after the plasma rotation is below approximately 2 to 4kHz
across most of the profile, the *n*=1 locked-mode signal increases
rapidly and leads to a rapid decay in *~P~* prior to beam turn off at
t=600ms. Clearly, understanding the origin of the bursting *n*=1 modes
and the other continuous and long-lived modes they trigger at high *~P~*
and *~N~* is an important element to further lengthening NSTX discharges
and raising *~N~*.

![](media/image11.wmf){width="3.3437007874015747in"
height="3.0625984251968505in"}To attempt to better understand the
limiting modes observed in Figure 3.1.10 above, the time-evolution of
the *n*=1 ideal MHD stability criteria computed with the DCON \[19\]
code both with and without a conducting wall is shown in Figure 3.1.11
for discharge 108420. The RWM growth time as computed by the coupled
DCON and VALEN \[20\] codes is 15 ms as *~N~* increases beyond the
no-wall beta limit, *~Nno-wall~* 5 near t= 300ms. However, as *~N~*
reaches a peak value of over 6.1, VALEN shows a greatly decreased mode
growth time of 30 s, indicating that the with-wall beta limit,
*~Nwall~*, is being approached and passive wall stabilization has become
less effective. At this point, a beta collapse occurs in the plasma
reducing *~N~* to 4.8. The ideal *n*=1 no-wall stability criterion
computed by DCON shows this value to be close to marginal stability. The
collapse occurs over a few hundred microseconds, consistent with an
ideal mode being heated through the stability limit. In addition, this
initial and subsequent beta collapses correlate exactly with collapses
of the measured neutron rate as shown in Figure 3.1.12. Since neutron
creation occurs almost exclusively in the plasma core, the collapses
indicate that the mode is internal. Using the relatively large value of
*~wall~* = 15 ms for the *n*=1 RWM perturbation computed with DCON and
VALEN when *~N~* initially exceeds *~Nno-wall~*, a conservative estimate
of the plasma duration with *~N~* /*~Nno-wall~* greater than unity is
18*~wall~*. The fast, repeated beta collapses shown in Figure 3.1.10 are
correlated with the magnitude of *~N~*, since similar plasmas have been
maintained for longer pulse lengths (duration of greater than
20*~wall~*) at a nearly constant value of *~N~* = 5.6 *without* fast
beta collapses. For the discharge shown in Figure 3.1.10, DCON shows
that the plasma is also unstable to the *n*=2 mode shortly after *n*=1
instability is determined. Plasma instability to multiple *n* values was
anticipated at high *~N~*, and future work will investigate the presence
of *n*=2 and possibly *n*=3 signatures measured by the new internal
sensor arrays.

***Resistive wall mode physics: rotation damping and passive
stabilization --- Results***

As stated above, long pulse ST plasma operation on the order of the
global resistive diffusion time with *~N~* \> *~Nno-wall~* is a goal of
NSTX. Since sufficient plasma rotation is required to stabilize low-*n*
kink/ballooning modes in the absence of external feedback, rapid
rotation damping associated with RWM destabilization is potentially a
major impediment in reaching this goal. However, as shown in the
previous section, present results have already shown significant
progress in maintaining *~N~* \> *~Nno-wall~* for many
![](media/image13.wmf){width="2.999212598425197in"
height="2.350787401574803in"}resistive wall times. A key to this success
has been operation with increased applied toroidal field. Figure 3.1.13
shows the evolution of the toroidal rotation frequency in the core of
the plasma for several values of *B~T0~*. Also shown is the EFIT
computed *q~min~* (without internal magnetic field measurements from
MSE) for each plasma at peak *~N~*. RWMs are observed in the discharges
with *B~T0~* = 0.34T (*q~min~* = 1.4) and *B~T0~* = 0.39T (*q~min~* =
1.7), leading to the rapid core rotation damping. However, as *B~T0~* is
raised to 0.44T (*q~min~* = 1.9), the *n*=1 signature of the RWM is no
longer apparent in the locked mode detector signal, the rotation damping
rate significantly decreases, and the pulse length is extended. The
fourth case shown also has *B~T0~* = 0.44T, but has slightly different
plasma cross-section (increased elongation) and the computed *q~min~*
rises to slightly above 2. Empirically, systematic analysis of EFIT
reconstructions finds that only plasmas with *q~min~* \> 2 have
maintained high *~N~* for long pulse lengths of order the current
relaxation time.

![](media/image14.png){width="3.8751968503937007in"
height="2.6736220472440944in"}Recent plasmas with reduced static error
field and increased *~N~* exhibit significantly different behavior than
RWMs at lower *~N~*. First, it is rare to find pure RWM activity
separate from tearing mode activity. This observation might be due in
part to an increased difficulty in measuring the RWM field perturbation
with the present locked mode detector (LMD) at the reduced static error
field. LMD signals of between 0.6--1.0 G are now more typical during the
RWM (see Figure 3.1.14). A common feature between RWMs at high and low
*~N~* is the strong toroidal rotation damping observed in both in spite
of increased neutral beam momentum input over lower beta plasmas. The
magnitude of the rotation damping, as well as the detail of the rotation
profile dynamics distinguishes the RWM from tearing mode activity and
suggests a very different physical mechanism for rotation damping
between the two modes. In plasmas exhibiting rotating modes alone,
rotation damping is relatively weak. Figure 3.1.14b illustrates the
toroidal rotation profile dynamics for a plasma initially exhibiting
*n*=1 and 2 rotating mode activity, with *n*=2 largely damped
approximately 60 ms after the mode onset. Magnetic pickup coils show
*n*=1 oscillations with a frequency slowly decreasing from 8 kHz,
consistent with the observed toroidal rotation frequency, *F*, decrease
in the region of the EFIT computed *q*=2 surface. The rotation damping
rate at *q*=2 is nearly constant at -29kHz/s. The profile dynamics show
the damping to be diffusive, originating near the *q*=2 surface, and
penetrating slowly to the plasma core. Mode locking eventually occurs
0.2s later, when rotation at *q*=2 drops to the critical value of
approximately half the initial value, ~0~/2. This process is in
agreement with the theory of rotation damping due to a magnetic island
in the presence of a conducting wall \[21\]. In contrast, Figure 3.1.14a
shows toroidal rotation damping occurring across most of the plasma
cross-section simultaneously when the RWM is present. The process
appears non-diffusive, and similar to the rotation damping process
observed in error field induced locked modes when field penetration
occurs \[16\]. The rotation damping rate near *q* = 2 in the RWM case is
-174 kHz/s, six times more rapid than in the case of islands alone. It
is also clear that the RWM shows only a weak signal in the locked-mode
detector and is accompanied by n=1 rotating mode activity as the RWM
grows. The locked- mode detector signal reaches just 0.6G before the
accompanying island locks. The RWM therefore greatly reduces the time it
normally takes the island to reach ~0~/2. Another remarkable detail of
the rotation damping process is that the edge rotation remains
essentially unchanged during RWM induced rotation damping, whereas the
case of slow rotation damping due to islands shows a viscous drag
outside of *q* = 2. This can be qualitatively explained by invoking a
model of neoclassical viscous drag in the nearly static magnetic field
perturbation of the RWM \[22,23\]. This model has been successfully used
to describe error field induced locked mode damping in JET \[16\]. By
this physics, local rotation damping scales as *B~r~^2^T~i~^0.5^*, where
*B~r~* is the local perturbed field, and *T~i~* is the ion temperature.
Therefore, it is expected that the rotation damping would be greatly
reduced in the colder outer region of the plasma, consistent with the
observation.

### Resistive wall mode physics: rotation damping and passive stabilization --- Plans

> *Goal: Measure and understand flow damping from, and rotational and
> dissipative stabilization of, the resistive wall mode across toroidal
> devices.*

FY2003-04 Propose similarity experiment with DIII-D and MAST to explore
(i) aspect ratio effects of these physics topics (DIII-D), and (ii)
comparison of plasmas approaching and surpassing the no-wall beta limit
with and without conducting structure (MAST). Perform experiments
designed to investigate the nature of RWM stabilization mechanism in the
presence of rotation and investigate role of the RWM itself in modifying
rotation. Using MARS code, perform theoretical assessment of expected
critical rotation frequency for RWM stabilization and associated scaling
with safety factor, magnetic field, shape, and aspect ratio.

FY2004-05 Theoretically and experimentally determine the feasibility of
operation in the "second stability region" of the resistive wall mode.
Explore the existence of toroidally localized, intermediate-*n*
kink/ballooning modes and associated RWMs created through error fields
or tearing modes. Establish with MSE data if low *n* RWMs can be
stabilized and/or rotation damping minimized through elevated *q~min~*
and finite rotation for high *~N~* operational regimes. In regimes where
RWM is passively unstable above the no-wall limit, benchmark codes such
as DCON+VALEN and/or MARS+VACUUM used in predicting RWM structure,
growth-rate, and frequency, against measurements from the internal
RWM/EF magnetic sensor set.

FY05-future Examine the role of RWMs of multiple simultaneous unstable
*n* values. Using experimental results and comparison to theory, assess
rotation required for stabilization of RWM in long-pulse high- operating
regimes. Use knowledge gained to test active feedback stabilization
physics in regimes with low rotation speed and to project to future ST
devices.

***Active RWM stabilization --- Motivation***

While *~N~* values above the no-wall beta limit have been sustained for
a significant number of conducting wall times in toroidally rotating
NSTX plasmas at increased toroidal field, sustaining such plasmas
indefinitely and at lower *q\** may require fast active feedback
stabilization of global MHD modes. Of particular interest for NSTX is
the sustainment of high *~N~* when error-field correction and rotation
from NBI heating are insufficient to provide rotational stabilization of
the RWM, i.e. when the toroidal rotation frequency is below the critical
rotation frequency for RWM destabilization. Such a system would
therefore allow the study of mode stabilization under the low-rotation
conditions that might be expected in an ST reactor.

![](media/image15.wmf){width="2.750787401574803in"
height="2.9925196850393703in"}A physics design of an active feedback
system planned to be installed in NSTX has been conducted with the DCON
and VALEN codes, using equilibrium input from NSTX experiments. These
calculations incorporate the NSTX conducting structure designed to
provide passive stabilization of the RWM. VALEN uses a finite element
representation of thin shell conducting structures in an integral
formulation to model arbitrary conducting walls, combined with a circuit
representation of stable and unstable plasma modes. The VALEN code also
has the capability to model arbitrary control coils, magnetic flux
sensors, simple power supplies and control schemes that would be used to
connect these items together to provide stabilization of plasma
instabilities through active feedback. Previous calculations using VALEN
for the DIII-D device indicate that the most effective systems have
control coils positioned as close as possible to the plasma and as far
away as possible from major conducting structures. A mode control scheme
typically uses a global array of magnetic sensors placed inside the
vacuum vessel as close as possible to the plasma and oriented to sample
the poloidal field of an instability while being orthogonal to the field
produced by the closest control coils. The structure of the instability
may then be identified with feedback logic determining the currents or
voltages applied to the control coils.

A near optimal active feedback system designed to suppress the *n*=1
instability in NSTX has been studied computationally. In this case, the
modeled sensors are positioned inside the vacuum vessel on the plasma
midplane and measure the poloidal field of the instability. As shown in
Figure 3.1.15, control coils were placed inside the vacuum vessel. Six
equal size picture frame coils, which produce local radial fields, cover
the mid-plane circumference of NSTX and are connected 'anti-pairwise'
(control coils diametrically opposite each other are in a series circuit
and their radial fields are in the same direction). The sensors have a
single turn and an area of 1cm^2^. The flux from the sensors is
multiplied by a constant gain to determine the voltage applied to the
control coils. Here, the system gain is expressed as the ratio of the
control coil voltage to input field perturbation amplitude. Figure
3.1.16 illustrates the performance of this system. At a gain of 0.1
*V/G* the plasma is stable for beta normal less than 5.39. Further
improvement in performance may be obtained by increasing the gain up to
about 1.0 *V/G* where the plasma is stable for beta normal less than
6.83. The active feedback system shows no further improvement for
additional increases in gain. Therefore, this system can stabilize the
mode up to *~N~* = 94% where *~N~* *~N~* (ideal-wall) - *~N~* (no-wall).
Alternatives to this 'near optimal' active feedback system have also
been considered, and the 'next best' system has poloidal field sensors
inside the vacuum vessel, but moves the control coils outside the vacuum
vessel. This system reaches a maximum stabilized *~N~* = 72% --- a
decrease of 22% from the near optimal design. Due to considerations such
as cost, system complexity and risk, implementation schedule, and the
capability of performing error-field correction and RWM control with low
effective supply ripple in a single system, it has been decided that
this 'next-best' exterior active coil design will be the first system
implemented on NSTX. This decision does not preclude the installation of
a higher-performance in-vessel coil system at a later date.

### Active RWM stabilization --- Plans

> *Goal: Design and implement an active global mode suppression system,
> and use it to sustain operation near the ideal wall limit.*

FY2003-04 Finalize design of active coil set using DCON+VALEN analysis.
System design will include control of low-*n* modes equal to and greater
than unity. System will be compatible with power/current and
frequency/bandwidth requirements to simultaneously correct error fields
and provide fast feedback for RWM control.

FY2004 Install active coils and power supplies (see section on
error-fields for more detail).

FY2005-06 Develop techniques to control rotation speed independent of
beam heating power to decouple rotation from . Flow damping from
non-resonant error-field excitation using active coils and/or controlled
error-field amplification of the RWM would be possible means. In regimes
where RWM is passively unstable above the no-wall limit, develop
feedback algorithms to stabilize the RWM up to the ideal-wall limit.
Investigate stabilization of multiple-*n* modes, possibly including
toroidally localized ballooning modes. Utilize the implemented multi-*n*
control coil system to create a spectrum of static *m/n* error fields to
determine the effect on the RWM. Also, use non-resonant error fields to
modify NTM island formation.

FY06-future Apply passive and active RWM stabilization to increase safe
operating distance above no-wall stability limit in high- long-pulse
discharges. Utilize RWM feedback to sustain high *~N~* operation close
to the ideal-wall limit in optimized long-pulse discharges.

### Neoclassical tearing modes --- Results

![](media/image18.png){width="2.6354330708661418in"
height="1.9874015748031495in"}

Prior to error-field reduction and before routine H-mode operation, the
effect of *q(0)* crossing 1 varied from mild sawtoothing (if *l~i~* was
sufficiently high) to the development of large radius *n*=1 sawteeth or
kink modes (for low *l~i~*) often resulting in locked modes that
disrupted the plasma. In regimes with *q(0)* \> 1, *n*=2 modes were
often observed to be destabilized prior to the *m/n*=1/1 becoming
unstable whenever *~P~* exceeded 0.4 to 0.5. This trend is evident in
Figure 3.1.3 for the FY2001 data (black symbols) for discharges with
*q\** between 2 and 3. These *n*=2 modes had many of the characteristics
of 3/2 neoclassical tearing modes including island width evolution
consistent with the modified Rutherford equation. As seen in Figure
3.1.17, the island width evolution is fit reasonably well using equation
parameters similar to those of standard aspect ratio tokamaks until
t=260ms. At t=270ms, a 1/1 mode is measured to become unstable possibly
explaining both the degraded fit just prior to 1/1 onset and the
oscillations in island width as inferred from the measured magnetic
perturbation after t=270ms. At present, it is not clear if the *n*=2
mode in the high *~P~* discharge of Figure 3.1.10 is similar to the 3/2
NTM shown in Figure 3.1.17.

### 

### Neoclassical tearing modes --- Plans

> *Goal: Understand NTM stability physics in low aspect ratio geometry
> and feedback stabilize these modes if they significantly impact
> performance.*

FY2003-04 Implement more accurate wall shape model in PEST-III for
wall-stabilized tearing mode stability studies. Implement algorithms in
PEST-III to predict Mirnov signals from rotating islands, compare to
experimental data, and estimate island widths.

FY2004-05 Using measured *q* profiles, assess seeding mechanisms for
NTMs in NSTX standard and advanced operating regimes. Determine if modes
are excited "spontaneously" via proximity to an ideal limit or if seeded
directly from other observable MHD modes. Investigate non-linear
coupling of NTMs of different helicities.

FY2005-06 Measure poloidal mode numbers magnetically utilizing improved
poloidal Mirnov array. Correlate magnetically inferred *m/n* data to
island position measurements from Soft X-ray (SXR) and possibly EBW
radiometer. Infer island widths from measurements and improved modeling
to assess current drive needs for EBW-CD feedback stabilization of the
NTM. Perform initial NTM stabilization studies with 1 MW EBW system in
2006.

FY2006-08 Perform preliminary assessment of changes in NTM stability due
to changes in current profile resulting from EBW current drive and
electron heating. Assess EBW power requirements for NTM stabilization
based on measurements of CD efficiency and required CD for mode
stabilization. Demonstrate direct NTM suppression with pre-programmed
control of launcher and plasma conditions. Verify CD requirements with
NTM modeling of stabilization.

FY08-future Incorporate EBW launcher control into PCS and demonstrate
active feedback stabilization/suppression of the NTM.

### Edge localized modes --- Results

The detailed stability characteristics of edge-localized modes (ELMs)
have not yet been thoroughly investigated in NSTX. Empirically,
separatrix configuration and shaping appear to play a large role in the
type of ELMs observed. Most NSTX long-pulse discharges have favored
lower single null operation both for easier H-mode access and for the
longest durations free of large ELM activity. In contrast, double-null
operation has thus far been more prone to larger ELMs disrupting
long-pulse flattops. Understanding this difference is very important, as
the strong shaping of highly triangular double null plasmas should
enhance no-wall global stability relative to single null operation.
However, ELM size also appears to be strongly related to edge fueling.
Thus, edge collisionality and density effects may be complicating the
interpretation of the types of ELMs observed through the edge
neoclassical bootstrap current. In some modes of operation, edge MHD
with some of the characteristics of an ELM can penetrate far past the
pedestal region into the core plasma. This may be the result of enhanced
poloidal mode coupling resulting from the enhanced toroidicity of the ST
geometry. Understanding and avoiding such modes will continue to be an
important element in improving long-pulse operations.

### Edge localized modes --- Plans

> *Goal: Measure and understand ELM characteristics as function of
> boundary shape and edge plasma conditions.*

FY2003-04 Perform experiments to assess impact of divertor
configuration, shaping, collisionality, and plasma-wall gaps on ELM
stability properties. Characterize pedestal energy loss in various
ELMing regimes and destabilization of NTMs and other modes due to ELMs.

FY2004-05 Commission very high-*n* array data acquisition for
measurement of ELM toroidal mode numbers. Correlate measured mode
numbers with ELM type.

FY2005-06 Use reflectometer or other high-resolution near-edge profile
diagnostic to perform preliminary measurements of ELM structure.

FY06-08 Using kinetic EFITs with MSE and all available profile
information, reconstruct discharges from controlled experiments designed
to excite different types of ELMs. Compare ELM stability threshold, mode
structure, and toroidal mode numbers to predictions from ELM stability
codes such as ELITE, DCON, GATO, or PEST.

FY03-future Throughout next five-year research period, continue to
develop best H-mode discharges in long-pulse discharges by balancing
highest thermal confinement against tolerable ELM size and frequency.

## ![](media/image19.wmf){width="3.0in" height="2.5744094488188978in"}Influence of rotation on equilibrium and stability --- Results

The high rotation speed of many NSTX discharges not only impacts limits
through wall stabilization, but can also modify the underlying
equilibrium itself. The centrifugal force of the spinning plasma most
strongly modifies force balance near the magnetic axis where the
pressure gradient would otherwise be small. An outward major-radial
shift in the electron density is indeed sometimes observable as shown in
Figure 3.1.18, which plots profiles of electron temperature, electron
density, and thermal Alfvén Mach number *M~A~* for an MHD-quiescent
L-mode discharge heated with 1.7MW of 80keV neutral beams. For this
relatively low-density discharge, approximately 2*/*3 of the outward
centrifugal force near the axis comes from the fast-ion component. The
solid line overlaying the density profile in the figure represents the
gradient expected from force balance arguments and is in good agreement
with the measured core gradient when the fast-ion centrifugal force is
included.

![](media/image20.png){width="2.3751968503937007in"
height="2.266535433070866in"}In addition to strong flow modifying
equilibria, flow shear may also impact MHD stability. Calculations using
the M3D \[24\] code for NSTX find that for self-consistent ideal MHD
equilibria with flow included, linear growth rates of *n*=1 internal
pressure-driven kink modes with *q(0)* *\<* 1 can be reduced by as much
as a factor of 3 due to flow-shear. Non-linearly, if sufficient shear
flow is maintained and if the pressure is locally highest within the
island, *m/n*= 1/1 mode saturation can occur. The large saturated 1/1
mode from M3D simulations shown in Figure 3.1.19 is consistent with the
experimentally observed modes at high toroidal as shown in Figure 3.1.9.
This physics likely plays a role in the saturation of and the gradual
decay of the plasma rotation ultimately leading to mode locking and
disruption.

### Influence of rotation on equilibrium and stability --- Plans

> *Goal: Determine the impact of thermal and fast-ion centrifugal force
> on core force balance and include rotation in equilibrium
> reconstructions and stability calculations.*

FY2003-04 Assess the impact of toroidal rotation in equilibrium
reconstructions. Determine change in inferred stored energy due to
inclusion of centrifugal force. If effects are significant, incorporate
rotation effect in control room equilibrium analysis when charge
exchange recombination spectroscopy data is available. Utilize newly
developed FLOW equilibrium code to include toroidal and poloidal flow
and pressure anisotropy effects.

FY04-06 Use core density gradient at magnetic axis as measurement of
total centrifugal force. Compare fast-ion centrifugal force to thermal,
and possibly use changes in central gradient to infer changes in
fast-ion population due to MHD activity. Cross check against beam-ion
profile diagnostics if available, NPA, and fast-lost ion probe (FLIP).
Develop stability code including flows based on FLOW equilibrium.

## Fast ion induced MHD --- Results

### 

### Overview

![](media/image21.wmf){width="2.8570866141732285in"
height="2.3019685039370077in"}

The ST in general, and NSTX in particular, is susceptible to
fast-ion-driven instabilities due to the relatively low Alfvén speed
compared to the neutral beam injection velocity, which is typically 2--4
times higher. Indeed, a wide variety of beam driven instabilities has
been seen in NSTX at frequencies ranging from 10's of kHz to many MHz.
Three beam driven instabilities commonly seen on NSTX have been
identified thus far. These include: Toroidal Alfvén Eigenmodes (TAE) or
Energetic Particle Modes (EPM), fishbone-type instabilities, and
Compressional Alfvén Eigenmodes (CAE). In addition, less well-identified
modes have also been observed. An example of a typical spectrum of MHD
activity in the frequency range up to 150 kHz during NBI on NSTX is
shown in Figure 3.1.20. This range includes the EPM, TAE, and fishbone,
but excludes the "compressional" Alfvénic mode (CAE) activity. The first
shear Alfvénic gap --- the toroidal Alfvén eigenmode gap --- for NSTX
occurs at frequencies between about 50 and 150 kHz. These instabilities
have, for the most part, an insignificant effect on fast-ion confinement
or performance. One exception is during operation at reduced plasma
current where bursts of TAE modes have been well correlated with abrupt
neutron rate drops of order 5--10% and the expulsion of fast ions.

#### TAE modes and fast-ion loss

The non-chirping modes in Figure 3.1.20, typically with toroidal mode
number between 2 and 6, are identified as TAE modes \[25\]. A somewhat
surprising observation is that, unlike beam driven TAE modes in
conventional aspect ratio tokamaks, these modes generally seem to have a
relatively small affect on the fast ion population. No obvious impact is
seen on the neutron rate, nor is there an increase in the measured fast
ion loss. However, in plasma conditions in which the central *q* is high
and the beam ![](media/image22.wmf){width="2.482677165354331in"
height="3.2255905511811025in"}heating is intense, the TAE evolve from
continuous modes to bursting modes, with multiple modes of different *n*
present. When the multiple *n* number bursting TAE modes are present,
significant fast ion losses are observed. In Figure 3.1.21 are shown
waveforms of the plasma current, magnetic fluctuations as measured with
a Mirnov coil, neutron rate, and D light. Coincident with the strong
magnetic fluctuation bursts, sharp drops in the neutron rate and
increases in the D light are seen. These observations are consistent
with losses of 5--10% of the most energetic fast-ion population. In
Figure 3.1.22 is shown a spectrogram of magnetic fluctuations with an
overlay of symbols indicating the toroidal mode numbers. MHD bursts
which are correlated with the fast-ion losses are indicated by vertical
dashed lines. As can be seen, the bursts appear to consist of several
modes with *n* ranging from 2 to 4.

### ![](media/image23.wmf){width="2.6188976377952757in" height="2.101574803149606in"}

### Bounce fishbone modes 

The chirping modes with toroidal mode number *n* = 1 in Figure 3.1.22
are believed to be a new variant of the precession resonance fishbone
\[26,27\] mode commonly observed in conventional aspect ratio tokamaks.
The modes occur when the central *q* is believed to be well above unity.
The fast-ion resonance condition is no longer the precession drift
frequency, but at the fast-ion bounce frequency \[28\]. Subtracting the
plasma central rotation rate, it is seen that the plasma-frame frequency
of the mode chirps downward from about 45 kHz to 25 kHz. In Figure
3.1.23, this range of chirping is compared to the bounce frequencies
from the ORBIT code for the fast-ion distribution calculated with
TRANSP. The modes are seen to be resonant with the large population of
beam ions with energies
![](media/image24.wmf){width="2.3751968503937007in"
height="2.1161417322834644in"}between 10 and 30 kV. The modes appear
relatively weak; they are barely detectable in the soft X-ray emission
and there is not a measurable effect on the neutron rate, implying no
strong loss of fast ions. This observation of bounce-resonance fishbones
has implications for conventional aspect ratio reactors in that the
drift reversal expected to stabilize the fishbone instability may no
longer be sufficient if the fast-ion distribution has a fast-ion
population such that the average bounce angle is large, allowing
resonance at the bounce frequency to drive the modes.

### Compressional Alfvén Waves 

![](media/image25.wmf){width="2.852755905511811in"
height="2.0in"}Compressional Alfvén Eigenmodes (CAE) \[29\] are
calculated to have a unique structure in low aspect ratio devices
\[30\]. The strong gradient in toroidal field from the inboard to
outboard plasma edge translates to a strong poloidal gradient in
magnetic field strength. As a result, the modes should be localized in a
"well" on the outboard edge of the plasma. The experimental observations
of the CAE mode are, so far, in good agreement with the predicted mode
characteristics. It was also predicted that multiple CAE modes of
sufficiently high amplitude could stochastically heat thermal ions
\[31,32\]. Coupled with early measurements that suggested anomalous ion
heating in NSTX, this has encouraged study of the CAE modes \[33\].
Experiments designed to place constraints on the fraction of beam energy
available to drive the CAE instability have demonstrated that it is not
likely that the *observed* CAE modes can be entirely responsible for an
anomalously high ion/electron temperature ratio. As seen in Figure
3.1.24, there is a clear threshold in beam energy necessary to trigger
these CAE instabilities. The threshold has a strong offset linear
dependence on beam voltage and toroidal field, and the threshold is more
complicated than a simple V~beam~ / V~Alfvén~ threshold. For typical
NSTX parameters, the beam energy threshold is at least 55 kV. With only
66% of the beam power in the full-energy component, this means that less
than ≈ 20% of the power of 80 kV beams is available to drive the CAE. As
the 60-80 kV beam population is disproportionately responsible for the
neutron production, a symptom of significant CAE-ion heating would be a
lower than expected neutron rate and a faster decay of the neutron rate
following the end of NBI, neither of which is seen.

### Fast-ion MHD similarity experiments

![](media/image26.png){width="2.4543307086614172in"
height="2.113779527559055in"}In addition to the increased ratio of
fast-ion velocity relative to the Alfvén speed in ST geometry, the
strong toroidicity of the ST can also influence fast ion MHD
characteristics. To better understand this physics, TAE similarity
experiments have been performed on NSTX and DIII-D. In these
experiments, the core Alfvén speed and fast-ion injection energy and
species were matched, as was the plasma shape. Figure 3.1.25 shows that
the excitation threshold is at a similar value of beam beta in both
devices. The most unstable TAE modes are expected to have poloidal
wavelengths approximately 6 times the fast-ion Larmor radius. For NSTX
parameters, this scaling implies that NSTX should observe toroidal mode
numbers roughly 2--3 times lower than in DIII-D because NSTX plasmas
have a higher safety factor at fixed toroidal field due to increased
toroidicity (lower aspect ratio). As seen in Figure 3.1.26, lower
toroidal mode numbers are observed in NSTX --- consistent with
expectations.

### Fast-ion MHD --- Plans

> *Goal: Measure Alfvén Eigenmode stability thresholds and structure,
> compare to theory, and assess the impact of these modes on fast-ion
> confinement.*

FY2003-04 Perform similarity experiments on NSTX and DIII-D
investigating the CAE to assess role of toroidicity on characteristic
frequencies, stability threshold, growth rates, etc. Assess if fast
ion-driven modes at low frequency such as fishbone or rTAE (*f*
=20-40kHz) play a role in high *~P~* disruptions due to elevated *q* or
destabilizing *q* profile (requires MSE).

FY2004-05 Perform first measurements of CAE poloidal amplitude
distribution and poloidal wavelength with new outboard poloidal Mirnov
array (at Bay H). Assess role of *q* profile in controlling gap
structure for TAE modes. Correlate fast-ion loss measurements from FLIP
with mode amplitude, frequency, etc. and determine the energy of ions
preferentially lost.

FY2005-07 Utilize internal diagnostics including reflectometer, EBW
spectrometer, or upgraded bandwidth SXR to measure internal structure of
TAE, CAE, and GAE modes. Utilize fluctuation signatures and frequencies
to distinguish between modes. Compare to theory and modeling with NOVA,
HINST, and HYM. Assess if "pitch-angle anisotropy model" can explain
drive for instabilities and thus how much energy is available to drive
modes.

FY04-future Develop beam-ion profile diagnostic to determine fast-ion
pressure profile. Use profile shape in ideal stability calculations and
for fast-ion MHD instability drive calculations. Assess influence of
fast-ion MHD on fast-ion population properties, such as neutron rate,
power deposition, fast-ion angular momentum, etc. Techniques to be
considered include a neutron collimator, a 3 MeV profile diagnostic, an
array of active neutral particle detectors, and D-alpha light from
re-neutralized beam ions.

***Impact of divertor pumping and secondary passive plate modifications
--- Motivation***

A final complicating factor in achieving high beta and bootstrap
fraction for many current diffusion times in the H-mode discharges
discussed above is the uncontrolled density rise in the H-mode phase. If
internal disruptions and resistive wall modes can be better controlled
in such scenarios with the techniques discussed above, it is expected
that density limit disruptions may begin to occur unless the density
saturates below the Greenwald limit. Further, having little control of
the plasma density in high performance discharges makes it very
difficult to assess the dependence of MHD stability on density and
collisionality. The potential operational and physics capabilities
offered by density control have motivated the consideration of divertor
pumping by the NSTX research team. As has been experienced in several
other tokamak experiments, density control through divertor pumping
comes at the cost of reduced flexibility in discharge shape. Since MHD
stability can be a sensitive function of plasma boundary shape and
proximity of nearby conducting structure, the design of a pumped
divertor will be closely tied to MHD equilibrium and stability
considerations.

### 

### Impact of divertor pumping and secondary passive plate modifications --- Plans

> *Goal: Study and optimize the design of a divertor pumping system
> consistent with acceptable shape flexibility and minimal negative
> impact on stability.*

FY2003-04 Identify (experimentally and computationally) high-performance
DND and SN discharges that are compatible with upper and/or lower
divertor cryo-pumping. Use boundary and SOL geometry from these
discharges to generate preliminary design for pumps and ducts. Determine
passive plate modifications consistent with pump design. Calculate
impact of passive plate modifications on wall stabilization of present
experimental and future target discharges. Assess which plasma shapes
would no longer be achievable with the modified divertor, and which
shapes can be pumped.

FY2005-08 Assuming the cryo-pumps are installed, operational, and can
pump: assess the impact of pumping on MHD stability. Assess changes in
pressure peaking due to pumping and correlate with changes in global
stability limits. Measure changes in NTM and ELM modes with reduced core
and edge collisionality. Measure changes in Alfvén Eigenmode structure
and amplitude caused by lower density operation. Assess impact of
changes in NBI and BS current density profiles on global, NTM, ELM, and
AE stability.

4.  ***Summary of Research Goals for FY2004-2008***

The major NSTX MHD research goals by topical area from section 3.1.3 are
re-stated below to summarize the proposed research plan for the upcoming
five-year period. The proposed research program time line is shown
following these goals.

### Influence of profiles and shape on global stability

> Measure and control the discharge shape and profiles to optimize
> stability and maximize the pulse duration at high performance.

### Error fields and locked modes

> Measure, then correct non-axisymmetric error fields through
> engineering improvements and externally applied and controlled *n*=1
> radial fields.

### Resistive wall mode physics: rotation damping and passive stabilization 

> Measure and understand flow damping from, and rotational and
> dissipative stabilization of, the resistive wall mode across toroidal
> devices.

### Active RWM stabilization

> Design and implement an active global mode suppression system, and use
> it to sustain operation near the ideal wall limit.

### Neoclassical tearing modes

> Understand NTM stability physics in low aspect ratio geometry and
> feedback stabilize these modes if they significantly impact
> performance.

### 

### Fast-ion MHD

> Measure Alfvén Eigenmode stability thresholds and structure, compare
> to theory, and assess the impact of these modes on fast-ion
> confinement.

### Edge-localized modes

> Measure and understand ELM characteristics as function of boundary
> shape and edge plasma conditions.

### Impact of divertor pumping and secondary passive plate modifications

> Study and optimize the design of a divertor pumping system consistent
> with acceptable shape flexibility and minimal negative impact on
> stability.

## ![](media/image28.png){width="6.473611111111111in" height="4.197916666666667in"}

## 

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