Efficient estimation of drift orbit island width for passing ions in a shaped tokamak plasma with a static magnetic perturbation

Shinohara, K.; Bierwage, Andreas; Matsuyama, Akinobu; Suzuki, Y.; Matsunaga, G.; Honda, M.; Sumida, S.; Kim, Junghee

doi:10.1088/1741-4326/aba0c8

“…The condition for a charged particle to resonate with the internal kink can be expressed as h ≡ ω tor / ω pol = 1, where the orbit helicity is the ratio of toroidal and poloidal transit frequencies and can be thought of as the kinetic counterpart of the field helicity modified by the combined effect of magnetic drifts v d and the mirror force 39 – 42 . The radial excursion caused by the magnetic drift is given by , so it is proportional to a particle’s mass-to-charge ratio M /( Z e ) and velocity v , and inversely proportional to the plasma current 43 .…”

Section: Resultsmentioning

confidence: 99%

Energy-selective confinement of fusion-born alpha particles during internal relaxations in a tokamak plasma

Bierwage

¹

,

Shinohara

²

,

Kazakov³

et al. 2022

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Long-pulse operation of a self-sustained fusion reactor using toroidal magnetic containment requires control over the content of alpha particles produced by D-T fusion reactions. On the one hand, MeV-class alpha particles must stay confined to heat the plasma. On the other hand, decelerated helium ash must be expelled before diluting the fusion fuel. Here, we report results of kinetic-magnetohydrodynamic hybrid simulations of a large tokamak plasma that confirm the existence of a parameter window where such energy-selective confinement can be accomplished by exploiting internal relaxation events known as sawtooth crashes. The physical picture — a synergy between magnetic geometry, optimal crash duration and rapid particle motion — is completed by clarifying the role of magnetic drifts. Besides causing asymmetry between co- and counter-going particle populations, magnetic drifts determine the size of the confinement window by dictating where and how much reconnection occurs in particle orbit topology.

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“…Furthermore, we pay significant attention to the radial shift of the drift orbit islands with respect to the corresponding magnetic islands formed by field line tracing (FLT). This radial shift was mentioned but not intentionally studied in references [13,14]. This radial shift is certainly important in understanding the EP transport in ITER due to RMP fields.…”

Section: Introductionmentioning

confidence: 99%

“…We note that drift orbit islands formed by passing EPs have recently been carefully studied in references [13,14] for the purpose of finding a reduced model with which to estimate the orbit island width. A so-called orbit pitch parameter, in analogy with the magnetic field-line pitch (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…the safety factor), was introduced in reference [13], in order to calculate the orbit island width. A refined technique, based on a Hamiltonian approach, was developed in reference [14] to better estimate the orbit island width-a technique also exploited in an earlier work [15]. As examples, KSTAR plasmas with vacuum RMP fields were considered in references [13,14] and it was found that the reduced model can predict the orbit island size to within an error range of 15%-25%, as compared to that estimated from the Poincaré map.…”

Section: Introductionmentioning

confidence: 99%

“…Instead, we directly evaluate the orbit island size based on the Poincaré plots of the EP drift orbits. In contrast to references [13,14], we employ a more automatic technique to quantify the orbit island size, by plotting the minimal and maximal values of the canonical toroidal angular momentum traced by each particle on the Poincaré plane. Furthermore, we pay significant attention to the radial shift of the drift orbit islands with respect to the corresponding magnetic islands formed by field line tracing (FLT).…”

Section: Introductionmentioning

confidence: 99%

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Drift orbit islands of energetic particles due to 3D fields in ITER

Liu

¹

,

Li

²

,

Loarte

³

et al. 2021

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In this paper, we report a comparative study of the orbit islands formed by the guiding center drift motion of test energetic particles (EPs), including both high-energy deuterium ions and fusion-born α-particles, with respect to the magnetic islands formed by tracing the field lines, for an ITER plasma representing the 15 MA baseline scenario. The particle drift orbit is modified by the presence of static resonant magnetic perturbations (RMPs) of different toroidal mode numbers n (n = 1 and 3 in this study), forming orbit islands in the Poincaré plane by passing EPs. The key findings are as follows. (i) With an n = 1 RMP field, the size of the orbit islands combined with the total RMP field, including the plasma response, is about three times smaller than that obtained by assuming the corresponding vacuum field. (ii) The orbit island size is not sensitive to the EP energy, and is comparable to those of the magnetic islands. (iii) Passing EPs with outward radial orbital drift form orbit islands that shift inward with respect to the corresponding magnetic islands, and vice versa. This radial shift, ΔΨ, measured in the normalized equilibrium poloidal flux, is quantified as ΔΨ ≃ 0.03X for the ITER baseline plasma and assuming n = 1 RMPs, with X ≡ ( M / M p ) 1 / 2 ( E [ M e V ] ) 1 / 2 Z − 1 , where M is the particle mass, M p is the proton mass, E is the particle energy, and Z is the particle charge number. (iv) Trapped EPs do not form drift orbit islands, even in the presence of the 3D fields produced by the 90 kAt ELM control coil current in ITER, and thus possess good confinement properties. Nevertheless, the deformation of the trapped particle drift orbits in the Poincaré plane shows that the canonical toroidal angular momentum of EPs is no longer conserved in the presence of the RMP fields.

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Kinetic vs magnetic chaos in toroidal plasmas: A systematic quantitative comparison

Moges,

Antonenas,

Anastassiou

et al. 2024

Physics of Plasmas

2

0

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Magnetic field line chaos occurs under the presence of non-axisymmetric perturbations of an axisymmetric equilibrium and is manifested by the destruction of smooth flux surfaces formed by the field lines. These perturbations also render the particle motion, as described by the guiding center dynamics, non-integrable and, therefore, chaotic. However, the chaoticities of the magnetic field lines and the particle orbits significantly differ in both strength and radial location in a toroidal configuration, except for the case of very low-energy particles whose orbits closely follow the magnetic field lines. The chaoticity of more energetic particles, undergoing large drifts with respect to the magnetic field lines, crucially determines the confinement properties of a toroidal device but cannot be inferred from that of the underlying magnetic field. In this work, we implement the smaller alignment index method for detecting and quantifying chaos, allowing for a systematic comparison between magnetic and kinetic chaos. The efficient quantification of chaos enables the assignment of a value characterizing the chaoticity of each orbit in the space of the three constants of the motion, namely, energy, magnetic moment, and toroidal momentum. The respective diagrams provide a unique overview of the different effects of a specific set of perturbations on the entire range of trapped and passing particles, as well as the radial location of the chaotic regions, offering a valuable tool for the study of particle energy and momentum transport and confinement properties of a toroidal fusion device.

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Efficient estimation of drift orbit island width for passing ions in a shaped tokamak plasma with a static magnetic perturbation

Cited by 5 publications

References 37 publications

Energy-selective confinement of fusion-born alpha particles during internal relaxations in a tokamak plasma

Energy-selective confinement of fusion-born alpha particles during internal relaxations in a tokamak plasma

Drift orbit islands of energetic particles due to 3D fields in ITER

Kinetic vs magnetic chaos in toroidal plasmas: A systematic quantitative comparison

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