Circulating-Ion-Driven Fishbone Instabilities in Plasmas with Weak-Shear Core

Ya.I. Kolesnichenko*, V.S. Marchenko*, R.B. White**
*Institute for Nuclear Research, Prospect Nauky 47, Kyiv, 03680, Ukraine
**Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey, 08543, USA
Abstract. New energetic particle mode instabilities of fishbone type are predicted. The considered instabilities are driven
by the circulating energetic ions. They can arise in plasmas of tokamaks and spherical tori with a weak magnetic shear in
the wide core region and strong shear at the periphery, provided that the central safety factor is close to the ratio m/n,
where m and n are the poloidal mode number and toroidal mode number, respectively. The instability with m=n=1 has
interchange-like spatial structure, whereas the structure of instabilities with m/n>1 is similar to that of the infernal MHD
mode (except for the region in vicinity of the local Alfven resonance).
Keywords: Fishbone Mode, Quasi-Interchange Mode, Infernal Mode.
PACS: 52.55Pi
The purpose of this work is to consider possible fishbone instabilities driven by circulating energetic ions in
plasmas with the safety factor close to unity or other low-order rationals in a wide core region surrounded by a
region with large magnetic shear. Such behavior of q(r) is typical for spherical tori. In addition, q(r) is close to unity
in the plasma core in many tokamaks experiments and this will be the case in the ITER third operational scenario, so
called “hybrid” regime [1]. Note that fishbone oscillations with m ≠ n ≠ 1 were observed in plasmas with q(0) ~ 2
of the National Spherical Torus Experiment (NSTX) [2]. We consider both the modes with m=n=1 and m ≠ n .
Our analysis will be based on the approach of Ref. [3] extended to the case when the plasma contains a small
number of the energetic ions. This will be done in the assumption that only non-adiabatic response of the energetic
ions is important.

Let us consider a possibility of the destabilization of infernal fishbones in NSTX plasmas with q0 ~ 2. This is of
interest because bursting fishbone instabilities with m / n > 1 were observed in NSTX [2]. We use the following
parameters: R ≈ 100cm, a = 65cm, B = 0.3T, Εα = 90keV, vα / vA = 3, m = 2, n = 1, q0 = 1.7 . For
realistic model profiles of the background plasma pressure and ι (r)we have found
σ 2 = 1/ 8,σ res,2 (ω ) = const ≈ 0.55 . Then we find from Eqs. (18), (19) that Ω ≈ 0.5, ˆ crit ≈ 6×10−2
βα .
Taking into account that r0 ≈ 0.6a ≈ 40cm, ρα ≈ 20cm, we obtain from Eq.(13) that the threshold β of
energetic ions is crit ≈ 15%
βαo . The mode frequency in dimensional units is
f ≡ω /(2π ) = 0.5(2ι 0−1)vα /(2π R) ≈ 40 kHz . The obtained threshold magnitude of βα and the mode
frequency are quite reasonable. In particular, a bursting fishbone instability with m=2 and the initial frequency in the
plasma frame f ≈ 45kHz was observed when the central safety factor was q0 ≈ 1.7 in the NSTX shot #106218
We have predicted new circulating-ion-driven fishbone instabilities in toroidal plasmas with q0 ~ m/ n ≥ 1
and low magnetic shear in the core region. The instabilities have the frequency determined by energetic particles,
ω ~ k||0vα , i.e., they belong to the class of Energetic Particle Modes (EPM). This implies that the considered
instabilities are potentially dangerous being able to lead to escaping the energetic ions from the core region to the
wall or plasma periphery. The mode numbers, m and n , are not necessarily equal unity, and determine the spatial
structure of the modes. When m=n=1, the structure of the considered mode strongly differs from the rigid kink
displacement taking place during conventional fishbone oscillations. Although our instability is caused by the same
resonance (ω = k||v|| ) as the conventional one< its physics differs from that of the conventional instability. The
reason is that all the energetic ions in the core region (rather than only particles crossing q=1 surface) contribute to
the destabilization of the mode.
This work was supported in part by the CRDF Project UKP2-2643-KV-05, and by the U.S. Department of
Energy Grant DE-FG03-94ER54271.
1. X. Litaudon et al., Plasma Phys. Control. Fusion 46, A19 (2004).
2. E.D. Fredrickson, L. Chen, R. White, Nucl. Fusion 43, 1258 (2003).
3. F.L. Waelbroeck, R.D. Hazeltine, Phys. Fluids 31, 1217 (1988).
4. M.N. Bussac et al., Phys, Rev. Lett. 35, 1638 (1975).
5. F.Porcelli, R. Stankevich, W. Kerner, H.L. Berk, Phys. Plasmas 1, 470 (1994).

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