Fusion Plasma Physics Annual Report Fusion Plasma Physics School of Electrical Engineering KTH Royal Institute of Technology

Transcription

1 Fusion Plasma Physics Annual Report 2013 Fusion Plasma Physics School of Electrical Engineering KTH Royal Institute of Technology Stockholm, December 2014

2 Fusion Plasma Physics School of Electrical Engineering KTH Royal Institute of Technology SE Stockholm, Sweden 2

3 Contents 1. Introduction Research projects MHD stability and control Subspace identification analysis at RFX-Mod and EXTRAP T2R SIM analysis of data from the full 2x64 sensor coil array at T2R Model Predictive Control in EXTRAP T2R ASDEX-Upgrade enhancement project T2R feedback system as a tool for tokamak-relevant physics studies Flow braking due to non-resonant perturbations Resonant magnetic perturbation penetration Tearing mode locking-unlocking mechanism Plasma - wall interactions Tungsten migration studies Erosion-deposition diagnostic tools for JET with ITER-Like Wall Microanalysis of divertor surfaces in JET A 10 Be marker experiment on beryllium migration in JET Theoretical fusion plasma physics ICRH scenarios for DEMO and the SELFO-light code Integrated Tokamak Modelling Task Force Collaboration and exploitation of JET Quasilinear versus non-linear wave particle interactions Requirements for ICRF control of sawtooth instabilities in ITER Monte Carlo schemes for pitch angle scattering Monte Carlo modelling of orbit averaged equations Computational methods for fusion plasmas Theoretical and numerical modelling of RFP confinement The Generalized weighted residual method (GWRM) Confinement physics Pedestal properties and confinement in JET ELM control by resonant magnetic perturbations Education and research training Basic and advanced level education Research training Personnel Income & Expenditure Bibliography

4 4 Fusion Plasma Physics Annual Report 2013

5 1. Introduction The main activity in the European fusion research programme is the ongoing construction of the ITER experimental facility in France. The accompanying physics programme, co-ordinated through the European Fusion Development Agreement (EFDA), and carried out at the existing research facilities in Europe is centred on the preparation for the operational phase of ITER. There are a number of university based research groups participating, and the research training of young fusion scientists is also an important part of the European programme. The Department of Fusion Plasma Physics is extensively involved in the accompanying physics programme. Activities in 2013 has mainly been in priority areas such as the development of MHD stability and control methods, experimental studies of plasma-wall interaction at plasma facing components and improved understanding through numerical simulations of wave heating and current drive experiments. The research activities at the Department of Fusion Plasma Physics continue to be very productive, with over 60 published papers in international journals and conference proceedings during This Annual Report summarizes the main research results. Fusion Plasma Physics participates during 2013 in the EFDA BeFirst training program. The aim of the BeFirst program is the education and training or early stage researchers in the area of Beryllium plasma facing components. At the end of 2013, the Department successfully applied for membership in FuseNet, an organization for increasing, enhancing and broadening fusion science and technology training in Europe. The Department of Fusion Plasma Physics is deeply involved in the education at KTH. The Department is responsible for basic level courses as well as advanced level courses in the Electrophysics Master Programme. The post-graduate research education is part of the Electrical Engineering Doctoral Program track on Plasma Physics. Per Brunsell Department Head Fusion Plasma Physics 5

6 2. Research projects 2.1. MHD stability and control P. Brunsell, L. Frassinetti, R. Fridström (PhD student), A. C. Setiadi (PhD student), and J. R. Drake In collaboration with: W. Suttrop, V. Igochine, Max-Planck-Institut für Plasmaphysik, Garching T. Bolzonella, G. Marchiori, G. Manduchi, Consorzio RFX, Padova C. R. Rojas, H. Hjalmarsson, EES/Automatic Control, KTH The research program at KTH on active MHD mode control is aimed at the development of methods applicable to both tokamak and reversed field pinch devices. The EXTRAP T2R reversed field pinch has been utilized for the development and testing of various algorithms. The process control system strategy has been adapted for RWM mode control; system identification followed by controller design based on the identification results. The work on active RWM stabilization is also carried out at the RFX-Mod reversed field pinch experiment. On a longer time-scale, the goal is to implement control algorithms for RWM control at the ASDEX Upgrade tokamak. Figure EXTRAP T2R device at Alfvén Laboratory KTH Parameters of the EXTRAP T2R device are listed in Table below. 6

7 Table EXTRAP T2R parameters Parameter Notation Value Unit Major radius R 1.24 m Minor radius a m Wall diffusion time t v 6.3 ms Plasma pulse length t d <100 ms Plasma current I p <150 ka Plasma electron temperature (typical) T e 300 ev Plasma electron density (typical) n e 1x10 19 m -3 A MHD mode control system is based around an array of control coils placed outside the conducting shell. Arrays are distributed over the toroidal surface as shown in Fig Figure Two-dimensional arrays of sensor flux loops and active saddle coils installed at EXTRAP T2R. The main features of system are: 128 magnetic flux loop sensors at 4 poloidal and 32 toroidal positions inside the thin shell. 128 active saddle coils at 4 poloidal and 32 toroidal positions outside the thin shell. Saddle coils and sensor flux loops are pair-connected at each toroidal position to form 64 independent m=1 coils and sensors. 32 power amplifiers units providing at total of 64 independent channels. Audio amplifiers are used with output power of Watt providing maximal radial magnetic field at the coil centre of about 3 mt. An integrated digital controller unit, contained in one VME bus crate including CPU board, ADCs and DACs. Control algorithms are implemented in software. 7

8 Subspace identification analysis at RFX-Mod and EXTRAP T2R Subspace system identification methods (SIMs), introduced in the 1990s, have become widely spread in process control practice. A particularly attractive feature of SIMs is their ease-of-use for Multi-Input Multi-Output (MIMO) systems and the way non-linear and/or non-convex optimization is avoided by the usage of numerical linear algebra. The system identification literature suggests that SIMs perform well on generic discrete-time linear time invariant systems. Figure Output prediction (one-step and many-steps) for T2R and RFX response experiments. Left: The black solid line shows the measured output y. The green solid line is the many-step predicted output y pf. The dashed blue line is the one-step predicted output y p. The dashed-dotted red line is the one-step prediction residual y-y p. The dotted cyan line is the many-steps prediction residual y-y pf. Right: Decay of the deviation accounted for versus the horizon length f. Top panels (a) are RFX data, while bottom panels (b) are T2R data. A subspace system identification analysis aiming to characterize the resistive wall mode response has been carried out at two reversed field pinch experiments: T2R and RFX-Mod. The T2R system to be identified is obtained by analysing the 64 coil current inputs and the 64 sensor outputs signals, while the corresponding RFX-Mod analysis utilizes 192 inputs and 192 outputs. The RFP datasets, which are samples of the distributed magnetic field dynamics, are naturally divided into smaller batches due to the pulsed-plasma operation of the experiments. Using subspace system identification techniques and randomized cross-validation methods to minimize the generalisation error, state-space orders of the empirical systems are suggested. These system orders are compared to stabilization diagrams commonly used in experimental modal analysis practice. The relation of the cross-validation system order to the decay of the singular values from the subspace method is observed. Both stable vacuum diffusion and unstable plasma response datasets are analysed. Apparent simulation 8

9 and prediction errors are quantified for both cases using a deviation-accounted-for index. These results are purely data-driven. Differences and similarities between T2R and RFX-Mod are observed. It was noted that it is possible to obtain full black-box MIMO models with reasonable short-time predictive capabilities for both devices. T2R analysis has previously generated seemingly reliable and interpretable results, and T2R techniques and practical confidence has been developed over several years. RFX-Mod turns out to be more challenging to analyse so far. Possible explanations for this are (i) unfavourable timescale ratio of flat-top to nominal long wall time, (ii) the possible errors-in-variables issues with the measured active coil current inputs. It may be possible to circumvent these problems by further developments of the estimation methods and by acquisition of more data SIM analysis of data from the full 2x64 sensor coil array at T2R Considerable research effort has recently been devoted to the development of closedloop system identification methods for analysis of EXTRAP T2R experimental data. Plausible detection of RWMs was made with a subspace system identification method (SIM) using data from a sensor array consisting of 2x32=64 coils. These previous data were suggestive of potential under-sampling, leading to aliasing of toroidal mode numbers. Figure Left: Empirical RWM dispersion relation for T2R. Red colour indicates high model density (highly probable location of the plasma response eigenvalues) in the logarithmic scale. A stable pole is located in z<1, an unstable pole is located in z>1. The discrete-time normalisation is with respect to the control cycle rate t s 1 =10 khz. The continuous-time growth rate is given by γ= t s 1 ln z. Right: Resistive wall MHD eigenvalues for discrete toroidal wave numbers n transformed to discrete evolution on the T2R control cycle time scale. The symbols (a) to (e) correspond to different RFP equilibria. Recently, sensor coil signals from the full 2x64=128 coil array has been analysed with the SIM code. These sensors are connected to a separate data-acquisition system with its own clock signal. The real-time system input (the active coil currents) was accurately post-shot synchronized with the non-real-time high spatial resolution system output (the 2x64 radial field coil array time-integrated voltages), based on the common sensors shared with the real-time 2x32 array. A collection of 114 feedbackstabilized randomly perturbed T2R plasma discharges was processed. This collection 9

10 corresponds to a sum-total of 3.8 seconds of steady-state slices of RFP data, each slice being of similar length. The used data is fully new and disjoint with the set used for previous analysis. In this method the RFP plasma response is represented by a by a discrete-time linear time-invariant state-space system: x( t+ t s ) = Ax() t + Bu() t + Ke() t y() t = Cx() t + e() t The system is evolved in steps of single control cycle times t s =100 µs. The vector y represents the radial magnetic field sensor array signals and the vector u represents the coil currents. The vector x is the state vector. In this model the state vector does not have any simple physical interpretation. The vector e is a residual that models the noisy part of the data, and K is a filter gain. Finally, the system is represented by the constant matrices A, B, C, which are determined in the system identification process. The state order selected was dim(x) = 600. With a 2x64 sensor array it was possible to avoid the aliasing problem. Using the extended sensor array of 2x64 coils, the method has provided the first generic and simultaneous measurement of the full RWM dispersion relation in reversed field pinch plasma. By generic it is meant that no assumption of the MHD model is built-in to the signal processing. Instead, the multivariate magnetic diagnostic data is regarded as a direct noisy time-domain eigenvalue problem. By simultaneous it is meant that all the RWMs are excited concurrently. The RWM growth rate spectrum obtained compares well to the MHD model calculation Model Predictive Control in EXTRAP T2R A numerical study of fast Model Predictive Control (MPC) in EXTRAP T2R has been carried out. A variant of predictive controller has been designed utilizing the system identification algorithm that has recently been implemented in T2R. Predictive control, which belongs to a class of optimal control, is known to generally outperform a generic control such as Proportional-Integral-Derivative (PID) control. Furthermore, the predictive control treats Multiple-Input Multiple-Output (MIMO) system and actuation constraints explicitly. Numerical simulations of Model Predictive Control in T2R have been carried out, which assess the performance of the proposed predictive controller, in particular concerning the implementation feasibility of the controller for a system with fast time scale. A discrete linear time-invariant system is considered. The aim of the MPC is to generate an optimal input that minimizes a cost function based on prediction of the system over some finite time horizon. If the optimization problem is unconstrained, then the optimal solution can be found analytically. If the optimization problem is constrained with linear constraints, then the MPC is a Quadratic-Program (QP). Furthermore, if the constraints are box input constraints, then the Fast Gradient method can be used. The proposed MPC has been shown to be able to stabilize EXTRAP T2R with a reasonable computing time (latency) of around 0.1 ms. 10

11 ASDEX-Upgrade enhancement project The on-going ASDEX Upgrade enhancement project for active MHD control is carried out in collaboration between Max-Planck-Institut für Plasmaphysik and includes 24 in-vessel saddle coils with power supplies. KTH involvement is mainly in the design of the RWM controller. At present, 16 coils have been installed at poloidal positions above and below the mid plane, and manufacture of power amplifiers is ongoing at Max-Planck-Institut für Plasmaphysik T2R feedback system as a tool for tokamakrelevant physics studies L. Frassinetti, P. Brunsell, S. Menmuir, M.W.M. Khan (PhD student), R. Fridström (PhD student) In collaboration with: Y. Sun, Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China F. A. Volpe, Dept. Applied Physics and Mathematics, Columbia University, USA External magnetic perturbations are an important tool in tokamaks to mitigate edge localized modes and/or to influence the neoclassical tearing mode island dynamics in order to optimize ECCD stabilization. On the other hand magnetic perturbations produce also undesired effects such as plasma flow braking. A clear study of the corresponding underlying physics is relatively complicated in tokamaks because of the limited number of active coils that inevitably produces a broad spectrum of sideband harmonics. The EXTRAP T2R reversed-field pinch is equipped with a set active and sensor coils that can produce external magnetic perturbations (MPs) with a specific harmonic in a controlled fashion (i.e. with defined amplitude and phase). The feedback system of EXTRAP T2R has the capability of suppressing the entire RWM and error-field spectrum and simultaneously producing a clean external MP. EXTRAP T2R is therefore a useful machine to investigate the magnetic perturbation effect on the plasma dynamics. During 2013 a series of studies aimed at the understanding of the mechanisms that lead to the flow braking have been conducted Flow braking due to non-resonant perturbations The non-resonant magnetic perturbation (MP) braking is studied in EXTRAP T2R and the experimental braking torque is compared with the torque expected by the neoclassical toroidal viscosity (NTV) theory. The non-resonant MP produces velocity braking with an experimental torque that affects a large part of the core region. 11

12 The application a non-resonant MP is characterized by a single harmonic allows study of the harmonic role in the braking mechanism. The experimental torque is not clearly related to the amplitude of the external applied MP, as shown in figure (a) where the volume averaged torque versus the volume averaged radial field is shown. On the other hand, a correlation is clear with the plasma displacement as shown in figure 2.2.1(b). These results are in optimal agreement with the results expected by the NTV theory. From a quantitative point of view, the experimental torque and the torque determined by the NTV theory differs by a factor 3-4. However, it must be highlighted that this difference might be related to a very uncertain estimation of the plasma viscosity, which is a key parameter for the estimation of the experimental torque. Figure Experimental torque versus the volume averaged applied MP (a) and versus the plasma displacement (b) Resonant magnetic perturbation penetration Resonant magnetic perturbations (RMPs) and/or error-fields can lead to wall locking of rotating tearing modes (TMs) and eventually to disruptions. The TM locking occurs both via the electromagnetic torque that acts locally on the rotating island and via the neoclassical toroidal viscosity torque that tends to damp the toroidal rotation to an offset velocity. At critical RMP amplitude, a bifurcation in the TM torque balance appears leading to an abrupt transition from branch with a fast rotating TM to a branch with a slowly rotating or wall locked TM. This critical RMP amplitude is referred to as the error-field penetration or locking threshold. Experimental results indicate that the RMP penetration threshold in EXTRAP T2R increases with the plasma temperature in the present parameter range. The toroidal TM velocity as a function of the applied RMP field amplitude is shown in Fig The RMP penetration threshold is identified as the abrupt transition from fast TM rotation to slow (or locked) TM rotation. 12

13 The threshold at the low temperature of T i 250 ev is around b r th 0.2 mt. At the high temperature T i 600eV the threshold is increased to around b r th 0.6 mt. The results show a clear dependence of the RMP penetration on the plasma current. The experimental results show a reasonable agreement with model described in reference [Fitzpatrick R. and Yu P., Phys. Plasmas 7, 3610 (2000)] assuming a dependence of the kinetic viscosity on the plasma current. Figure TM velocity vs RMP amplitude for two different sets of plasmas; i) high current and high temperature (red dots) and ii) low current and low temperature (black dots) Tearing mode locking-unlocking mechanism The tearing mode (TM) locking and unlocking process due to an external resonant magnetic perturbation (RMP) is experimentally studied in EXTRAP T2R. The RMP produces a reduction of the natural TM velocity and ultimately the TM locking if a threshold in the RMP amplitude is exceeded. During the braking process the TM slows down via a mechanism composed of deceleration and acceleration phases. During the acceleration phases the TM can reach velocities higher than the natural velocity. Once the TM locking occurs, the RMP must be reduced to small amplitude to obtain the TM unlocking showing that the unlocking threshold is significantly smaller than the locking threshold and that the Figure TM velocity vs RMP amplitude for a set of similar shots in which the harmonic (1,-12) was applied. The full symbols correspond to shots in which an RMP with squared waveform was applied. The open symbols correspond to shots in which an RMP with triangular waveform followed by a plateau was applied. For the open symbols, data are time averaged during the plateau phase before the termination of the discharge. process is characterized by hysteresis. This is shown in figure where the TM velocity versus the amplitude of the external resonant MP is shown. Experimental results are in qualitative agreement with a model that describes the locking-unlocking process via the balance of the electromagnetic torque produced by the RMP that acts to brake the TM and the viscous torque that tends to re-establish the unperturbed velocity. 13

14 2.3. Plasma - wall interactions M. Rubel, H. Bergsåker, D. Ivanova, P. Petersson, I. Bykov (PhD student), A. Garcia-Carrasco (PhD student), P. Ström (PhD student), A. Weckmann (Ph.D. student) In collaboration with G. Possnert (Uppsala University) Plasma-wall interactions (PWI) comprise all processes involved in the exchange of mass and energy between the plasma and the surrounding wall. Two inter-related aspects of fusion reactor operation - economy and safety - are the driving forces for studies of PWI. The major issues to be tackled are: (i) lifetime of plasma-facing materials (PFM) and components (PFC), (ii) accumulation of hydrogen isotopes in PFC, i.e. tritium inventory; (iii) carbon and metal (Be, W) dust formation. PWI is one of the primary areas where integration of the Physics and Technology programmes is being achieved. The work at KTH in the field of PWI and fusion-related material physics has been fully integrated with the international fusion programme: (i) EU Fusion Programme, (ii) International Tokamak Physics Activity (ITPA), (iii) International Atomic Energy Agency (IAEA), (iv) Implementing Agreements of International Energy Agency (IEA). It is demonstrated by the participation in: European Task Force on Plasma Wall Interactions (EU-TF-PWI), EFDA-JET Work Programme: Task Forces and JET Enhancements (Phase 1 and Phase 2) including the ITER-Like Wall (ILW) Project, i.e. full metal wall at JET, EFDA-JET Fusion Technology Programme, ITPA, IAEA and IEA activities. Experimental work is carried out at home laboratory, JET, TEXTOR, ASDEX- Upgrade and Tore Supra. The research programme is concentrated on: Material erosion, migration and re-deposition. Fuel retention studies and fuel removal techniques. Dust generation processes in fusion devices. Characterization of plasma-facing materials and components including testing of high-z metals. Development and testing of diagnostic components. Development and characterization of wall materials for ILW at JET. Development of diagnostic methods for PWI studies Tungsten migration studies Broad application of tungsten in tokamaks requires development of techniques enabling studies of its migration. One concept can relies on Mo markers as it is applied to study erosion-deposition phenomena in the tungsten divertor of JET-ILW. The changes in the layer thickness can be measured with ion beam analysis (IBA) methods. A potential risk for the assessment is Mo-W inter-diffusion and/or alloying at high temperatures. Another approach may be based on application of a volatile compound, e.g tungsten hexafluoride (WF 6 ). In addition, the use of tungsten PFC requires impurity seeding for improved edge radiation. The injection of neon (Ne), argon (Ar), or nitrogen (N 2 ) is performed for that purpose. Among many issues related to the injection is the in-vessel residence of gas by implantation, co-deposition 14

15 or by compound formation with PFC materials. The latter may become important in the case of nitrogen-tungsten combination. To address W transport and the change of PFC surface morphology in the presence of nitrogen dedicated experiments were performed in the TEXTOR tokamak by injection of WF 6 and 15 N 2. The aim was to assess: (a) material balance by qualitative and quantitative determination of a global and local deposition pattern of tungsten and local of nitrogen; (b) material mixing; (c) fluorine residence in PFC. Experiments with the localised WF 6 injection were performed at the TEXTOR tokamak prior to the major shutdown connected with the retrieval of tiles for ex-situ analysis. They were done using a test limiter lock located at the bottom of the machine. Fig (a) shows the location of the lock with respect to the nearest blades of the toroidal belt pump limiter ALT-II (Advanced Limiter Test) which is the main PFC of TEXTOR. An assembly of the test limiter is shown in Fig (b): a roof-shaped block with a polished plate (both made of graphite) with a hole for WF 6 puffing. It was placed the scrape-off-layer (SOL). The experiment was performed on the last operation session when puffing of 1.93x10 20 W atoms in 13 shots heated neutral beam injection (NBI) was accompanied by puffing two other markers: Nitrogen-15 from the toroidal inlets and 13 CH 4 from the upper test limiter. Figure : Top view into the TEXTOR vacuum vessel showing the location of the test limiter with respect to ALT-II limiter blades with marked position of corner tiles (a); test limiter assembly with marked components of the set-up (b). Local spectroscopy measurements were focused on the test limiter where NII (451.4 nm), WI (400.8) nm, CII (426.7 nm), FII (389.8 nm) and D ε (397.0 nm) lines were recorded. The exposures were followed by detailed ex-situ studies of components by means of surface-sensitive ion and electron spectroscopy methods. Temporal evolution of W and F fluxes at the test limiter is plotted in Fig for the first and the last shot with WF 6 injection. The data are normalized with respect to the intensity of the D ε line. For a given species the signals are fairly similar. This weak memory effect may indicate that fluorine retention on the test limiter is not pronounced, i.e. species is effectively transported to other PFC or to pumps. 15

16 Figure : Normalized spectroscopy signals of WI and FII lines for the first and the last discharge with the WF 6 injection. Spectroscopy The injection of WF 6 lead to the formation of a co-deposit on the graphite plate in the vicinity of the gas inlet, as seen in the photo, Fig (b). The deposited layer, as identified with ToF HIERDA contains a mixture of light and heavy species: H, D, He, 10 B, 11 B, 12 C, 13 C, 14 N, 15 N, 16 O, F and W accompanied by small quantities of Inconel components (Ni, Cr, Fe). The concentration varies, but the greatest amounts are found near the gas inlet: up to 1x10 18 W cm -2, N-15 (3x10 16 cm - 2 ), F (2x10 16 cm -2 ) and He (1x10 17 cm -2 ). These measurements reveal only a small quantity of fluorine in comparison to other species, especially to tungsten. They also prove and confirm nitrogen retention in deposits. Helium originating from regular glow discharge wall conditioning and He-beam diagnostics is identified in deposit from TEXTOR. Its concentration is fairly high with respect to other gaseous elements in the analysed layer. On the molybdenum catcher plates attached to the test limiter base the quantities of W, 15 N and F are below the detection limit. Tungsten balance The integrated quantity of tungsten found on the graphite plate near the gas inlet corresponds to 2-3% of the injected amount. This very small local deposition of W may be attributed to at least two factors: low sticking probability of the injected gas to the plate and/or efficient erosion of the locally deposited tungsten. The large Larmor radius of W ions would eventually increase the migration of W from the vicinity of the injection point. The integrated amount on ALT-II tiles, 10.5% of the injection W atoms, is also small. Summing up the amount from the test and toroidal limiter only 13% of the species could be identified. Therefore, for the first time several DED tiles from various locations were studied. The W content ranges from 1 to 25x10 15 cm -2. Taking 3x10 15 cm -2 as a mean value, the integrated amount on DED is approximately 2x10 20 W atoms, i.e. exceeding the amount puffed. It is impossible to assess accurately the amount originating from the last experiment because the tiles were in TEXTOR for eight years. As determined by RBS, the tiles also contain other metals, e.g. Inconel components. The results lead to a conclusion that the inner bumper is a major residence place for high-z metals eroded from the TEXTOR liner, various test limiters, and those introduced by injection. Also the deuterium content on the DED tiles is significant: 3-4x10 18 cm -2 leading to the integrated amount in the range x10 23 D atoms accumulated in that region. 16

17 In conclusion, volatile WF 6 can be used as a high-z transport marker without a major risk of leaving large quantities of fluorine sticking (co-deposited) to PFC and then released to plasma during subsequent pulses. The statement is justified by two facts: (i) the memory effect is not pronounced, as proven by spectroscopy and (ii) small quantities of F (maximum 2x10 16 cm -2 versus 1x10 18 cm -2 ) are found even near the injection point. The most important outcome of the experiment is the direct demonstration of tungsten erosion and its subsequent migration over long distances by re-erosion ionization re-deposition steps. The transport is gradual (see Fig. 4) but very effective under experimental conditions, i.e. edge T e ~ 60 ev. One may assume that so significant W migration will be at least partly suppressed at low edge temperature and high divertor densities, as expected in ITER. However, this would not eliminate metal erosion followed by prompt re-deposition and local formation of modified mixed material layers Erosion-deposition diagnostic tools for JET with ITER-Like Wall The Joint European Torus (JET) is the largest present-day tokamak. Its main scientific mission is to develop plasma operation scenarios for a reactor-class machine such as ITER. It is equally important to test the performance of plasma-facing components and divertor configurations. Since late JET has been operated with the ITER- Like Wall (JET-ILW Material erosion and fuel inventory studies are among top priorities. A large number of diagnostic tools has been developed and manufactured to elucidate the overall material migration scenario. Two major categories are: (i) markers for studies of beryllium and tungsten erosion and (ii) active and passive deposition monitors. They are placed in locations crucial for obtaining a global and local pattern of material migration. Beryllium marker tiles and coatings on inner wall cladding A marker is a regular beryllium tile coated first with a high-z metal film acting as an interlayer and then with a Be layer of density similar to that of bulk beryllium. It is important to ensure good adherence and thermo-mechanical, and physical properties of the coating: best possible match of linear thermal expansion coefficients (α LTE ) and a melting point of the marker higher than that for beryllium, T m (Be) = 1551 K. Nickel [T m (Ni) = 1726 K] was selected as an interlayer (2-3 µm) material to separate the bulk Be tile from a 7-10 µm thick beryllium coating. In the development phase marker coupons were examined by material analysis techniques before and after high-heat flux (HHF) testing with an electron beam in the JUDITH facility. HHF screening tests allowed for the determination of the power and energy density limits deposited onto the surface at which damage to a marker occurred. A cyclic test served to assess the thermal fatigue under repetitive power loads. The major results may be summarised by the following: (i) the markers survived without noticeable damage at power loads of 4.5 MW m -2 for 10 s (energy density 45 MJ m -2 ) or for fifty repetitive pulses performed at 3.5 MW m -2 each lasting 10 s, i.e. corresponding to the total energy deposition of 1750 MJ m -2 ; (ii) in both cases the surface temperature measured with an infrared camera was around 873 K; (iii) damage to the Be coating occurred at power loads of 5 MW m -2 for 10 s. Plots in Fig show depth profiles obtained by secondary ion mass spectrometry (SIMS) for two marker coupons: (a) unexposed to heat loads and (b) after HHF test carried out for 10 s at a power density of 4 MW m -2, i.e. total energy density of 40 MJ m -2. Both profiles are quite similar (Be coating thickness ~9.5 µm) thus indicating that the applied power loads neither damage the coating nor cause intermixing of Be and 17

18 Ni. There are some impurity species (Al, Si, Fe) but their content is below 1 % as determined by ion beam analysis, energy and wavelength dispersive X-ray spectroscopy. Metallographic cross-section of the HHF tested coupon revealed a clear separation of beryllium and nickel thus proving durability of the coating. Figure : SIMS depth profiles for two markers: (a) as produced ; (b) HHF tested at 40 MJ m -2. The inner wall cladding and the dump plate tile carriers are made of cast Inconel. These tiles are in the shadow of bulk Be tiles, but to minimize the risk of high-z impurity (Ni, Cr, Fe) influx, the Inconel is protected by about 8 µm thick evaporated Be coatings. During regular plasma operation in JET, the estimated power load to the cladding is MW m -2 for 10 s corresponding to energy deposition of 5-7 MJ m - 2. HHF testing indicated that the Be coating on Inconel would melt at energy loads exceeding 30 MJ m -2. Such tiles themselves serve as Be erosion markers in recessed areas, but even more precise tools for material migration studies are wall inserts, called also sachets made of Inconel 600. These are metal buttons inserted in the cladding. One half of each button (i.e. sample) surface is coated by nominally 40 nm W using physical vapour deposition and the other half is covered by nominally 3 μm Be. To draw conclusions regarding erosion-deposition on the inserts one has to determine the difference in composition and thickness of the marker layers (Be and W) before and after the exposure to plasma during the whole campaign. The exact initial thickness was determined using ion beam analysis methods. Tungsten markers Marker tungsten migration studies are placed in the divertor, both on W-coated CFC blocks and in the W-LBSRP. These are standard tiles or lamellae respectively first coated with a molybdenum interlayer (3-4 or 6-7 µm dependent on the location) and then with a tungsten film of the thickness of 4 or 5-6 or 12 µm dependent on the location. The choice of Mo-W system is related to the similarity of crystallographic structures (both are bcc metals) and α LTE coefficients, 4 5 x10-6 K -1. This ensures mutual adhesion and thermo-mechanical integrity of the Mo-W layer under thermal excursions. Though metals have high melting points, T m (Mo) = 2896 K, T m (W) = 3695 K, such shocks may lead to coating detachment from CFC because of α LTE mismatch: below 1x10-6 K -1. The other possible cause for marker destruction is inter-diffusion and W-Mo alloying at operation temperatures above 1700 K, thus making post exposure depth profiling with ion beam analysis inconclusive. The potential benefits for material migration studies overweigh the possible difficulties. The layers were obtained by means of combined magnetron sputtering and ion implantation (CMSII), i.e. the technique applied to coat CFC divertor tiles with tungsten. Images in Fig (a) and (b) show respectively a microstructure of the 18

19 W-Mo layers and a W-LBSRP with marked positions of marker lamellae in the center and in a shadowed part of the stacks. Figure : Mo-W markers: (a) cross-section of the coating; (b) a W-LBSRP unit showing the banks of solid W lamellae, with the positions of the rows with markers. Deposition monitors Probes, active and passive, are installed in locations protected from direct plasma impact, i.e. deep into the scrape-off layer on the main chamber wall or in areas protected by the divertor tiles. Their role is to monitor material transport to various places in the machine. QMB devices are active monitors which have previously provided data after individual discharges; e.g. to relate operation scenario with erosion-deposition processes. Information from passive monitors is obtained by surface analysis techniques after an entire campaign when devices have been retrieved from the vacuum vessel during a major shut-down. For the use at JET- ILW a new set of EDP was installed after a design review and necessary modification of earlier monitors in order to meet requirements of operation with metal walls. The rotating collector is a diagnostic based on a drive mechanism powered by the magnetic field. Every pulse for which the field coils are energised, will advance the first wheel in a gear chain by one step. Erosion - deposition is monitored during over ~3000 pulses with a time resolution of either 25 or 50 pulses. Since the units need no electrical connections, they can be fitted to the outer vessel wall in addition to the divertor locations. Passive diagnostic tools comprise divertor deposition monitors, louver clips and mirror test units. Clips are clamped on the water-cooled louvers in the shadowed region in the outer and inner divertor. The device consists of two jaws, Inconel probes fixed to the jaws and a spring. Divertor deposition monitors are traps for particles transported to remote regions. Polycrystalline molybdenum mirrors are installed in eight cassettes located in the divertor (base, inner, outer), and two on the main chamber wall, as mentioned above. The so-called First Mirror Test, is carried out for ITER because metallic mirrors will be essential components of all optical spectroscopy and imaging systems for plasma diagnosis in a reactor-class device. Optical and surface morphology of mirrors is studied before and after exposure. 19

20 Concluding remarks and outlook All marker tiles and deposition monitors will be retrieved for ex-situ examination during the shut-down. Ex-situ structural studies of Be and W tiles will give insight into their power handling capabilities. Fuel retention in gaps between tiles (spaces equal to castellation) and in remote areas will be measured using ion beam methods. The ultimate goal is to obtain a global picture of material performance and migration. The key point is in the correlation of surface measurements on various erosiondeposition diagnostic tools with time-resolved data recorded in-situ by spectroscopy, thermocouples, Langmuir probes and cameras both during discharges and highresolution inspection of the vessel during the shut-down period. These results will eventually be essential for modelling of material transport in JET assessment of phenomena in ITER operated with a full metal wall. 20

21 Microanalysis of divertor surfaces in JET The erosion and migration of first wall material gives rise to several critical plasma-surface interactions issues for ITER and for other future big and high duty cycle fusion devices. The balance between erosion and deposition at different surfaces in the device determines the net erosion rate and consequently the life time of the plasma facing component. Deposition of thick layers at some surfaces is linked with co-deposition of fuel and consequently to the tritium inventory in a reactor. The build-up of thick deposited layers also entails dust production due to subsequent breaking and flaking of the layers. Materials migration and mixing may also modify the erosion rate and other surface properties. To study these issues at JET, microscopy, ion beam analysis techniques and SIMS Figure have been frequently used for post mortem analysis of plasma facing surfaces. Figure shows a poloidal cross section of the inner JET divertor indicating positions where surface samples were taken. The surfaces are difficult to analyse due to surface roughness and microscopically non uniform composition. Different methods provide complementary information. E.g. nuclear reaction analysis from the surface (NRA) is element specific but can be difficult to quantify properly when the layer thickness or variations in depth distributions of elements are comparable to the accessible depth Figure

22 Proton backscattering is less elementally specific but has larger accessible depth. SIMS has good spatial resolution but is very hard to make quantitative. Analysis from the side of cross sections of deposited layers is necessary to fully characterize layers thicker than about 20 µm. Figure shows an example of how elemental mapping with NRA of cross sections from the side compares with broad beam SIMS from the surface. The layers were from position 3/2 and had been deposited in and in The dashed lines indicate the interface between carbon CFC substrate and deposited layers. The NRA maps of deuterium and beryllium are quantitative within the limits of the spatial resolution of about 10 µm, the nickel maps are quantitative up to a constant factor. The SIMS profiles on the right hand side however are clearly not quantitative, either in terms of depth distribution or comparison between elements; they do however provide qualitative information with better spatial distribution in the depth direction. Figure Figure shows NRA maps of the deuterium distribution at a surface at position 3/8 after exposure through The proton spectrum in panel a) allows a separation of surface deuterium (depth < 15 µm, panel b) from deeper deuterium (panel c). Overlaying with a SEM image from the same region clearly shows that surface deuterium is largely concentrated to cracks and pits at the surface, while deeper deuterium is also associated with buried, hidden structures. The close up in panel d shows a half buried particle, which is rich in deuterium. It also shows an example of the typical elongated structures at the surface, indicating that columns have grown in systematic directions, which can be related to the direction of incident ions at the surface. Careful quantification based on a combination of analysis methods, as well as good microscopic spatial information is necessary for accurate determination of the overall amount of fuel trapped at the plasma facing surfaces. The detailed spatial information related to surface roughness and other effects is also helpful in understanding the 22

23 processes of fuel trapping. It is also highly relevant for the assessment of in situ fuel removal methods A 10 Be marker experiment on beryllium migration in JET An isotopic marker experiment has been designed to study the migration of beryllium from the main chamber to the divertor in JET with ITER-like wall. One of the beryllium tiles at the inner wall in JET has been enriched with 10 Be through irradiation with thermal neutrons in a fission reactor. The tile was installed in JET in 2011 and exposed to the plasma throughout the first period of operations with ITERlike wall. Figure shows a numerical simulation predicting the 3D large scale redistribution of the marker using the ASCOT code, with a particular set of Figure assumptions. Using the extremely sensitive accelerator mass spectrometry (AMS) method, the 10 Be content in re-deposited beryllium layers all over the JET can be investigated after the first JET shut down in summer 2012, down to five orders of magnitude dilution with respect to the primary marker tile. Several numerical models exist for the materials migration and mixing problem in JET with ITER-like wall and the marker experiment is designed for comparison with the numerical models. Figure shows a representation of the inboard wall in JET, with the 16 vertical beams of inner wall guard limiters (IWGL). The marker tile position is indicated with a cross and the red line shows the direction of a typical magnetic field line at the plasma boundary. 23

24 Figure The yellow arrows show tiles that were permanently removed for post mortem analysis after the first period of operations with ITER-like wall. However, for more complete information it was necessary to sample also IWGL tiles that had to go back into JET. A method to do this was developed and figure shows the first AMS analysis results from the IWGL. The coloured spots show the measured areal densities of 10 Be within the sampling depth of about 4 µm. The blue spots show samples that were not yet analysed in For comparison the data are compared with an ASCOT simulation of the expected spatial distribution function for deposited 10 Be at the JET surfaces during the limiter phase, given certain assumptions. There is qualitative agreement e.g. in the right/left asymmetry above the mid plane at beam 2X and in the vicinity of the source tile in 5Z. Quantitatively though, a large fraction of the estimated total amount of eroded 10 Be is missing at the IWGL. Further analysis and modelling is clearly necessary to draw any definite conclusions. The most relevant modelling can be obtained with ASCOT (a 3D code for impurity transport, not including any modelling of the erosion and other surface processes), WallDyn (a 2D code including detailed modelling of surface processes and materials mixing at the surfaces) and ERO (a 3D code focusing on local erosion and deposition). AMS analysis of the 2012 samples is being completed in 2014 and a second set of samples is expected to be collected in the JET shut down in fall

25 2.4. Theoretical fusion plasma physics T. Hellsten, T. Johnson, A. Hannan (PhD student), J. Höök (PhD student), Q. Mukhtar (PhD student), S. Tholerus (PhD student) In collaboration with CEA, CCFE, IST, TEKES, CRPP, ENEA associations The theoretical fusion plasma physics group is focused on studying wave-particle interactions relevant for fusion experiments, in particular for heating, current drive and excitation of waves by fast particles. The group is particularly active in developing numerical models and codes for studies of ion cyclotron resonance heating, ICRH, and in validating them against experiments. This work is well integrated into the European fusion program through participation in: the Integrated Tokamak Modelling Task Force, and the exploitation of the JET facility. The three main codes developed by the group are PION, FIDO and SELFO. PION was the first self-consistent code for modelling ICRH and NBI heating using a model for the power deposition and solves a simplified Fokker-Planck equation for the distribution function. PION has become the standard code for routine simulation at JET. The Monte Carlo code FIDO calculates the distribution functions of the resonant ion species taking into account effects caused by finite orbit width and RF-induced spatial transport due to absorption of the momentum of the wave. The SELFO code calculates the wave field, using the LION code, and the distribution function, using the FIDO code, self-consistency is obtained by means of iterations. The FIDO code is being upgraded to include interaction with MHD waves allowing self-consistent studies MHD modes during ICRH; at the moment by using simple models of the MHD-modes. A new code, SELFO-light, for routine simulation to be used as an ITM tool and for analysing JET experiments is being developed ICRH scenarios for DEMO and the SELFO-light code The SELFO-light code is ICRF code that couples a particle description (a Fokker- Planck solver) and a wave solver [T. Hellsten et al 2013 Nucl. Fusion ]. The code is less advanced than e.g. SELFO, but significantly fast, which makes it suitable for rapid analysis, parameter scans and long pulse modelling. Both SELFOlight and SELFO use the global wave solver LION for calculating the wave field, which is based on finite element, see figure A problematic issue in modelling wave propagation in plasmas is the spatial dispersive effects. New methods suitable for FEM codes to include have been developed to take into account these effects. 25

26 Figure Comparison of ICRF wave field in reactor size plasma (to the left) and the type of wave field common in today s machines (to the right). The higher temperatures, densities and plasma dimension of a reactor plasma changes the character of the wave field from an ergodic field to a beamlike wave that is absorbed in the plasma centre. The SELFO-light code has been used to identify the most suitable ICRF current drive scenarios for DEMO [A. Hannan et al 2013 Nucl. Fusion ]. It has been found that due to the strong damping by alpha particles only four wave frequency regimes are available in ITER. For each of these frequencies the optimum toroidal mode number has been identified, which restricts the design on the geometry of the ICRF antenna. It has been shown that the optimal mode number appears where the phase velocity being around 1.23 times the thermal velocity Integrated Tokamak Modelling Task Force The group participates in the Integrated Tokamak Modelling Task Force, where Thomas Johnson is Deputy Project Leader for IMP5; the integration project for Heating, Current Drive and Fast Particle Effects (previously lead by Torbjörn Hellsten). During 2013 the main contributions have been in the further development of the ITM infrastructure, in the integration of heating and current drive codes into the European Transport Solver (ETS), in the adaptation of heating codes to the ITM framework and the development of advanced Fokker-Planck models. The work has resulted in the publication [G.L. Falchetto et al 2014 Nucl. Fusion ]. IMP5 infrastructure The developments of the heating and current drive specific infrastructure (IMP5 infrastructure) has during 2013 has been focussed the porting codes and workflows to the new version of the data model, 4.10a, and the development of generic tools for handling machine parameters within ITM workflows have been implemented. In addition technical tools for e.g. automated actorgeneration have been implemented and automated transformation of name lists into xml-files, schemas and FORTRAN interface. Heating and current drive workflow The workflow for heating and current drive, IMP5HCD, has been upgraded to use all available actors in 4.10a. This development has enabled both advanced and rapid modelling of NBI heating by selecting different codes (actors) and multiple alternative EC codes within the workflow. As a result the workflow now works as a standard module in both the ETS-A and ETS-C workflow, including EC, NBI and alpha sources. 26

27 RFOF library for RF modelling in orbit averaged Monte Carlo codes. The work on RFOF has continued and the library is now part of two orbit following Monte Carlo codes, ASCOT (TEKES/Finland) and SPOT (CEA/France). The coupling to ASCOT has been developed in collaboration with TEKES Collaboration and exploitation of JET While the group has not participated in any JET experiments during 2012, the group have still been active in the analysis of JET data. Modelling for ICRF control of sawtooth instabilities During 2013, experiments on ICRF control of the sawtooth instability in H-mode plasmas. The group participated in these experiments and performed extensive ICRF modelling using the SELFO code. The work resulted in the publication [Graves et al, to be published in Plasma Physics Controlled Fusion]. Non-linear stabilisation of tokamak micro-turbulence by fast ions Using fast ion profiles from SELFO along with the gyro-kinetic code GENE previously unexplained improvement of confinement has been explain through a non-linear mechanism involving the fast ion pressure gradient, see figure The results extrapolate favourably for a reactor operating in an advance tokamak configuration [Citrin et al, 2013 Phys. Rev. Lett. 111, ]. Figure 2.4.2: Comparison of nonlinear GENE simulations and experimental ion heat flux measurements for the five separate discharges at ρ=0.33. The importance of the fast ion contribution is underlined by the sensitivity studies carried out for discharges and The dashed lines connect the results of the nominal and simulations with results obtained at reduced R/LTi Quasilinear versus non-linear wave particle interactions Excitation of Alfvén waves by fast particles can lead a loss of fast ion confinement and therefore to degradation of fast ion heating schemes and damage to plasma facing components. A common assumption when modelling the interaction between the fast ions and the Alfvén waves is that the long-time evolution can be described by quasilinear theory, which can be justified if the interactions are decorrelated on sufficiently short time scales. However, the collision frequency may not be sufficiently high to decorrelate the interactions to use the quasi-linear approximation. A non-linear model, suitable for describing excitation of Alfvén waves in Monte Carlo codes, has therefore been developed to study wave-particle interactions at an arbitrary rate of decorrelation. It has been found that the quasilinear model represents well the effective growth rates of the generalised model when the decorrelation time is shorter 27

28 than the bounce time of ions deeply trapped in the wave field induced phase-space island Requirements for ICRF control of sawtooth instabilities in ITER A detailed study of the power requirements for sawtooth control in ITER was performed. The study identifies that the power planned for the ICRF system is sufficient to shorten the sawtooth and thereby reducing the beta threshold for triggering NTMs. The study was performed primarily with the SELFO code, but complementary modelling using the SCENIC strengthens the reliability of the results Monte Carlo schemes for pitch angle scattering Monte Carlo techniques are commonly in plasma physics, in particular to model interparticle collisions. One component of collision process that is particularly tricky to handle is the pitch-angle scattering. Yet, most codes use a simple numerical scheme to represent the pitch angle scattering that is easy to implement. To improve on this scheme, two new schemes have been proposed. The schemes are constructed using an operator splitting technique, along with analytical solutions to equations similar to the equation for pitch angle scattering. The result is a second order scheme that has been shown to outperform the standard scheme already at very long time-steps. The scheme has been implemented in the Monte Carlo code ASCOT Monte Carlo modelling of orbit averaged equations The bifurcation between passing and trapped guiding centre orbits gives rise to difficulties in modelling collisional transport in tokamaks. To study this bifurcation a simple 2D Monte Carlo model has been developed from the orbit averaged Fokker- Planck equation. The model has a discontinuity in the diffusion coefficient at the trapped passing boundary, which is non-trivial to resolve with Monte Carlo techniques. To resolve the singularity we suggest adding an ad-hoc Monte Carlo drift term. Three alternative models for the drift term have been derived. Neither solves the problem exactly, but preserves the key properties of the exact solution of the original partial differential equation. The model has also been extended to include model Monte Carlo operators for driving the density profile to a prescribed shape. This is of important when modelling long time-scales, where the thermal particle density is obtained from experimental measurements or from a transport code. The model operator has been extended to 3D by including energy scattering. As a first step the model has been tested in conjunction with an RF-operator to model RF-heating demonstrating the importance of the evolution of the thermal particle density profile for modelling ICRH. 28

29 2.5. Computational methods for fusion plasmas J. Scheffel and A. Mirza (PhD student) In collaboration with: D.D. Schnack, Univ. Wisconsin-Madison, USA and H. Nordman, Chalmers University of Technology Our research within computational methods concerns stability and confinement of reversed-field pinch (RFP) plasma configurations as well as the development of new, time-spectral methods for solving systems of partial differential equations. In the first research area, resistive pressure-driven resistive instabilities are studied, because of their detrimental effect on confinement in the RFP. The second research area concerns a new, general method for solving problems with strongly separated time scales. A brief report on progress during 2013 follows Theoretical and numerical modelling of RFP confinement A non-linear resistive MHD numerical study of confinement improvement in the RFP using a static model for current profile control (CPC) has been performed [Scheffel 2013]. CPC has the aim of reducing current driven resistive (tearing) modes by flattening the current density profile in the centre of the plasma. It can be achieved by using RF techniques such as lower hybrid or electron Bernstein current drive. Our numerical models include the fully nonlinear resistive MHD code DEBSP as well as linear codes, with the effects of perpendicular and parallel heat conduction taken into account. By tailoring the parameters of the CPC model, an advanced mode of operation, characterized by up to a three-fold increase in energy confinement and a 30% increase in poloidal beta up to values of 0.27, is reached (Figures 2.5.1a and 2.5.1b). The edge heat flux is reduced to about a third of that in the conventional RFP case. The high-confinement phase may, however, finally be interrupted by a crash, with a rapid decrease in confinement. The power that goes into the CPC during the high-confinement phase is non-negligible although not prohibitive; it contributes to a 10 15% reduction in the confinement time in optimized scenarios. Plasma fluctuations are substantially decreased by CPC; poloidal cross section Poincare plots show less stochastic flux surfaces. Magnetic power spectra show that essentially only two unstable modes remain in the high-confinement regime; these are the (m, n) = (1, 2) and (1, 8) modes. All m = 0 modes are reduced to negligible levels. Contrary to the (1, 2) mode, the (1, 8) mode is resonant near the reversal region, where instability is shown to arise due to the combination of high pressure and a high pressure gradient. The mode is analysed using both theory and a linear full resistive MHD code based on the GWRM [Scheffel 2011, Mirza 2012]. It is found that the current profile is stable against tearing modes but that, using the traditional adiabatic energy equation, there is a significant growth of the linear (1, 8) pressure-driven resistive g-mode prior to the crash. Pressure-driven instability is also found using a delta prime model with thermal effects included in the energy equation, above a Lundquist number threshold, and for all current Lundquist numbers in the GWRM model. Stability below a critical Lundquist number is consistent with our earlier results showing that, at higher 29

30 Lundquist numbers, the heat conductivity causes linear growth rates to be only weakly dependent on the Lundquist number (Figure 2.5.2). Heat conduction effects, as applied to this model, thus do not inhibit resistive g-mode instability in reactor relevant (high Lundquist number) plasmas in the RFP; the unfavourable curvature effects are too strong. It remains to determine whether kinetic effects due to the relatively large Larmor radii in the RFP may quench the resistive g-modes in this regime. The crash obtained in the DEBSP simulations subsequently establishes a lower beta and a weaker global pressure gradient. A similar behaviour is obtained for simulations at high aspect ratios. Further studies are required to establish whether stable plasma behaviour can be obtained in the high-confinement regime using static current profile control. The required practical implementation of RF techniques such as lower hybrid and electron Bernstein current drive need also be assessed. Figure Poloidal beta (a) and energy confinement time (b) versus time (resistive time units) for aspect ratio R/a = 4 (red graphs) compared with reference (no CPC) and CPC cases with R/a = Figure Growth rate (γ) of the m = 1, n = 8 mode versus resistivity (1/S0) for t = 0.54 obtained by the model. 30