Holzhauer, E.

Köhn, A.

Leddy, J.

Thomas, M.

Vann, R.

English

MPG.PuRe

Perturbations of microwaves due to plasma density fluctuationsA. Köhn1,2, M. Thomas3, R.G.L. Vann3, E. Holzhauer1, J. Leddy31 IGVP, University of Stuttgart, Germany2 Max Planck Institute for Plasma Physics, Garching, Germany3 York Plasma Institute, Department of Physics, York, U.K.Electromagnetic waves in the microwave regime play an important role in present plasmaexperiments as they are used for heating [1] and diagnostics purposes [2]. In both cases, themicrowaves have to traverse the plasma boundary. In fusion related plasma, substantial densityfluctuation levels are known to occur there [3] which can significantly distort the traversingmicrowave beam and thus lead to reduced coupling efficiencies to the plasma or to ambigu-ous diagnostics results. This work aims to investigate the average perturbation of a fluctuatingplasma on a microwave beam by means of full-wave simulations. The advantage of a full-wavetreatment is that no a-priori assumptions about the strength or size of the plasma density per-turbations need to be made. The 2D full-wave code IPF-FDMC [4] is used to study the effectof a fluctuating plasma density on a propagating microwave beam. It is a finite-difference time-domain code based on a cold plasma description.Ensemble averaging over a number of density profiles is required in order to be statisticallyrelevant. The density fluctuations appear to be frozen in the frame of the microwave since theyvary on the kHz scale [3], whereas the microwave oscillates on the GHz scale. The fluctuationsitself are created by a Hasegawa-Wakatani drift-wave turbulence model within the BOUT++framework [5]. A slice of fluctuating plasma density is then superimposed onto a homogeneousbackground density n0 with a value of n0 = 0.5ne,cut-off, where ne,cut-off is the correspondingcut-off density of the injected microwave.The numerical grid has a size of 10λ0 in the x-direction, where λ0 is the vacuum wavelengthof the injected microwave, and 5λ0 into the y-direction. It is surrounded by absorbing (non-radiating) boundaries. The fluctuating density slice extents along the whole x-direction but onlyfrom y = 1 . . .4λ0. The microwave beam is injected along y = 0 and along y = 5λ0, a receivingantenna is placed. The injected beam has a Gaussian shape with the beam waist located inthe antenna plane having a radius of w0 = 2λ0. The polarization is such that an O-mode isinjected and the background magnetic field points into the direction perpendicular to the 2Dnumerical grid with a constant strength of Y =ωce/ω0 = 0.5, where ωce is the electron cyclotronfrequency.Figure 1 shows two snapshots of the absolute value of the wave electric field taken after the42nd EPS Conference on Plasma Physics P1.1890 2 4 6 8 10x / λ0012345y /λ0|E|012345y /λ0Figure 1: Snapshots of the absolute value of the wave electric field after the steady state solu-tion is achieved. Top: for the case of a homogeneous plasma with n0 = 0.5ne,cut-off everywhere;bottom: for the case of a turbulence slice with an average structure size of cL ≈ 0.5λ0 (whitesolid and dashed lines correspond to positive and negative density perturbations, respectively).steady state solution is achieved. The top snapshot shows the case for a homogeneous plasmawith a density of n0 = 0.5ne,cut-off and the bottom snapshot for a fluctuating plasma with anaverage size of the density structures of cL ≈ 0.5λ0 and an average fluctuation level of σ ≈4%. The average size cL is taken as the distance where the spatial auto-correlation drops to avalue of 0.5 and the fluctuation level is taken as the standard deviation of the mean-free densityfluctuations. Comparing the two snapshots, it can be seen how the microwave beam is perturbedby the plasma density fluctuations. In this case, the position of the maximum signal is slightlyshifted to the left and a sidelobe at the very right hand side occurs.To quantitatively investigate the effect of the fluctuations on the microwave beam, the rms-value of the wave electric field Ẽ is continuously recorded at the detector antenna as a functionof the coordinate x: Ẽrms = ∑t(|Ẽ|/√T), where t is the time coordinate and T the wave period.42nd EPS Conference on Plasma Physics P1.1890 2 4 6 8 10x / λ0020040060080010001200Erms/ a.u.w/o turb.w/ turb.Figure 2: Detector antenna signal for the homogeneous case(red) and for a few turbulence slices with an average structuresize of cL ≈ 0.5λ0.This signal is then comparedwith the signal of the homoge-neous case, Erms. Figure 2 showsthis comparison for the case ofthe average structure size whichyielded the largest perturbation.The effect of the density fluctu-ations is obvious. Note, that forthis plot only a few of the realiza-tions from the ensemble of den-sity profiles are shown. A scatter-ing parameter α is defined as thesum of the squared deviations ofthe rms-signals, allowing to quantify the result of one full-wave run with a single value:α =∑x(Ẽrms −Erms)2∑x E2rms. (1)1000 2000 3000N-0.2-0.10.00.10.2∆/λ0Figure 3: Average value of the spatial difference of the maximum signalat the detector antenna (compared to the position of the maximum signalfor the homogeneous case) as a function of the number of ensembles foran average structure size of cL ≈ 0.5λ0 (the red curve corresponds tothe average and the dashed orange curves to the error).Looking at Fig. 2, thenecessity of sufficient en-semble averaging is appar-ent. To check the qualityof the averaging process,the average position of themaximum signal in the de-tector antenna plane, x̃max,is compared with the posi-tion for the homogeneouscase, xmax. The differenceof these two values shouldvanish, ∆ = x̃max−xmax!= 0.Only then, the results willbe statistically relevant. The average value of ∆ is plotted in Fig. 3 as a function of the numberof ensembles N. It can bee seen that N is sufficiently large, since an asymptotic value of ∆ = 0is reached (within the errorbars).42nd EPS Conference on Plasma Physics P1.1890.0 0.2 0.4 0.6 0.8 1.0 1.2structure size / λ00.0000.0020.0040.0060.0080.0100.012scatter parameterαFigure 4: Scattering parameter α (defined by Eq. (1)) as a function ofthe average size of the density structures for an average fluctuation levelof σ ≈ 4%.The average size of thedensity structure is var-ied from cL ≈ 0.2λ0 . . .1λ0.With increasing structuresize cL, the number of en-sembles N is also increasedas a smaller number ofdensity structures fit intoone turbulence slice. Fig-ure 4 shows the scatteringas a function of the aver-age structure size. A max-imum scattering at a size ofcL ≈ 0.5λ0 can be clearlyseen. For decreasing and increasing sizes, the average scattering is decreasing.Note that in a previous study, the influence of a single blob-like structure on a traversingmicrowave beam was studied [6], and the deterioration was found to peak at a larger structuresize. This is, however, not in contradiction to the result presented here, as we are interestedin the average perturbation whereas in the previous study we were interested in the maximumperturbation.Further investigations are performed at the moment in order to elaborate the role of thestrength of the fluctuations and of the size of the turbulence region.References[1] V. Erckmann and U. Gasparino Plasma Phys. Control. Fusion 36 1869 (1994)[2] H.-J. Hartfuss and T. Geist Fusion Plasma Diagnostics with mm-Waves (Wiley-VCH, Weinheim, 2014)[3] S. J. Zweben et al., Plasma Phys. Control. Fusion 49 S1 (2007)[4] A. Köhn et al., Plasma Phys. Control. Fusion 50 085018 (2008)[5] B Dudson et al., Comp. Phys. Comm. 180 1467 (2009)[6] T. Williams et al., Plasma Phys. Control. Fusion 56 075010 (2014)Acknowledgements Part of the simulations were performed on the HELIOS supercomputersystem at Computational Simulation Centre of International Fusion Energy Research Centre(IFERC-CSC), Aomori, Japan, under the Broader Approach collaboration between Euratomand Japan, implemented by Fusion for Energy and JAEA.42nd EPS Conference on Plasma Physics P1.189

Perturbations of microwaves due to plasma density fluctuations

http://hdl.handle.net/21.11116/0000-0008-82A3-C

Perturbations of microwaves due to plasma density fluctuations

Abstract

Similar works

Full text

Available Versions

MPG.PuRe