Radial magnetosonic eigenmodes in a toroidal plasma with an ion-ion hybrid layer

Cotsaftis, Michel; Sy, W. N. C.

doi:10.1016/0375-9601(83)90045-2

Cited by 6 publications

(5 citation statements)

References 3 publications

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“…x n 3 --• (18) In this limit, the form of the FLR corrections coincides with the one first obtained in Refs [24,25]. Equation (1) becomes a system of ordinary differential equations, which has been widely used to investigate mode conversion and absorption near cyclotron resonances [7][8][9][10]16]. In these references a thorough discussion of the physics involved in the FLR wave equations can be found.…”

Section: Plane Stratified Limit and Dispersion Relationsupporting

confidence: 72%

“…In the ICR frequency range, however, ray tracing is only marginally justified, even in the largest devices. Moreover, one-dimensional simulations with a plane stratified plasma model including the appropriate variation of |B| but no shear (see, for example, Refs [7][8][9][10]) suggest that cavity eigenmodes could play an important role. This has reoriented the modelling efforts towards the development of global twodimensional codes.…”

Section: Introductionmentioning

confidence: 99%

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Numerical simulation of ion cyclotron heating of hot tokamak plasmas

1988

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The authors have written a code for the solution of the integro-differential equations describing coupling, propagation and absorption of high frequency waves in the ion cyclotron frequency range in tokamak plasmas, taking into account finite Larmor radius effects and parallel dispersion. The wave equations are discretized by a semi-spectral approach, using cubic Hermite finite elements in the radial direction and an expansion in Fourier modes in the poloidal direction. The latter permits analytic evaluation of the orbit integrals along magnetic field lines in the presence of a poloidal component of the static magnetic field. Thus, the code describes mode conversion to ion Bernstein waves, ion cyclotron damping at the fundamental and at the first harmonic, and electron transit time and Landau damping in full toroidal geometry. A few simulations of ion cyclotron heating of the ASDEX tokamak are presented. They show generally good agreement with the predictions of simpler models, namely plane layered models and ray tracing. Furthermore, the simulations can be used to identify a few interesting toroidal effects, particularly regarding the efficiency of mode conversion and the propagation of ion Bernstein waves.

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Section: Plane Stratified Limit and Dispersion Relationsupporting

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Numerical simulation of ion cyclotron heating of hot tokamak plasmas

1988

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“…It is an outstanding characteristic of this case that the plasma density which yields the maximum loading resistance increases with increasing toroidal magnetic field strength. This tendency is well understood, provided the local cavity mode predicted by the theory [8][9][10][11] is really present; as the toroidal magnetic field BT increases, the resonance cut-off double layer shifts towards the low-field side, thereby reducing the volume of the cavity. For the RF frequency kept constant, the cavity resonance can only be satisfied by the shorter wavelength realized in the case of higher plasma density.…”

Section: Discussionmentioning

confidence: 99%

“…is known to be a quantity which can be used to measure the separation between a resonance layer and a cut-off layer [6,8]. Here, R is the major radius.…”

Section: Discussionmentioning

confidence: 99%

ICRF heating experiments on JIPP T-II

et al. 1984

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Data of JIPP T-II ICRF heating experiments are presented. The experiment covers three typical cases: the low-concentration hydrogen minority case, the high-concentration hydrogen minority case, and the 3 He-minority case. The best heating efficiency is obtained for the 3 He-minority case. It is shown through power balance analysis that the two H-minority cases are different in the wave energy deposition profile. The difference is explained by the presence of a local cavity mode in the high-concentration minority case. The ion temperature stops rising at a power density level of 0.65 W-cm" 3 for the hydrogen minority experiments. No such deterioration is found in the case of the 3 He minority experiment up to a power density level of 0.45 kW'cnf 3 . This is the maximum possible to attain within the maximum power injection (180 kW) up to which the experiment is conducted. An analytic solution of the Fokker-Planck equation is derived in order to interpret the deterioration of the heating efficiency.

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“…In field theory it provides a simple zero-dimensional model possessing a non-polynomial Lagrangian [9]. The δ > 0 case is useful in toroidal plasma [14]. The corresponding radial Schrödinger equation reads…”

Section: Non-polynomially Modified Oscillatormentioning

confidence: 99%

Unified derivation of exact solutions for a class of quasi-exactly solvable models

Agboola

Zhang

2012

Journal of Mathematical Physics

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We present a unified treatment of exact solutions for a class of four quantum mechanical models, namely the anharmonic singular potential, the generalized quantum isotonic oscillator, the soft-core Coulomb potential, and the non-polynomially modified oscillator. We show that all four cases are reducible to the same basic ordinary differential equation, which is quasi-exactly solvable. A systematic and closed form solution to the basic equation is obtained via the Bethe ansatz method. Using the result, general exact expressions for the energies and the allowed potential parameters are given explicitly for each of the four cases in terms of the roots of a set of algebraic equations. A hidden sl(2) algebraic structure is also discovered in these models.

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Radial magnetosonic eigenmodes in a toroidal plasma with an ion-ion hybrid layer

Cited by 6 publications

References 3 publications

Numerical simulation of ion cyclotron heating of hot tokamak plasmas

Numerical simulation of ion cyclotron heating of hot tokamak plasmas

ICRF heating experiments on JIPP T-II

Unified derivation of exact solutions for a class of quasi-exactly solvable models

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