Proceedings of ITC/ISHW2007

Energetic ion driven MHD instabilities and their impact on ion
transport in Heliotron J plasmas
Satoshi YAMAMOTO1), Gen MOTOJIMA2), Shinji KOBAYASHI3), Tohru MIZUUCHI3),
Hiroyuki OKADA3), Kazunobu NAGASAKI3), Boyd BLACKWELL4), Katsumi KONDO2),
Yuji NAKAMURA2), Noriyoshi NAKAJIMA4) and Fumimichi SANO3)
1) Kyoto University Pioneering Research Unit for Next Generation, Gokasho, Uji 611-0011, Japan
2) Graduate School of Energy Science, Kyoto University, Gokasho, Uji 611-0011, Japan
3) Institute of Advanced Energy, Kyoto University, Gokasho Uji 611-0011, Japan
4) Research School of Physical Science and Engineering, The Australian National University, Canberra, Australia5) National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, Japan
Energetic ion driven MHD instabilities such as global Alfvén eigenmode (GAE) are observed in NBI-heated
Heliotron J plasmas. In order to investigate the configuration effect on GAEs, we changed the magnetic
configuration with regard to iota profile due to the variation of plasma current and coil current. The characteristicsof observed GAEs are related to the iota profile and magnetic shear. The GAEs are excited by the sidebandexcitation. The bursting GAE might be effect on energetic ion transport because the some plasma parameters aresimultaneously modulated with bursting GAEs.
Keywords: MHD instability, advanced stellarator, low magnetic shear, Alfvén eigenmodes, energetic ion
transport.

1. Introduction
To clarify the MHD instabilities destabilized byenergetic ions is important for the Deuterium-Tritium(D-T) fusion plasmas because the MHD instabilities
could lead to the loss of alpha particles from confinement
region before their thermalization and the ejected alphaparticles might cause significant damage of first wall of afusion device. Therefore, MHD instabilities destabilized
by the energetic ions such as Alfvén eigenmodes (AEs)and energetic particle modes (EPMs) are being
extensively studied in many stellarators/heliotrons as wellas tokamaks using the Alfvénic ions produced by neutralbeam injection (NBI), ion cyclotron resonance heating(ICRH) and D-T reactions.
The characteristics including the existence and thedamping mechanisms of AEs such as continuum damping
mainly depend on the structure of magnetic field.
Toroidicity-induced AEs (TAEs), which can exist in theTAE frequency gap formed by the poloidal mode
coupling m and m+1 (m: poloidal mode number) of shear
Alfvén continua, are observed and effect on the energetic
ion transport in the CHS [1] and LHD [2] with highand/or moderate magnetic shear. In the low shear
stellarator/heliotron W7-AS [3] and Heliotron J [4],Global AEs (GAEs), which can exist on just below ofupper continuum and above of lower shear Alfvén
author’s e-mail: syama@iae.kyoto-u.ac.jp

continuum
aretypicallyobserved.
Moreoverhelicity-induced AEs (HAEs), which are observed in
W7-AS and LHD [5], can exist in the HAE frequency
gaps formed by both toroidal and poloidal mode coupling.
It will be more important AEs as well as GAEs inadvanced stellarators with low toroidal field period Nf(e.g. Nf = 2~5) because AEs having the frequency
comparable with ion diamagnetic frequency could havelarge growth rate and the frequency of HAE is scaledwith the number of toroidal field period [6]. Therefore, it
is important and of interest to investigate the GAEs andHAEs in the Heliotron J plasmas for advanced stellarator
type fusion reactor with low magnetic shear and toroidal
field period.

2. Configuration effect on global AEs
Heliotron J [7] is the helical-axis heliotron device
with major and effective mirror radii R=1.2 m and<aeff>=0.15~0.22 m, simultaneously. The magnetic
configuration of Heliotron J is characterized by the low
magnetic shear for the avoidance of the rational surface
with low mode number and the combination of local
quasi-isodynamic and bumpy (mirror) magnetic field forthe good particle confinement. The Heliotron J plasmas
are produced by the second harmonic electron cyclotron
heating (ECH) with 70GHz, and can be additionallyProceedings of ITC/ISHW2007
heated by the ECH, NBI and ICRF. We utilize theAlfvénic energetic ions produced by the tangentially co.and counter-injected Hydrogen neutral beams with theenergy of 24~27 keV for the destabilization of GAEs.
The toroidal and poloidal magnetic probe array candetermine the toroidal and poloidal mode number n and mof observed coherent MHD modes were installed on thevacuum vessel of Heliotron J.
In the NBI-heated Heliotron J plasmas, some GAEs
with m=2/n=1 and m=4/n=2 are typically observed [4].
These modes propagate in the ion diamagnetic drift
direction and of which frequency is correspond to that ofdiscrete mode obtained from CAS3D3 [8] analysis where
poloidal mode coupling are only taken into account. The
magnetic fluctuation amplitudes of GAEs are in the orderof bθ/Bt ~ 10-6 at the position of the magnetic probes.
In order to investigate the configuration dependenceon GAEs, we changed the magnetic configuration withregard to the differences of iota profiles. The plasma
current and coil current can internally and externally vary
the iota profile. In the plasma for AE excitation
experiment, the plasma current consists of neutral beam
driven current and bootstrap current. We changed theFig. 1. Time evolution of (a) amplitude of observed
m=2/n=1 GAEs, (b) plasma beta obtained fromdiamagnetic signals, (c) line averaged electron
density and (d) plasma current.

bumpy field in order to change the bootstrap current
which is related to the confinement of trapped particle.
The time evolution of amplitude of observed m=2/n=1
GAE and some plasma parameters are shown in Fig. 1,
where the plasma beta obtained from diamagnetic loop,
and line averaged electron density are almost same in theplasmas with different bumpy field. Both neutral beam
driven and bootstrap currents flow in the co.-directionthat increases the rotational transform. The differences ofplasma current shown in Fig. 1 (d) are mainly resulted
from the differences of bootstrap current. The amplitudes
of observed m=2/n=1 GAEs are different in eachmagnetic configurations and is scaled with the amount of
the plasma current.
In order to clarify the differences the amplitude ofobserved GAEs, We compared these observed
frequencies at t = 0.26 s in each plasmas shown in Fig. 1
with shear Alfvén spectra that are calculated forequivalent two dimensional (2D) magnetic configuration

Fig. 2. Shear Alfvén spectra for n=1 for t = 0.26 s
shown in Fig. 1 where poloidal mode coupling istaken into account. (a) Low bumpy case (b) middle
bumpy case and (c) high bumpy case. (d) Profiles ofrotational transform for each configuration.

Proceedings of ITC/ISHW2007
where toroidal mode coupling is ignored. Shear Alfvén
continua for n = 1 and profiles of rotational transform forthe each configurations are shown in Fig. 2. In Fig. 2(a) ~(c), red and blue lines denote the shear Alfvén continuumof m = 2/n = 1 and frequency of observed GAEs with m =2/n = 1. As seen from Fig. 2, the observed mode
frequencies lie just below the shear Alfvén continuum ofm = 2/n = 1. The shear Alfvén spectra and rotationaltransform are almost same in each configurations invacuum. The differences of shear Alfvén spectra shownin Fig. 2 (a) ~ (c) is caused by the plasma current
including bootstrap current. The observed frequency does
not clearly intersect the shear Alfvén continua, therefore,
the GAEs would not be suffer from strong continuum
damping. There are no differences in the electron and ion
temperatures that indicates electron and ion Landau
damping are same in each configuration. The bumpy field
effects on the confinement of trapped particle, whichcannot resonantly couple with the AEs. The reason ofdifferences in observed GAEs amplitude might be
explained by the differences of structure of GAEs. We
need measurement of structure of observed GAEs andcalculation of global mode analysis.
We also changed the iota profile due to the changeof coil current shot by shot (named as iota scanexperiment) and investigated the dependences of themon GAEs. In the iota scan experiments, we fixed themagnetic axis position and plasma volume andstrength of bumpy field. The clear differences inamplitude of observed GAEs were not observed. The
frequency of observed mode is related to the iota value.

3. Parametric studies of GAEs
AEs excited by the energetic ions will be destabilized
when a certain threshold conditions are satisfied. The
linear growth rate of AEs being proportional to thepressure gradient of energetic ions must be large enoughto overcome the damping rate of the waves. Moreover,the velocity of energetic ions vb// is required to satisfy theresonance condition with the Alfvén wave. The GAE
resonance condition for the fundamental excitation isvb///vA >1 and sideband excitation via the drift modulationof energetic ion orbit is vb///vA > k//(m, n) / k//(m±1, n) =[mi-n]/[(m±1)i-n]. Here, k//(m, n) and k//(m±1, n) are theparallel wave number of waves, and i the rotationaltransform. The resonance condition for sideband
excitation between m = 2 and m = (2+1)/n = 1 is vb///vA >0.2. We investigated the resonance condition with vb///vA
changing the electron density <ne>. The m ~ 2/n = 1
GAEs are destabilized in the condition of vb///vA > 0.25 asshown in Fig. 3. The linear growth rate of AEs is related
to the velocity ratio vb///vA as well as energetic ion beta
<βb//> and has a peak at unity. The fluctuation amplitude
of observed GAEs increased with an increase in vb///vA.
These results of parametric study for vb///vA agree with thelinear theory of AEs.

Fig. 3. The dependence of amplitude of observed
m=2/n=1 GAEs against the ratio of energetic ion
velocity and Alfvén velocity.

4. Energetic ion loss induced by the GAEs
In the plasma with magnetic configuration having
the higher bumpy field, bursting GAEs (m = 4/n = 2), of
which amplitude is two times larger than that ofcontinuously observed GAEs are often observed, as
shown in Fig. 4 (a)~(b). The frequency of bursting GAEs
usually chirps down quickly. The time interval between
each bursting GAEs increases with the increased inamplitude of bursting GAEs. This phenomenon can beexplained by predator-prey model between energetic ion
driven mode and energetic ions and might indicate theenergetic ion transport induced by the energetic ion
driven mode. The some plasma parameters such as Hα/Dαand, ion saturation current and plasma floating potential
which are obtained from Langmuir probes located at
outside last closed flux surface of plasma, aresimultaneously increased with bursting GAEs, as shownin Fig. 4 (c)~(e). The increasing of ion saturation current
is related to the increasing of amplitude of GAEs.
Although the increasing in Langmuir probe signals
cannot directly indicate the loss of energetic ion from theconfinement region, the simultaneous increasing of thesome plasma parameters indirectly indicates the energetic

Proceedings of ITC/ISHW2007
ion loss induced by the busting GAEs. The degradation of
stored plasma energy induced by the bursting AEs
observed in LHD and W7-AS were not observed inHeliotron J plasmas.

Fig. 4. Time evolution of (a) frequency spectrumand (b) amplitude of observed m=4/n=2 GAEs, (c)Hα/Dα signals, and (d) ion saturation current andfloating potential obtained from Langmuir probes.

5. Conclusion
We investigated the dependence of magnetic
configuration on GAEs using the variation of plasma
current and coil current. In the high bumpy configuration,
m=2/n=1 GAEs with the largest amplitude were observed.
We compared with the observed frequencies and shear
Alfvén spectra for n = 1. The differences of amplitude ofobserved GAEs in each configuration cannot beexplained by the change of damping rate. GAEs wereexcited by the sideband excitation. The bursting GAEs
with intense magnetic fluctuations might be affecting theenergetic ion transport.

References[1] K. Toi, et al., Nucl. Fusion 40, 1349 (2000).
[2] S. Yamamoto, et al., Nucl. Fusion 45, 326 (2005).
[3] A. Weller et al., Phys. Plasmas 8, 931 (2001)[4] S. Yamamoto, et al., Fusion Sci. Technol. 51, 92(2007).

[5] S. Yamamoto, et al., Phys. Rev. Lett. 91, 245001(2003).
[6] N. Nakajima, C.Z. Cheng and M. Okamoto, Phys.
Fluids B 4, 1115 (1992).
[7] T. Obiki, et al., Plasma Phys. Control. Fusion 42,1151 (2000).
[8] C. Nührenberg Phys. Plasmas 6, 137 (1999).