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© 2020 The Author(s). The SPARC tokamak is a critical next step towards commercial fusion energy. SPARC is designed as a high-field (T), compact (m, m), superconducting, D-T tokamak with the goal of producing fusion gain 2$]]> from a magnetically confined fusion plasma for the first time. Currently under design, SPARC will continue the high-field path of the Alcator series of tokamaks, utilizing new magnets based on rare earth barium copper oxide high-temperature superconductors to achieve high performance in a compact device. The goal of 2$]]> is achievable with conservative physics assumptions () and, with the nominal assumption of, SPARC is projected to attain and MW. SPARC will therefore constitute a unique platform for burning plasma physics research with high density (), high temperature (keV) and high power density () relevant to fusion power plants. SPARC's place in the path to commercial fusion energy, its parameters and the current status of SPARC design work are presented. This work also describes the basis for global performance projections and summarizes some of the physics analysis that is presented in greater detail in the companion articles of this collection.

The pressure gradient of the high confinement pedestal region at the edge of tokamak plasmas rapidly collapses during plasma eruptions called edge localised modes (ELMs), and then re-builds over a longer time scale before the next ELM. The physics that controls the evolution of the JET pedestal between ELMs is analysed for 1.4 MA, 1.7 T, low triangularity, delta = 0.2, discharges with the ITER-like wall, finding that the pressure gradient typically tracks the ideal magneto-hydrodynamic ballooning limit, consistent with a role for the kinetic ballooning mode. Furthermore, the pedestal width is often influenced by the region of plasma that has second stability access to the ballooning mode, which can explain its sometimes complex evolution between ELMs. A local gyrokinetic analysis of a second stable flux surface reveals stability to kinetic ballooning modes; global effects are expected to provide a destabilising mechanism and need to be retained in such second stable situations. As well as an electronscale electron temperature gradient mode, ion scale instabilities associated with this flux surface include an electro-magnetic trapped electron branch and two electrostatic branches propagating in the ion direction, one with high radial wavenumber. In these second stability situations, the ELM is triggered by a peeling-ballooning mode; otherwise the pedestal is somewhat below the peeling-ballooning mode marginal stability boundary at ELM onset. In this latter situation, there is evidence that higher frequency ELMs are paced by an oscillation in the plasma, causing a crash in the pedestal before the peeling-ballooning boundary is reached. A model is proposed in which the oscillation is associated with hot plasma filaments that are pushed out towards the plasma edge by a ballooning mode, draining their free energy into the cooler plasma there, and then relaxing back to repeat the process. The results suggest that avoiding the oscillation and maximising the region of plasm, QC 20171204

Studies of the pedestal stability in low triangularity, d=0.2, JET ITER-Like Wall discharges are presented, following the evolution between ELMs. The pressure gradient tracks the ideal MHD ballooning threshold, only lagging behind it when the threshold rises rapidly as the plasma penetrates the second stability region. This is consistent with a role for the kinetic ballooning mode in the pedestal structure. When the plasma has second stability access, e.g. for low gas puff discharges, the peeling-ballooning mode is marginally stable at ELM onset. In cases where there is no second stability access the discharges are some way short of the peeling-ballooning threshold, so this alone cannot be the trigger for the ELM. A low amplitude sinusoidal oscillation in the Be-II emission is observed that correlates well with the ELMs, and has an associated high frequency magnetic field fluctuation, ~100-250kHz, with modulated amplitude. This might be associated with a new filamentary equilibrium state., QC 20190614

First systematic measurements of pedestal structure during Ohmic and NBI-assisted Type I ELMy H-modes were performed on the COMPASS tokamak in two dedicated experimental campaigns during 2015 and 2016. By adjusting the NBI heating and a toroidal magnetic field, the electron pedestal temperature was increased from 200 eV up to 300 eV, which allowed reaching pedestal collisionality nu(ped)* < 1 at q(95) similar to 3. COMPASS has approached conditions for the Identity experiment done at JET & DIII-D, complementing the range of scanned rho(ped)*. The pedestal pressure was successfully reproduced by the EPED model. The dependence of pedestal pressure width on nu(ped)* and beta(pol)(ped) is discussed., QC 20170510

We present the pedestal structure, as determined from the high-resolution Thomson scattering measurements, for a database of low and high triangularity (δ ≈ 0.22-0.39) 2.5 MA, type I ELMy H-mode JET plasmas after the installation of the new ITER-like wall (JET-ILW). The database explores the effect of increasing deuterium fuelling and nitrogen seeding with a view to explain the observed changes in performance (edge and global). The low triangularity JET-ILW plasmas show no significant change in performance and pedestal structure with increasing gas dosing. These results are in good agreement with EPED1 predictions. At high triangularity, for pure deuterium fuelled JET-ILW plasmas, there is a 20-30% reduction in global performance and pressure pedestal height in comparison to JET-C plasmas. This reduction in performance is primarily due to a degradation of the temperature pedestal height. The global performance and pressure pedestal height of JET-ILW plasmas can be partially recovered to that of JET-C plasmas with additional nitrogen seeding (Giroud et al 2013 Nucl. Fusion 53 113025). This observed improvement in performance is predominately due to a significant increase in density pedestal height as well as a small increase in the temperature pedestal height. A key result with increasing deuterium fuelling for JET-ILW plasmas is there is no improvement in pressure pedestal height however the pedestal still widens which is inconsistent with the Δ = 0.076√βpol,ped scaling. Furthermore, a key result with increasing nitrogen seeding is the pressure pedestal widening is due to an increase in the temperature pedestal width whilst the density pedestal shows no clear trend. The comparison of EPED1 predictions with the measurements at high triangularity is complex as, for example, for pure deuterium fuelled plasmas there is very good agreement for the pedestal height but not the width. In addition, current EPED1 runs under-predict the pedestal height and width at high nitrog, QC 20150609

Rapid bifurcations in the plasma response to slowly varying n=2 magnetic fields are observed as the plasma transitions into and out of edge-localized mode (ELM) suppression. The rapid transition to ELM suppression is characterized by an increase in the toroidal rotation and a reduction in the electron pressure gradient at the top of the pedestal that reduces the perpendicular electron flow there to near zero. These events occur simultaneously with an increase in the inner-wall magnetic response. These observations are consistent with strong resonant field penetration of n=2 fields at the onset of ELM suppression, based on extended MHD simulations using measured plasma profiles. Spontaneous transitions into (and out of) ELM suppression with a static applied n=2 field indicate competing mechanisms of screening and penetration of resonant fields near threshold conditions. Magnetic measurements reveal evidence for the unlocking and rotation of tearinglike structures as the plasma transitions out of ELM suppression.

Type I ELMy H-mode operation in JET with the ITER-like Be/W wall (JET-ILW) generally occurs at lower pedestal pressures compared to those with the full carbon wall (JET-C). The pedestal density is similar but the pedestal temperature where type I ELMs occur is reduced and below to the so-called critical type I-type III transition temperature reported in JET-C experiments. Furthermore, the confinement factor H-98(y,H- 2) in type I ELMy H-mode baseline plasmas is generally lower in JET-ILWcompared to JET-C at low power fractions Ploss/P-thr,(08)< 2 (where P-loss is (P-in-dW/dt), and P-thr,(08) the L-H power threshold from Martin et al 2008 (J. Phys. Conf. Ser. 123 012033)). Higher power fractions have thus far not been achieved in the baseline plasmas. At Ploss/P-thr,P- 08 > 2, the confinement in JET-ILW hybrid plasmas is similar to that in JET-C. A reduction in pedestal pressure is the main reason for the reduced confinement in JET-ILW baseline ELMy H-mode plasmas where typically H-98((y, 2)) = 0.8 is obtained, compared to H-98((y, 2)) = 1.0 in JET-C. In JET-ILW hybrid plasmas a similarly reduced pedestal pressure is compensated by an increased peaking of the core pressure profile resulting in H-98((y, 2)) <= 1.25. The pedestal stability has significantly changed in high triangularity baseline plasmas where the confinement loss is also most apparent. Applying the same stability analysis for JET-C and JET-ILW, the measured pedestal in JET-ILW is stable with respect to the calculated peeling-ballooning stability limit and the ELM collapse time has increased to 2ms from typically 200 mu s in JET-C. This indicates that changes in the pedestal stability may have contributed to the reduced pedestal confinement in JET-ILW plasmas. A comparison of EPED1 pedestal pressure prediction with JET-ILW experimental data in over 500 JET-C and JET-ILW baseline and hybrid plasmas shows a good agreement with 0.8 < (measured p(ped))/(predicted p(ped), EPED) < 1.2, but that, QC 20140508

The confinement in JET baseline type I ELMy H-mode plasmas is compared to that in so-called hybrid H-modes in a database study of 112 plasmas in JET with the carbon fibre composite (CFC) wall. The baseline plasmas typically have βN ∼ 1.5-2, H98 ∼ 1, whereas the hybrid plasmas have βN ∼ 2.5-3, H98 < 1.5. The database study contains both low- (δ ∼ 0.2-0.25) and high-triangularity (δ ∼ 0.4) hybrid and baseline H-mode plasmas from the last JET operational campaigns in the CFC wall from the period 2008-2009. Based on a detailed confinement study of the global as well as the pedestal and core confinement, there is no evidence that the hybrid and baseline plasmas form separate confinement groups; it emerges that the transition between the two scenarios is of a gradual kind rather than demonstrating a bifurcation in the confinement. The elevated confinement enhancement factor H98 in the hybrid plasmas may possibly be explained by the density dependence in the τ98 scaling as n0.41 and the fact that the hybrid plasmas operate at low plasma density compared to the baseline ELMy H-mode plasmas. A separate regression on the confinement data in this study shows a reduction in the density dependence as n0.09±0.08. Furthermore, inclusion of the plasma toroidal rotation in the confinement regression provides a scaling with the toroidal Alfvén Mach number as and again a reduced density dependence as n0.15±0.08. The differences in pedestal confinement can be explained on the basis of linear MHD stability through a coupling of the total and pedestal poloidal pressure and the pedestal performance can be improved through plasma shaping as well as high β operation. This has been confirmed in a comparison with the EPED1 predictive pedestal code which shows a good agreement between the predicted and measured pedestal pressure within 20-30% for a wide range of βN ∼ 1.5-3.5. The core profiles show a strong degree of pressure profile consistency. No beneficial effect of core density pea, QC 20130207

We present the results from a new fuelling scan database consisting of 14 high triangularity (delta similar to 0.41), type I ELMy H-mode JET plasmas. As the fuelling level is increased from low, (Gamma(D) similar to 0.2 x 10(22) el s(-1), n(e),(ped)/n(GW) = 0.7), to high dosing (Gamma(D) similar to 2.6 x 10(22) el s(-1), n(e, ped)/n(GW) = 1.0) the variation in ELM behaviour is consistent with a transition from 'pure type I' to 'mixed type I/II' ELMs (Saibene et al 2002 Plasma Phys. Control. Fusion 44 1769). However, the pulses in this new database are better diagnosed in comparison to previous studies and most notable have pedestal measurements provided by the JET high resolution Thomson scattering (HRTS) system. We continue by presenting, for the first time, the role of pedestal structure, as quantified by a least squares mtanh fit to the HRTS profiles, on the performance across the fuelling scan. A key result is that the pedestal width narrows and peak pressure gradient increases during the ELM cycle for low fuelling plasmas, whereas at high fuelling the pedestal width and peak pressure gradient saturates towards the latter half of the ELM cycle. An ideal MHD stability analysis shows that both low and high fuelling plasmas move from stable to unstable approaching the ideal ballooning limit of the finite peeling-ballooning stability boundary. Comparison to EPED predictions show on average good agreement with experimental measurements for both pedestal height and width however when presented as a function of pedestal density, experiment and model show opposing trends. The measured pre-ELM pressure pedestal height increases by similar to 20% whereas EPED predicts a decrease of 25% from low to high fuelling. Similarly the measured pressure pedestal width widens by similar to 55%, in poloidal flux space, whereas EPED predicts a decrease of 20% from low to high fuelling. We give two possible explanations for the disagreement. First, it may be that EPED under predicts th, QC 20130920

Type-I edge-localized modes (ELMs) have been suppressed in DIII-D (Luxon et al 2003 Nucl. Fusion 43 1813) H-mode discharges with a H98Y2 confinement factor near 1.0 using magnetic perturbations (MPs) with dominant toroidal mode number n = 2. This expands

Multidevice pedestal scaling experiments in the DIII-D, ASDEX Upgrade (AUG), and JET tokamaks are presented in order to test two plasma physics pedestal width models. The first model proposes a scaling of the pedestal width Delta/a proportional to rho*(1/2) to rho* based on the radial extent of the pedestal being set by the point where the linear turbulence growth rate exceeds the E x B velocity. In the multidevice experiment where rho* at the pedestal top was varied by a factor of four while other dimensionless parameters where kept fixed, it has been observed that the temperature pedestal width in real space coordinates scales with machine size, and that therefore the gyroradius scaling suggested by the model is not supported by the experiments. The density pedestal width is not invariant with rho* which after comparison with a simple neutral fuelling model may be attributed to variations in the neutral fuelling patterns. The second model, EPED1, is based on kinetic ballooning modes setting the limit of the radial extent of the pedestal region and leads to Delta(psi) proportional to beta p(1/2). All three devices show a scaling of the pedestal width in normalised poloidal flux as Delta(psi) proportional to beta p(1/2), as described by the kinetic ballooning model; however, on JET and AUG, this could not be distinguished from an interpretation where the pedestal is fixed in real space. Pedestal data from all three devices have been compared with the predictive pedestal model EPED1 and the model produces pedestal height values that match the experimental data well., QC 20110721

The dependence of the H-mode edge transport barrier width on normalized ion gyroradius (rho* = rho/a) in discharges with type I ELMs was examined in experiments combining data for the JET and DIII-D tokamaks. The plasma configuration as well as the local normalized pressure (beta), collisionality (nu*), Mach number and the ratio of ion and electron temperature at the pedestal top were kept constant, while rho* was varied by a factor of four. The width of the steep gradient region of the electron temperature (T-e) and density (n(e)) pedestals normalized to machine size showed no or only a weak trend with rho*. A rho(1/2) or rho(1) dependence of the pedestal width, given by some theoretical predictions, is not supported by the current experiments. This is encouraging for the pedestal scaling towards ITER as it operates at lower rho* than existing devices. Some differences in pedestal structure and ELM behaviour were, however, found between the devices; in the DIII-D discharges, the n(e) and T-e pedestal were aligned at high rho* but the ne pedestal shifted outwards in radius relative to T-e as rho* decreases, while on JET the profiles remained aligned while rho* was scanned by a factor of two. The energy loss at an ELM normalized to the pedestal energy increased from 10% to 40% as rho* increased by a factor of two in the DIII-D discharges but no such variation was observed in the case of JET. The measured pedestal pressures and widths were found to be consistent with the predictions from modelling based on peeling-ballooning stability theory, and are used to make projections towards ITER, QC 20110301 36th European-Physical-Society Conference on Plasma Physics, Natl Palace Culture, Sofia, BULGARIA, JUN 29-JUL 03, 2009