Faustin, Jonathan Marc Philippe

Graves, Jonathan

Johnson, T.

Lanthaler, Samuel

Lerche, E.

Patten, Hamish William

Van Eester, D.

Infoscience - École polytechnique fédérale de Lausanne

Modelling the Fast-ion RF-Pinch Effect with a Toroidally Localised ICRFAntennaH. Patten1, J.Graves1, J.Faustin1, S.Lanthaler1, D. Van Eester2, E.Lerche2,T.Johnson3 and JET Contributors4∗1 SPC-EPFL, Lausanne, Switzerland2 Association Euratom-Belgian State, LPP-ERM-KMS, B-1000 Brussels, Belgium3 Alfvén Laboratory, Association EUROATOM/VR, Sweden4 EUROfusion Consortium, JET, Culham Science Centre, Abingdon, OX14 3DB, UKE-mail: hamish.patten@epfl.chIntroductionThe Finite Orbit Width (FOW) of a fast ion can greatly influence the interaction between theion and Ion Cyclotron Range of Frequency (ICRF) waves, and what is not clear is what impactthe toroidal localisation of the antenna might have on the behaviour of the ions at high energies,especially with it’s anisotropy. The work carried out here studies the differences in the RF-Pincheffect when simulating toroidally localised ICRF waves.The results presented in this paper were carried out using JET plasma profiles determined fromshot number 89199 from the M15-27 ‘ICRH scenarios for DT’ experiments. The data imple-mented in the simulations here was taken using EFIT data, which gave a q0 and q95 of 1.5and 5.5 resp., Ti0 and Te0 of 4.4keV and 6.1keV resp. and ne0 of 4.9e19m−2. Within this shot6.6MW of ICRF heating was applied using the minority heating scheme on the 3He ions whichconsisted of 3% of the plasma, of which the time average for EFIT was 51.25± 0.25s. Usingthis data, the SCENIC [1] package was used to study interactions of ICRF heating with fast3He particles. Consisting of three main codes; ANIMEC, the anisotropic flavour of VMEC, toproduce the 2D ideal-MHD equilibrium, LEMan, the wave-propagation code with warm plasmamodel and 0th order FLR effects, and finally VENUS-LEVIS, the guiding-centre particle fol-lowing code. Within this work the phasing remains at +90, with 6.6MW of power applied to theminority 3He species of 3% and each simulation run for a total of 4.5 times the slowing downtime on the electrons for convergence.Antenna ModelIn order to toroidally localise the wave in LEMan, the total electric field will be the summa-tion of the different toroidal wave numbers, the contribution of each wave weighted accordingToroidal Mode Number nϕ-60 -40 -20 0 20 40 60|σ n|200.0020.0040.0060.0080.010.0120.014JET Antenna Toroidal Mode Spectrum+90Dipole-90ϕ Toroidal Angle-pi 0 piNormalised |E2 |00.20.40.60.81+90 Phasing - Toroidal Localisation1 Mode : n ∈ [12]3 Modes : n ∈ [11,13]9 Modes : n ∈ [8,16]106 Modes : n ∈ [-53,53]Figure 1: The toroidal localisation of the JET antenna: a) the toroidal fourier spectrum coefficients ofthe jantenna decomposition, b) the influence of the number of toroidal modes used on the electric fieldproduced by LEManto the antenna current spectrum given by:Jnϕ =∑kj(nϕ )ksin(nϕR Wk)nϕR Wkexp(− nϕdR)with jnϕk = j0kexp(inϕRzk + iϕk)(1)Where Wk is the half width of the antenna strap, zk is the strap location and ϕk is the phasingof the antenna. Note that the exponential term includes the effect of the plasma damping onthe wave for the ROG distance d. The toroidal mode spectrum obtained from this equation isplotted on the left of figure 1. Therefore LEMan calculates the electric field for each toroidalmode number and the Monte-Carlo ICRF operator implemented in VENUS-LEVIS ensures acoherent reconstruction of the wave according to equation 1. Furthermore, the antenna that isimplemented in LEMan is constructed independantly in s,θ and ϕ:Jant = σs(s)σθ (θ)∑nσneinϕ ~eant (2)Where this box function representation is constructed in the same way for s and θ :σα(α) = fB(α−α1α2−α1)(1−χ2α)2 (3)For α = s,θ and fB the box function. In order to calculate the effects of the antenna localisation,+90 phasing was used to provide insight into the differences in the inward pinch of using mul-tiple toroidal modes. Thus three different simulations were made: using one mode of nϕ ∈ [12],3 modes of nϕ ∈ [11,13] and 9 modes of nϕ ∈ [8,16], chosen according to the magnitude of themode contribution. The results shown in figure 2 indicate that by localising the wave toroidally,the total fast ion pressure reduces. In this case the losses associated with toroidally localising theantenna increase, such that for 1, 3 and 9 modes the lost particles from the fast ion populationare 43.3%, 54.7% and 58.1%. Additionally, the collisional power on the background electronsρ~r/a0 0.1 0.2 0.3 0.4 0.5 0.6Fast-Ion Pressure [Pa]×10 40.511.522.531 Mode nϕ ∈ [12]3 Modes nϕ ∈ [11, 13]9 Modes nϕ ∈ [8, 16]PotatoLFS CherryHFS Cherry% of Fast-ion Population02468101 Mode nϕ ∈ [12]3 Modes nϕ ∈ [11, 13]9 Modes nϕ ∈ [8, 16]Figure 2: Influence of toroidally localising the antenna on fast ion population: left) the fast ion pressure,right) percentage of exotic orbitsand deutrium ions increases as 3.34MW, 3.54MW 3.62MW for 1, 3 and 9 modes respectively.Further evidence that using one toroidal mode induces a larger inward RF-pinch effect is tostudy the number of different types of exotic particle orbit behaviours in the plasma, as with ahigher inward pinch the trapped resonant particles tend to be driven more towards the passinglimit. Thus three different exotic particle orbit types are defined here: potato orbits are trappedparticles that circle the magnetic axis, and Low Field Side (LFS) and High Field Side (HFS)cherry orbits, which are co and counter-current passing particles (resp.) which do not circle themagnetic axis. In order to classify the orbits, a simple consideration of the background magneticequilibrium and the constants of motion of a particle suffices to allow a categorisation of the ex-otic orbits[2], noting that there has been more extensive research into more complicated orbitsdescribed by the work of L-G Eriksson and F. Porcelli, also based on the constants of motion[3]. A simple method to achieve this is to rearrange the equation for the toroidal momentum ofthe particle in terms of the dimensionless variable Hp = B0/Bparticle, the toroidal magnetic fluxψ and the constants of motion of the particle. This can provide insight into the drift a particlewill undergo from it’s average flux surface during it’s motion around the tokamak, carried outextensively in [4]. With this information a simple categorisation of the particle orbits can beevaluated.The bar graph shown on the right of figure 2 indicates that more exotic particles are found whenthe antenna is not toroidally localised, implying that when the wave is toroidally localised theinward pinch is not as effective on the particles. The reason for the larger inward pinch for using1 mode only is most likely due to a broadening of the doppler shift of the wave, where reso-nance occurs at ω =Ω+v||k||, and as k|| = nϕ/R, by including a broader range of toroidal modenumbers the inward pinch of the particle might not be as peaked on the resonance layer. Despitethe small percentage concentration of these types of orbits, they can have a large influence onρ ≃ r/a0 0.2 0.4 0.6 0.8 1Current Density [Am-2 ]×10 4012345671 Mode nϕ ∈ [12]3 Modes nϕ ∈ [11, 13]9 Modes nϕ ∈ [8, 16]PotatoLFS CherryHFS Cherry% of Fast-ion current0510152025301 Mode nϕ ∈ [12]3 Modes nϕ ∈ [11, 13]9 Modes nϕ ∈ [8, 16]Figure 3: Influence of changing Bres on the RF-Pinch: pressure of minority ion speciesthe fast-ion current, which is shown in figure 3. The LFS cherry orbits provide a large currentcontribution as they are produce by trapped particles that have their bounce tips aligned with theresonance layer such that the bounce tips collapse to form a LFS cherry orbit; high energy pass-ing particles still aligned with the resonance layer; thus almost continually accellerated. For thepotato orbits, despite usually being exhibited by high energy particles, due to the fact that theyare still nonetheless trapped, the potato orbits do not tend to induce large currents. Finally, theHFS cherry orbits also tend not to contribute as much of a current as those on the LFS becauseif their anisotropy further increases then there is a limit to which they will become re-trapped,and therefore there will be a net co-directional current from the LFS orbit ions.ConclusionThe effects of toroidally localising the ICRF antenna on the RF-pinch effect in tokamak plas-mas was investigated, to find that most likely due to the larger doppler-shifted broadening ofthe resonance layer, the results suggest that using multiple toroidal modes for a +90 phasingICRF antenna has a reduced inward pinch, which reduces the number of exotic particle orbitsobserved after convergence of the mean energy of the fast ion distribution.AcknowledgementThis work has been carried out within the framework of the EUROfusion Consortium and has re-ceived funding from the Euratom research and training programme 2014-2018 under grant agreementNo 633053. The views and opinions expressed herein do not necessarily reflect those of the EuropeanCommission.References[1] M. Jucker, et al., Comput. Phys. Commun. 182, 912–925 (2011)[2] J. Hedin, et al., Nuc. Fus. 42, 527–540 (2002)[3] L. G. Eriksson, F. Porcelli, Plasma Phys. Con. Fus. 43, R145-R182 (2011)[4] C. T. Hsu, D. J. Sigmar, Phys. Fluids B 4, 6 (1992)

Modelling the Fast-ion RF-Pinch Effect with a Toroidally Localised ICRF Antenna

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Modelling the Fast-ion RF-Pinch Effect with a Toroidally Localised ICRF Antenna

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