Accessibility and Energy Depositon of Lower-Hybrid Waves in a Tokamak with Density Fluctuations

Abstract

A wave kinetic equation, including electromagnetic effects, to study the effects of scattering by density fluctuations on the accessibility of lower hybrid waves is derived. A Monte Carlo solution of the wave kinetic equation shows that the scattering, combined with toroidal effects and magnetic shear, can cause large upshifts in k\\ 9 thus allowing inaccessible waves to penetrate to the plasma center and heat. The implications of these results for past and future lower-hybrid-heating experiments are discussed.PACS numbers: 52.50. Gj, 52.25.Gj, 52.25.Ps, 52.55.Gb Recently, measurements have been made of density fluctuations (presumably drift waves) in tokamaks, by using laser and microwave scattering techniques. 1 * 2 Here we investigate the effect of these fluctuations on the accessibility of a lower-hybrid heating wave. The issue of accessibility is a fundamental one. For a straight plasma cylinder with a smooth density profile and field (B) aligned along the axis of the cylinder, the accessibility condition is that n\\ be greater than a critical value which we denote by n a ? where n l} = k ]l c/oj and £"=£• B/|B|. Forn"<« a (n\\>n a ) waves cannot (can) propagate to the plasma interior. The results of our work demonstrate that waves which would be inaccessible in a tokamak without density fluctuations can still propagate to the plasma center and heat if fluctuations are present. The physical mechanism for this is the following. As an inaccessible lower hybrid wave propagates in the low-density region of the plasma, the poloidal mode number m is typically quite small, m «0. Then, for a constant value of the toroidal mode number n, and the ordering \B r \ 2 <<\B e \ 2 <<\B^, k^[k T B r + {m/r)B Q +{n/R) x J B </J ]|B|" 1 = 5* B/|B| remains essentially constant as the wave propagates. However, as the wave scatters from density fluctuations, the angle of £ x =£-fc"B/|B| changes and the wave acquires finite values of m. As the wave continues to propagate, k\\ can be modified due to a combination of toroidal effects 4 (variations inm) and magnetic shear. 5 (We note that even in the absence of scattering, accessibility can also result purely from toroidal effects. 4 This requires sufficiently low aspect ratio and/or «" values not too far below n a . We reserve further discussion of this aspect of the problem to a future publication.)Density fluctuation scattering becomes especially interesting in light of recent puzzling results of the Alcator-A lower-hybrid-heating experiment, where it was found that the power coupled to the plasma was independent of the phasing of the two wave-guide grills used to launch the microwaves, 6 thus indicating that the inaccessible part of the power spectrum was able to propagate to the plasma center and heat. Furthermore, a high level of density fluctuations, peaked at the limiter radius, 1 was observed in Alcator-A. The energy density of lower hybrid waves in the plasma was observed to vary linearly 7 with the applied power (over a fairly large range), suggesting that the phenomena...

Non-linear coupling to lower-hybrid waves in a tokamak plasma

“…This equation is very similar to the one-dimensional equation derived for the travelling-wave excitation, eq. (24). It merely has a more complicated "effective" density modification.…”

“…The coupling of a smaller four-waveguide array with j phasing is still qualitatively described by eq. (24) provided no = r is not too close to 1; roughly, we require that no > 3. For nO < 3, we have had success with the coupling model described in Section 7.…”

Scattering of radio frequency waves by blob-filaments

“…10,11 Scattering of an incident slow wave is found to be significant, as expected from previous work that employed a density fluctuation formalism. 15,16 Since the SW wavelength for LH waves can be order-of-magnitude comparable to the size of turbulent blob structures, various regimes of the critical parameter =k Ќ a b are of interest. A typical value of the scattering width is the larger of the two quantities 1 / k Ќ and a b .…”

“…It is to be expected that propagating waves would be scattered by the plasma fluctuations. Indeed, both experimental evidence for such scattering 13,14 and previous theoretical treatments of the problem [15][16][17][18] have been reported. Recent contributions to the literature have studied rf scattering from turbulence in the LH and electron-cyclotron frequency ranges 19,20 as well as the high harmonic fast wave regime.…”

ICRF wave field measurements in the presence of scrape off layer turbulence on the ASDEX Upgrade tokamak (invited)

“…These are field-aligned perturbations, which are responsible for regulating heat and particle transport across the SOL 3 . RF wave dynamics in turbulent magnetized plasmas have been extensively examined both theoretically and experimentally [4][5][6][7][8] , with the RF waves in the lower hybrid frequency range receiving the most attention due to the wavelength size being comparable to the characteristic cross-field scale length of turbulent structures 4,5,7,8 . In our case, we are interested in studying the wave-turbulence interaction between ICRF waves and turbulence in the SOL, the region where the fast ICRF wave is typically evanescent 9,10 and the plasma density perturbations introduced by turbulence are large enough that the fast wave becomes propagating within the filaments 10 .…”