Penetration of the rotating magnetic field into the plasma1Correspondence. Prof Karl Finken, Institut for Plasma Physics, Forschungszentrum Juelich, Association EURATOM-KFA, D-52415 Juelich, Germany.1

Low frequency heating and flow driven by the dynamic ergodic divertor in tokamaks

“…Note that very similar distributions of LF fields and dissipation are found in calculations for TCABR plasmas [9]. Turning to the [6,2] scenario, 311 × 79 radial×poloidal mesh points in the plasma (45 radial points in vacuum) are used to calculate the radial electric field distribution excited by 6/2, 5/2, and 4/2 antenna modes shown in figure 7. Taking J (M, N) = 1 A m −1 and f = 10 kHz the following respective values of normalized LF field dissipation result: W norm = 1.04 × 10 −3 , 1.99 × 10 −3 , 0.726 × 10 −3 .…”

“…In standard right-handed coordinates, (r, θ, φ), the DED coil helicity requires the use of −θ c in the place of θ c , or equivalently −'n 0 ' in the place of 'n 0 ' in the formulae derived therein. Note that the scalar coil current density J in equations (5) and (6) refers to the full component of current J flowing along the coil, with components J θ,φ (r, θ, φ, t) and J θ,φ (M, N) following from the θ, φ projections which introduce the sine or cosine of the angle between the coil and cylinder-axis (φ) directions.…”

“…In TEXTOR, the DED coils have been designed to excite poloidal modes having integral numbers of poloidal wavelengths, the final design admitting situations involving as lowest order pairs: three poloidal wavelengths for an N = 1 excitation, six for N = 2, and 12 for N = 4. In cylindrical geometry, this dictates coil design and phasing such as to excite antenna spectra centred on the specific M 0 /N pairs 3/1, 6/2, 12/4 [2], this entailing θ c = Nπ/M 0 = π/3 as shown in equation (6). The above choice of θ c = 35.6f or the coil array implies a different ratio of N to M 0 , this choice having been made in anticipation of an effect of the poloidal non-uniformity of dφ/dθ seen in toroidal geometry (note that [2] uses M 0 /N = 5).…”

“…In figures 3 and 4 we show the dependence of antenna impedance on frequency, and the distribution of the E r -component of the LF field and of the absorbed power density as a function of radius for TEXTOR parameters. Three coil settings [M 0 , N] = [3, 1], [6,2], [12,4] are analysed. If for a given coil setting we normalize the current spectrum in equation (6) that the strength of LF field absorption from the central spectral amplitude, M 0 /N = 3, diminishes strongly with growing mode number (resonance near fixed position, r s = 42 cm for TEXTOR).…”

“…Related earlier experimental and theoretical studies on penetration of rotating low frequency (LF) fields into tokamak plasmas [3,4] continues in recent experiments on the HYBTOK-II tokamak [5]. More exclusively theoretically oriented study is an active endeavour [6][7][8][9][10][11][12] which includes modelling of DED coils for the Tokamak Chauffage Alfvén Brésilien (TCABR) [9]. The present work models the DED coils recently installed on TEXTOR, treating them as an antenna producing energy deposition and associated plasma flow in the upper DED frequency band 5-10 kHz, these quantities being presumably linked to the positive DED features cited above.…”