Response of the COMPASS Plasma to Magnetic Perturbation Experiments T

WDS'15 Proceedings of Contributed Papers — Physics, 252–257, 2015. ISBN 978-80-7378-311-2 © MATFYZPRESS

Response of the COMPASS Plasma to Magnetic Perturbation Experiments T. Markoviˇc,J. Havl´ıˇcek, and M. Imr´ıˇsek Institute of Plasma Physics CAS, Prague, Czech Republic. Faculty of Mathematics and Physics, Charles University in Prague, Prague, Czech Republic. P. Cahyna, R. P´anek, P. Bohm, M. Komm, and J. Urban Institute of Plasma Physics CAS, Prague, Czech Republic.

A. Havr´anek Institute of Plasma Physics CAS, Prague, Czech Republic. Faculty of Electrical Engineering, Czech Technical University in Prague, Prague, Czech Republic. Y.Q. Liu Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, United Kingdom.

Abstract. It has been demonstrated on several tokamak devices that application of a Resonant Magnetic Perturbation (RMP) field on plasma can suppress or mitigate the Edge-Localized Mode (ELM) instabilities. One of the leading theories describes a reaction of the plasma to the RMP as an induction of screening currents on resonant surfaces. This manifests itself by generation of radial magnetic field, which can be measured in the experiment. In this work, magnetic diagnostics installed on the COMPASS tokamak are utilized to measure the RMP response field for two different RMP coil configurations. The measured plasma response field is compared to the original RMP field, as well as to the response field calculated by linear MHD code MARS-F. Consequently, the similarities and differences between the model and the experiment are discussed. Depth of penetration of resonant components (aligned with the pitch angle of magnetic fieldlines) of the RMP into plasma are calculated by the MARS-F code, and presented as well.

Introduction In toroidal devices with diverted plasma configuration it was observed that once certain threshold of heating power is overcame, plasma energy confinement is suddenly increased by factor of 1.5–2.0 [Wagner, 1982]. This regime is referred to as the High confinement mode (H-mode), and is associated with formation of edge particle transport barrier, which features high radial gradients in plasma density and temperature. Due to their gradual growth over time, the gradients are periodically relaxed by mechanism of MHD instabilities called Edge Localized Modes (ELMs). In large devices the ELMs pose a threat to the plasma divertor, since the transient heat loads which they cause may exceed the engineering parameters of the divertor material components and capabilities of heat exhaust system [Evans, 2013]. ELM-induced damage can be mitigated by increasing the ELM repetition rate (and hence lowering the accumulated plasma energy that is carried by them) by the ELM pacing techniques, reviewed in [Evans, 2013]. These include an injection of high-velocity pellets of frozen Deuterium into plasma [Lang, 2004], rapid changes of vertical plasma position [Degeling, 2003] and application of Resonant Magnetic Perturbation (RMP) field [Evans, 2006]. The principle of the RMP field method is based on the stochas- tization of the edge plasma regions, which effectively prevents the build-up of the edge gradients over certain threshold. However, (according to the one of the leading RMP theories, also supported by recent experimental observations in [Denner, 2014]) due to the rotation and high conductivity of the plasma, there are currents generated in plasma, which effectively screen the components of RMP field that are aligned with the pitch of the magnetic fieldlines of plasma equilibrium. This complicates the interpre- tation of the experiment and prediction of the plasma behavior and hence is subject to simulations by a wide range of MHD codes [Turnbull, 2012]. In this paper, the recent results of the RMP experiments on the COMPASS tokamak are presented. Namely, the measurements of the spatial profile and magnitude of the magnetic field induced by screening

252 MARKOVIC ET AL.: RESPONSE OF THE COMPASS PLASMA TO RMP EXPERIMENTS

Figure 1. Full RMP coil conﬁguration. Blue lines represent the RMP coils, which consist of 3 diﬀerent rows in toroidal direction — large coil row on the midplane and two smaller coil rows in the top and bottom parts of the tokamak. Green arrows show direction of currents, red lines represent plasma separatrix.

currents are compared to the original perturbation field, as well as to the plasma RMP response field calculated by the linear MHD code MARS-F [Liu, 2000]. First, the characterization of RMP field generation system on the COMPASS tokamak is provided, followed by the description of the measurement method used to obtain the experimental values of the original RMP fields, as well as those of plasma response. The MARS-F code and its inputs are then introduced and the comparison of original RMP field, of measured and of modelled plasma response field is shown and discussed subsequently, inluding the estimation of depth of penetration of RMP into the plasma. Lastly, the main findings are discussed, conclusions drawn and future endeavors outlined.

RMP Experimental Arrangement on the COMPASS Tokamak RMP Field Coils On the COMPASS tokamak, the RMP windings consist of series of independent conductors, located ex-vessel and divided into 4 toroidal quadrants [Cahyna, 2009]. By their appropriate connection (see current directions illustrated in Fig. 1), it is possible to create saddle-shaped coils for generation of radial magnetic field. This perturbative field is n = 2 periodic in the toroidal angle φ in manner of ∼ exp inφ. There are two configurations of such field studied in this work, a full RMP configuration, featuring all the windings depicted in Fig. 1, and an off-axis RMP configuration featuring only top and bottom rows of these coils (i.e., without the large midplane coil row). Power sources for the RMP coils allow a single pulse per tokamak discharge. The duration of current flat-top and ramp-up/down phases can be set to last from units of milliseconds to tens of milliseconds, enabling triangular, trapezoidal or near-rectangular waveform of the pulse. As can be seen in Fig. 1, top and bottom RMP coil rows have the same polarity per quadrant (so called even parity configuration), while midplane coil is of opposite polarity to them.

RMP Field Measurements The COMPASS tokamak is equipped with a network of 104 diagnostic saddle loops that fully cover its vacuum vessel from the outside. Like RMP coils, the saddle loops are organized among 4 toroidal quadrants, with 26 loops each. Radially they are located between the separatrix and the RMP coils — see Fig. 2a. Due to their ex-vessel position, skin effect on conducting chamber cuts-off the signal of frequency above 40 kHz, however, the measurements during the flat-top phase of the RMP are unaffected (and during ramp-up/down phases as well, provided these are sufficiently slow). Besides n = 2 periodic RMP field, the saddle loops also detect an axisymmetric n = 0 poloidal magnetic field Bθ generated by the bulk plasma current and poloidal field coils. By summation of row of saddle loops on the poloidal position of θ across 4 toroidal quadrants, correspondingly to the signs in the top of Fig. 2 b): B2(θ) = BSE(θ) − BNE(θ) + BNW(θ) − BSW(θ), (1) an effective n = 2 pass filter is obtained. The B2 quantity represents the superposition of the original RMP perturbation Bvac and plasma response field Bresp. Hence the plasma response field can be obtained from: Bresp(θ) = B2(θ) − Bvac(θ). (2)

253 MARKOVIC ET AL.: RESPONSE OF THE COMPASS PLASMA TO RMP EXPERIMENTS

Figure 2. (a) Poloidal cross-section of the arrangement. Both plasma separatrix (red) and tokamak chamber (blue) are located underneath the network of diagnostic saddle loops. Each loop spans on poloidal range between two neighboring orange symbols. The same applies for RMP coils (green). (b) Scheme of 104 COMPASS saddle loops covering the vacuum vessel. θ and φ represent poloidal and toroidal angle, respectively. The signs in the top represent the combination in eq. (1).

The quantity of Bvac (θ) is calculated from relation:

4 i 1 Mi(θ) B (θ)= ( 1) − I , (3) vac − S (θ) · RMP i=1 i

where index i denotes toroidal segment, Mi(θ) represents mutual inductance between the RMP coils and diagnostic saddle loop on poloidal position θ of toroidal segment i, obtained from calibration vacuum discharge (i.e., RMP pulse without plasma discharge). Surface of the loop Si(θ) is calculated from loop geometry, taking into consideration the curvature of the tokamak chamber. IRMP is current in RMP coils, measured with Rogowski coil.

MARS-F Code Reaction of plasma of COMPASS to the applied RMP field was modelled with linear MHD code MARS-F code [Liu, 2000]. Principally, the code solves the forced stability eigenvalue problem, where the axisymetric plasma equilibrium is perturbed by the RMP field [Turnbull, 2012]. The unperturbed magnetic equilibrium of COMPASS plasma in the standardized eqdsk form was provided by the EFIT++ code [Lao, 1985], which uses magnetic measurements as its main input. The remapping of this equilibrium into the straight fieldline coordinate system (i.e., into the coordinate system used in the MARS-F code) was carried out by equilibrium solver CHEASE [Lutjens, 1996]. The radial profile of plasma electron density ne was measured by the High Resolution Thomson Scattering (HRTS) system [Bilkova, 2010], while the profiles of electron and ion temperatures (Te and Ti, respectively) were provided by the METIS code [Artaud, 2010], with Te being validated with respect to the measurement of this quantity by HRTS. Lastly, the profile of toroidal plasma flow vφ was obtained from scaling relation that corresponds to plasmas similar to those described in this paper [Scarabosio, 2006]:

Ti(ρ∗) vφ(ρ∗) 12.5 . (4) ≈ Ip

In the above relation, ρ∗ corresponds to normalized plasma radius and Ip to total plasma current. In MARS-F, the RMP coils are represented as toroidally symmetric conductors of finite width, carrying the spatially harmonic current of exp inφ. This, at first glance, differs from the real coil geometry presented in Fig. 1, however, by comparison∼ of the RMP field components that are aligned with the pitch angle of magnetic equilibrium fieldlines, calculated by MARS-F code (using this simplified coil geometry), to those calculated by Biot–Savart’s law-based code ERGOS [Nardon, 2007] featuring the full coil geometry, only the magnitude difference below 6 % was observed. Hence the MARS-F coil representation was deemed satisfactory.

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Figure 3. Poloidal distribution of measured Bvac (black line and axis), measured Bresp (blue line and red axis) and modelled Bresp (red line and axis). The x-axis represents normalized poloidal angle θ/π. (a) Full RMP configuration discharge. (b) Off-axis RMP configuration discharge.

Figure 4. Radial profile of resonant components of modelled vacuum and plasma-screened RMP field. Plotted bres quantity comes from eq. (5), with n = 2, m = nq(ρ∗). (a) Full RMP configuration. (b) Off-axis| RMP| configuration.

The output of the MARS-F code provides a wide variety of physical parameters that characterize the plasma response to the RMP ﬁeld. In this paper, only the total n = 2 plasma response ﬁeld Bresp on radial and poloidal positions of diagnostic saddle loops, and depth of RMP resonant component penetration into plasma are discussed.

Measured and Modelled Plasma Response Field The effect of the two RMP configurations is studied on two different L-mode, diverted plasma discharges, #8078 and #9655 for full and off-axis RMP configuration, respectively. Both of the discharges 19 3 were of similar parameters: plasma current I 230 kA, line-averaged electron density n 6 10 m− , p ≈ e ≈ · central electron temperature Te 750 eV, central ion temperature Ti 500 eV, safety factor at the plasma edge q 3.5 and the central≈ toroidal plasma flow velocity v ≈ 26 km/s. The current in the 95 ≈ φ ≈ RMP coils was IRMP =1.5 kA in the discharge #8078 and IRMP =1.8 kA in the discharge #9655, respectively. The measured poloidal distributions of plasma response field Bresp and vacuum RMP field Bvac (see eq. (2)), for the both RMP configurations, are plotted in Fig. 3. Both quantities are localized on the radial position of diagnostic saddle loops. Note that there is an order in magnitude difference between these two fields, as the Bvac data correspond to the black axis on the left side of the plot, while the Bresp correspond to the red axis on the right. The θ localization of the data is given by the poloidal position of the diagnostic saddle loops. Bresp modelled by the MARS-F code is represented by the red line and red y-axis and was calculated across the whole poloidal range of π<θ<π. −

255 MARKOVIC ET AL.: RESPONSE OF THE COMPASS PLASMA TO RMP EXPERIMENTS

Fig. 4 shows a resonant part of the modelled RMP ﬁeld for both the original RMP perturbation and the one screened by plasma response. Note that the plotted quantity represents the m, n spectral components of the RMP ﬁeld [Nardon, 2007]:

1 2 b · ∇ψ |bmn| = 2 (5) R0B0dψn/ds Beq · ∇φ

and hence is different from the Bresp quantity, which represents the total RMP field. |bres|, in Fig. 4 1 ∗ shows the radial dependence of the |bmn| components, where the condition q(ρ ) = m/n is fulfilled, i.e., the components that are aligned with the pitch angle of the equilibrium magnetic field Beq. Note that each data point in the plots corresponds only to the single m component of the spectrum, therefore even ∗ ∗ ∗ though |bres|(ρ ) → 0, following may apply at the same time: Bresp(ρ ) + Bvac(ρ ) 6= 0.

Discussion and Conclusion Both measurements and model in Fig. 3 show, that for the both studied RMP configurations, the plasma response field Bresp is in anti-phase with respect to the original RMP perturbation field Bvac. This implies that the plasma screening is dominant over the penetration of the RMP field into the plasma. This is further supported by Fig. 4, which shows that the components of the RMP field aligned with the pitch of magnetic equilibrium fieldlines |bres| are effectively screened even in the edge regions of the ∗ plasma of high ρ . An order of magnitude difference between Bvac and Bresp in Fig. 3 shows, that while the screening of the resonant components in the RMP spectrum is strong, this does not necessarily mean that RMP field as a whole is significantly altered. The main difference between the RMP configurations in this study was the presence/absence of the large coil row on the midplane. Comparison of Fig. 3a to 3b shows, that the main effect this coil row has on the vacuum RMP field is on the magnitude of the field around θ ≈ 0 position. Surprisingly, the poloidal profile of the Bresp remains the same, regardless on the presence of the midplane coil row. This implies, that the screening currents of the plasma have the same spatial structure in both studied RMP field configurations. From Bresp field in Fig. 3, or resonant vacuum field |bres| in Figs. 4a and 4b can be seen, that the midplane coils are responsible for the half of the RMP field magnitude. While the strongest Bresp was measured on the midplane θ ≈ 0 for the both of the RMP configurations, Fig. 3 also shows that this effect was not fully reproduced by the model. However, there is a good agreement between measured and modelled Bresp on the θ ≈ ±0.4π positions, where the top/bottom RMP coil rows are localized, moreover the discrepancy does not disappear when the midplane RMP coil row is not used. This implies that the cause is most likely not due to the approximation of the RMP configuration by MARS-F code. Nonetheless, future studies will include comparison of the vacuum RMP field by MARS-F, to the real-geometry vacuum field representation by the ERGOS code and to the experimental measurements as well. One of the possible causes for this difference in the midplane response field might be due to the uncertainty in the vφ profile. The empirical scaling relation in eq. 4 was validated on a different devide than COMPASS and thus the magnitude, as well as the radial profile shape of the vφ might be different. These issues will be addressed in the future studies by modelling the plasma with quasilinear code MARS-Q [Liu, 2013], which takes into account also the mo- mentum transport effect on the rotation profile, and later on by measuring the Ti and vφ directly, using the Charge-exchange recombination spectroscopy. Moreover, the direct measurements of the screening currents using the diagnostics and method described in [Denner, 2014] are envisioned as well.

Acknowledgments. This work was supported by the Ministry of Education, Youth and Sports CR grant numbers 8D15001 and LM2011021, and by the Grant Agency of the Czech Republic grant number GA14-35260S.

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