1 Pellet fuelling of lasmas with mitigation by resonant magnetic erturbations in MAST M Valovič, G Cunningham, L Garzotti, C Gurl, A Kirk, G Naylor, A Patel, R Scannell, A J Thornton and the MAST team EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon, OX14 3DB, UK email: martin.valovic@ccfe.ac.uk Abstract. Shallow fuelling s are injected from the high field side into lasmas in which s have been mitigated using external magnetic erturbation coils. The data are comared with ideal assumtions in the ITER fuelling model, namely that mitigated s are not affected by fuelling s. Firstly it is shown that during the evaoration an is triggered, during which the amount article loss could be larger (factor ~1.5) than the article loss during an which was not induced by. Secondly, a favourable examle is shown in which ost- article losses due to mitigated s are similar to the non- case, however unfavourable counter-examles also exist. 1. Introduction In future tokamak fusion devices like ITER the frequency of naturally occurring edge localised modes (s) is exected to be low causing large modulations of the energy flux that can not be handled by the divertor. One of the techniques for active control of the frequency which has been successfully demonstrated, and is considered for ITER, is the alication of resonant magnetic erturbations (RMPs). An imortant ste in the develoment of mitigation is to test its comatibility with density control as mitigation often affects the article confinement, e. g. see [1]. In ITER, the main density control tool is likely to be the injection of frozen deuterium s from the high field side (HFS) of the lasma. First data on fuelling with mitigation by RMPs have already been collected from major tokamaks. On JET low field side s have been used to refuel lasmas with RMPs resulting in a further increase of frequency and an additional reduction of ower deosited to the outer divertor targets during s [2]. On DIII-D fuelling of a lasma with fully suressed s sometimes results in a return to y H-mode [3]. On ASDEX-Ugrade, with fuelling into a discharge in which tye I s have been suressed, some energy losses synchronous with s were observed [4]. Note that the estal collisionality is lower and deosition is shallower in the DIII-D case comared to the ASDEX-Ugrade exeriment. This aer resents the results of the first exeriments on the Mega Am Sherical Tokamak (MAST) on the interaction of HFS s with RMP mitigation. The focus is to examine the deviation from the fuelling model which assumes that mitigation is indeendent of fuelling s. 2. Pellet fuelling model Before resenting the exerimental results it is useful to define the ideal state of affairs against which the exerimental data can be comared. This model for ITER has been described reviously in dedicated aers [5, 6]. Here we resent its simlified version in which we assume that s are
2 mitigated by resonant magnetic erturbations and not by acing. This means that we are not concerned about cometition between fuelling and acing for overall article throughut. The starting oint of the model is the assumtion that we have erfect control over the frequency f. This frequency is set to the value: f = α P / δw (1) where P is the ower loss, α is the fraction of ower loss due to s [7] and δ W is the maximum energy loss er which can be handled by a divertor. For the resent ITER divertor δ W =.6 MJ so that for the standard scenario with P= 1MW the frequency is f ~ 33Hz (with α =.2 ) [6]. The next ste is to assume that the number of articles lost er, δ N, is roortional to the relative energy loss (so called convective s): δw δw δ N = N = (2) W T Here N and W are the article and energy content of lasma related to the estal resectively and T is the estal temerature. The assumtion (2) that s are conductive reresents the most unfavourable case from the fuelling oint of view. However in resent devices convective s are observed mostly at high collisionality and as the collisionality decreases significant temerature dro is observed during s suggesting that conductive loss mechanism is dominant [8, 9]. Therefore on ITER with low collisionality estal δ N / N < δ W / W is exected. Nevertheless to asses the uer limit for fuelling requirement for ITER one usually takes the case of convective s [6] so that δ N / N = δ W / W =.6. The final ste of the model is to assume a steady state situation so that the article loss by s is balanced by the fuelling rate Φ : Φ = f N = f δ N (3) Here f is the frequency of fuelling s and N is the article content. The diameter in ITER is set to 5mm ( N / N ~.3 ) so that the frequency is f ~ 8Hz [5, 6]. el N s Nmin time Figure 1. Schematics of the idealised fuelling and mitigation. Note that s and s are not synchronised and the -averaged article loss is constant (indicated by broken line). Figure 1 schematically illustrates the ideal fuelling and mitigation scenario. The density feedback system controls the density at N = Nmin. In this regime all s are equal in size. This model imlicitly assumes that s are small comared to the lasma article content which
. 26. 28. 3. 32. 34. 36. 38 5. 1 19 4. 5 1 19 4. 1 19 3. 5 1 19. 6. 4. 2. 1. 5 1.. 5. 1 1 18 9 1 17 8 1 17 7 1 17 6 1 17 3 means that the estal temerature is not modulated over the cycle ( T = const( t) ) so that the energy loss er is also constant ( δ W = const( t) ) as follows from equation (2). The situation described above reresents the ideal state of affairs: Particle and heat flux arrive to the divertor in small and equal (for each ) amounts. s and s are not synchronised. When averaged over the cycle, these fluxes are not modulated due to discrete fuelling i.e. the ost density decay is linear (dashed line in figure 1). are: The exeriment can deviate from such ideal situation for many reasons. The most likely ones s become synchronised with s Particle losses immediately after the are enhanced These effects can result in transients which counterbalance the mitigation effort. In addition these deviations can reduce fuelling efficiency and result in higher fuelling rate, if density is controlled by feedback. Higher Φ will reduce estal temerature because of the relationshi between article and heat fluxes, Φ = α P / T, if ower is fixed. Lower fuelling efficiency will also reduce the burn-u fraction of a fusion reactor. 3. Exerimental conditions The lasma used in this study has a single null divertor configuration (major radius R geo =.88m, minor radius a=.49m, elongation κ = 1.65, lasma current I = 55 64kA, toroidal magnetic field B T =.45T ). The lasma is heated by neutral beams. s are mitigated with RMP coils in an n = 6 configuration with coil current I RMP = 5.6 ka-turns (4 turns), located at the lower-outer side of the lasma. This is the best lasma and RMP setu for mitigation so far (for details see reference [1]). Pellets are injected from the to-high field side of the lasma (figure 2a). The injector roduces cylindrical s with nominal diameter and length d el = Lel = 1.3 mm 19 ( N el = 1.3 1 atoms), and velocities ~3m/s. For more details on injection see [11]. Deuterium is used for gas fuelling, s and neutral beams..5 z [m] #27355 5 a) density b) [1 19 m -3 ] [V] 4.6 D α -.5 RMP -1..5 1. 1.5 [ka] [1 18 D2/m -3 ] 1 1.6 neutrals RMP n=6.26.28.3.32.34.36.38 Time (Sec) Figure 2. (a) Plasma cross section, geometry of injection and RMP coils. (b) Tyical waveforms for mitigation and fuelling exeriment (from to to bottom): line averaged density, D α emission, RMP current and neutral density in the vacuum vessel. Plasma current I = 64kA and injected neutral beam ower P = 1.9MW. NBI
4 Figure 2b shows tyical waveforms in the exeriment. Alication of RMPs increases the frequency, decreases their amlitude and simultaneously decreases the lasma density. This density um-out is artially comensated by an additional gas uff as seen from the increased main chamber neutral gas density. Pellets are injected during the flat to of the RMP current. Gas and fuelling was used in feed forward mode based on exerience from revious lasmas. 4. Mitigated s without s To assess the effect of s on s, it is necessary to have a non- comarison. Figure 3a shows the analysis of mitigated s without, using a fast interferometer signal. The frequency is f = 25Hz. The waveform of line integrated density nl shows two very clear breakin-sloe oints during an [12]. This suggests that the article losses occur during the well defined time interval. Good temoral localisation allows evaluation of the number of articles lost er 19 2 : δ ( nl) ( nl) = 3.2% ( nl= 3.6 1 m ). The article loss associated with s without s is then: 2-2 -1 Φ noel fδ nl = (4), ( ) 2.9 1 m s Figure 3b shows the Thomson scattering rofiles taken just before and after the s in figure 3a. Such measurement is enabled by oerating this diagnostic in burst mode. It is seen that the radial extent of the affected area is δ r a ~.18. In this aer we concentrate only on fuelling asect of the mitigation roblem and by size we mean the article loss and not the energy loss. Plasma used as a target for fuelling in this work is art of a larger dataset of lasmas with RMP mitigation on MAST. This dataset is described in the secialised aer [13] which includes detailed analysis of energy loss er and its arametric deendencies. Here we restrict ourselves only to showing the changes of electron temerature and electron ressure rofiles during the s (figures 3c and 3d). It is seen that the relative dro of electron density and electron temerature are comarable and both contribute to the energy loss.
5 nl [1 19 m -2 ] #27351 3.7 3.6 3.5 5 a) n b) e [1 19 m -3 ] 4 3 2 D α [a.u.] 1.34.36.38.31.312 time [s] 1.25 1.3 1.35 1.4 1.45 T e [ev] 5 4 3 2 1 3 c) d) e [Pa] 25 2 15 1 5 1.25 1.3 1.35 1.4 1.45 1.25 1.3 1.35 1.4 1.45 Figure 3. The size and affected area of s mitigated by RMP. (a) line integrated density nl from fast interferometer, D α emission and vertical lines showing the timing of Thomson scattering. (b) electron density, (c) electron temerature and (d) electron ressure rofiles from Thomson scattering before (red-solid line) and after (blue-dotted line) the s. 2 s are overlaid. I = 64kA, P NBI = 1.9MW. Interferometer and Thomson scattering measurements are taken along the major radius with vertical offset of z=.27m relative to the magnetic axis. 5. Pellet - synchronisation The first ossible deviation from the fuelling model resented in section 2 is the triggering by s. Figure 4 shows the data from 5 s on a relative time scale. Figure 4a shows the increment of interferometer signal ( nl) during the evaoration and deosition. This rocess lasts δ t el =.8 1.6ms. Figure 4b shows the D α emission from the lower outer leg of the divertor which is sensitive to s but not to the light from the evaorating. It is seen that for each there is an inside the time interval of evaoration. A closer look shows that the s are synchronised not with the beginning, but with the end of the evaoration rocess. Because the frequency in ITER is about 5 times larger than the frequency, the extra s triggered by s increase the frequency by 2% and thus should not cause a significant roblem. This however assumes that the triggering of an by the is not increasing the size. Direct measurement of the article loss due to the triggered is comlicated by the fact that the density rofile during evaoration is 3 dimensional due to the existence of an intense local article source from the. This is illustrated in figure 4c showing clear in-out asymmetry in the density rofiles during the deosition. The effect of the is clearly seen from the difference between re- and ost density rofiles at the outer art of the
6 lasma (shaded area in figure 4c). The change in the line integrated density due to the at the 17 2 outer art of the lasma is δ( nl) = 8.3 1 m. This is 1.5 times larger than for an, outer without the shown in figure 3b illustrating that the triggered s could be associated with larger article loss comared to non- s. Note that the affected area at the outer art of the lasma, δ r / a ~.15, is aroximately the same as for the non- in figure 3b so that the difference is due to the amlitude. As already mentioned a recise evaluation of article loss is comlicated due to the 3D character of the loss rocess. In this context it is interesting to note that the 3D erturbation (over-ressure bum ) caused by has been observed during -trigged s on JET [14] and it is also reroduced in MHD modelling [15, 16]. Finally note that the size of the deosition area is about rel / a ~.3, which is similar to that exected in ITER [17, 18]. (nl) [1 19 m -2 ] 1..5.2 D α 27355 27816 28241 28244 28245 s TS a) b) #27816 n e 1.95ms.65ms [1 19 m -3 ] c) 8 6 4 [a.u.].1 -.65ms 2-3 -2-1 1 2 3 relative time [ms].4.5.6.7 1.3 1.4 Figure 4. Synchronisation of s and s. (a) increment of interferometer signal ( nl) during the s. (b) D α emission from lower outer divertor target. (c) Density rofiles for one shot marked by squares on ( nl) and D α traces at times indicated by markers in anel (a). 6. Post- article losses The second assumtion of the idealised fuelling model shown in section 2 is that the ost losses occur due to s of constant size and frequency which are the same as for mitigated s without s. Figure 5 shows the first examle when these assumtions are not satisfied. It is seen that immediately after the the density decays 4.8 times faster than the ideal rate calculated for a non case in eq (4). This fast article loss is caused by a comound, i.e. an followed by a transient L-mode-like hase. The evolution of the density rofile during this hase is shown in figure 5b. It is seen that the area affected by raid article loss encomasses the whole deosition zone. It is also noticeable that the rofile evolution comrises mainly outward loss and virtually no inward diffusion. The corresonding article flux Γ / ne can be estimated from the R continuity equation Γ ne ~ 1 ne n e tdr, where the time derivative is evaluated by ne t from two subsequent density rofiles during the density decay and the source term due to gas is omitted. The magnitude of this article flux Γ / ne is shown in figure 5b. It is seen that the eculiar feature of the outward article loss in the zone with ositive density gradient ( R= 1.2 1.28 m ) can be exlained by a convection with a velocity of ~ 3m/s. In the zone with conventional negative
7 density gradient (say at R = 1.34m ), the article flux is Γ / ne ~1m/s. If this flux is fully attributed 2 to diffusion then the coefficient is D ~ 1.5 m /s ( Ln = 1/ R ln ne ~.15m ). The reason for this in out asymmetry of ost transort is not known. This effect could be imortant for fuelling of next ste devices and therefore it needs to be understood. For comleteness figure 5a shows temoral evolution of the lasma energy W determined by equilibrium reconstruction. At the onset of -triggered comound a small dro of W can be observed but the main effect is the change in sloe in temoral evolution of W ( t ). Small change in W during ost- density decay is consistent with the observable increase of electron temerature measured by Thomson scattering. In this context it is useful to note that initial density losses due to s (so called first filament ) can occur even without triggered [14, 15, 16]. W 5 [kj] 4 Figure 5. (a) Change in line integrated density ( nl), D α emission and the lasma energy W (blue 19 2 solid line) for shot with and mitigated s. The density offset of nl= 3.4 1 m and the time offset of.3218s are subtracted. Broken line is the decay rate without from equation (4) and dotted line is 4.8 larger than this rate. (b) Density rofiles at times shown by markers on anel (a). Broken line is the normalised article flux Γ n. I = 6kA, P = 3.6MW. / e The second examle shown in figure 6 reresents a favourable situation where the ost losses are similar to the ideal fuelling model. The size and frequency of the s have not changed significantly (~2%) due to the as seen from the traces of line integrated density, D α emission and the lasma energy W. The averaged ost- density decay is aroximately linear and is similar to that calculated from mitigated s without s in equation (4). Density rofiles are not available for this, however, a bremsstrahlung image shows that the evaoration zone is rel.85a (figure 6b). This is similar to deosition in ITER and shows that the favourable ost- behaviour is not the result of dee enetration. This is the closest scenario to that exected in ITER which has been obtained on MAST so far in terms of similarity of / ratio and ost density decay. The reason for the difference in the examles shown above is not well understood. Both lasmas have identical RMP current and configuration, identical heating ower, similar shaes and similar densities and sizes. The most significant difference is that the favourable examle has somewhat lower lasma current comared to the unfavourable case. It should be noted that in the unfavourable examle (figure 5), comound s are resent also before the. Nevertheless, during these s, the density decay rate is not significantly higher than redicted by the ideal case as seen in figure 5a about 7 ms before the. NBI
8 In all analysis we have ignored the article source from gas fuelling. The imortance of this term in our lasmas is clearly seen from the sontaneous increase of lasma density during the inter H-mode hases in examles shown in figures 3 and 5. An evaluation of the gas sources requires 2D simulations in order to account for the oloidal modulation of neutrals around the lasma. Such an analysis is outside the scoe of the resent aer and is lanned in the future. W 5 [kj] 4 Figure 6. (a) Change in line integrated density ( nl), D α emission and the lasma energy W 19 2 (blue solid line) for shot with and mitigated s. Density offset of nl= 3.9 1 m and time offset of.3668s are subtracted. Broken line is the decay rate without from equation (4). (b) oen shutter visible bremsstrahlung image of the. The contour labels are r / a= ψ N, where ψ is the normalised oloidal magnetic flux. I = 55kA, P = 3.6MW. N NBI 7. Conclusions This aer reorts on the first exeriments on MAST with simultaneous fuelling and mitigation by RMP coils. The data are comared with the fuelling model which has been formulated for ITER. It is shown that the fuelling s trigger s and their size could be larger than non- induced RMP-mitigated s. Concerning the ost loss an examle is shown in which similarity with the ideal fuelling model is demonstrated simultaneously in the following asects: deosition is ITER-like, rel / a>.7 to article ratio is ITER-like, N ell / δ N ~ 6 ost- loss rate is constant and the same as due to mitigated s without The relative ratio of to lasma article content is larger on MAST than on ITER as is the case in the majority of resent devices. Clearly a larger dataset is needed to understand article losses under the condition of simultaneous fuelling and mitigation by RMPs. The aim is to demonstrate fuelling with mitigation which is simultaneously comatible with the lasma core, divertor and overall fuel balance. A high frequency injector in MAST Ugrade would further increase the similarity with the ideal fuelling model, in articular by reducing the contribution of gas fuelling. Acknowledgement This work was funded by the RCUK Energy Programme under grant EP/I5145 and the Euroean Communities under the contract of Association between EURATOM and CCFE. The views and oinions exressed herein do not necessarily reflect those of the Euroean Commission. Authors
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