Proceedings of ITC/ISHW2007

Stability of Super Dense Core Plasmas in LHD
J. H. Harris1, R. Sanchez1, D. J. Spong1, N. Ohyabu2 , K. Watanabe2, J-A. Jimenez1
1Fusion Energy Division, Oak Ridge National Laboratory, USA2

National institute of Fusion Science, Toki, Japan
3

CIEMAT, Madrid, Spain

Author affiliations should be centered 10-point italic type
(Received 16 October 2007)
Recent experiments [1] using pellet injection into reduced-recycling discharges in the Large Helical Device
have yielded Super Dense Core (SDC) plasmas with very peaked density profiles, high central density ~ 4.5 × 1020
m-3, and improved confinement. We have examined ideal MHD stability of these SDC configurations the using the3-D COBRA stability code [2]. These calculations show that the core region inside the zero-shear radius has directaccess to second stability, i.e., the stability margin increases with β. Outside the zero-shear radius, the plasma
becomes unstable to ballooning modes at average β ~3-4%. Of course, resistive versions of the modes are expected
to appear at lower β. These MHD effects may play a role in improving core confinement, and may also provide a
useful mechanism to constrain the plasma pressure in the outer plasma region and thus help maintain the favourable
SDC state. Experiments like this in LHD and other stellarators such as the TJ-II heliac could also help elucidate thenature of ballooning modes in three-dimensional confinement systems.
Keywords: stellarator, heliotron, magnetohydrodynamic stability, ballooning modes, high-beta

1. Inroduction
Magnetohydrodynamic ballooning modes have long
been thought to set the upper limit of normalized pressure
β = 2µ0p/B2 in stellarator plasmas. As yet, however, theirexistence has not been confirmed experimentally, even inparameter ranges where they were expected, such as
recent experiments in the Large Helical Device (LHD) in
which values of β of nearly 5% were obtained [1]. It istherefore of great interest to look for specificexperimental conditions in which the excitation andobservation of ballooning modes might be possible.
Experiments [2] using pellet injection into
reduced-recycling discharges in the Large Helical Device
have yielded Super Dense Core (SDC) plasmas with very
peaked density profiles, high central density > 5 × 1020
m-3, improved confinement, and values of β in the rangeof 1-2%. Figure 1 shows sample profiles of density andpressure for one these plasmas taken from Reference 1.
These plasmas have good confinement, and exhibit aninternal diffusion barrier, whose mechanism is understudy [3]. Since the maximum density in stellarators islimited only by input power, operation at very highdensities > 1 × 1022 m-3 may make alternative reactor
author’s e-mail: harrisjh@ornl.gov

scenarios with low temperatures accessible.

Fig. 1.Sample density and pressure profiles for an SDC plasmain LHD.

2. Stability calculations
We have examined the ideal MHD ballooning
stability of these LHD SDC configurations the using the3-D COBRA stability code [3], with a model pressure
profile that approximates that seen in the experiment.
Figure 2 shows the radio profiles (against normalizedminor radius) of rotational transform (ι = 1/q, where q
is the safety factor) and specific volume V′ = ∫ dl/B,

Proceedings of ITC/ISHW2007
where the integral is along field lines, and V′′ < 0corresponds to a magnetic well. The equilibria show verystrong outward Shafranov shifts, a non monotonic ιprofile in which the core region has tokamak-like shear(ι′ < 0) and a pronounced magnetic well, and surroundedby an edge or “mantle” region with stellarator-like shear(ι′ > 0) and a magnetic well.
COBRA calculations of ballooning growth rates(plotted in inverse Alfven times in Fig 2 show that thecore region inside the zero-shear radius has direct accessto second stability, i.e., the stability margin increases with
β. Outside the zero-shear radius, the plasma becomes
unstable to ballooning modes at average β ~3-4%.
Studies of the eigenfunctions show that the modes are
localized in the region of bad curvature in each field
period. Radially, the inner edge of the region of
ballooning instability is inside the magnetic well, afurther indication of the mode’s ballooning (as opposedto interchange) character. Of course, resistive analoguesof the modes are expected to appear at the lower β values
accessed in the experiments so far.
These MHD effects may play a role in improving
core confinement, and may also provide a usefulmechanism to constrain the plasma pressure in the outerplasma region and thus help maintain the favourable SDC
state. Ongoing studies on LHD of radially resolved
transport are expected to shed some light on this in thefuture.
Experience with tokamaks (TFTR) suggests thatballooning modes will be difficult to observe on external
magnetic coils because of their short coherence length, sothat internal diagnostics like local ECE emission will
have to be used. So far, magnetic fluctuationmeasurements in high-beta LHD plasmas show only low
mode number resistive interchanges that appear and thendisappear as the plasma pressure is raised.
The non-monotonic rotational transform profile
calculated for these equilibria is not surprising, but still
merits experimental confirmation; the most convincing
measurement would be a motional Stark broadening
measurement of the poloidal magnetic field, a techniqueFig. 2. Radial profiles of finite-beta rotational transform,
specific volume, and ballooning growth rate for model
sequence of LHD SDC equilibria.

Fig. 3 Radial profiles of rotational
ballooning growth rate for TJ-II.

transformand

Proceedings of ITC/ISHW2007
which is widely used in tokamaks, but needs to beimported to stellarators.
Similar computational studies have been carried out
for the TJ-II heliac [4]. Figure 3 shows profiles ofrotational transform and ballooning growth rate for abroad pressure profile p = p0(1-ρ2) and several different
values of β. Ballooning modes appear in the outer region
for modest values of volume-averaged β < 1%, whichshould become accessible with the 1-2 MW of neutralbeam power (from injectors originally used at ORNL)
expected to become available on TJ-II within the next
year. Joint experiments by TJ-II and ORNL staff in 2007
have already succeeded in obtaining simultaneous
operation of both injectors with a total injected power ofjust under 1 MW. These trials will continue when TJ-II
re-commences operation in October, 2007.

3. Acknowledgements
Research supported by the US Department ofEnergy under Contract DE-/AC05-00OR22725 withUT-Battelle, LLC, MEXT-Japan, and by the Spanish
Ministry of Science and Technology under project
FTN2003-08337-C04-0.2.
[1][2][3][4]

H. Yamada, invited paper, this conference.
N. Ohyabu et al, Phys. Rev. Lett. 97, 055002 (2006).
R. Sanchez et al, Comp. Phys. Comm 141, 55 (2001).
E Ascasíbar et alPlasma Phys. Control. Fusion 44, B307
(2002).