Appel, L.

Denner, P. J.

Gryaznevich, M. P.

Lilley, M. K.

Martin, R.

Pinches, S. D.

Sharapov, S. E.

Vann, R. G.L.

Willis, C. T.N.

White Rose Research Online

This is a repository copy of Modelling observations of mode polarisation from MAST.White Rose Research Online URL for this paper:https://eprints.whiterose.ac.uk/175779/Version: Submitted VersionProceedings Paper:Vann, R. G.L. orcid.org/0000-0002-3105-2546, Appel, L., Denner, P. J. et al. (6 more authors) (2008) Modelling observations of mode polarisation from MAST. In: 35th EPS Conference on Plasma Physics 2008, EPS 2008 - Europhysics Conference Abstracts. 35thEuropean Physical Society Conference on Plasma Physics, EPS 2008 Combined with the 10th International Workshop on Fast Ignition of Fusion Targets, 09-13 Jun 2008 35th EPS Conference on Plasma Physics 2008, EPS 2008 - Europhysics Conference Abstracts . , GRC , pp. 1506-1509. eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. 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. Modelling observations of mode polarisation from MASTR G L Vann1, L Appel2, P J Denner1, M P Gryaznevich2, M K Lilley3, R Martin2,S D Pinches2, S E Sharapov2, C T N Willis1 and the MAST team1 Department of Physics, University of York, Heslington, York YO10 5DD, UK2 Euratom/UKAEA Fusion Association, Culham Science Centre, Abingdon,Oxfordshire OX14 3DB, UK3 Department of Physics, Imperial College of Science, Technology & Medicine,Exhibition Road, London SW7 2AZ, UKSuperthermal energetic particles (EPs) play an important role in the plasmas ofmagnetically-confined nuclear fusion experiments [1]. Sources of EPs include neutralbeam injection (NBI) heating, ion cyclotron resonance heating (ICRH) and fusion-produced alpha-particles. It is critical to the success of any future fusion reactor boththat the kinetic energy of these EPs is contained within the plasma sufficiently long tosustain the fusion process and also that the presence of these particles does not destabi-lize the plasma. Alfvénic eigenmodes are of particular interest as an example of collectiveinstabilities that may be resonantly excited by EPs [2, 3]. In this paper we categorizemagnetic activity on the Mega-Amp Spherical Tokamak (MAST) [4] by direct measure-ment of the orientation, polarisation and handedness of the magnetic perturbation. Wecalculate these quantities by combining the signals from a Mirnov probe which containsthree concentric coils oriented radially, vertically and toroidally (denoted below by sub-scripts r, z and φ, respectively). These probes are mounted sufficiently far from thewall that they can measure the radial field, and are therefore an advance on previousorientation measurements made on NSTX [5]. We take the Hanning-windowed Fouriertransform of the perturbed magnetic field time signals to obtainδB =∑j∈{r,z,φ}êjδBj cos (ωt+ θj) (1)where the {δBj ≥ 0}. δB traces out an ellipse and can be writtenδB = δBmajor cos(ωt+ ψ) + δBminor sin(ωt+ ψ) (2)wherecos(2ψ) =∑j∈{r,z,φ}δB2j cos 2θj sin(2ψ) =∑j∈{r,z,φ}δB2j sin 2θj. (3)The vectors δBmajor and δBminor are the major and minor axes, respectively, of the ellipsetraced out by δB. It is important to recognise that δBmajor and δBminor are not them-selves basis vectors but are composed of the basis vectors δBjej. Two scalar measuresof the mode orientation are the angles between the equilibrium field B0 and the majorFigure 1(a) Amplitude Figure 1(b) Toroidal mode number nFigure 1(c) Orientation of major axis Θmajor Figure 1(d) Ellipticity R (polarisation)Figure 1(e) ΘH < 90◦: right-handed modes Figure 1(f) ΘH > 90◦: left-handed modesFigure 1: Experimental observation of Alfvénic activity in NBI-heated MAST shot 18690.This analysis (see text for details) suggests that the waves at ω/2π ∼ 110kHz aretoroidicity-induced Alfvén eigenmodes (TAEs) and the waves at ω/2π ∼ 700kHz arecompressional Alfvén eigenmodes (CAEs) (corresponding to shear and fast magnetoa-coustic waves, respectively).and minor axes, denoted by Θmajor and Θminor, respectively. The polarisation is given byR = |δBminor|/|δBmajor|: R = 0 implies plane polarisation; R = 1 implies circular polari-sation. Furthermore, let us define ΘH as the angle between δBmajor×δBminor and B0 (i.e.ΘH = arccos ((δBmajor × δBminor) .B0/|δBmajor| |δBminor| |B0|). Since the minor axis isrealised a quarter period after the major axis, ΘH < 90◦ implies that the perturbation isright-handed with respect to B0; ΘH > 90◦ implies that the perturbation is left-handed.Additionally we calculate the toroidal mode number n using coils at equivalent poloidallocations and distinct toroidal locations.To characterize modes on MAST [4] we use signals from the “OMAHA” Mirnov array,capable of sampling at 10MHz and situated 20cm above the midplane at a major radiusof 1.7m. Five vertically-oriented coils at relative toroidal locations {0◦, 13◦, 27◦, 45◦, 79◦}are used for calculating the toroidal mode number. The equilibrium field B0 is calculatedusing the EFIT equilibrium reconstruction code [6]. In this paper we study NBI-heatedMAST shot 18690 in the time range 0.27-0.31s. The data are displayed in Figure 1 –the subplots show quantities as functions of time and frequency. Subplot (a) shows theamplitude on a logarithmic scale: there are two families of modes: one at ∼ 110kHz andone at ∼ 700kHz. Subplot (b) shows the toroidal mode numbers: the lower frequencymodes have 0 < n < 5; the higher frequency modes have negative toroidal mode num-ber. Subplot (c) shows the angle between the major axis of the perturbation and theequilibrium field. The lower frequency modes are oriented approximately perpendicularto the equilibrium field and the higher frequency modes are oriented quasi-parallel. Theorientation of the minor axis has not been plotted; it is quasi-perpendicular for bothsets of modes. Subplot (d) shows the polarisation of the modes: the lower frequencymodes are more circularly polarised. Subplots (e) and (f) isolate left- and right-handedperturbations, respectively. The higher frequency modes are right-handed with respectto the equilibrium field, whilst the lower frequency modes are left-handed. (I.e. thehigher (lower) frequency modes rotate (anti-)clockwise about the equilibrium field.) Onthe basis of this analysis, these lower and higher frequency modes are identified as be-ing toroidicity-induced Alfvén eigenmodes (TAEs) and compressional Alfvén eigenmodes(CAEs), respectively.We notice in the amplitude plot a strong signal from 0.28s with frequency 690kHz thatfollows the statistics of the lower frequency modes rather than the other higher frequencymodes – it is quasi-perpendicular, circularly polarised, left handed and it has positivetoroidal mode number. It cannot be a toroidicity-induced (poloidal mode number mcoupling to m+ 1) mode since its frequency is too high, but it shares the characteristicsof a shear wave. We therefore identify it as a higher gap mode: either an ellipticity (mcoupling to m+ 2) or triangularity (m coupling to m+ 3) induced mode. We note thatthis wave cannot be distinguished from the compressional wave by looking only at thewave’s frequency.We have performed the analysis described above for a large number of MAST shotsand have found that the characteristics discussed above are general, rather than specificto this particular shot and time window. The resulting statistics are shown in Table 1.The first row catalogues the relatively low frequency mode while the second row cata-Mode Θ1 Θ2 ω/2π (kHz) Ellipticity R Mode number n HandednessTAE & 60◦ & 60◦ (60, 150) (0.4, 0.8) 0 < n . 8 LeftCAE . 40◦ & 60◦ & 150 (0.2, 0.5) −20 . n . −5 RightTable 1: Characteristics of candidate TAEs and CAEs from a number of observationsfrom MAST. The two types of mode can be distinguished without referring to theirfrequency. This is crucial when differentiating between a CAE and a higher-gap shearmode such as an ellipticity or triangularity induced eigenmode (EAE or NAE).logues the relatively high frequency mode.A key question is to what extent the local measurements made at the probe reflectthe wave properties at the mode location within the plasma. To tackle this question wehave begun theoretical modelling using the equilibrium codes EFIT [6] and HELENA [7],and the eigenfunction code CASTOR [8]. The Alfvén continuum may be plotted as thelocation of discontinuities in computed eigenfunctions. In principle, the eigenfunctionscan be compared directly with what is measured in experiment. However, before thiscan be done, the following challenges have to be overcome: (i) our current use of straightfield line coordinates causes problems at the separatrix; how much does it affect theeigenfunction if only plasma up to normalised ψ = 90%, say, is considered? (ii) thespectrum at the edge is strongly dependent on the pedestal profile, (iii) calculatingthe remnant of the wavefunction that tunnels through the continuum is difficult (iv)MHD breaks down as the cyclotron frequency is approached, so a more sophisticatedtreatment [9] is needed.This work was partly funded by the UK EPSRC, the Nuffield Foundation and theEuropean Communities under the Contract of Association between EURATOM andUKAEA. The views and opinions expressed herein do not necessarily reflect those of theEuropean Commission.[1] S. D. Pinches et al., Plasma Physics and Controlled Fusion 46 B187 (2004)[2] W. W. Heidbrink, Phys. Plasmas 15 055501 (2008)[3] L. Appel et al., “Compressional Alfvén eigenmodes on MAST” submitted to PlasmaPhysics Control. Fusion (2008)[4] A. Sykes et al., Nucl. Fusion 41 1423 (2001)[5] N. N. Gorelenkov, E. D. Fredrickson, W. W. Heidbrink, N. A. Crocker, S. Kubotaand W. A. Peebles, Nucl. Fusion 46 S933 (2006)[6] L. L. Lao, H. E. St John, R. D. Stambaugh, A. G. Kellman and W. Pfeiffer, Nucl.Fusion 25 1611 (1985)[7] G. T. A. Huysmans, J. P. Goedbloed and W. Kerner CP90 Conf. on Comp. Physics(Singapore: Word Scientific) p371 (1991)[8] W. Kerner, J. P. Goedbloed, G. T. A. Huysmans, S. Poedts and E. Schwarz, J.Comp. Phys. 142 271 (1998)[9] M. K. Lilley and S. E. Sharapov, Proc. 35th EPS Conference on Plasma Physics,Crete (2008)

Modelling observations of mode polarisation from MAST

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Modelling observations of mode polarisation from MAST

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