RF stabilization of high-density plasma in an axisymmetric mirror I: Identification and stabilization of flute mode

Yasaka, Yasuyoshi; Itatani, Ryohei

doi:10.1088/0029-5515/24/4/005

Cited by 50 publications

(31 citation statements)

References 15 publications

(26 reference statements)

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“…Recent experiments demonstrating radiofrequency (RF) stabilization [1][2][3] have stimulated theoretical interest in the subject [4][5][6][7][8]. In this letter, we present a theoretical description which unifies and generalizes previous work that has emphasized either mode coupling [4] or ponderomotive force [5,6].…”

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confidence: 61%

“…Recent RF stabilization experiments [1][2][3] have focused on attempting to correlate stability with RF power W and frequency (co-fyVfy. It has been difficult so far to obtain a unified understanding of the various experimental results.…”

Section: =mentioning

confidence: 99%

“…In the high-m interchange limit, r 3r (2) where p = nnij is the mass density, CJ S the interchange mode frequency, K the radial component of the curvature, and p the plasma pressure. To obtain RF stabilization, we must h a v e^r ~ 5F ~ O(|E| 2 ) where E is the RF electric field amplitude.…”

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confidence: 99%

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Surfaces of Nonpositive Extrinsic Curvature in Spaces of Constant Curvature

Borisenko¹

1982

Math. USSR Sb.

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Geodesic loops on polyhedra were studied only for Euclidean space and it was known that there are no simple geodesic loops on regular tetrahedra. Here we prove that: 1) On the spherical space, there are no simple geodesic loops on tetrahedra with internal angles π/3 < α i < π/2 or regular tetrahedra with α i = π/2, and there are three simple geodesic loops for each vertex of a tetrahedra with α i > π/2 and the lengths of the edges a i > π/2. 2) On the hyperbolic space, for every regular tetrahedron T and every pair of coprime numbers (p, q), there is one simple geodesic loop of (p, q) type through every vertex of T .

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confidence: 61%

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confidence: 99%

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Surfaces of Nonpositive Extrinsic Curvature in Spaces of Constant Curvature

Borisenko¹

1982

Math. USSR Sb.

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“…Therefore, if | VlogAip | «: | VlogE a |, the perturbed rf field can be neglected in Eq. (2). I shall restrict myself to this case by considering only q profiles with small inversion radii.…”

Section: Wrf=i[ ^Tz-vxmej^s-viej 2 )mentioning

confidence: 99%

“…2 This phenomenon has been interpreted 2 " 4 to be a consequence of a ponderomotive force exerted by the radiation on the plasma. Recently it has been proposed 5,6 that the same mechanism can be employed to stabilize the ballooning modes in tokamaks.…”

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Ion-Cyclotron-Frequency Stabilization of Internal Kink Mode and Sawtooth Oscillations in Tokamaks

Litwin

1988

Phys. Rev. Lett.

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It is proposed that the ponderomotive force due to applied ion-cyclotron-resonance-frequency waves can stabilize the internal-kink mode in tokamaks. The sufficient stability criterion is derived and the necessary power estimated. It is concluded that at the rf power level present in the Joint European Torus experiment, the ponderomotive force effects are significant and may be responsible for the modification of the sawtooth activity observed in recent experiments. PACS numbers: 52.55.Fa, 52.40.Db Stabilization of interchange instabilities by an applied radio-frequency (rf) radiation has been demonstrated in experiments at the Phaedrus Tandem Mirror at the University of Wisconsin 1 and at Kyoto University. 2 This phenomenon has been interpreted 2 " 4 to be a consequence of a ponderomotive force exerted by the radiation on the plasma. Recently it has been proposed 5,6 that the same mechanism can be employed to stabilize the ballooning modes in tokamaks. However, the rf power required to stabilize these modes in a large-size tokamak is much higher than in present-day experiments. 6 Heuristically, since the magnetic field curvature in tokamaks is much larger than in the tandem mirror central cell, the ballooning modes are driven more strongly in tokamaks than in mirrors. It can be expected, however, that the ponderomotive force will be more efficient in the stabilization of more weakly driven modes. An example of such a mode is the internal kink.The internal-kink mode has been considered 7,8 responsible for the sawtooth oscillations in tokamak experiments 9 which are associated with the electron-temperature variation in the plasma core. In the Kadomtsev 7 picture, the current profile becomes more peaked as the electron temperature increases until the safety factor on the axis, qo, falls below unity. This leads to growth of a magnetic island with the poloidal mode number m = 1. Subsequent reconnection restores qo to above unity. Bussac et a/. 8 suggested that the sawtooth crashes are caused by an ideal internal kink. While the Kadomtsev picture appears to describe properly the sawtooth activity in early tokamak experiments, 9 recent observations 10 indicate that sawtooth crashes occur on the ideal MHD time scale.Ponderomotive stabilization of the internal-kink mode would be of considerable experimental interest. Besides being an interesting physical phenomenon in itself, it would make possible sawtooth-oscillation control and allow for a higher electron temperature than in the absence of the rf radiation. In fact, it is not implausible that ponderomotive-force effects on sawtooth oscillations have already been observed. In experiments at Joint European Torus (JET) the sawtooth activity has been seen to be strongly affected by the ion cyclotronresonance-frequency (ICRF) heating. Usually 11 the presence of ICRF leads to sawteeth characterized by both larger amplitude and longer period than in the case of purely Ohmic heating. In most cases the sawtooth ramp phase is terminated by an m=n = l instability (n is the tor...

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The ponderomotive force of an electromagnetic wave in a collisional plasma

Sawley

1984

J. Plasma Phys.

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The nonlinear propagation of a circularly polarized, electromagnetic wave in a collisional, infinite, magnetized plasma is considered. The presence of collisions leads to spatial variation in the amplitude of the wave field which gives rise to a time-independent ponderomotive force. The ponderomotive potential for a left (right) circularly polarized wave attains a maximum at the ion (electron) cyclotron frequency. In the vicinity of the cyclotron frequency it is shown to be always positive. A decrease in both the particle density and the real and imaginary parts of the complex wavenumber is shown to result from the effect of the ponderomotive force.

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RF stabilization of high-density plasma in an axisymmetric mirror I: Identification and stabilization of flute mode

Cited by 50 publications

References 15 publications

Surfaces of Nonpositive Extrinsic Curvature in Spaces of Constant Curvature

Surfaces of Nonpositive Extrinsic Curvature in Spaces of Constant Curvature

Ion-Cyclotron-Frequency Stabilization of Internal Kink Mode and Sawtooth Oscillations in Tokamaks

The ponderomotive force of an electromagnetic wave in a collisional plasma

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