Physics | Flexibility » Valisa-Agostini-Alonso - The Value of Flexibility, The Contribution of RFX to the International Tokamak and Stellarator Programme

Source: http://www.doksinet EXP/P3-11 The Value of Flexibility: the Contribution of RFX to the International Tokamak and Stellarator Programme M Valisa1, M. Agostini1, J A Alonso2, F Avino3, M Baruzzo1, P Bettini1, T Bolzonella1, D Carralero2, L Carraro1, R Cavazzana1, A. Fasoli3, I Furno3, M Gobbin1, D Hanson4, S P Hirshman5, L Marrelli1, P Martin1, E Martines1, G Marchiori1, B. Momo1, R Paccagnella1, P Piovesan1, L Piron1, M E Puiatti1, A Scaggion1, P Scarin1, S. Spagnolo1, G Spizzo1, M Spolaore1, D Terranova1, C. Theiler3, N Vianello1, P Zanca1, B Zaniol1, L Zanotto1 , M Zuin1 1 Consorzio RFX, Associazione EURATOM-ENEA sulla Fusione, Padova, Italy EURATOM-CIEMAT Association, Madrid, Spain 3 CRPP –EPFL, Association EURATOM-Suisse, Lausanne, Switzerland 4 Auburn University, Physics Department, Auburn, AL, USA 5 ORNL, Fusion Energy Division, Oak Ridge, TN, USA 2 E-mail contact of main author: marco.valisa@igicnrit Abstract This paper highlights the contribution of RFX-mod

Reversed Field Pinch to the wider fusion science program. This is done by illustrating some of the issues that tackled in the Reversed Field Pinch configuration find strong commonalities in Tokamak and/or Stellarators, and describing the direct cross configuration studies carried out on RFX-mod. The RFP has an intrinsic helical nature in the core which makes it an excellent test bed for the validation of Stellarator tools for equilibrium reconstruction. RFX can also be run as a circular low current Tokamak, which has been experimented down to sub q=2 equilibria in a stable way. Non circular shapes are being sought as well. RFX has unique capability of studying 3D physics, including details of turbulent structures at the edge, whereby ideas for possible control of the universal edge filamentary structures have been envisaged. Expanding the parameters space and tackling basic physics issues is the way the flexible RFX-mod device is contributing to secure the track towards ITER and DEMO.

1 Introduction The highest priority of the fusion program worldwide is participation in the international ITER experiment which is based on the Tokamak concept. The burning plasma of ITER represents an intirely new regime that none of the current experiments can explore, whith a large portion of the sustaining power that is self-generated by the plasma through fusion reactions and the liason between micro, meso and macro-scale physics that is expected to be largely modified by the presence in the phase space of a significant population of fast particles [1]. In the same time it is widely recognized that several issues of relevance to the demonstration reactor will not be completely solved by ITER. What will be the most suitable operation scenario for DEMO is for instance still matter of debate. To assure the exploitation of ITER and secure the development of a demonstration reactor it is important that the possibility to pursue basic research and expand the experimental parameter space

is maintained, in order to increase the chances to find novel solutions to the many unresolved problems. In this paper we wish to concentrate on the contribution that RFX-mod, the largest Reversed Field Pinch in operation, has given in the recent past to the fusion science program by conceiving research plans in which the potential of the experiment is exploited to tackle urgent physics and technological issues of general interest. Such direction has been facilitated by the particular characteristics of flexibility of RFX-mod. Flexibility refers first to the possibility for RFX to perform cross-configuration studies by making direct comparisons with both Stellarators and Tokamaks. With Stellarators because of the intrinsic helical nature of the Reversed Field Pinch equilibrium and with Tokamaks because RFX can be run also as a low current Tokamak. However, flexibility reflects here also the possibility for RFX to Source: http://www.doksinet EXP/P3-11 perform a number of experiments

on 3D physics that are of general interest, particularly thanks to its state-of-the-art equipment for magnetohydrodynamic (MHD) mode control [2]. Considering the equilibria of the three major configurations explored in magnetically confined fusion, Tokamak, Stellarator and Reversed Field Pinch (RFP), the safety factor profile of the RFP lays below all of the others, with q well below 1 and reversing its sign at the edge. This is exemplified in Fig 1 where the q space covered by the various configurations is schematically shown. One may notice how RFX expands the region of the explorable q by running as a RFP, as Tokamak capable of a low q operations, and Fig 1. Schematic of the region of the as a Ultra Low q [3]. If we consider the RFP as a way safety factor q explored by the three to study a hot magnetized plasma in the region of the major configurations: Tokamak parameters space characterized by low toroidal Stellarator, Reversed Field Pinch and magnetic fields at the edge, then it

may be not Ultra-Low-q. In red the contribution of RFX completely surprising that many basic physics issues addressed in the RFP (density limit, turbulent transport, 3D physics, transport barriers, MHD stability and control, etc.) find strong commonalities in both Tokamak and Stellarators. The intrinsic helical nature of the equilibrium that is reached when RFX-mod approaches the Single Helicity RFP state [4] sets a strong similarity with the Stellarator topology and establishes a robust bridge between the interests of the two communities. In particular, the use of equilibrium and transport analysis codes developed for the Stellarator has been successfully applied to the RFP, so that the same tools can now be adopted to analyze the three main configurations. A direct contribution to the international Tokamak programme derives from the possibility to run RFX-mod as a low current ( up to 150 kA) Tokamak. RFX has shown that with its flexible MHD feedback control system the equilirium of a

Tokamak can be streched in a stable way to values of q well below 2, thus widening the parameter space usually covered by nowadays experiments with consequent potential improvement of confinement and or economical convenience. The flexibility of RFX has aroused lively interest in the scientific community and has led to important collaborations with laboratories worldwide (JT60-SA, DIII-D, AUG, PPFL, PPPL, Auburn University, ORNL). In the following the contribution that RFX-mod has provided to the Tokamak and Stellarator programmes is reported with an emphasis on three main aspects and some common physics issues: the contribution resulting from the experience of RFXmod run in the Tokamak configuration, the experience gained adapting Stellarator analysis tools to the RFP and the deep commonalities found in the intimate nature of turbulence at the edge of RFX, which has been compared to that of both Tokamaks and Stellarators. We will notice how 3D physics is a common denominator of the

various aspects that will be analysed. 2 RFX- mod run in the Tokamak configuration 2.1 Low q operation RFX can be run as a low current ( maximum toroidal field = 0.55 T ), 1 s long , circular cross section, high aspect ratio, ohmic Tokamak. One of the most interesting results is that the possibility to control MHD modes, in particular the (2,1) mode, has allowed exploring equilibria down to qcyl(a) of 1.6 Fig2 shows an example of Tokamak discharge with q at the edge below 1.8 Source: http://www.doksinet EXP/P3-11 In absence of active feedback control the (2,1) current driven Resistive Wall Mode (RWM) grows exponentially on the resistive shell time constant ( penetration time of the vertical field is 50 ms) when qcyl(a) is still above 2. Active feedback control instead suppresses the mode completely for the entire duration of the pulse. A necessary condition for the successful mode control is the removal from the radial field measurements of the aliasing of the vacuum sidebands

harmonics generated by the feedback coils placed outside the conducting shell [5]. It is important to notice that, instead, such suppression was not necessary in the RFP configuration for stabilizing RWM [2]. The relevance of this finding is that the stabilization of the RWM can be performed with radial field sensors, provided that Fig. 2- Example of current (top) and q(a) the feedback is in Clean Mode Control. These (bottom) in a Tokamak RFX plasma pulse. sensors in fact offer the tecnological advantage to allow an arrangement outside the plasma facing structures, while the more generally poloidal ones, though less affected by sideband pollution, need to be placed in front of the plasma. Let us also recall that Clean Mode Control is superior compared to the Plasma Response or Explicit Mode Control when applied to radial sensors [6]. Experiments in this configuration as well as the comparison between sideband cleaning and plasma response with poloidal sensors are part of the future

programme, where testing the experimental verification of the feedback laws for RWM control will continue. Thanks to the flexibility of the active MHD control system, for the first time, the effect of different reduced sets of correction coils have been tested on the same target plasma. Active control of RWM in RFP configuration and control of the 2/1 RWM in the tokamak configuration have been experimented using less and less number of coils instead of the full machine coverage [5]. Mode stabilization has been obtained with a very limited number of active coils, although in the most extreme cases severe degradation of the plasma performance may occur due to the control sidebands harmonics. The results suggest that tokamak operation at low q-edge is possible with the use of an active coils number comparable, but not equal, to the spatial periodicity of the controlled mode. 2.2 Non circular plasmas In view of expanding the above exercise to plasmas with different shapes, and in

particular with an internal X point, the possibility of producing non circular plasmas has been explored and high a triangularity plasma with double null has been produced. Fig. 3 shows a MAXFEA reconstruction of the plasma equilibrium in one of the attempts to reach a double null configuration. This has been obtained by reversing the current in two of the 8 couples of field shaping coils, with each couple of coils connected in series to assure a top-bottom symmetry ( see Fig. 4) The exercise, of preliminary nature, required the implementation of a new horizontal Fig 3 – MAXFEA equilibrium reconstruction of a RFX-mod Tokamak plasma with double null. Source: http://www.doksinet EXP/P3-11 Fig. 4 Current direction in the field shaping coils for Double Null plasmas. Colors represent different direction of the current in the coils. position controller that basically incorporates the possibility to add a current distribution over the field shaping coils to the usual feedback

controller of the horizontal shift. Success in estabilishing a stable double null or a single null equilibrium could open the way not only to experiment low q regimes in non circular plasmas but could also facilitate the access to an ohmic H mode, with the possibility of important studies on ELM’s control. The absence of an active pumping divertor could be compensated by wall conditioning techniques such as liquid lithium coating. Toroidal flow (km/s) 2.3 Non resonant perturbation and flow The flexibility of the mode control grid of saddle coils has been applied also to the important studies on the effects of resonant and non resonant magnetic perturbations (NRMP) both in RFP and Tokamak plasmas. Non resonant pertubations, like any symmetry-breaking sources or error fields, can produce torques on the plasma via the generation, for instance, of neoclassical toroidal viscous forces (NTV) proportional to the square of the relative amplitude of the non-axisymmetric fields [7]. This is

of relevance because in both present and future devices magnetic field errors of the order of 10E-4 may be inevitable and also because plasma rotation in tokamak plasmas has beneficial impact on confinement and stability by shielding resonant magnetic field perturbations, stabilizing Resistive Wall Modes and reducing transport. Spontaneous torques are of particular interest because they may induce toroidal rotation and the beneficial avoidance of locked modes even in absence of beam injection. Experiments of flow breaking have been carried out in several tokamak experiments ( DIII-D, NSTX, JET and MAST ]. On RFX-mod tokamak plasmas we have studied magnetic flow breaking during the application of m=2, n=1 non-resonant magnetic field perturbations of various amplitudes in discharges with q(a) below 2. An example of the experimental evidence is shown in Fig 5 where the velocity of hydrogen-like carbon is plotted as a Including NTV+stochasticity function of the perturbation normalized

amplitude. Including NTV Application of the perturbation reduces the Including stochasticity spontaneous flow in the counter current direction Unperturbed solution and eventually reverses it in the co-corrent direction. Preliminary considerations suggest that Co-IP the experimental evidence can be explained assuming that in the 1/ν collisional regime of RFX-mod a NTV torque [8] and especially a torque due an ambipolar electric field in the Counter-IP plasma edge due to a region of stochastic magnetic field 9] are present. Indeed visco2,1 Br amplitude / BT(a) resistive MHD simulations done with the Fig 5 . Black sympbols: toroidal flow of PIXIE3D code [10] show that in presence of the hydrogen-like carbon as a function of the (2,1) NRMP the plasma edge becomes stochastic. applied m=2, n=1 mode amplitude. Color Fig. 5 shows how the inclusion of the stochastic curves: solutions of the momentum balance equation including torques as in the legenda term well reproduces the experimental data

[11]. Source: http://www.doksinet EXP/P3-11 2.4 Density limit An important subject that is relevant in all of the configurations and in which the contribution of the RFP can be significant is that of the maximum operational density which is experimentally found not to exceed the so called Greenwald limit in RFP‘s and Tokamaks [12]. Stellarators appear to have instead a much higher threshold, the Sudo limit, which is clearly an edge density limit [13]. The reason for this picture is not clear yet, however recent developments have shown some interesting commonalities between the RFP and the Tokamak phenomenology regarding the role of 3D fields on the onset of precursors of the density limit. In RFX-mod a (m=0, n=1) mode resonating near the wall breaks the toroidal symmetry and a convective cell produces a density peaking near the wall with the same (m=0,n=1) structure [14]. The edge convection is driven by edge radial electric fields which are space modulated by the plasma wall

interaction and the related alternation of ion and electron dominant losses. The picture is corroborated by 3D measurements of the electric potential, which has been shown to be well correlated with the magnetic perturbations. The analogy is in particular with MARFEs (density limit precursors observed in Tokamaks) but extends also to the ambipolar electric field formation due to a modification of the electron to ion diffusion ratio following the use of MPs [15] to suppress ELMs. 3. 3D Physics The RPF is a configuration that relies on internal self-generated currents to build and sustain the toroidal flux and the whole system is externally driven by applying a toroidal loop voltage. The toroidal field at the edge reverses its sign with respect to the core. The main practical consequence of this peculiarity is that the toroidal magnetic field to be provided by external coils is small, of the order of tens of Fig. 6 Reconstructed 3D core and egde mT, against the several T of the Tokamak

Equilibrium of RFX-mod in a Quasi Helicity. configuration, with enormous simplification of case. The grid of 192 external correction coils is also plotted the toproidal circuit and also much less severe consequencwes in case of plasma disruptions. The dynamo mechanism that converts poloidal into toroidal flux in advanced RFP relies on the QSH state, that follows the development of one MHD mode (in RFX-mod the m=1, n=-7) that grows at the expense of all of the other modes to the point that the plasma core is helically shaped with conformal thermal and, following pellet injections, density structures. When the separatrix of the associated island is expelled the original O-point becomes the new toroidal and helical axis of the plasma [16]. The edge remains quasi symmetric, with reminiscences of the large core deformation. Fig 6 shows the structure of the (1,-7) mode in the plasma core during a QSH and the quasy symmetric last closed magnetic surface. The onset of this helical state

breakes the axial symmetry and leads to the necessity of providing a 3-dimensional description of the equilibrium for a correct comprehension of the experiments, based on direct available measurements. The 3D codes already developed to predict the behavior of the MHD modes in the RFP [17] are not suitable to decipher the experimental situation of many plasma pulses. The equilibrium reconstruction determines the internal magnetic surfaces, Fig. 7 - q profile evaluated by VMEC in a Single Helicity equilibrium case. the current density and magnetic field and pressure Source: http://www.doksinet EXP/P3-11 profiles, which must satisfy the time dependent MHD equations. An in-house equilibrium reconstruction code SHEq that neglects pressure has been developed [18] but it has been spontaneous to look at the Stellarator community and to their mature, fully 3D suite of codes. In turn, the exercise of describing the RFX-mod equilibrium represents a good test-bed for those numerical codes

conceived to deal with 3D effects in Stellarators and Tokamaks. Also in Tokamaks 3D physics has become increasingly important for the description of the physics of external magnetic perturbations or MHD phenomena like the so called snakes [19]. The equilibrium codes VMEC and V3FIT [20] imported from the Stellarator community have been successfully adapted to reconstruct RFX-mod equilibria with the inclusion of diagnostics [21] and these equilibria have been used to perform stability and transport analysis [22]. VMEC is the equilibrium solver and V3FIT minimizes the difference between modeled and available experimental signals in presence of a prescribed boundary magnetic surface, although VMEC and V3FIT can deal with free boundary conditions. The choice for the fixed boundary condition implies that all the fields outside the last closed surface are generated by internal currents and imposes the independent computation of the fields generated by external structures for a correct

comparison with the magnetic signals, which are collected outside the magnetic boundary. The RFX-mod equilibria reconstructed in such a way show a good agreement with the results of SHEq, but providing also information on the role of pressure, neglected in the latter code. The inclusion of diagnostics besides the magnetic probes, especially the ones providing profile information such as the multipoint Thomson scattering for the electron temperature and multi-chord interferometer for the electron density, reduce significantly the equilibrium degeneracy. Also Soft X-ray emissivity has been considered. It has been shown that the assumption that the thermodynamic quantities Te, ne are flux functions Fig 8- Remapping of the of the thermal is already a good constraint for the reconstruction, plasma content after equilibrium although the use of the full profile assures the most reconstruction based on a pressure profile consistent with experimental robust result. Fig. 7 shows one example of

the q profile measurements In the corner, the 2D equilibrium and the Thomson scattering reconstructed by VMEC in a case of Single Helicity. laser path. The safety factor has a non monotonic radial profile and the presence of a maximum where usually a strong thermal barrier develops [23]. Fig8 instead shows the remapping of the electron temperature profile on the equilibrium reconstruction by V3FIT carried out using as a constraint a pressure profile consistent with experimental electron temperature and density. The inclusion of more constraints in V3FIT such as the thermal content profiles or a local q measurement from MSE is ongoing to further increase the reliability of the magnetic equilibrium evaluation. 4 Fig 9 Conditional average potential and current perturbations associated to blobs at a time scale corresponding to 250 kHz (black) in a RFXTokamak discharge. Edge turbulence in RPF, Tokamak and Stellarator The plasma edge of magnetically confined plasmas is accessible in a

relatively simple way by a number of diagnostics that can measure local magnetic and electrostatic fluctuations. Source: http://www.doksinet EXP/P3-11 There the granularity of the plasma has been identified in great detail, with 2D and 3D reconstructions in order to study the intimate nature of energy and particle transport. RFX offers the possibility to study the coherent structures that emerge at the edge of the plasma both in RFP and Tokamak configuration in the same device, as well as to investigate the effect on those structures of 3D fields that at the edge accompany the presence of large helical core deformation during the single helicity states of the RFP. Magnetic field-aligned filamentary structures appear at the edge of all of the configurations: an associated parallel current density and a vorticity represent their electromagnetic and electrostatic nature, respectively. Similar current carrying filamentary structures have been found also in ASDEX Upgrade in type I ELMs

events suggesting that a better knowledge of their characteristics could suscitate ideas for ELM suppression or mitigation [24]. In the RFX experience the driving mechanism of the filamentary structure, which is the seed that generates a charge separation from which the structure develops has a drift kinetic Alfvén origin. In the Tokamak configuration, small scales current filaments have also been found (an example is given in Fig 9) but the nature of the instability at their origin has still to be singled out. The Drift-Kinetic Alfven footprint of the structures in the RFP consist in the fact that parallel vorticity and parallel current are in phase, together with the evidence that the measured perpendicular velocities are consistent with the Alfven velocity fluctuations induced by the magnetic perturbation that accompanies the current carrying filament. Interestingly, same measurements carried out on the TORPEX experiment have shown that in a simple magnetized toroidal plasma, blobs

are originated by ideal interchange waves. In the last case, for the first time, the cross-field map of the parallel current density in the filaments has been revealed. Regardless of the driving mechanisms, in all of the configurations the filamentary structures show very similar charatcteristics. Taking advantage of the multi-experiment database however, a more general picture can be drawn by putting together the various measurements and observing their dependence on certain local parameters [25]. In this respect similar studies carried out on the TJ-II Stellarator device, where a range of plasma beta can be explored have Fig. 10 Vorticity peak of coherent been particularly useful. One can draw the conclusion structures vs local average E × B flow for instance that the ExB shearing rate influences the shear in various devices intensity of vorticity, in particular of its parallel component: the higher the shearing rate the larger the vorticity, as shown in Fig 10. The intensity of the

parallel current associated to the structures, normalized to the magnetic field, appears instead to increase with the electron beta (Fig.11) The higher the electron beta, the higher the parallel current. One important experiment carried out on RFX suggests that the filamentary structure could in the future be controlled, to some extent [25]. As Fig. 11 δJ///B0 vs local electron beta in mentioned above, in presence of a helical perturbation various devices. of the core also the properties of the edge manifest a helical pattern. In particular flow, pressure gradient and the connection lengths at the edge have a helical modulation, well correlated with the local plasma wall interaction. Inducing artificially the rotation of the helical deformation of the plasma in the RFP configuration it has been possible to measure the characteristics of the coherent structures in relation to the position of the perturbation. In particular it has been seen that the higher part of both current Source:

http://www.doksinet EXP/P3-11 and vorticity frequency spectra are helically modulated, suggesting therefore that external means can interfere and possibly control the quality of the filamentary structures. Final considerations RFX has oriented in an integrated way its experimental and theoretical [26] programs in order to address themes that are of interest to the general fusion community, estabilishing direct connections in particular with Tokamak and Stellarators. This has been possible in virtue of the flexibility of the experiment and in particular of the powerful equipment for 3D physics control featured by RFX. The application of Stellarator tools to describe the RFP equilibrium and the achievement of stable sub q=2 tokamak equilibria are important outcomes of such a direction. Also, a deep comparison of the role on local transport of granular structures produced by the edge turbulence has estabilished the universal similarity of the filamentary sructures in the various

configurations regardless of the driving instability, and suggested possible ways to control them, to some extent. RFX offers also the possibility to help disentangling some common issues of fusion devices such as the density limit. In summary RFX has helped expanding the parameter space explored so far in the attempt to find new solutions for a successful exploitation of ITER and a reliable design of DEMO, and keeps going on in this direction. References [1] [2] [3] [4] L CHEN, F ZONCA- Eur. Phys Lett, 96 (2011) 35001 R. PACCAGNELLA et al Phys Rev Lett (2006 )97 075001 D BONFIGLIO et al. Nucl Fus 48 (2008) 115010 M VALISA et al. Plasma Phys Control Fus (2008) & R Lorenzini et al Nature Phys (2009) 570 [5] M BARUZZO et al. Nucl Fus 52 (2012) 103001 & R Pacagnella et al Nucl Fus (2002) 1102 [6] P ZANCA et al. Plasma Phys Control Fus 54 (2012) 094004 and P ZANCA et al., "Advanced feedback control of MHD instabilities: comparison of compensation techniques for radial sensors

", accepted for pub. in Plasma Phys Control Fus (2012) [7] K C SHAING and J. D CALLEN, Phys Fluids 26, 3315 (1983) [8] A J COLE et al. , Physics of Plasmas 15, 2008 [9] M De BOCK et al., Nucl Fus 48, 2008 [10] L CHACON, Physics of Plasmas 15, 2008 [11] L PIRON et al submitted to Plama Phys. Contr Fus [12] M GREENWALD, Plasma Phys. Contr Fus 44 R27 (2002) & ME Puiatti et al Nucl Fus 49 (2009) 045012 [13] S SUDO et al, Nucl. Fus 30, 11 (1990) [14] G SPIZZO et al., Nucl Fus52 (2012) 054015 [15] Rozhansky, Nucl. Fusion 52 (2012) 054011 [16] D T ESCANDE et al. Phys Rev Lett 85, 3169 (2000) [17] S CAPPELLO, Plasma Phys. Contr Fus 46 B313 (2004) [18] MARTINES et al. Plasma Phys Contr Fus 53 (2011) 035015 [19] A WELLER, et al., Phys Rev Lett, 59, 2303, (1987) [20] S P HIRSHMANet al., Phys Fluids 26 (1983) 3554 & JD Hanson et al, Nucl Fusion 49 (2009) 075031 [21] W COOPER et al Plasma Phys Contr Fus 53 (2011) 074008 & M GOBBIN et al Phys. Plasmas 18, 062505 D [22] TERRANOVA et

al., to be submitted to Nuclear Fusion [23] M E PUIATTI et al 2011 Nucl. Fusion 51 073038 [24] N VIANELLO et al Phys Rev Lett 106 125002 (2011) [25] M SPOLAORE et al. submitted to PPCF [26] S CAPPELLO et al. “Nonlinear Modeling for Helical Configurations in Toroidal Pinch Systems”, TH/P2-16, This conf