Proceedings of ITC/ISHW2007

Transport Studies in HSX at 1 Tesla
J. Lore, F.S.B Anderson, J.M. Canik, W. Guttenfelder, K.M. Likin, J.N. Talmadge, K.Zhai
HSX Plasma Laboratory, University of Wisconsin
Initial results at B=1.0T at HSX demonstrate a reduction in particle and heat transport due to quasisymmetry,
supporting the results of B=0.5T operations. Electron temperature and density profiles from Thomson scattering
for several injected powers show a factor of 2-2.5 increase in the core temperature and a more peaked density
profile for the quasi-helically symmetric configuration (QHS) as compared to the configuration where thesymmetry is spoiled (Mirror). In a case where the temperature profiles are matched (requiring 2.3 times theinjected power in Mirror) the core electron thermal diffusivity has been measured to be reduced by a factor of 3.
The particle transport was analyzed using the neutral gas transport code DEGAS to obtain the source rate. Theseresults indicate that for a given temperature gradient the particle flux, which is dominated by thermodiffusion, issmaller in QHS. Additional work is required on neoclassical calculations before conclusions on the effect ofquasisymmetry on anomalous transport can be made.
Keywords: Neoclassical transport, quasisymmetry, DKES, DEGAS, HSX, Thermal transport

1. Introduction
The Helically Symmetric Experiment (HSX) is a
mid-sized stellarator at the University of Wisconsin. The
magnetic field of HSX can be varied from a quasi-helicallysymmetric configuration (QHS) to a configuration with thesymmetry intentionally degraded by a set of toroidal fieldcoils (Mirror). Aside from the magnetic spectrum, otherproperties such as the rotational transform, plasma volumeand well depth are very similar. The change in themagnetic spectrum can be quantified by the effective ripple,
which is increased in the core from 0.007 in QHS to 0.05
in Mirror with the largest change occurring in the core of
the plasma. In this paper the effect of spoiling thesymmetry on particle and electron heat transport will bediscussed.

2. 0.5 Tesla Operation
A transport analysis at B=0.5T demonstrated that boththe particle and electron heat transport were reduced in theQHS configuration [1]. For the same injected power thedensity profiles were peaked in QHS and hollow in Mirror
due to a reduction in the thermodiffusive particle flux. Itwas also shown that 2.3 times the injected power isrequired in Mirror to match the temperature profiles
between the configurations, and that for this matched casethe electron thermal diffusivity is reduced in the core for
the QHS configuration. The reduction in the corediffusivity was comparable to the calculated difference inthe neoclassical diffusivities.
The transport analysis at B=0.5T was complicated by
the presence of a suprathermal electron population driven
by the 2nd harmonic X-Mode electron cyclotron heating.
This suprathermal tail was observed by measurements
author’s e-mail: jlore@wisc.edu

from several diagnostics including the ECE system, hard
X-ray detectors and a diamagnetic loop. Due to thecontamination of the diamagnetic loop signal, the absorbed
power was measured using many discharges while varying
the Thomson scattering firing time around the ECH turnoff
time. This limitation meant that very few configurations
could be studied at B=0.5T.

3. 1.0 Tesla Operation
HSX has recently began regular operation at B=1.0T.
At the higher field strength fundamental frequency
O-Mode heating is used greatly reducing the drive of asuprathernal population. Fundamental frequency heating
also allows for operation at higher densities, increasing thedamping on a tail population. Measurements from theECE system and the diamagnetic loop indicate that thesuprathermal contamination has been greatly suppressed at
B=1.0T allowing for a transport analysis to be performed atseveral injected powers in both QHS and Mirror.

4. Profiles from Thomson Scattering
A ten channel Thomson scattering system installed on
HSX has been used to measure the electron density andtemperature profiles in the QHS and Mirror configurations
for four injected powers: 26, 44, 70 and 100kW.
The profiles shown in Figure 1 clearly show that foreach injected power the central electron temperatures are
2-2.5 times greater in the QHS configuration. Also, foreach injected power above 26kW the density profiles are
more peaked for QHS. The greatest differences in theprofiles are seen in the core, where the change in effective
ripple is the largest and neoclassical transport is significant(see Section 7). These profiles indicate that transport
properties change between the two configurations and that

Proceedings of ITC/ISHW2007
An expression for the diffusivity can be obtained by taking
the flux surface average of the energy continuity equation
(1).

d ⎛3
⎞
⎜ neTe ⎟ = −∇ ⋅ q + pin − p out
dt ⎝ 2⎠(1)

Where pin and pout are generic power sources and sinks.
Assuming that the heat flux is purely diffusive, theeffective electron thermal diffusivity can be written as seenρin (2).

χe =Fig.1 QHS and Mirror electron temperature(left) and density (right) profiles for several
injected powers.
both particle and electron thermal transport are improvedin the QHS configuration.
Due to the differences in the temperature gradients,
the profiles cannot be exactly matched between theconfigurations. To minimize the difference in the profiles
over the whole minor radius 2.3 times the injected power(1.8 times the absorbed power) is needed in the Mirror
configuration, again demonstrating the improvement inelectron thermal transport (Figure 2).

Profiles demonstrating that 2.3 times theinjected power is required in Mirror to minimize
the difference in the temperature profiles.

5. Electron Thermal Transport
To quantify the change in thermal transport seen inFigure 2 the electron thermal diffusivities were calculated.

0∂T
2
ne V ' e ∇ ρ∂ρ(2)Where V’=dV/dρ and ∇ ρ account for the deviationof the geometry from a straight cylinder.
For the following calculations the power sinks such asradiation and ionization losses were ignored. Theselosses are small compared to the total injected power for
HSX plasmas and were found to be similar between theconfigurations at B=0.5T [2].
A ray-tracing code is used to calculate the power
deposition profiles based on the local temperature anddensity from the Thomson scattering profiles. The power
deposition profiles are volume integrated and scaled tomatch the absorbed power calculated at ECH turnoff fromthe diamagnetic loop.
Figure 3 shows the effective thermal diffusivities forthe profiles in Figure 2. The diffusivity in the core has
been reduced by a factor of three due to quasi-symmetry.

Fig.3
Fig.2

− ∫ V ' ( pin − pout )dρ 'Experimental and neoclassicaleffective thermal diffusivities for theQHS and Mirror profiles in Figure 2.

6. Particle Transport
The density profiles seen in Figure 1 indicate that theparticle transport changes in the core of the plasma
between the two configurations. At B=0.5T it was foundthat the thermodiffusive component of the particle flux wasreduced in the QHS configuration.
At B=1.0T

Proceedings of ITC/ISHW2007
neoclassical calculations show that the thermodiffusive
component is the dominant particle flux drive in bothconfigurations (Figure 4).

calculated using the DKES code to find the monoenergetic
diffusion coefficients [4][5]. At each radial location themonoenergetic diffusion coefficients are numericallyintegrated over a Maxwellian by using a fit form to theDKES results to yield the neoclassical transport coefficientmatrix. The particle and heat fluxes can then be
calculated for a given radial electric field. The radial
electric field is then determined by the ambipolarity
constraint.

Fig.4 Components of the neoclassical particle fluxfor QHS (left) and Mirror (right). In eachconfiguration the dominant component isthermodiffusion.
To calculate the experimental particle flux the particle
source rate is required. To obtain the source rate theneutral transport code DEGAS was used [3]. DEGAS is a
3D Monte Carlo code that can calculate several quantities
including, significantly, the Hα emission. The code is run
for each set of Thomson scattering profiles on a fully 3Dcomputational grid representing the HSX vacuum vessel.
The results of the code are coupled to experiment using asuite of absolutely calibrated Hα detectors located on themachine.
For each set of profiles DEGAS is run for two cases.
One of the cases is for the main fuelling source, a puffvalve located on the vessel wall. DEGAS calculates theHα emission to be localized toroidally for this case, and theresults are then scaled to match the measured Hα emission
from a poloidal array located at the puff valve. The othercase is for a recycling source, located at the locations
where the magnetic field lines just outside the separatrix
intersect the vessel. The results from this case are scaled
to match the measured emission from a toroidal array ofdetectors. The scaled results of the two cases are thenadded to obtain the total source rate.
The particle flux can be calculated by taking the flux
surface average of the particle continuity equation (3) ins
steady state yielding (4).

∂n+∇⋅Γ = S
∂t
Γ=1

ρ

∇ρ V ' ∫0

V ' S ( ρ ' )dρ '(3)(4)

The dependence of the particle flux on thetemperature gradient is plotted at ρ=0.3 in Figure 5.
Figure 5 shows that for a given temperature gradient theparticle flux is lower in the QHS configuration.

7. Neoclassical Calculations
The neoclassical particle and thermal transport wereFig.5

Dependence of the experimental andneoclassical particle flux on temperature
gradient.

The neoclassical electron thermal diffusivity profiles
for the temperature and density profiles in Figure 2 can beseen in Figure 3. The diffusivity is reduced in the coreregion due to the strong positive radial electric fields which
greatly reduce the ion flux. Figure 3 shows that unlike at
B=0.5T, the reduction in the neoclassical transport is notenough to account for the reduction in the experimental
transport. This could indicate a reduction in anomaloustransport due to quasi-symmetry, however further work on
the neoclassical calculations is required as will beexplained below.
In Figure 5 the neoclassical calculations also showthat for a given temperature gradient the particle flux is
expected to be smaller in the QHS configuration.
However, the large difference in the neoclassical values is
not seen in the experimental results.
As mentioned above, several additional effects andcorrections can be applied to the neoclassical calculations,
two of which will be briefly described here. The
monoenergetic diffusion coefficients calculated by DKES
were fit to an analytic form to allow a fast numericalintegration over a Maxwellian.
The analytic form
however did not account for the effect of the poloidal
resonance of the radial electric field on the ion flux. To
correct for this the analytic form was modified to include
this effect. This effect will in the future be moreaccurately accounted for by performing a very fine DKES
scan and directly interpolating the results instead of fitting
to an analytic form.

Proceedings of ITC/ISHW2007
The above method has been applied to manystellarators[6], however DKES only considers pitch angle
scattering which results in a collision operator that is not
momentum conserving. Due to the symmetric nature of
HSX the effect of momentum conservation may be
important, as in a tokamak. To address this, the PENTA
code [7], which uses a momentum conserving collision
operator will be run and compared to the results obtainedusing DKES and ambipolarity.

8. Conclusion
Initial results at B=1.0T demonstrate a reduction inparticle and electron thermal transport due toquasi-symmetry.
Profiles from Thomson scattering
clearly show an improvement in electron thermal transport,with 2.3 times the injected power required to match theelectron temperature profiles. A large (factor of three)
reduction in the core electron thermal diffusivity has also
been measured. A particle transport analysis indicatesthat for a given temperature gradient the particle flux is
reduced in the QHS configuration. Finally, neoclassicalcalculations suggest a reduction in anomalous transport in
the QHS configuration, but further work is required toconfirm this.

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S.P. Hirshman et al., Phys. Fluids 29, 2951 (1986).
W.I. van Rij and S.P. Hirshman, Phys. Fluids B 1, 563(1989).
C.D. Beidler et al., Proceedings of the 14th ISW,
Greifswald, Germany, Sept. 29-Oct. 1, 2003.
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