A Shimizu

C Suzuki

K Ida

K Matsuoka

K Nagaoka

K Ogawa

K Toi

M Isobe

S Nishimura

S Okamura

T Akiyama

T Minami

Y Todo

Y Yoshimura

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Energetic-particle modes driven by supra-thermal electrons 
in second harmonic ECRH plasmas of the Compact Helical System 
 
M. Isobe1, K. Toi1, Y. Yoshimura1, A. Shimizu1, Y. Todo1, K. Ida1, C. Suzuki1, T. Akiyama1, 
T. Minami1, K. Nagaoka1, S. Nishimura1, K. Ogawa2, K. Matsuoka1 and S. Okamura1 
1National Institute for Fusion Science, Toki, 509-5292 Japan 
2Department of Energy Science, Nagoya University, Nagoya, 464-8603, Japan 
 
1. Introduction 
Fast-particle-driven MHD instabilities such as the fishbone (FB) mode and toroidicity-
induced Alfvén eigenmodes (TAEs) are one of key physics issues in magnetically confined 
fusion plasma experiments because those instabilities may lead to anomalous transport of 
alphas in a future burning plasma.  In existing toroidal devices, experiments concerned with 
this subject have been so far performed by use of beam ions, perpendicular fast ion produced 
by ICRH and alphas born from D-T reactions.  It should be pointed out that compared with 
alphas in ITER, in existing experiments, those ions mentioned above are fairly energetic, 
having much higher ratio of Larmor radius to minor radius and also showing significant shift 
of banana orbits from flux surfaces [1].  Supra-thermal electrons are also capable of 
destabilizing those modes since excitation of those modes depends on precessional drift 
frequency of particle, not on mass [2].  They are characterized by small dimensionless orbit, 
similarly to alphas in reactor-relevant plasmas.  In this point of view, it could be mentioned 
that instabilities driven by supra-thermal electrons are relevant to alpha-particle-driven modes 
in burning plasmas.  After the FB mode excited by supra-thermal electrons produced by 2nd 
harmonic ECRH was first found in the DIII-D [3] and Compass-D [4], FB modes associated 
with supra-thermal electrons have been observed in several tokamaks [5,6].  In regard to 
helical system, global AEs were excited due to supra-thermal electrons in the weak magnetic 
shear stellarator HSX with 2nd harmonic ECRH [7].  In this paper, we report bursting MHD 
instabilities in low-density plasmas with 2nd harmonic ECRH in CHS. 
 
2. Energetic-particle modes in second harmonic ECRH plasmas 
Figure 1a) shows bursting recurrent MHD instabilities in fairly low-density plasmas 
(ne<0.5!10
19 m-3) of inward shifted configuration (Rax/Bt=0.949 m/0.97 T) with high-power 
off-axis ECRH (PECRH~275 kW).  The focused X-mode wave of which frequency is 54.5 GHz 
35th EPS Conference on Plasma Phys. Hersonissos, 9 - 13 June 2008 ECA Vol.32D, P-1.056  (2008)
and power is up 300 kW was perpendicularly injected into the CHS vacuum chamber from the 
upper diagnostic port at the vertically elongated poloidal cross section.  The wave frequency 
was 2nd harmonic because Bt ranged from 0.88 T to 1 T.  The resonance layer was located at 
the place between a pair of helical winding coils, i.e. bottom of helical magnetic field ripple 
(see Figure 1b)).  In such a heating scheme, helically trapped energetic electrons are primarily 
created.  The Mirnov coil array indicates that the observed mode has a structure of m=2/n=1, 
propagating poloidally in parallel to the ion-diamagnetic direction and toroidally in parallel to 
the direction of helical field coil current equivalent to plasma current in tokamak in a 
viewpoint of increasing the rotational transform.  Here, m and n stand for the poloidal and 
toroidal mode numbers, respectively.  The mode is characterized by the rapid frequency 
downshift from ~70 kHz to ~50 kHz in the time scale of ~1 ms.   It is noted that strong MHD 
activities can be seen in inward shifted configurations (Rax∀0.949 m) that provide improved 
orbit of trapped particle compared with that in outward shifted configurations.  The X-ray 
detector suggests that an appreciable amount of perpendicular supra-thermal electrons exists 
in plasmas of ne less than 0.5!10
19 m-3 whereas they do not at ne of 1!10
19 m-3.  It should be 
noted that the direction of toroidal precession drift of helically trapped electrons matches the 
toroidal direction of the observed mode propagation.  Figure 2 shows shear Alfvén continua 
for n=1 and n=2 modes of the discharge shown in Fig. 1.  It is obvious that the observed mode 
frequency is much lower than the TAE gap frequency.  In addition, the mode shows the 
periodic recurrence accompanied with the rapid frequency down shift.  Instabilities observed 
 
 
Figure 1a) Bursting MHD instabilities (m/n=2/1) in a low ne 2
nd harmonic ECRH plasma of 
CHS.  Time traces of ne, dB!/dt and its spectrogram are shown.  1b) 2
nd harmonic resonance 
layer position for the wave of 54.5 GHz. 
35th EPS 2008; M.Isobe et al. : Energetic-particle modes driven by supra-thermal electrons in second harmonic... 2 of 4
in CHS ECRH plasmas could be therefore classified into the energetic-particle mode (EPM). 
   The FB mode excited by trapped fast ions propagates poloidally in parallel to the ion-
diamagnetic drift velocity and toroidally in parallel to the precession velocity of deeply 
trapped ions in tokamak [8].  In tokamak plasmas with ECRH, the strong bursting MHD 
activities have been observed when the resonance layer position was placed on the high field 
side.  In such a heating condition, 
barely trapped electrons are primarily 
generated.  The toroidal precession 
direction of those electrons is the same 
as that of ions trapped deeply in the low 
field side because of the drift reversal 
and those electrons can excite the FB 
instability potentially [2].  The bursting 
instabilities observed in 2nd harmonic 
ECRH plasmas of CHS propagate 
poloidally in parallel to the ion-
diamagnetic direction and toroidally in 
parallel to the co-direction.  This mode 
behavior is the same as the ion FB 
mode excited in tokamak and is also the same as EPM driven by tangentially co-injected 
beam ions in CHS.  As mentioned before, helically trapped electrons are primarily produced 
in our condition.  The direction of toroidal precession drift of helically trapped supra-thermal 
electrons matches that the toroidal direction of observed mode propagation.  It looks that 
helically trapped supra-thermal electrons produced by ECRH play a dominant role in the 
mode excitation.  In the case of EPM excitation by trapped particles, it may be expected that 
the mode frequency would be !!!d, where ! and !d are the mode frequency and the bounce-
averaged toroidal precessional drift frequency of trapped particles, respectively [9].  We have 
estimated toroidal precessional frequency fd of deeply, helically trapped electrons by solving 
formulae for the particle drift in the r and ! directions in a model helical magnetic field given 
by Mynick et al. [10].  Figure 3a) shows examples of helically trapped orbits of energetic 
electrons.  Estimated fd of helically trapped electrons is shown in Figure 3b).  It can be seen 
that if energies of trapped electrons are about 70 keV, the mode frequency matches fd of those 
electrons. 
 
Figure 2a) Profiles of rotational transform (1/q) and ne 
for the discharge shown in Fig. 1.  2b) Shear Alfvén 
continua (2D) for n=1 and n=2 modes.  
35th EPS 2008; M.Isobe et al. : Energetic-particle modes driven by supra-thermal electrons in second harmonic... 3 of 4
In summary, bursting MHD instabilities were destabilized in fairly low ne 2
nd harmonic 
ECRH plasmas without neutral beams in CHS.  The mode of which frequency is lower than 
the TAE gap frequency is characterized by frequency downshift, rotating poloidally parallel to 
the ion-diamagnetic direction and toroidally in 
parallel to the co-direction.  The direction of 
the toroidal precession of helically trapped 
electrons is the same as the co-direction.  The 
observed mode is supposed to be due to 
helically trapped supra-thermal electrons 
produced by 2nd harmonic ECRH. 
 
Acknowledgements 
This work is supported by Grant-in-Aid 
from MEXT for Exploratory Research No. 
20656150 and for Scientific Research on 
Priority Areas No. 16082209.  This work is 
also supported by the JSPS-CAS Core-
University Program in the field of "Plasma and 
Nuclear Fusion". 
 
References 
  [1] A. Fasoli et al., Nuclear Fusion 47, S264 (2007). 
  [2] F. Zonca et al., Nuclear Fusion 47, 1588 (2007). 
  [3] K.L. Wong et al., Phys. Rev. Lett. 85, 996 (2000). 
  [4] M. Valovi# et al., Nuclear Fusion 40, 1569 (2000). 
  [5] P. Smeulders et al., 29th EPS Conference on Plasma Phys. and Contr. Fusion, Montreux,    
  17-21 June 2002 ECA Vol. 26B, D-5.016 (2002). 
  [6] X.T. Ding et al., Nuclear Fusion 42, 491 (2002). 
  [7] D.L. Brower et al., 32nd EPS Conference on Plasma Phys., Tarragona, 27 June – 1 July   
  2005 ECA Vol. 29C, O-2.001 (2005). 
  [8] K. McGuire et al., Phys. Rev. Lett. 50, 891 (1983). 
  [9] F. Zonca and L. Chen, Phys. of Plasmas 7, 4600 (2000). 
  [10] H.E. Mynick et al., Phys. Rev. Lett. 48, 322 (1982). 
 
 
Fig. 3a) Bounce-averaged orbits of helically 
trapped electrons with energy of 50 keV.  3b) 
Toroidal precession frequency of helically 
trapped electrons as a function of energy 
35th EPS 2008; M.Isobe et al. : Energetic-particle modes driven by supra-thermal electrons in second harmonic... 4 of 4


Energetic-particle modes driven by supra-thermal electrons in second harmonic ECRH plasmas of the Compact Helical System

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Energetic-particle modes driven by supra-thermal electrons in second harmonic ECRH plasmas of the Compact Helical System

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