A hybrid full-wave Markov chain approach to calculating radio-frequency wave scattering from scrape-off layer filaments

Abstract

The interaction of radio-frequency (RF) waves with edge turbulence modifies the incident wave spectrum, and can significantly affect RF heating and current drive in tokamaks. Previous lower hybrid (LH) scattering models have either used the weak-turbulence approximation, or treated more realistic, filamentary turbulence in the ray tracing limit. In this work, a new model is introduced which retains full-wave effects of RF scattering in filamentary turbulence. First, a Mie-scattering technique models the interaction of an incident wave with a single Gaussian filament. Next, an effective differential scattering width is derived for a statistical ensemble of filaments. Lastly, a Markov chain solves for the transmitted wave spectrum in slab geometry. This model is applied to LH launching for current drive. The resulting wave spectrum is asymmetrically broadened in angular wavenumber space. This asymmetry is not accounted for in previous LH scattering models. The modified wave spectrum is coupled to a ray tracing/Fokker–Planck solver (GENRAY/CQL3D) to study its impact on current drive. The resulting current profile is greatly altered, and there is significant increase in the on-axis current and decrease in the off-axis peaks. This is attributed to a portion of the modified wave spectrum that is strongly dampened on-axis during the first pass.

Verifying raytracing/Fokker–Planck lower-hybrid current drive predictions with self-consistent full-wave/Fokker–Planck simulations

“…Approximately 800 kW of LHCD power was coupled to a plasma with T e0 = 2.3 keV, ne = 5 × 10 19 m −3 producing a near non-inductive plasma operating at I p = 540 kA with a loop voltage of −0.2 V. This discharge has been modelled extensively in the past using both raytracing (Schmidt 2011) and full-wave simulations (Wright et al 2009(Wright et al , 2010(Wright et al , 2014Meneghini 2012). Furthermore, this shot is very similar to the shot #1101104011 that has also been subject to much analysis in the literature (Mumgaard 2015;Biswas et al 2020;Baek et al 2021;Biswas et al 2021).…”

“…A number of mechanisms that upshift the parallel refractive index N = k c/ω = c/v ph, , where k is the parallel component of the wave vector k and c is the speed of light in vacuum, closing the spectral gap have been proposed. These mechanisms include: toroidally induced increases in the parallel wavenumber and wave scattering from turbulence (Bonoli & Ott 1981, 1982Decker et al 2014;Peysson et al 2016;Biswas et al 2020Biswas et al , 2021, parametric wave interactions (Cesario et al 2004;Decker et al 2014;Peysson et al 2016) and diffractional broadening of the wave spectrum (Pereverzev 1992;Wright et al 2009Wright et al , 2010Shiraiwa et al 2011a;Wright et al 2014). Which N upshift mechanism is dominant in a given situation can profoundly affect wave damping and current drive efficiency.…”

An Assessment Of Full Wave Effects On Maxwellian Lower Hybrid Wave Damping

“…Quantitative agreement in this case was limited here by magnetic equilibrium resolution and computational resources, but these results indicated that even in weakly damped scenarios gap closure by full-wave effects such as diffraction and interference is unlikely. Spectral gap closure resultant from toroidal upshifts [21,22], interactions of LHWs with turbulence [17,24,25,62] and parametric broadening of the LHW spectrum [31] will almost certainly be more important. However, it is important to note that this revised TORLH analysis has so far been applied only to Maxwellian plasmas.…”

“…The velocity downshifted portion of the wave spectrum fills the spectral gap in the Landau plateau providing high energy electrons for the high velocity component of the spectrum to damp on. Various mechanisms have been proposed as sources of the downshift that provides spectral gap closure including: geometric downshift of the wave velocity [21,22,23], wave interactions with turbulence [21,22,17,24,25], diffractional broadening of the wave spectrum [26,27,28,29,30], and spectral broadening as a result of parametric wave interactions [31,17]. As each of these effects modify the wave spectrum differently, if the dominant effect or combination of effects is not properly included in a simulation then its results may differ substantially from the experimental measurements.…”

Radio-frequency sheath excitation at the extremities of scrape-off layer plasma filaments, mediated by resonant high harmonic fast wave scattering

“…Radio-frequency (RF) wave scattering in inhomogeneous magnetized plasmas has recently attracted much attention, in particular as a mechanism of RF power redirection at the periphery of magnetic fusion devices. Myra & D'Ippolito (2010), Ram & Hizanidis (2016), Lau et al (2020), Tierens et al (2020aTierens et al ( ,b, 2022a, Biswas et al (2021) and Zhang et al (2021) provide an overview of recent modelling work on this topic in the lower hybrid and ion cyclotron ranges of frequencies (ICRF). Scattering of fast magnetosonic waves, without change of polarization, is generally modest in the ICRF range, because the typical size of inhomogeneities transverse to the magnetic field does not match the typical transverse wavelength of the fast wave (Myra & D'Ippolito 2010).…”