Asymmetric toroidal eddy currents (ATEC) to explain sideways forces at JET

PAPER Asymmetric toroidal eddy currents (ATEC) to explain sideways forces at JET To cite this article: R. Roccella et al 2016 Nucl. Fusion 56 106010 View the article online for updates and enhancements. Related content Plasma current asymmetries during disruptions in JET S.N. Gerasimov, T.C. Hender, J. Morris et al. - Measurement of scrape-off-layer current dynamics during MHD activity and disruptions in HBT-EP J.P. Levesque, J.W. Brooks, M.C. Abler et al. - JET and COMPASS asymmetrical disruptions S.N. Gerasimov, P. Abreu, M. Baruzzo et al. - Recent citations Dependence of disruption forces on the plasma position inside the vacuum vessel in tokamaks V D Pustovitov - Extension of Shafranov’s Equilibrium Theory to the Description of Current Quenches Affected by Resistive Wall Dissipation in Tokamaks V. D. Pustovitov - Disruptive plasma simulations in EAST including 3D effects S.L. Chen et al - This content was downloaded from IP address 87.218.223.151 on 11/08/2020 at 16:38 1 © 2016 EURATOM Printed in the UK 1. Introduction Plasma asymmetries during VDEs are measured in several tokamaks (JET [1], ASDEX upgrade [2], DIII-D [3]) but evidence of associated strong asymmetric loads are observed only at JET. These observations provide, in ITER, the basis for definition of asymmetric VDE loads. They are assessed, using the source and sink model, through extrapolation of the amplitude of the plasma current asymmetry and duration from JET. The source and sink model gives a quantitative estimate of the sideways force consistent with the measured JET vessel displacement. Applied to ITER vacuum vessel (VV) analyses the same model predicts about 45 MN of sideways forces in locked AVDEs [4]. In case of asymmetry rotating at frequencies close to the ITER VV natural frequency the VDE duration extrapolated from JET data, would cause important amplification of the vessel deformations. In addition to these loads, Nuclear Fusion Asymmetric toroidal eddy currents (ATEC) to explain sideways forces at JET R.Roccella1, M.Roccella2, V.Riccardo3, S.Chiocchio1 and JET Contributorsa EUROfusion Consortium, JET, Culham Science Centre, Abingdon, OX14 3DB, UK 1 ITER Organization, Route de Vinon-sur-Verdon, CS 90 046, 13067 St Paul Lez Durance Cedex, France 2 LTCalcoli Srl, Piazza Prinetti 26/B, 23807, Merate (LC), Italy 3 CCFE, Culham Science Centre, OX14 3DB, Abingdon, UK E-mail: [email protected] Received 13 October 2015, revised 4 March 2016 Accepted for publication 30 March 2016 Published 9 August 2016 Abstract During some JET vertical displacement events (VDEs) plasma current and position are found to be toroidally asymmetric. When asymmetries lock, the vessel has been observed to move horizontally, consequently strong horizontal forces are expected following plasma asymmetries, whether locked or rotating. The cause of horizontal forces is, as already identified in previous works, the asymmetric circulation of current in the structures. The physics mechanism responsible for these asymmetric currents is instead an open issue and it is the object of the present analysis. In particular it will be shown that the asymmetry is not due to a direct exchange of current between plasma and structure (as in the case of halo currents) but to asymmetric conductive paths which arise, in the structures, when the plasma column asymmetrically wets the wall. Simulations of this phenomenon using finite element (FE) models have been conducted to reproduce the JET observation during locked and rotating asymmetric VDEs. Estimated sideways force, asymmetry ( I p asym ) and normalized asymmetry ( A p asym ) of plasma current, vertical position at different toroidal locations during the disruption and halo current asymmetry have been compared with measurements done at JET during upward AVDEs. The substantial match between experiments and simulations confirms the soundness of the assumptions. Furthermore, the same physical model applied to downward VDEs shows that divertor support and coils, together with the geometry of the limiting surfaces, considerably lessen asymmetric loads as experienced at JET after installing those components. Keywords: JET, ITER, asymmetric vertical displacement events, sideways forces, halo currents, ATEC (Some figuresmay appear in colour only in the online journal) R. Roccella etal Printed in the UK 106010 NUFUAU © 2016 EURATOM 2016 56 Nucl. Fusion NF 0029-5515 10.1088/0029-5515/56/10/106010 Paper 10 Nuclear Fusion IOP International Atomic Energy Agency a See the appendix of [9]. 0029-5515/16/106010+11$33.00 doi:10.1088/0029-5515/56/10/106010 Nucl. Fusion 56 (2016) 106010 (11pp) R. Roccella etal 2 the halo current asymmetry measured during AVDEs would produce relevant tilting moments on the ITER structures. Understanding the causes of sideways forces and of asymmetric halo currents measured in JET during AVDEs is, then, essential to confirm the basis for the loads estimate on the ITER VV and it is the aim of this analysis. In the following sections, we present a model for locked and rotating Asymmetric VDEs (AVDEs) which: (a) provides a likely explanation of the phenomenon of the AVDEs showing the mechanism triggering the asymmetric flow of current in the structures; (b) is consistent with the JET magnetic measurements during upward AVDEs; (c) is consistent with the sideways forces predicted by the source and sink model and inferred from JET vessel displacement during AVDEs; (d) demonstrates the fundamental identity between measured plasma and halo current asymmetries; (e) explains why, at JET, the divertor structure prevents the raise of asymmetric loads during downward VDEs. 2. AVDE sideways force mechanism The JET disruption shown in figure1 (38070, [1]) caused large sideways displacement and is a clear case of locked AVDE. The minimum and maximum asymmetry of toroidal plasma current (Ip) and vertical position (zp) are measured at octant 3 and 7 respectively and do not move significantly during the disruption. During the current quench the asymmetric instability arises and pushes one side (octant 7) of the plasma column against the in-vessel upper structures that at the date of this event were Inconel dump plates (DP) covered with carbon fibre composite (CFC) tiles. At the opposite side of the torus, octant 3, no significant vertical movement is measured. The asymmetry starts with the plasma column already displaced 1.25 m upward and the average difference in vertical position during the current quench (CQ) phase is about 0.2 m. During the asymmetric phase the first wall (FW) surface at the top of the machine deeply intersects the plasma column around octant 7. Under certain conditions of plasma temperature (and thus resistivity) it is possible that neighbouring dump plates are short-circuited in toroidal direction through the plasma. In this configuration, part of the toroidal current induced in the vacuum vessel (VV), which has the same sign as the plasma current, will flow in the dump plates of the sectors wetted by the plasma. On the opposite side of the machine (around octant 3), where the plasma and structure are not in contact the short circuit cannot be established. A schematic view of the asymmetric path of the induced current is shown in figure 2(a). The eddy current (green) is induced only in the vacuum vessel where the plasma vertical position is measured low (octant 3) but where the plasma wets the structure, part of it is transferred to the dump plates. The poloidal path of the eddy current from the VV to the DPs in octants 3 to 7 (and its anti-symmetric counterpart from the DPs to the VV on the opposite side of the machine) interacts with the toroidal field resulting in a net sideways force. Figure2(lower part) shows a simplified view of the kink mode configuration of pulse 38070. In the octant 3 the entire induced toroidal current flows in the vessel and only the plasma current is measured by the pick-up coils; in the octant 7 the part of induced current that flows toroidally in the dump plates falls inside the contour of in-vessel poloidal field pick-up coils (in red) and contributes to the measure of the plasma current. This scheme implies that the plasma current is the same at all toroidal locations. The measured asymmetry is not due to plasma current which, in some sectors, flows toroidally in the vessel as it would be in case of toroidal halo current. The cause of the asymmetry is, instead, current induced in the vessel structures which flows internally to the pick-up coils loop where the plasma column wets the top dump plates. 3. Analysis models Two finite element models have been prepared in ANSYS® to assess locked (180° model) and rotating (360° model) AVDEs. The geometry is based on JET CAD drawings of the vacuum vessel and includes sector double shell, port openings and bellows. All modelled structures except for the CFC tiles and, of course, the halo current (HC) region, are made of Inconel. The assigned resistivity is: 1.3 * 10−6 Ω·m for vessel bosses and dump plates and 5 * 10−6 Ω·m for CFC tiles. The bellows are simulated with straight plates of 3 mm thickness with an orthotropic equivalent resistivity calculated of 1.4 * 10−6 Ω·m radially and poloidally resistivity and 5 * 10−6 Ω·m toroidally. The resulting toroidal resistance of JET vessel is Rtor ~ 370 * 10−6 Ω against an expected value of about 330 * 10−6 Ω reported in [5]. 4. Procedure for calculation of locked and rotating AVDE The plasma AVDE is described via finite element (FE) models as following: the plasma current is approximated by means of Figure 1. JET AVDE (pulse 38070) with measured plasma current and vertical position in two opposite octants. Reproduced with permission from [1], copyright 2000 IOP Publishing Ltd. Nucl. Fusion 56 (2016) 106010 R. Roccella etal 3 a set of axisymmetric elements (green in figure3) located at the vertical position of the plasma when the asymmetry starts, zp = 1.25 m (from figure1). The plasma elements are not conductive (in this way no eddy current is induced in these elements during transients) and a total current (Ip) is imposed to reproduce the current quench behaviour from 2.7 MA linearly down to 0 in about 40 ms. A halo region (HR) of about 15 cm radial width is in contact with the dump plates through a thin (2 mm) interface layer. The halo region is, like the plasma, an axisymmetric comp onent and covers most part of the dump plates in the poloidal direction. The halo region resistivity is evaluated through Spitzer’s formula [6]: / η=⋅ −T2.8108e 32 (Ω·m) with Te in keV for the component of current parallel to the magnetic field and ηη=⋅ ⊥1.96 for the component of current perpendicular to the magnetic field. Several cases have been analysed for electron temperatures in the range between ⋅− 510 3 and ⋅− 210 2 keV which correspond to parallel resistivity between ⋅− 710 5 and ⋅− 8106 Ω·m and normal resistivity about two times higher. The resistivity of the HR is thus orthotropic. It has been assigned equal to the parallel resistivity in the toroidal and in the poloidal direction, and to the normal resistivity in the radial direction. The asymmetry is reproduced by changing the radial resistivity of the thin interface layer between HR and CFC tiles with the toroidal angle. At low toroidal angles the resistivity is set very high preventing short-circuit of CFC tiles then it gradually decreases (in the toroidal direction) to simulate the Figure 2. Schematic view of eddy current patterns in JET structures during AVDEs. Toroidal sectionat vessel top (a); vertical sectionof the machine (b). The black spots approximately indicate the location of the toroidal field pick-up coils. Figure 3. Detail of the upper region: an axisymmetric 15 cm halo region (purple) wets the CFC tiles (orange elements). The resistivity of the contact element (green) between halo region and CFC tiles changes with the toroidal angle (with the function of figure4). The plasma current, located in the vertical position it has when the asymmetry starts is also axisymmetric. Nucl. Fusion 56 (2016) 106010 R. Roccella etal 4 increase of wetting area associated with the asymmetry evolution. The curve of resistivity versus toroidal angle is shown in figure4. Variation in the curve would impact the distribution of the asymmetry in the toroidal direction. The sideways force (Fy) is evaluated by the following formula: ()( )() ∑ =⋅ ⋅⋅F Ji Bi i2vol y n z 1 tor el180 (1) Where nel_180 are all elements of conducting structures in the 180° model (vessel, bellows, dump plates and their connecting bosses and CFC tiles); Jz(i) is the vertical component of the current density in the generic element i; vol(i) the volume of the element i and ()Bi tor is the toroidal field at the location of the element i consistent with the toroidal field of the analysed pulse of 2.85 T at 3 m from the tokamak axis. In the analysis of the rotating AVDE the same sum is extended to all elements of the 360° model and the resulting force is not doubled. The net toroidal current in the HR is prevented (by isolating its nodes at the 0° boundary) to make sure that the overall current quench time is not modified by this current. A similar procedure has been applied to a 360° FE model for the rotating case with the difference that after the first 10 ms of locked asymmetry, it starts rotating and completes 5 revolutions in 30 ms (during the last 10 ms of the current quench no rotation is imposed). The plasma temperature for the rotating case has been assumed around 15 eV. 4.1. Asymmetries during upward VDEs Several cases have been analysed to verify whether the proposed model is able to reproduce the typical locked AVDE measurements of JET pulse 38070. Sideways force and asymmetry of the plasma current have been assessed for a range of plasma parallel resistivity which goes from − 10 5 to ⋅− 710 5 Ω·m (roughly corresponding to temperature of pure hydrogen plasma from 20 to 5 eV). The amplitude ( I p asym ) and the normalised amplitude ( A p asym ) of the plasma current asymmetries [7] are calculated as: ( )=−II I p asym p7 p3 2 for locked AVDE analysis, ( )( ) =−+−IIIII p asym p7 p3 2p5 p1 2 for rotating AVDE and /= AII p asym p asym p dis for both locked and rotating AVDE. Another relevant measured parameter is the first plasma current vertical (and radial) moment which gives the position of the plasma centroid normalized over the total current; it has been deduced as following from the simulation results: =∑⋅⋅MJAZ IZ iiii tor where Ji tor is the toroidal component of current density in the element i ; Ai is the area of element i orthogonal to the toroidal direction and Zi is the vertical position of the element i . The sum is extended to all elements carrying toroidal current inside the vacuum vessel. The plasma current (calculated at octants 1, 3, 5, and 7), plasma current asymmetry and calculated vertical position are shown in the following figure5 and should be compared with the measurements of the target pulse 38070 (figure 1). In the simulations, the initial slow vertical drift of the plasma is not taken into account as it is located at the position occupied at the asymmetry onset. In figure5, Ip_oct3 indicate the total toroidal current inside the poloidal field pick-up coils loop at octant 3 (0°) and Ip_oct7 the current at octant 7 (180°) for plasma temperatures from 5 to 20 eV; DIp is the plasma current asymmetry (total current at octant 7–octant 3); zp_max is the vertical position of plasma current centroid calculated at octant 7. The asymmetry of the plasma current ( I p asym ) is extracted from the simulation results approximately every 12° (at the VV bellow locations) and is shown, together with the current entering in the DP from the vessel at each assessed toroidal location, in figure6. For the locked AVDE case it gives 10% of A p asym . The I p asym is evaluated by the line integral of B along Figure 4. Resistivity of the thin interface layer between plasma HR and CFC tiles. Nucl. Fusion 56 (2016) 106010 R. Roccella etal 5 Figure 5. FE simulation results of JET pulse 38070 with plasma temperature between 5 and 20 eV: plasma current plasma (blue lines) and plasma centroid vertical positions (red lines) in two opposite octants (3 and 7); in green the plasma current asymmetry. Figure 6. Toroidal current flowing in the dump plates versus the toroidal angle and angular current density flowing from VV to dump plates versus toroidal angle. Table 1. Values of plasma temperature and resistivity and main locked AVDEs simulation results. Plasma temp. Parallel resistivity ()Ω⋅m Normal resistivity ()Ω⋅m Max plasma current asymmetry (kA) Max normalized plasma current asymmetry Max plasma vertical asymmetry (m) Max sideways force (MN) 5 eV ⋅− 7.92 10 5 ⋅− 1.58 10 4 91 0.033 0.15 0.85 10 eV ⋅− 2.8 10 5 ⋅− 5.6 10 5 195 0.072 0.23 1.75 15 eV ⋅− 1.5 10 5 ⋅− 3 10 5 285 0.105 0.27 2.5 20 eV ⋅− 1105 ⋅− 2105 353 0.13 0.3 3.2 Nucl. Fusion 56 (2016) 106010 R. Roccella etal 6 a path which follows the VV inner shell contour retracing the JET array of in-vessel poloidal pick-up coils (red dashes in figures2 and 13). Table1 summarises the imposed values for the plasma temperature and resistivity and the main simulation results ( ∆IAzF;; ; p asym p asym ymax max ). So far, only one case of rotating AVDE has been analysed due to the demanding computational resources. The 360° FEM implements about 400 000 elements and the transient simulation solved 260 time steps to reproduce the rotating event. In order to assess the influence of the rotation on the sideways force the same case has been analysed with locked asymmetry. The plasma current in the 4 octants (1, 3, 5 and 7) and normalised asymmetry are reported in figure7 and should be compared with the JET measurements of pulse 72926 where Figure 7. Top: calculated plasma current in 4 octants during a rotating AVDE (plasma temperature ~13 eV); bottom: normalized amplitude of the plasma current asymmetry. The AVDE begins locked, at 10 ms the fast rotation starts completing 5 loops in 30 ms (~170 Hz). Figure 8. Measured plasma current in 4 octants, normalised asymmetry of plasma current and phase of the asymmetry rotation during JET pulse 72926. Reproduced with permission from [7], copyright 2014 EURATOM. Nucl. Fusion 56 (2016) 106010 R. Roccella etal 7 5 rotations are completed in about 30 ms (figure 8 from [7]). Both the plasma current in the four octants and the normalised asymmetry are consistent with the simulation and a strong damping of the sideways force due to the rotation has been found. Figure9 shows a reduction of almost one order of magnitude in the sideways force exerted during the rotating (blue) case with respect to the corresponding locked (red) case. It can be noticed that even though the A p asym is about 80% of the locked case (0.08 against 0.1 of the locked AVDE) the force that is produced by this asymmetry decreases to about 10% of the locked case. The proposed model of ATEC implies that part of the difference in the plasma vertical position in opposite octants is not caused by the real plasma deformation (m = n = 1 mode) but by the induced current flowing at a fixed height (dump plates). A clear phase relationship between the plasma cur rent asymmetry (ΔIp) and the first vertical current moment (ΔMIZ) is thus expected as the latter is the sum of the moment of the current ΔIp flowing in the plates and the moment of quenching plasma current, which in the simulation does not change position (because the plasma kink is not modelled). The slope of the ΔMIZ − ΔIp phase relationship depends, then, in the FE analysis, only on the vertical position of the DP where the ΔIp flows: → ∆=−=⋅+∆⋅ −⋅ =∆ ⋅∆ ∆= π MMMIzI zI z Iz M Iz IZ IZ IZ IZ FE 0 pp pDPpp pDP FE p DP (2) In JET, on the other hand, the measurement of MIZ includes the kink of the plasma column: ⎜⎟ ⎜⎟ ⎛ ⎝ ⎞ ⎠ ⎛ ⎝ ⎞ ⎠ ∆=⋅+ ∆ +∆ ⋅−⋅− ∆ =⋅∆+∆⋅ =∆ +∆ MIzzIz Iz z Iz Iz MM 22 ; IZ IZ IZ JETpp kink pDPppkink pkinkpDP kink FE (3) where zDP is the average vertical position of the top dump plate; ∆zkink and ∆ M IZ kink are respectively, the variations of plasma vertical position and plasma current first moment due to the kink only; superscripts FE and JET label quantities evaluated in the FE analysis or measured during JET experiments. In the end, the difference between the simulated and the measured ΔMIZ is the variation of plasma current first moment due to the kink alone. This result is independent from the amplitude of ∆Ip and from the assumptions on the plasma position made in the simulation. Figure 10(left) shows the measured ΔMIZ − ΔIp phase relation: the slope is almost constant for all the reported disruptions and close to the slope of the evaluated phase relation equal to zDP (figure 10(right)). This confirms that ΔIp is actually flowing at the DP level. The small distance between the two lines at equal ΔIp gives, as shown above, ()∆ =∆ −∆MMM IZ IZ IZ kink JETFE . This is much smaller than the measured ΔMIZ and of the same order of the measured ΔMIZ (0.05 ÷ 0.1) as expected in case of asymmetries dominated by an m = n = 1 mode [7]. 4.2. Asymmetries during downward VDEs Both upward and downward asymmetric VDEs were experienced at JET before installing the divertor coils and structure. After this major upgrade no relevant asymmetries have been measured during downward VDEs. The divertor structures prevent somehow plasma toroidal current asymmetries. Preliminary analysis of downward AVDEs have been carried out on the base on the hypothesis that, in case of plasma asymmetries, ATEC could also flow in the lower structures of the JET vessel. The main structures added with the divertor upgrade are the four active divertor coils (green in figure11) and, starting Figure 9. Comparison of calculated modulus of sideways force for locked and rotating AVDE (plasma current before disruption and current quench time are same for both cases). Nucl. Fusion 56 (2016) 106010 R. Roccella etal 8 from MkII, the divertor support structure (red in figure11). The coils (in copper) are made of 15–20 turns each (about 65 turns total). During disruptions they can be considered, in most cases, short-circuited through their power supplies. The divertor support is a toroidally continuous U-shaped Inconel structure of about 10 cm thickness. In case of downward VDEs important currents are induced both in divertor coils and support partly shielding the vessel for longer time than current quench duration. In this qualitative analysis the AVDE of figure1 has been simulated with the divertor structures modelled at the machine top, the halo temperature fixed to 15 eV and the plasma asymmetry modelled in the same way as in the upward AVDEs analyses. The divertor support has been modelled by connecting all top dump plates in toroidal direction and their resistivity has been modified to take into account that the divertor support is about three times thicker than the dump plates. The divertor coils have been modelled by means of a single stranded coil, insulated from the rest of conductive structures, positioned between the dump plates and the vessel (orange elements in figure12). The resistivity of the coil in the FE model has been chosen to allow comparable induced current to the total induced in the divertor coils during a downward VDE (about 15–20% of Ip). The analysis results show about one order of magnitude reduction in measured plasma current asymmetry ( =A0.01 p asym ) and sideways force ( =F0.23 MN y max ) with respect to the corresponding upward case. Most part of the reduction is caused by divertor support. In fact the same analysis run without the divertor coil gives only slightly higher asymmetry and sideways force ( =A0.015 p asym and =F0.28 MN y max ). The asymmetric short-circuit of tiles through the plasma (responsible of important sideways forces Figure 10. Measured (at JET left) and calculated (right) phase relationship between plasma current (ΔIp) and first plasma current vertical moment (ΔMIZ) asymmetries. Reproduced with permission from [7], 2014 EURATOM. Figure 11. Toroidally continuous components in the divertor (MkII) region: divertor support structure (red) and divertor coils (green). Nucl. Fusion 56 (2016) 106010