Holzhauer, E.

Köhn, A.

O'Brien, M.

Ramisch, M.

Vann, R.

Williams, T.

White Rose Research Online

This is a repository copy of Influence of density perturbations on the O-X mode conversion.White Rose Research Online URL for this paper:https://eprints.whiterose.ac.uk/175769/Version: Published VersionProceedings Paper:Köhn, A., Holzhauer, E., O'Brien, M. et al. (3 more authors) (2013) Influence of density perturbations on the O-X mode conversion. In: 40th EPS Conference on Plasma Physics, EPS 2013. 40th EPS Conference on Plasma Physics, EPS 2013, 01-05 Jul 2013 40th EPS Conference on Plasma Physics, EPS 2013 . European Physical Society (EPS) , FIN ,pp. 1142-1145. eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse This article is distributed under the terms of the Creative Commons Attribution (CC BY) licence. This licence allows you to distribute, remix, tweak, and build upon the work, even commercially, as long as you credit the authors for the original work. More information and the full terms of the licence here: https://creativecommons.org/licenses/ Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Influence of density perturbations on the O–X mode conversionA. Köhn1, E. Holzhauer1, M. O’Brien2, M. Ramisch1, R. Vann3, T. Williams31 IGVP, University of Stuttgart, Stuttgart, Germany2 EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon, U.K.3 York Plasma Institute, Department of Physics, York, U.K.Microwave heating is widely used to transfer energy to plasmas. If, however, the plasma den-sity exceeds the corresponding cutoff density of the injected microwaves, the plasma becomesinaccessible and the waves are reflected. Electron Bernstein waves (EBWs) provide a methodto overcome this limitation: they are electrostatic waves that have no high-density cutoff andare very well absorbed at the electron cyclotron resonance layer and its harmonics. Due to theirelectrostatic nature, EBWs cannot propagate in a vacuum but need to be coupled to injected elec-tromagnetic (EM) waves. A possible coupling mechanism is the O–X–B mode conversion [1]: ifan O-mode is injected at the optimum angle it is converted into an X-mode in the vicinity of theplasma frequency layer. This X-mode is then reflected and propagates outwards until it reachesthe upper-hybrid resonance layer, where it is transformed into a backwards propagating EBW.Figure 1: Dispersion relation of the O- and X-modeas obtained from simulations (crosses) and coldplasma theory (solid lines).The efficiency of the whole process stronglydepends on the efficiency of the O–X conver-sion which itself is mainly dependent on theinjection angle. The optimum injection angleis determined by the normalized density gra-dient k0Ln = k0 ·n/|∇ n| (where k0 is the vac-uum wave number of the injected microwaveand n the plasma density) at the O–X modeconversion layer, which is usually situated atthe plasma boundary. This is a region withstrong gradients leading to instabilities or per-turbations of the density profile. These per-turbations can influence the conversion pro-cess and the propagating microwave in gen-eral. We have studied theses effects using the full-wave code IPF-FDMC [2].The full-wave code IPF-FDMC is a 2D finite-difference time-domain code which simulateswave propagation in a cold magnetized plasma. It has been used previously to study the fea-sibility of heating scenarios relying on the O–X–B mode conversion process [3]. To check the40th EPS Conference on Plasma Physics P4.173Figure 2: Simulation of a microwave beam propagation in a plasma with a background density ofn = 0.4ncuto f f and without magnetic field for the case (a) without a density perturbation, (b) the Gaus-sian shaped perturbation being elongated inside the simulation plane and (c) the perturbation beingelongated perpendicular to the simulation plane; shown is |E|.validity of the code, the dispersion relations for O- and X-mode have been deduced from itand compared with the analytic solutions from cold plasma theory. As can be seen from Fig. 1,excellent agreement is found.To investigate the role of density perturbations one could in principle generate an ensembleof density profiles with randomly generated fluctuations and average over this ensemble to seehow the conversion process is, on the average, influenced. This can be easily realized for 1Dsimulations [4] but is significantly more demanding in terms of computational resources for a2D geometry due to the large ensemble necessary to get a reliable average. Furthermore, theinsight gained into the underlying process altering the conversion is limited by just looking atthe average effect.We have therefore chosen to reduce the problem to the case of the interaction between anelectromagnetic wave and a single density perturbation of Gaussian shape which is added ata specific position to the background density profile. The perturbation is characterized by itswidth wñ, its peak density ñpeak and its position on the simulation grid: ñ(r)= ñpeak exp(−r2/w2ñ).These perturbations resemble so-called blobs or filaments, perturbations of the plasma densitythat are elongated along the magnetic field lines and appear at the plasma boundary where theyare responsible for a significant fraction of particle and heat losses. Therefore, the treatment ofsuch isolated perturbations is not just a simplification but the inclusion of an important physicalproblem.In fusion plasmas, injected microwave beams have to traverse the plasma boundary whereblobs usually occur. Therefore, it is of interest to investigate the general interaction processof electromagnetic waves with blobs. Such a process is illustrated in Fig. 2(b) and Fig. 2(c),40th EPS Conference on Plasma Physics P4.173Figure 3: Contour plots of the spatial distribution of Erms in the receiving antenna plane located at thetop of the simulation grid (see Fig. 2) (a) as function of the horizontal position of the blob-like structureand (b) as function of the width of the blob-like structure.where a Gaussian beam with a beam waist of wbeam = 3 · λ0 is injected from the bottom into ahomogeneous plasma with a density of n = 0.4 · ncutoff with (b) a blob-like structure elongatedinside the simulation plane and (c) elongated perpendicular to it. The perturbation is the same inboth cases with a width of wñ = 1 ·λ0 and a peak density of ñpeak = 0.8 ·ncutoff. For comparison,the unperturbed case is shown in Fig. 2(a). It is obvious that the modification of the beam isconsiderably stronger for the blob elongated perpendicular to the simulation grid. The followingstudies will therefore emphasize this case. To systematically investigate the deterioration of theinjected beam, a receiving antenna is added to the simulation at the top of the grid. To getinformation about the spatial distribution of the wave field, the antenna is expanded over thewhole width of the computational grid.Figure 3(a) shows the signal of the aforementioned receiving antenna as function of the hor-izontal position of the blob-like structure, which has the same size and structure as before. Themicrowave is significantly distorted if the blob approaches a position within the (Gaussian)beam width of the microwave beam whose value is in the relatively small grid considered herestill very close to the beam waist. The influence of the width of the blob-like structure can bededuced from Fig. 3(b): Only weak distortion is found if the width of the Gaussian-shapedperturbation is wñ < λ0/2 or wñ > 10λ0. Strong impact is found for values in between, mostpronounced if the size of the density perturbation is on the order of the vacuum wavelength ofthe injected microwave. Having such strong influence on the wave electric field, these perturba-tions are expected to significantly alter the process of mode conversion which is sensitive to thespectral distribution of the microwave at the conversion layer.40th EPS Conference on Plasma Physics P4.173Figure 4: O–X conversion efficiency as function ofinjection angle for the case with and without densityperturbation as depicted in the plot.The efficiency of the O–X conversion de-pends on the injection angle of the microwavebeam, as mentioned in the beginning. For alinear density profile with k0Ln = 30 and aconstant background magnetic field of Y =ωce/ω0 = 0.8, the angular dependence isshown in Fig. 4. A pronounced maximum atan injection angle of θ ≈ 42◦ with an effi-ciency of η ≈ 0.8 is found. Figure 4 alsoshows the case for the same density pertur-bations as considered in the simulations dis-cussed above. The center of the perturbationis located at a background density value ofn = 0.4 · ncutoff and for the perpendicular case, it is located approximately at the center of themicrowave beam when injected at the optimal angle.A strong reduction of the conversion efficiency is found for the perpendicular case and onlya negligible influence when considering a perturbation along the background magnetic field,as expected from the simulations discussed above. For the perpendicular case, the maximumconversion efficiency is not only reduced by a factor of 2, but the injection angle for optimumconversion is also shifted by approximately 6◦ here.To summarize, the influence of an isolated density perturbation on microwave propagationand on the O–X conversion has been simulated with a full-wave code. The influence of the sizeand position of the perturbation and its impact on the wave electric field has been systematicallyinvestigated. Strong modification was shown to occur depending on the size and position ofthe perturbation. The O–X conversion is sensitive to the orientation of the phase fronts of themicrowave at the conversion layer and, hence, strong reduction was demonstrated to occur forcase considered here. As a next step, a similar scan as the one performed for the impact on thewave electric field will be performed for the impact on the conversion efficiency.References[1] H. Laqua, Plasma Phys. Control. Fusion 49, R1 (2007) [2] A. Köhn, Ph.D thesis, Universität Stuttgart, Stuttgart, 2010 [3] A. Köhn et al., Plasma Phys. Control. Fusion 50, 085018 (2008) [4] A. Köhn et al., 38th EPS Conf. on Plasma Phys. (ECA 35G, P2.020, Strasbourg, 2011) 40th EPS Conference on Plasma Physics P4.173

Influence of density perturbations on the O-X mode conversion

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Influence of density perturbations on the O-X mode conversion

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