A variational principle for studying fast-wave mode conversion

Abstract

A variational principle for studying one-dimensional wave propagation and damping near the ion-ion hybrid conversion region in a tokamak is presented. In its variational form, the wave equation is closely related to the power balance equation: substituting the electric field for the test function in it yields the generalized Poynting theorem. The guiding centre position rather than that of the particle is adopted as the independent variable. Toroidal and oblique incidence effects are retained but the poloidal magnetic field is neglected. A strictly positive power density for Maxwellian plasmas is ensured by starting from a general formalism due to Lamalle (Lamalle PU 1993 Phys. Lett. 175A 45;1997 Plasma Phys. Control. Fusion 39 1409 and expanding the operator acting on the electric field in the expression for the absorbed power per guiding centre orbit (rather than expanding the dielectric tensor, as is usually done) in terms of the assumed small parameter ε = k ⊥ ρ, where k ⊥ is the perpendicular wavenumber and ρ the Larmor radius. The general formulae for the dielectric response are provided and explicit expressions are given for the case where up to second-order corrections in ε are retained in the operator. As an illustration, the absorption of radio frequency power in a (H)-D-(Ar) TEXTOR plasma typical for the radiative improved mode is discussed.

On all-FLR order numerical modelling of RF wave propagation and damping

“…Electron absorption scaling with k⊥ 2 when adding the electron Landau and transit time magnetic pumping contributions [9,10], the absence of electron absorption suggests that the considered spectrum not containing high enough k x -modes. More in depth analysis confirms this is indeed the case: see the inset for the corresponding evaluation using the TOMCAT differential equation solver [11] which shows a small but finite electron absorption exhibiting both long (fast wave) and short (Bernstein wave) wavelength structure. …”

Efficient generation of energetic ions in multi-ion plasmas by radio-frequency heating

“…Equation (2) predicts that 3 He ions should efficiently absorb RF power in H-D or H- 4 He plasmas, if the hydrogen concentration is ~ 67%. This is supported by modeling with the TOMCAT code 11 , using plasma parameters relevant for the JET experiments described below. A direct comparison of the heating performance of the three-ion discharges was not possible for the JET discharges discussed here.…”

Kinetic theory of plasma waves

“…SOME ASPECTS OF NONUNIFORM PLASMA MODELING III.A. Mode Coupling [38][39][40][41][42][43][44][45][46][47][48][49][50][51] Before commenting on the particular issues brought about by the impact of the plasma inhomogeneities on the orbits of the particles and the challenges this leads to when trying to write down a rigorous expression for the dielectric response, a simplified problem is looked at first, namely that of the wave propagation in a tokamak in absence of a poloidal field i.e. where the guiding center orbits are assumed to simply being given by ϕ(t) = ϕ(t o ) + v // (t − t o ).…”

“…Removing the differential operators from the test function vector components F by partial integrations allows to find the corresponding expression for the dielectric tensor, and the so obtained surface terms immediately provide the expression for the kinetic flux [38].…”

“…The action-angle formalism is discussed in [33][34][35][36][37]. Comments on how to solve the relevant set of equations -with a focus on accounting for the realistic geometry -are given in [38][39][40][41][42][43][44][45][46][47][48][49][50][51] while the role of decorrelation is the key subject in [52][53][54][55].…”