Proceedings of ITC/ISHW2007

Experimental Tests of Quasisymmetry in HSX
J.N. Talmadge, F.S.B. Anderson, D.T. Anderson, C. Deng, W. Guttenfelder, K.M. Likin, J. Lore, P.H.
Probert, J.C. Schmitt, K. Zhai
HSX Plasma Laboratory, University of Wisconsin-Madison, USA(Received)

This paper discusses the results from experiments in HSX testing the properties of a quasisymmetric stellarator.
HSX is a quasihelical stellarator with minimal toroidal curvature and a high effective transform. The high effective
transform was verified from passing particle orbits as well as from the magnitude of the Pfirsch-Schlüter andbootstrap currents. The passing particle orbit shift, the helical structure of the Pfirsch-Schlüter current and the
direction of the bootstrap current were all consistent with minimal toroidal curvature. Good agreement wasobserved between data from plasma currents obtained by a set of magnetic pick-up coils and the results of the
V3FIT code. Good confinement of trapped particles was observed with quasisymmetry. These particles may be
responsible for a coherent global MHD mode that was detected during ECH at B = 0.5 T. It was found that the
breaking of quasisymmetry increased the hollowness of the density profile and the damping of plasma flow while
decreasing the core electron temperature, in good agreement with neoclassical models. At 0.5 T, anomaloustransport appeared unaffected by the degree of quasisymmetry; more work is need to understand if this still holds at
1.0 T. The experimental energy confinement time and electron temperature profile could be reproduced reasonably
well with a combination of neoclassical transport and a modified Weiland model for ITG/TEM turbulence.
Keywords: quasisymmetry, HSX, quasihelical symmetry, transport, effective transform, bootstrap current,
Pfirsch-Schlüter current, turbulence

1. Introduction
The poor neoclassical transport in the low
collisionality regime of conventional stellarators has
spurred efforts to design stellarators which combine thegood single particle confinement of the tokamak and thesteady-state, disruption-free characteristics of stellarators.
The paper by Mynick [1] summarizes various approaches
by which neoclassical transport in stellarators might be
improved. One such approach is the quasisymmetricstellarator, pioneered by Nührenberg and Zille [2] and by
Garabedian [3]. A quasisymmetric stellarator is one inwhich the magnetic field spectrum is dominated by a single
harmonic. Aside from the tokamak-like neoclassicaltransport, quasisymmetric stellarators possess a directionof symmetry in |B| and hence minimal parallel viscousdamping in that direction. Such a property may be
advantageous for improving anomalous transport.
The quasisymmetric approach to improving transport
in stellarators is the thrust of the U.S. stellarator program.
The Helically Symmetric Experiment (HSX) [4] is the firstquasisymmetric stellarator in the world. The symmetry inthis experiment is in the helical direction. The
quasi-axisymmetric
National
Compact
Stellarator
Experiment (NCSX) [5], is symmetric in the toroidal
direction and is currently under construction at PPPL.
author’s e-mail:talmadge@wisc.edu

Finally, the proposed Quasi Poloidal Stellarator (QPS) [6]at ORNL has a direction of symmetry in the poloidal
direction.
In Boozer coordinates, the magnitude of the magnetic
field for a quasihelically symmetric (QHS) stellarator canbe written as
B B0 = 1 − bnm cos(nφ − mθ )(1)where φ is the toroidal angle and θ is the poloidal angle.
In a straight field-line coordinate system given by θ = ιφ ,where ι is the rotational transform, the magnetic field
variation on the field line is given by
B B0 = 1 − bnm cos([n − mι ]φ )(2)This is similar to the variation along a field line in atokamak with the substitution ι eff = n − mι for therotational transform. For HSX, with n = 4, m = 1 and ι ≥ 1 ,the effective transform ι eff is about 3.
The combination of quasisymmetry and high effective
transform in HSX results in small drifts of passing particles
from a flux surface, small banana widths, small plasma
currents, low neoclassical transport and low parallelviscous damping. On the other hand, the high curvatureProceedings of ITC/ISHW2007
and small connection length in HSX may be responsible
for somewhat larger anomalous transport. This paper
discusses what recent experimental results from HSX cantell us about the properties of a quasisymmetric stellarator.

around the magnetic axis poloidally, |B| undergoes justunder 3 oscillations. For the corresponding tokamak withthe same transform, there is 1 oscillation. Another way tolook at it is to see that the gradient of |B| changes sign overa much smaller spatial scale in a QHS device than in atokamak, resulting in smaller deviation from a flux surface.
Figure 2 shows the measured electron orbit in HSX
after mapping to Boozer coordinates. The deviation of theorbit from a flux surface is due to the n = 4, m = 1 helicalfield on the right side of the experimental data and to then = 1, m = 1 earth’s field on the left. The earth’s field issignificant in this case because the experiment was done ata magnetic field of only 90 g; at higher fields the earth’s
field can be neglected. To the right of the data is acalculated orbit of the electron if it were in a tokamak (andneglecting the earth’s field). Comparing the two figures it
can be seen that indeed the orbit shift is outside the flux
surface for the QHS case and inside the surface for the
tokamak. Also, the orbit shift is smaller for the QHS casebecause of the higher effective transform.

Fig.1 Contours of constant |B| for a quasihelicallysymmetric configuration (top) and for a tokamak (bottom).
Also shown is a magnetic field line with a rotationaltransform of 1.06. The arrows point in the direction ofincreasing |B| in the poloidal direction. Red is the
maximum field, blue is the minimum.

2. Drift Orbits
The leading m ≠ 0 terms of the vacuum magnetic
field spectrum in HSX were determined by measuring theorbit shift of passing electrons from a flux surface [7]. At
low energies, the electrons injected with a filament stayclose to the flux surface and were used to map the lab
coordinate frame into Boozer coordinates using a neuralnetwork. At higher energies, the electrons deviate fromthe flux surface and measurement of this deviation atseveral toroidal locations yields the spectrum.
The direction of the shift of the electron from amagnetic surface is a verification of the lack of toroidal
curvature in HSX. Figure 1 is a comparison of thecontours of constant |B| in HSX and in a tokamak. Alonga magnetic field line close to a toroidal angle of zero
degrees, the direction of increasing B is oppositely
directed in the two cases. Since the radial drift velocity inBoozer coordinates for a curl-free magnetic field is given
by B0 r dr dt = − (mv||2 eB) dB dθ , the radial drift fromthe home flux surface should be in the opposite direction
for the two configurations. Figure 1 also illustrates thehigh effective transform that is characteristic ofquasihelically symmetric stellarators. For the QHS
configuration, as the magnetic field line rotates once

Fig. 2 Experimental data from HSX mapped into Boozer
coordinates (left) and a calculation of the orbit of the same
electron in a tokamak magnetic field (right).

2. Pfirsch-Schlüter and Bootstrap Currents
Because of the lack of toroidal curvature in HSX,
the Pfirsch-Schlüter (PS) and bootstrap currents havesome unique properties. For a quasihelically symmetricconfiguration, the PS current is given by Boozer [8],J PS =

1 dp nI + mgδcos(nφ − mθ )B0 dψ n − mι nm(3)and the bootstrap current has the expression [9],J BS =1.46 bnm

m g ⎡
dn
⎢1.67(Te + Ti )n − mι B0 ⎣dψ

+ 0.47ndTe
dT ⎤− 0.29n i ⎥
dψ
dψ ⎦

(4)

There are several things to notice about these expressions.
For one thing, both currents are reduced by the same factor,

Proceedings of ITC/ISHW2007

n − mι which is the effective transform. Also, thePfirsch-Schlüter current is helical so that from the
beginning of the field period to the half-period the dipole
currents reverse direction. Note that at φ = 0 0 where themagnetic field in a QHS device is tokamak-like (that is, thehigh field side is on the inboard side), the PS current
distribution is reversed from what it would be in a tokamak.
From the equation this appears as a sign change between an = 4, m = 1 and a n = 0, m = 1 configuration. Physicallythis effect occurs because of the reversal in the gradient of
the magnetic field between a QHS and tokamak
configuration, just like in the particle orbit. Note too, thatthe bootstrap current in a QHS device is in the opposite
direction from that in a tokamak, resulting in a rotationaltransform that decreases as the pressure gradient increases.
The transport however doesn’t degrade with the decreasein the transform, because the effective transform actually
increases slightly.
The reversal of the bootstrap current in a QHS devicecompared to a tokamak can be understood using the model
developed by Shaing and Callen [10]. The top plot of
Figure 3 shows how the parallel current flows in one
direction for HSX so that when added to the diamagnetic
current, the total current flows along the direction ofsymmetry. The bottom plot shows how this parallel current
has to flow in the opposite direction along the field line sothat the total current flows in the axial direction.

To measure the plasma current in HSX there is a
Rogowski coil and a belt to which is attached a set of 16
3-axis magnetic coils. Both are mounted outside thevacuum chamber of HSX. To measure the signals due tothe helical Pfirsch-Schlüter current, the belt containing theset of 16 triplets was first placed at the half-field period
and subsequently at the one-sixth period location. Figure 4
is an illustration of the helical nature of the current and theapproximate locations of the 16 triplets. The red and blue
colors denote currents that are flowing in the opposite
directions.

1
1/6 FP
Poloidal Station #1

1/2 FP

2

16
1
2

Fig. 4 Last closed magnetic surface and Pfirsch-Schlüter current
contours at two toroidal locations where the 16 3-axis magnetic
coils were located.

U||
UT
Ud

U||

Ud

UT

Fig. 3 Diamagnetic current (Ud), parallel bootstrap current(U||) and total current (UT) in HSX (top) and a tokamak(bottom) illustrating that the bootstrap current flows in the
opposite direction for the two configurations.

Figure 5 shows the polodial and radial magnetic fields
due to the plasma current at a time, late in the discharge,
just before the ECH is turned off. It can be seen from thefigure that the radial magnetic field at the 1/2 field period
is almost 1800 degrees out of phase with the signals at the
1/6 field period location. This confirms that indeed thePfirsch-Schlüter current in HSX is helical.
Another interesting feature of Figure 5 is that thepolodial magnetic field is offset vertically indicating that
there is a current flowing in the plasma in addition to thePfirsch-Schlüter current. We have made estimates of thebootstrap current in HSX using the BOOTSJ code [11]using the data from the Thomson scattering array as input.
However, since the magnetic diffusion time is generally
greater than the ECH pulse length, the total current
measured by the Rogowki coil has not reached asteady-state by the end of the discharge.
A comparison of the current calculated by BOOTSJ
with the measured current when the ECH turns off as wellas an extrapolated steady-state value of the total current isshown in Figure 6. The agreement is fairly good. In
addition, the direction of the measured current is opposite
from what it would be in a tokamak, as expected.

Proceedings of ITC/ISHW2007

B (T)

10

x 10

-4

3. Magnetic Flexibility

θ

5

0
0

Br (T)

5

x 10

2

6

8

10

12
14 I =16
V3POST
I BOOTSJ
tor
Exp. t = 50. ms

0

-5
0

10
B (T)

4

-4

x 10

2

4

6
8
10
Poloidal Station #

2

4

6

12

14

16

-4

θ

5

0
0

Br (T)

5

x 10

8

10

12
14
16
V3POST I = I

-4

tor

BOOTSJ

Exp. t = 50. ms

0

-5
0

2

4

6
8
10
Poloidal Station #

12

14

16

Fig. 5 Amplitude of magnetic field components (marked by ‘x’)in the polodial and radial directions at the 1/6 field period (top)and 1/2 field period (bottom) locations. Also shown are thecalculated values using the V3FIT code (dashed line).

To model the signals detected by the 16 coil array, we
use the V3FIT [12] code which takes as input the pressure
and current profiles. When we include the current profile
due to the bootstrap current in the V3FIT calculation, we
obtain reasonably good agreement with the data that
explains the vertical offset in the polodial magnetic field.
The calculation however does not take into account theevolution of the bootstrap current which could alter theagreement between the V3FIT code and the data. This will
be addressed in the future. More information is provided in
the paper by Schmitt [13].
1000
I

tor

800

@ t = ECH Off

Extrapolated I

SS

I tor

600

400

200

0
0

100

200

300

400

500

600

Boostrap Current -- BOOTSJ (A)Fig. 6 Bootstrap current calculated by the BOOTSJ code
compared with the measured current at the ECH turnoff (+) as
well as an extrapolated value (circles) of the current based on its
time evolution.

One of the best ways to test quasisymmetry is todegrade the symmetry and see what the result is on theplasma. To accomplish this, HSX has a set of 48 auxiliary
planar coils that are outside the modular coil set that
produces the quasihelical field. Depending on thearrangement of the coil distribution in the auxiliary coils, it
is possible to vary the magnetic field spectrum as well as
the rotational transform, well depth, neoclassical transport,
parallel viscous damping and MHD stability.
In particular, one configuration is termed ‘Mirror’
because it introduces spectral terms with (n,m) = (4,0) and(8,0). The effect of these extra spectral terms is to increase
the effective ripple at r/a ~ 2/3 from 0.005 to 0.04. The
increase in the effective ripple is even larger towards theplasma core. For this configuration, the plasma volume,rotational transform, magnetic axis and well depth vary
little from the QHS configuration. There is another, earlier,configuration which we term the “old Mirror”, which
differs slightly from the “Mirror” in the current distributionof the auxiliary coils. The “old Mirror” had about a 1 cm
magnetic axis shift between the QHS and “old Mirror” thatmade it difficult to obtain a Thomson scattering profile that
included the plasma core. For the “Mirror” the shift is only
about 1 mm. The first sets of experiments described below
were done at a magnetic field of 0.5 T; further in the article
we will discuss the 1.0 T data.

4. Trapped Particle Confinement
In the QHS configuration, calculations indicate thattrapped particles should be very well confined. Similarcalculations for the Mirror configurations show that thetrapped particle confinement should be considerably
degraded. We tested the trapped particle confinement by
mounting a collector disk inside the vacuum chamber at
the top and bottom of the confinement region andmonitoring the floating potential [14].
Figure 7 shows the floating potential versus plasma
density for the QHS and “old Mirror” configurations. Withquasisymmetry, the floating potential of the plates in boththe ion and electron drift directions show little change as
the density is varied. However, with the quasisymmetry
degraded, the floating potential becomes increasingly
negative at lower density. This is only observed in the
direction of the electron drift, as expected. For the plate in
the ion drift direction, the floating potential is relatively
unchanged.
Another indication of the improved confinement oftrapped particles with quasisymmetry is the higher x-ray
flux in this configuration [15]. The hard x-ray emission in
HSX was analyzed using a CdZnTe detector that washoused outside the vacuum vessel in a lead box with a 0.8
mm pinhole and a 200 mm SS filter. Pulse height analysis
was used to obtain the energy spectrum in a set of similar
ECH discharges. Figure 8 shows the spectrum for QHS
and ‘old Mirror’ at the same density of 2 × 1012 cm -3 . The
high-energy tail for the QHS configuration is indicative ofProceedings of ITC/ISHW2007
the improved confinement of the superthermal electrons
that gives rise to the more efficient heating during theECH.

approximate agreement with an Alfvén mode. However,
without a direct measurement of the electric field, it isdifficult to determine the scaling in the laboratory frame ofreference.

Fig. 9 Frequency spectrum of reflectometer signal for QHS andMirror configurations at r/a ~ 0.4.

Fig. 7 Floating potential versus plasma density for the QHS
configuration (top) and “old Mirror” configuration (bottom).
Shown are the data for the plate in the ion (+) and electron(triangles) drift directions.

The striking feature of the mode is that it decreases inamplitude with increasing quasisymmetry degradation.
Figure 9 shows a comparison of the frequency spectrum of
density fluctuations measured by the reflectometer for the
QHS and Mirror configurations [17]. The frequency of thereflectometer was tuned in this case to a spatial location ofr/a ~ 0.4. In contrast to the broad turbulent spectrum for the
Mirror configuration, the QHS spectrum is more quiescent,but with a large coherent mode at around 55 kHz. Thismode is absent in the Mirror spectrum. Based on themeasurements of an energetic tail population that is better
confined in the QHS configuration, as discussed in theprevious section, we infer that the coherent mode is most
likely driven by nonthermal electrons. Future work willconcentrate on whether the broader turbulent spectrum in
the Mirror configuration might be due to the larger fractionof trapped particles for that configuration, close to the core.

6. Particle, Momentum and Heat Transport at B =0.5 T

Fig. 8 X-ray spectrum for QHS and “old Mirror” configuration.

5. Fluctuations at B = 0.5 T
One distinguishing feature of the QHS configurationis the presence of a global coherent low-frequency modethat is observable from Langmuir probes, theinterferometer, the radiometer as well as magnetic pick-up
coils [16]. Indications from the interferometer, and more
recently from a reflectometer, are that the mode is localized
towards the plasma core. The estimated mode number is n
= 1, m = 1. From probe measurements, the mode
propagates in the electron diamagnetic direction. The mode
frequency decreases with increasing density, inA number of experiments were performed to compare
particle, momentum and heat transport between the QHS
and the Mirror configurations. More details are given in thepapers by Gerhardt [18] and Canik [19]. A common featureof the experiments is that the neoclassical reduction intransport could be observed by altering the magnetic field
spectrum, in approximate agreement with a neoclassicalmodel, but in each case there remained a large level ofanomalous transport that didn’t appear to change between
the configurations.
Figure 10 shows the density profiles measured with a
10 channel Thomson scattering system. For the Mirror
configuration, the profile is flat to hollow, which is typicalof ECH discharges in many other stellarators. For the QHS
configuration however, the profile is peaked. The
experimental particle flux was inferred from a set of HαProceedings of ITC/ISHW2007
detectors and the DEGAS [20] code. Inside r/a ~ 0.3, theexperimental particle flux in the Mirror was found to beclose to the neoclassical flux driven by temperature
gradients. This flux, termed the thermodiffusive flux, isreduced in the QHS configuration, accounting for thepeaked density profile. In the outer regions of the plasma
the experimental particle flux was found to be similar forthe two configurations and, in both cases, much greaterthan the neoclassical level.

time scales for the plasma flow, a faster and a slower timescale. The difference in the measured damping rates isroughly the same as the difference in the slow neoclassicalrates. However, for both configurations, there is anadditional source of flow damping that is unaccounted forin the neoclassical model.
The final comparison to be made is of the electron
thermal diffusivity. The bottom plot of Figure 10 shows theelectron temperature profile for the two configurations
with the same ECH input power. The central temperature isabout 800 eV for the QHS configuration and 500 eV for
the Mirror. The higher temperature for the quasisymmetricconfiguration is indicative of a lower neoclassical thermal
conductivity.
A more rigorous comparison was made of the two
configurations with the same temperature profile andsimilar density profiles, except for the core where
thermodiffusion dominates for the Mirror. A comparison of
the thermal conductivity for the two configurations isshown in Figure 11. At a r/a ~ 0.2 – 0.3, the electron
thermal conductivity is around 2 m2/s for QHS and around
4 m2/s for Mirror. This difference is comparable to thedifference in the neoclassical values. Towards the edge,
where the neoclassical thermal conductivity is small, thetwo configurations have comparable transport.

Fig. 11 Experimental and neoclassical thermal conductivities for
the QHS and Mirror configurations.

7. Electron Thermal Conductivity at B = 1.0 T

Fig. 10 Comparison of the density profile (top), flow decayrate (middle) and electron temperature profile (bottom) for QHS
and Mirror configurations.

The middle figure of Figure 10 shows the results of acomparative experiment using a biased electrode to spin up
the plasma in the two configurations. It was found that for
the quasisymmetric configuration, the plasma flow, as
measured by a Mach probe, increased more slowly androse to a higher value than for the Mirror configuration.
After the bias turn-off, the decay in the flow was faster forthe nonsymmetric configuration. The results werecompared to a neoclassical model which predicted two

For second harmonic extraordinary mode heating at
0.5 T, the transport analysis was complicated by thepresence of a superthermal electron population. This
prevented an estimate of the absorbed power from being
obtained based on the decay of the diamagnetic loop.
Rather, a fairly tedious process of estimating the absorbed
power was employed based on the time evolution of thetotal integrated kinetic energy obtained from Thomson
scattering measurements. For fundamental ordinary modeheating at 1.0 T however, the superthermal population wasmuch reduced based on diamagnetic, ECE and x-ray
measurements. This simplified the measurement of theabsorbed power and the calculation of the thermal
conductivity. Figure 12 shows that for 100 kW input power,
electron temperatures up to 2.5 keV were obtained for theProceedings of ITC/ISHW2007
QHS configuration, while around 1.5 keV was measured
for the Mirror.

T e (keV)

2.5

stellarator geometries, Rewoldt [22] found that HSX had afairly high growth rate because of this short connection
length and also because of the substantial bad curvature at
the location of the trapped particles.

2
1.5
1
0.5

1

0

0

0.5
ρ

1

Fig. 12 Electron temperature profile for QHS (red) and
Mirror (blue) with 100 kW input power.

The neoclassical and anomalous components of thetotal electron thermal conductivity were compared bymatching as close as possible the temperature and density
profiles. This required decreasing the QHS input power to
44 kW, while the Mirror input power stayed at 100 kW asin Figure 12. The experimental and neoclassical electron
thermal conductivities for the QHS and Mirror
configurations are shown in Figure 13. The large error bar
for the Mirror case is because of the difficulty obtaining
reproducible discharges. Still, roughly a factor of 3
reduction in the conductivity is observed at the plasma core
due to the quasisymmetry. Further analysis is needed
however at this point to understand how the anomaloustransport compares between the two configurations. Moredetails are given in the paper by Lore [21].

Fig. 14 Electron temperature profile from Thomson scattering(red circles) and model (black line).

To simulate anomalous transport in HSX, the Weiland
ITG/TEM model [23], originally used to describe transport
in tokamaks, was modified to approximate the local
geometry in HSX. This required the substitution of thehelical ripple in place of the toroidal ripple and a local
curvature about 3 times that of a tokamak with the same
major radius. The 3D gyrokinetic code GS2 [24] was thenused to confirm that the linear growth rates using themodified Weiland model were accurate to within 30%.
Details are given in the paper by Guttenfelder [25].

Mirror Exp

QHS Exp

Mirror Neo
QHS NeoFig. 13 Experimental and neoclassical electron thermal
conductivities for QHS and Mirror.

8. Modeling Anomalous Transport in HSXWith ECH, the electron temperature in HSX is muchhigher than the ion temperature so that the dominant longwavelength instability is the trapped electron mode (TEM)
Because of the quasisymmetry, the magnetic geometry in
HSX looks similar to that in a tokamak with high effective
transform. In a comparison of microinstabilities in different

Fig. 15 Comparison of model dependence of confinement time
(blue line) on absorbed power with experimental data (reddiamonds).

The temperature profile in HSX was modeled byassuming a thermal conductivity consisting of theneoclassical term and the Weiland contribution. The power
deposition profile is based on a calculation using a
ray-tracing code and the total absorbed power comes fromthe decay of the diamagnetic loop signal. Figure 14 shows
a comparison of the experimental data to the model
calculation. Outside the region of r/a ~ 0.3, the agreement
is quite good. Towards the core the agreement isn’t as good,Proceedings of ITC/ISHW2007
possibly because of the omission of non-linear effects orE × B shear suppression of turbulence. The predictedenergy confinement times agree well with the experimental
confinement times. The dependence of the experimental
confinement time on the absorbed power is slightly weaker
than the model prediction. This is shown in Figure 15.

9. Conclusions
This paper reviewed a number of different ways inwhich quasisymmetry was tested in HSX. A quasihelicallysymmetric configuration is noted for its lack of toroidal
curvature and high effective transform. The high effective
transform was observed in small deviation of a passing
particle orbit from a magnetic surface as well as the small
Pfirsch-Schlüter and bootstrap currents that were measured.
The lack of toroidal curvature was noted by the drift of anelectron to the inside of the flux surface, rather than to theoutside if toroidal curvature dominated. Also, the helicalPfirsch-Schlüter current and the direction of the bootstrap
current were also indication of a very small toroidal
curvature. Measurements of the polodial and radial
components of the magnetic field due to the plasma
currents showed good agreement with the V3FIT code.
Another feature of the quasisymmetric configurationis the good confinement of energetic trapped particles as
seen from collector plates and hard x-ray measurements.
This good confinement may be responsible for an MHD
instability which is observed to decrease in amplitude andthen disappear as the degree of quasisymmetry breaking
increases. First measurements of density fluctuations at theplasma core were obtained with a reflectometer andshowed a quiescent background with a large coherent
global mode for the QHS configuration, versus a broad
spectrum of turbulent fluctuations without the coherentmode for the Mirror configuration.
With ECH at a magnetic field of 0.5 T, the results
showed that the parallel momentum damping, particle
thermodiffusion and electron thermal conductivity could
all be decreased with quasisymmetry. The level of decrease
roughly agreed with the calculated decrease in the
neoclassical values, however a large anomalous component
to particle, momentum and heat transport still remained. To
date, there is no evidence in the data obtained at 0.5 T thatthe anomalous contribution differs substantially between
the quasisymmetric and nonsymmetric configurations.
At a magnetic field of 1.0 T, central electron
temperatures were up to 2.5 keV for the QHS configuration
when 100 kW ECH was injected into the plasma. With thequasisymmetry degraded, the core temperature fell to 1.5
keV. Analysis of the transport for similar temperature anddensity profiles showed substantial reduction in theexperimental thermal conductivity at the plasma core.
Further analysis is needed before it can be understoodwhether the anomalous transport for the QHS case wasdifferent from that in the Mirror configuration.
Finally, while the short connection lengths in HSX areshown to be good for decreasing particle orbits, plasma

currents and neoclassical transport, initial evidence seems
to indicate that the combination of the short connection
lengths and large curvature may be responsible forsomewhat higher anomalous transport. Calculations of thetemperature profile and energy confinement time based on
a combination of neoclassical transport plus a modified
Weiland model for anomalous transport, show reasonableagreement with the data. So far the model ignores zonal
flows, E × B shear suppression of turbulence, nonlinear
effects and the differences in the fraction of trapped
particles between the quasisymmetric and nonsymmetricconfigurations. Future work will concentrate onunderstanding how the degree of quasisymmetry affects
the radial electric field and plasma turbulence.
In summary then, initial experimental results indicatethat the quasisymmetric configuration has fulfilled its
promise of reducing neoclassical transport. More work isneeded to resolve what effect the quasisymmetricconfiguration has on anomalous transport.

Acknowledgments
The authors wish to thank the V3FIT team for the useof their code and especially Steve Knowlton for invaluableassistance. This work was supported by the U.S.
DepartmentofEnergyunderContract
No.
DE-FG02-93ER54222.

References
[1]
[2]
[3]
[4]
[5]

H.E. Mynick, Phys. Plasmas 13, 058102 (2006).
Nuhrenberg and R. Zille, Phys. Lett. A 129, 113 (1988).
P. R. Garabedian, Phys. Plasmas 4, 1617 (1997).
F. S. B. Anderson et al., Fusion Technol. 27, 273 (1995).
G. H. Neilson, M. C. Zarnstorff, J. F. Lyon and the NCSX
Team, J. Plasma Fusion Res. 78, 214 (2002).
[6] D. A. Spong, S. P. Hirshman, L. A. Berry et al., Nucl.
Fusion 41, 711 (2001).
[7] J. N. Talmadge, V. Sakaguchi, F. S. B. Anderson, D. T.
Anderson and A.F. Almagri, Phys. Plasmas 8, 5165 (2001).
[8] A.H. Boozer, Phys. Fluids 24, 1999 (1981).
[9] A.H. Boozer and H.J. Gardner, Phys. Fluids B2, 2408
(1990).
[10] K.C. Shaing and J.D. Callen, Phys. Fluids 26, 3315 (1983).
[11] K.C. Shaing et al., Phys. Fuids B4, 148 (1989).
[12] S.P. Hirshman, E.A. Lazarus, J.D. Hanson, S.F. Knowlton,
L.L. Lao, Phys. Plasmas 11, 595 (2004).
[13] J.C. Schmitt, J.N. Talmadge, P.H. Probert, D.T. Anderson,
Proceedings of ITC/ISHW2007.
[14] J.C. Canik, personal communication.
[15] A. Abdou, Ph. D. thesis, University of Wisconsin-Madison(2005).
[16] D.L. Brower, C. Deng et al., Transport Task Force, 2005.
[17] K. Likin et al., Proceedings of ITC/ISHW2007[18] S.P. Gerhardt, J.N. Talmadge, D.T. Anderson, J.M. Canik,
Phys. Plasmas 12, 56116 (2005).
[19] J.M. Canik, D. T. Anderson, F. S. B. Anderson, C. Clark, K.

Proceedings of ITC/ISHW2007
M. Likin,, J. N. Talmadge, and K. Zhai, Phys. Plasmas 14,056107 (2007).
[20] D. Heifetz et al., J. Comput. Phys. 46, 309 (1982).
[21] J. Lore et al., Proceedings of ITC/ISHW2007.
[22] G. Rewoldt, L.-P. Ku, W.M. Tang, Phys. Plasmas 12,102512 (2005).
[23] H. Nordman et al., Nucl. Fusion 30, 983 (1990).
[24] M. Kotschenreuther et al., Comp. Phys. Comm. 88, 128(1995).
[25] W. Guttenfelder et al., Proceedings of ITC/ISHW2007.