Hot plasma dielectric response to radio-frequency fields in inhomogeneous magnetic field

Svidzinski, V. A.; Kim, J. S.; Spencer, J. Andrew; Zhao, L.; Галкин, С. А.; Evstatiev, Evstati

doi:10.1063/1.4966638

Cited by 8 publications

(7 citation statements)

References 20 publications

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“…a procedure that directly reasons in terms of x // to capture the isolated parallel dynamics in some way) a further speed-up could possibly be realised. Deriving the hot plasma conductivity tensor for a tokamak, Svidzinski [31] explored a route to include the parallel dynamics by expressing the electric field at the position (R ′ , Z ′ ) in the orbit integral yielding the dielectric response in terms of its values at the grid points (R i , Z j ) later adopted for the actual numerical solving of the wave equation. Adopting a sufficiently refined grid, this allows him to locally represent the ⃗ E(R ′ , Z ′ ) using a low order polynomial (he uses second order Lagrange polynomials) and define a nonlocal conductivity tensor accounting for the poloidal field.…”

Section: Budé's Methods and Parallel Dynamicsmentioning

confidence: 99%

Solving the all-FLR ICRH integro-differential wave equation as a high-order differential equation for studying combined ICRH-NBI heating

Eester¹,

Lerche²

2020

Nucl. Fusion

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A fast and intuitive method is proposed to solve the integro-differential wave equation relevant for modelling ion cyclotron resonance heating (ICRH) at any cyclotron harmonic, for arbitrary ion distributions and retaining all finite Larmor radius effects. The method is inspired on recent work of Budé who proposed to fit the dielectric tensor in k-space by a higher order polynomial, allowing to derive a suitable differential operator that conveniently mimics the integro-differential operator in a sufficiently large k ⃗ -range to describe all physically relevant wave modes in k ⃗ -space. Eliminating a drawback of the Budé method by going back to first principles yields a wave equation dielectric response operator that guarantees a positive definite power absorption for populations in thermal equilibrium—as physically expected—and that can directly be used in the Fokker–Planck equation. The method is exploited for 1D application but retaining the toroidal curvature. Analytical expressions of the components of the dielectric tensor are available for Maxwellian distributions as well as bi-Maxwellians with a finite parallel drift. Numerical integration of the velocity space integrals allows to account for arbitrary distributions. A number of examples relevant for high performance tokamak plasma operation and exploiting simultaneous ICRH and neutral beam injection heating are given to illustrate the method’s potential.

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Section: Budé's Methods and Parallel Dynamicsmentioning

confidence: 99%

Solving the all-FLR ICRH integro-differential wave equation as a high-order differential equation for studying combined ICRH-NBI heating

Eester¹,

Lerche²

2020

Nucl. Fusion

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“…A similar approach can be applied for wave equations with a nonlocal hot plasma dielectric response model. 7 The boundary problem is formulated from Maxwell's equations…”

Section: Hybrid Iterative Approach For Solving Wave Equationsmentioning

confidence: 99%

“…Presently available advanced codes solving for full wave (without limiting approximation of small wavelengths relative to the size of the system) electromagnetic (EM) fields in plasma, which are driven by an antenna operating at fixed frequency x, are using direct linear solvers for solving the discretized linear wave equations in a frequency domain. For hot fusion plasma applications, such codes include TORIC, 1,2 AORSA 3 (used for 2D Tokamak geometry), AORSA3D, 4 PSTELION 5 (developed for 3D Stellarator geometry), STELEC 6 [3D Stellarator electron cyclotron heating (ECH) modeling], and FullWave 7,8 (recently developed for 2D Tokamak geometry at FAR-TECH, Inc.). An approach in which the hot plasma response is added iteratively to the cold plasma model in the full wave simulations [9][10][11][12] has recently demonstrated its merits in practical simulations of some RF scenarios.…”

Section: Introductionmentioning

confidence: 99%

Hybrid iterative approach for simulation of radio-frequency fields in plasma

et al. 2018

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A novel iterative approach for solving discretized linear wave equations in a frequency domain, which combines time evolution with iterative relaxation schemes, is presented. In this hybrid approach, each iteration cycle consists of evolution of electromagnetic (EM) fields in time over a specified number of field periods followed by several iterative relaxations. Provided that there is sufficient dissipation, both the time evolution and the iterative relaxations contribute to the convergence of the EM fields to the solution of the formulated full wave boundary value problem. Time evolution rapidly distributes EM fields, propagating with group velocity, over the simulation domain, while the iterative relaxations smooth the fields, reducing the numerical errors such that iteration cycles converge to a steady state solution, approximating the solution of the formulated problem. This approach is intended for large scale simulations which are beyond the capabilities of direct solvers presently used for solving wave equations in the frequency domain. The technique is demonstrated for solving wave equations on a regular grid using a cold plasma dielectric model with collisions for 2D modeling of EM fields in tokamak in an electron cyclotron frequency range.

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“…Several full-wave numerical simulation codes have been developed to describe waves in fusion toroidal devices [1][2][3], exploiting symmetry or ray-tracing technique; at the same time, only few methods have been developed to obtain selfconsistent solutions for nonaxisymmetric ECRIS plasma [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

“…Previous approaches to simulate RF fields in ECRIS using the conductivity kernel of 1-D mirror magnetic field are described in [6].…”

Section: Introductionmentioning

confidence: 99%

Modelling RF-plasma interaction in ECR ion sources

et al. 2017

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Abstract. This paper describes three-dimensional self-consistent numerical simulations of wave propagation in magnetoplasmas of Electron cyclotron resonance ion sources (ECRIS). Numerical results can give useful information on the distribution of the absorbed RF power and/or efficiency of RF heating, especially in the case of alternative schemes such as mode-conversion based heating scenarios. Ray-tracing approximation is allowed only for small wavelength compared to the system scale lengths: as a consequence, full-wave solutions of Maxwell-Vlasov equation must be taken into account in compact and strongly inhomogeneous ECRIS plasmas. This contribution presents a multi-scale temporal domains approach for simultaneously including RF dynamics and plasma kinetics in a "cold-plasma", and some perspectives for "hot-plasma" implementation. The presented results rely with the attempt to establish a modal-conversion scenario of OXB-type in double frequency heating inside an ECRIS testbench.

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Hot plasma dielectric response to radio-frequency fields in inhomogeneous magnetic field

Cited by 8 publications

References 20 publications

Solving the all-FLR ICRH integro-differential wave equation as a high-order differential equation for studying combined ICRH-NBI heating

Solving the all-FLR ICRH integro-differential wave equation as a high-order differential equation for studying combined ICRH-NBI heating

Hybrid iterative approach for simulation of radio-frequency fields in plasma

Modelling RF-plasma interaction in ECR ion sources

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