Operational space and performance limiting events in the first physics campaign of MAST-U

The MAST-U fusion plasma research device, an upgrade to the Mega Amp Spherical Tokamak, has recently completed its first campaign of physics operation. MAST-U operated with Ohmic, or one or two neutral beams for heating, at 400–800 kA plasma current, in conventional or ‘SuperX’ divertor configurations. Equilibrium reconstructions provide key plasma physics parameters vs. time for each discharge, and diagrams are produced which show where the prevalence of operation occurs as well as the limits in various operational spaces. When compared to stability limits, the operation of MAST-U so far has generally stayed out of the low q, low density instability region, and below the high density Greenwald limit, high beta global stability limit, and high elongation vertical stability limit. MAST-U still has the potential to reach higher elongation, which could benefit the plasma performance. Despite the majority of operations happening below established stability limits, disruptions do occur in the flat-top phase of MAST-U plasmas. The reasons for these disruptions are highlighted, and possible strategies to avoid them and to extend the operational space of MAST-U in future campaigns are discussed.


Introduction
The upgrade to the fusion research device Mega Amp Spherical Tokamak (MAST) [1], called MAST-U [2], was years in 4 See author list of Harrison J R et al 2019 Nucl. Fusion 59 112011. * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. the making, but recently completed its first physics campaign [3]. One of the main goals of the research in MAST-U is to exploit the new capabilities of the upgrade, including new poloidal magnetic field coils and a flexible divertor geometry, to study the performance of fusion plasmas in unique configurations. To this end, it is important to track the operational space of the plasmas within the multidimensional space of various key physics plasma equilibrium parameters, relative to stability limits.
The equilibrium states of magnetically confined plasmas are stable balance points between magnetic and plasma pressures. These equilibria must be reconstructed from diagnostic measurements of the plasma conditions [4]. Once the equilibrium reconstruction is performed, many important plasma parameters, such as the shape of the enclosing flux surfaces and the pressure are known. Measurements of density and temperature of the electron and ion components add to the knowledge of their state at a given time during a discharge. Typically, in fusion devices, the plasma current is ramped up, held at a steady level during the 'flattop', and then ramped down again if it has not been disrupted by various modes of instability of the plasma. In the first campaign of MAST-U the flattop current was between roughly 400-800 kA and lasted on the order of a half to one second. The ultimate design values of MAST-U are up to 5 s and 2 MA, though not simultaneously [3].
One of the goals of fusion research devices is to explore the parameter space and the limits of magnetically confined plasma operation to see where plasmas can be stably operated without disruption. These limits can be compared to theoretical expectations and used to project them to future devices. A straightforward way to do this is to create operational space diagrams, which show the frequency of operation at a given value of the key plasma equilibrium parameter over the course of months or years long campaign of experimentation. The Disruption Event Characterization and Forecasting (DECAF) code [5][6][7], which analyses the chains of events that lead to disruptions and their patterns in multiple machine databases, is also equipped to provide operational space diagrams. Additionally, because the DECAF code also determines the timing of disruptions and the chain of events that leads to them, the causes of those disruptions can be investigated, and potential solutions found for expanding the stable operating space. This paper is organized as follows. First, the database of MAST-U equilibrium reconstructions from the first physics campaigns is presented. Second, these are used to produce diagrams showing the operational space of MAST-U in the first physics campaign. Finally, examples of events which lead to disruption or limitations in the performance of MAST-U plasmas are illustrated, and methods for potentially overcoming them are discussed.

The MAST-U database
MAST-U was operated in various sets of discrete allowed scenarios in three main categories, which are logged for each discharge: the plasma current level, the shape of the divertor, and the level of neutral beam heating. In addition to a small number of limiter discharges where the closed flux surface impact on a metal 'limiting' structure in the machine, which we will exclude, all MAST-U discharges ran in the double null (DN) configuration, where magnetic field coils are used to pull the open field lines beyond the last closed flux surface to divertor targets at both the top and bottom of the machine. Therefore, we can categorize all MAST-U discharges into 24 categories based on the choice of three plasma current request levels, two divertor geometries, and four levels of beam heating. The three current levels used were 400-450, 600, and 700-750 kA. The two divertor geometries were conventional (CD) and super-X (SX) [8]; however, in a number of cases the divertor configuration was unspecified (UN). There were also just a couple of 'snowflake' divertor discharges in the first campaign as well [9], but these were not included. Finally, the four heating levels were Ohmic (OH, no beams), one beam from the 'southwest' beam (SW), one beam from the 'south' beam (SS), and two beams (2B). Therefore, every discharge in MAST-U is, in principle, labelled by the session leader after it is performed in a scenario, such as: DN-700-SX-1BSW. This categorization has been re-checked on a shot level. While it can be assumed that the current is maintained at a steady level, there is no guarantee that the SX divertor was maintained during that time, nor that the SW beam was on for the full flattop duration (often it was not). Additionally, the achieved plasma current could differ from the requested one, especially early in the run before Rogowski coil calibrations were updated (in one extreme example 810 kA was achieved for a programmed 750 kA discharge). Therefore, it is admittedly a somewhat crude categorization, and all equilibria derived from the example labelled discharge, DN-700-SX-1BSW, are labelled as such, even though there may be time points that have a conventional divertor, or Ohmic power only, or current that differs from 700 kA.
Nevertheless, these are convenient categories to split the discharges to look at differences in their operational spaces. Some discharges were not labelled at the time of their operation, in which case we retroactively categorized them by current and beam heating but not by divertor geometry. Automatic evaluation of the strike point location to determine the time and position of the SX divertor flux expansion is being developed. Comparisons between the strike point location from equilibrium reconstruction and peak heat flux locations or Langmuir probe data are also ongoing [10].
The underlying data that DECAF uses to produce these diagrams, for MAST-U, come from the EFIT++ equilibrium reconstruction code [10,11], which presently uses magnetic data only as an input. Kinetic profiles from Thomson scattering are routinely available, and charge exchange recombination spectroscopy and motional Stark effect diagnostics are also available for most discharges with the 'south' neutral beam injection, but using these in equilibrium reconstructions are a work in progress [10]. Additionally, the requested plasma current from the plasma control system [12], the measured plasma current, and the measured line density are used.
The measurements, reconstructed variables, and DECAF analysis results were stored in SQL databases on computers at the Princeton Plasma Physics Laboratory for easy access for U.S.-based researchers.
The database of MAST-U discharges derived from the magnetics-only equilibrium reconstructions utilized here for the operational space diagrams does not include all plasma discharges. Discharges before June, 2021 were excluded as the machine was in an early phase of operation. In the discharges used, in the range of shot numbers 44 114-45 484 from the months of June-October, 2021, there were some 'fizzle' cases that did not make it to the current flattop, some cases where not all the necessary data was available to run the reconstruction, and finally cases in which the equilibrium reconstruction was run but the χ 2 number indicating the goodness of the fit of the reconstruction to all the data that goes into it was too high (>30). We are left with a total of 855 discharges, separated into different scenarios according to table 1. In each discharge, the flattop is split into 5 ms intervals (the timing of the equilibrium reconstruction), so that for every second of flattop in the discharge, 200 individual equilibrium times are taken. In this way the total number of equilibria in the database was 108 826. The majority of the discharges and equilibria, in the first campaign had Ohmic heating only, and the two most frequent conventional divertor scenarios were at the extremes: low current Ohmic, and high current two beam. Finally, there are obvious gaps in the scenario map in table 1. For example, there are no discharges with the SW beam in 400 kA plasmas. This is by choice, as the confinement of the SW beam energetic particles, which are injected offaxis, was deemed to be too poor in lower current discharges, so they were not attempted.

Operational space
In general, the DECAF code can produce diagrams showing the probability of any DECAF event, such as disruption, Greenwald limit, vertical displacement event, etc … occurring within a given parameter space of tokamak operation [6]. Diagrams showing the frequency of disruption [13] and magnetic island widths [14] have been previously produced for the database of MAST discharges. Here however, we present DECAF-produced operational space diagrams, which more simply show the number of times the plasmas accessed a given space. A limited number of such diagrams have been independently illustrated for MAST-U in [3].
Operational space plots are useful for showing where the plasmas generally operate and the boundaries of that operation. Each square of the parameter space is plotted with a colour on a logarithmic scale ranging from 1 (blue) to 1000 (yellow), indicating how many equilibrium points from the database exist within that space. In this way the density of operations in a given space is illustrated. Usually, such diagrams are made with scatter plots of points, which does not show this, or sometimes with shading, which does but only qualitatively (some examples from MAST are in [15][16][17]). Generally, the two-dimensional spaces illustrated have a resolution of a 50 × 50 square grid. Squares are only plotted if they have three or more equilibria in them.

Hugill diagram
A well-known diagram in fusion plasma physics is the Hugill diagram [18], which plots the tokamak operation in the space of nR/B φ vs. 1/q 95 . Here, n is the line average density, R is the major radius of the magnetic axis, B φ is the toroidal magnetic field at the axis, and q 95 is the safety factor at 95% of the magnetic flux. The advantage of this diagram is that it shows both a low q limit due to current driven instabilities as a horizontal line on the plotfor example, as q 95 = 2 (at 1/q 95 = 0.5), and density limits as diagonal lines on the plot. The high density limit is perhaps more intuitively shown in a different Greenwald diagram, which will be discussed next. Figure 1 shows the Hugill diagram for MAST-U.
As a spherical tokamak, MAST-U generally has quite a high edge safety factor, as can be seen in the figure where almost all of the operation is between 5 < q 95 < 10. So far MAST-U has operated below any low q stability limits.
In MAST disruptivity was elevated generally in the low q 95 , low density upper left region, above 1/q 95 ∼ 0.2 and below nR/B φ ∼ 5 [13]. This area has so far been sparsely accessed in MAST-U. However, some discharges in MAST-U have suffered from low density locked modes. This sometimes occurs because the density is often kept low on purpose, for example in Ohmic plasmas, in order to get power into the divertor for dedicated divertor experiments.
It should be noted that in limited equilibrium reconstructions, including a measurement of the magnetic pitch angle from the motional Stark effect diagnostic, the q profile can be generally shifted slightly (∼0.5) lower than for magnetics only reconstructions [10], but this is not anticipated to make a large difference in the conclusions of the Hugill diagram.

Greenwald limit diagram
Tokamak fusion plasmas have long been known to be subject to a density limit, where the line average density n e [10 20 m −3 ] is limited to the so-called Greenwald density n G ≡ I p /πa 2 , where I p is the plasma current in MA and a is the plasma minor radius in m [19]. An easy way to illustrate this limit is to simply plot the measured density against the Greenwald density, and a diagonal line indicates the limit. In some ways, this diagram is a reconfiguration of the Hugill diagram [20], because the vertical axis is proportional to the plasma current so theoretically this diagram shows a current limit at the top. Additionally, at low density on the left, there is a possibility to see a low density runaway electron boundary, but this area is small on the diagram. Figure 2 shows that MAST-U has generally remained well below the Greenwald limit in the flattop to this point. Lower plasma current discharges need to maintain a lower density to stay below the limit, as illustrated in figure 3 where the database is split into three plasma current levels with coloured line contours containing a minimum of 30 equilibria. This does not show the details of where the operation was more prevalent in that space, but rather the general envelope of the operation. This style of plot uses a lower resolution plotting grid of 25 × 25 squares for less detail in the contours, to make the plot more readable.
As aforementioned, the plasma density was often relatively low in the first MAST-U campaign. Additionally, it was shown that the optimal Greenwald fraction for maximizing the plasma stored energy was about 0.6 [3]. However, there were occasional cases of flattop plasmas crossing the Greenwald limit, leading to disruptionfor example, 400 kA Ohmic discharges, which reached a Greenwald limit at 0.4 × 10 20 m −3 , as indicated in figure 2 where the operational space touches the line. These cannot be seen in figure 3 because there are less than 30 such cases. There were also purposeful ramps in density in some discharges in the first campaign. These individual probes of the density limit will be the subject of a future more focused study, comparing experiments to theories, such as a newly proposed limit formulation based on boundary turbulent transport [21].
Finally, the I p rampdown phase was not included in the database shown here, but it can lead to cases of plasmas crossing the Greenwald limit because the limit comes down with I p . One way to combat this is to purposefully shrink the plasma, so that the reducing a counteracts the reducing I p . This strategy has been employed successfully in some discharges in MAST-U.

Normalized beta diagrams
Another traditional diagram in fusion plasma physics that, in principle, shows more than one operational limit is a plot showing <β t > vs. l i I p /(aB 0 ). Here l i is the plasma internal inductance, l i ≡ <B p 2 >/B p 2 (a) (where B p is the poloidal magnetic field), which indicates peaking of the current profile. The plasma current here is in units of MA and a is the minor radius in m. β t is the toroidal beta, a ratio of plasma pressure to magnetic pressure defined by β t ≡ 2µ 0 <p>/B 0 2 ), where <p> is the volume-average plasma pressure. Clearly, from figure 4, much of the MAST-U operation so far has been at lower beta, which is consistent with what is seen in table 1, that the majority of plasmas so far have Ohmic heating only.
The macroscopic stability of fusion plasmas is known to decrease with an increasing ratio of normalized beta to internal inductance, although not necessarily monotonically [22]. The physical mechanism to explain this dependence is that larger β N means larger overall pressure and therefore larger destabilizing pressure gradients in the outer regions, while lower l i means a broader current profile and therefore lower stabilizing magnetic shear [23]. Conveniently, since β N ≡ <β t > aB 0 /I p , diagonal lines on this diagram represent levels of β N /l i . Figure 4 shows that the operational space of MAST-U reaches β N /l i = 3.3 so far. This is well below the socalled no-wall limit, which was projected to be about β N /l i = 7 for MAST-U [24]. Above this, limit resistive wall modes can become unstable without stabilizing effects, although modelling for MAST suggests that kinetic stabilization may be sufficient to maintain stability [25].
Secondly, this same diagram is meant to show a low q operational limit as the abscissa approaches 4. Once again, the MAST-U operation is well below this limit yet.
A more straightforward way of showing the macroscopic stability limit is a β N vs. l i diagram. This is simply another way of displaying the same information. Such diagrams from the early operating days of MAST showed plasmas reaching β N /l i of 6 [15,17]. Figure 5 shows the data plotted this way, again indicating that the maximum β N /l i so far in the early operation of MAST-U is about 3.3. The maximum transient values in the database of β N /l i = 3.37 and β N = 3.47 (both from discharge 45 477) cannot be seen in this diagram because equilibria with β N > 2.8 were too rare.
Not surprisingly, the highest β N operating points came during plasmas with both neutral beams injected. This can be seen in figure 5, where a steady increase in β N , and general decrease in l i , are seen from Ohmic to beam operation. A similar pattern was noted early in MAST operation [15]. Naturally, plasma stored energy increases with increased injected power in MAST-U [3]. Additionally, performance increased from SW to SS to 2B operation. The reason that the SS beam can generally lead to higher β N plasmas than the SW beam is that it is oriented to deposit energy on-axis, while the SW beam is off-axis, and the fast ion confinement is considerably higher for the on-axis beam [26].
One of the major focuses of the MAST-U program is to develop the super-X divertor for heat and power exhaust handling in a spherical tokamak. One can see from table 1 that the SX has been mostly operated in OH plasmas to date, with just a few one and two beam discharges. This is primarily for two reasons: first, there were a lot of initial Ohmic development discharges to establish the SX divertor operation, and second in SX divertor experiments the desire for substantial measured power in the divertor led generally to low density operation, and beam absorption was thought to be poor in MAST-U at low density, so there was not a strong desire for SX beam discharges. A greater number of beam heated SX discharges are anticipated in further campaigns.
A key consideration is whether the divertor configuration affects the core plasma. Of course, there are major differences between CD and SX in the divertor: SX having about twice the field line length and a much larger area of power deposition, a ten times reduction in peak heat flux was noted, as predicted [27]. Though it is not shown in the diagrams presented here, by comparing the achieved range of normalized beta between CD and SX Ohmic plasmas, at each of the plasma current levels, we have seen that there is no discernable difference so far between the CD and SX plasmas with respect to the core plasma pressure. Though there have been short periods of H-mode confinement obtained in SX plasmas, sustained and systematic SX H-modes were not a focus of the first campaign, so a comparison between CD and SX core plasmas in H-mode will be a future consideration.

Vertical stability
Elongated plasmas are potentially prone to vertical instability, in which control of the plasma position is lost and it either moves upwards or downwards until striking the surrounding material. Lower aspect ratio plasmas naturally have a higher elongation, κ, but there is a limit on that elongation that can be stably maintained, which is inversely proportional to the internal inductance [28]. Improvements to vertical stability control, of course, increase the achievable κ for a given l i [29]. By the time, a disruption of the plasma current has occurred due to the vertical instability process, the plasma may have shrunk to a lower κ and increased its l i , but the originating vertical displacement event generally begins at higher κ, lower l i [6,28]. Figure 6 shows that MAST-U plasmas operated as expected-lower l i plasmas had higher κ [3]. The dashed line shown is an upper limit of κ = 3.4-l i derived from the experience of NSTX for the design of future spherical tokamaks [30]. A boundary, such as this has been proposed for a model predictive control scheme for tokamaks [31]. This indicates that MAST-U still potentially has some margin to increase the elongation of its plasmas, especially as l i is lowered even further in future campaigns. It should be noted, however that the operational space achieved in the NSTX database of discharges was somewhat lower than the limit derived and shown [30].

Plasma performance improvement from plasma shaping
With the exception of vertical stability, increased elongation in spherical tokamaks tends to increase the stability of the plasmas. Additionally, it is associated with improved confinement of the plasma energy. In fact, the fusion power output scales approximately with elongation, normalized beta, and toroidal field all to the fourth power, so increases in elongation are quite important for spherical tokamaks [30].
Another way of considering the importance of elongation is to consider that increased elongation allows for an increase in the product of toroidal beta and bootstrap current (noninductive current) fraction. These two parameters are both important-βt for fusion gain and f bs for pulse length and sustainment of the discharge, but they are inherently competitive through the relation f bs βt ∼ A −1/2 (1 + κ 2 )β N 2 [30,32]. An increase of κ increasing the product of these parameters, however, meaning the ability to either simultaneously increase both or to increase one without detriment to another. The fraction of current being carried by the bootstrap effect can be determined per shot by analysis, but since bootstrap fraction scales with poloidal beta, it was recognized that a convenient way to visualize this benefit of elongation with global parameters was to plot βpβt vs. 1 + κ 2 [29]. Figure 7 shows this diagram for the first campaign of MAST-U. The units of the ordinate are not important (in our case the βt was in percentage, while the βp was not). What is important is the increase in value as elongation increases. Clearly, much of the operation of MAST-U thus far has been at low values of the βpβt product, and there is a lack of data in the range of κ ∼ 1.6-1.7 (1 + κ 2 ∼ 3.5-3.9) (which can also be seen in figure 6), but the potential for increase with high κ is possible. Additionally, a small increase in κ to about 2.45 would give a 1 + κ 2 of 7, the right side of the plot.

Other stability limits
In the present paper, we have thus far been discussing global stability limits. Examples of other stability aspects not indicated by the plots shown here are as follows: rotating or tearing magnetohydrodynamic (MHD) modes, and pedestal stability. This is primarily because the analysis of such more localized stability issues requires much more detailed calculations and parameters beyond just global equilibrium quantities. However, work is progressing, separately, on these issues as well.
As an example, high performance MAST-U plasmas have been seen to reach the peeling pedestal stability limit [3], and work is underway to analyse MAST-U pedestal stability, in the way that was done for MAST [33].

Disruptions and performance-limiting events
The plasma current in tokamak confinement devices is subject to disruptions due to instabilities that are typically the result of chains of physical events. The DECAF code's many separate physical event modules provide warnings and declare occurrences of certain events leading to disruption. In addition to operational space diagrams, the DECAF code also includes the ability to produce diagrams showing the probability of any DECAF event occurring within a given parameter space of the tokamak operation. Most commonly, the DIS event-the time of disruption-is used, resulting in a familiar disruptivity plot. Disruptivity diagrams have been produced for MAST in a previous study [13], and have previously been produced with DECAF and compared to other devices [7]. One must be somewhat cautious with disruptivity diagrams; however, as the regions showing low disruptivity in the diagram may also be important. In high event probability regions, plasma conditions can change significantly between the first problem detected and when disruption happens [6]. Consequently, disruptivity diagrams are not yet very insightful for MAST-U, though they may become so after years of operation.
DECAF could potentially be used to generate statistics on the common chain of events leading to disruption in MAST-U, and this is planned for future work. However, at this time, because of the relatively low number of discharges and because of specific present limitations in DECAF analysis (which will be mentioned, along with changes being implemented to overcome them) instead here we will focus briefly on some examples of individual causes of disruption that limit the performance of MAST-U, and strategies to avoid them to extend the operation space in future campaigns.

Density limit disruptions
In section 3.2 it was explained that there were not many MAST-U discharges that reached the Greenwald density limit, however there were some. Figure 8 shows an example of a 450 kA plasma where the measured density grows until it crosses the Greenwald density, and the plasma subsequently disrupts. This plot is an automatic output of the DECAF code, which very simply, in this case, shows that the warning level rises from 0 to 3 as the Greenwald fraction rises (level 3 indicating an impending disruption). This is a straightforward example of a DECAF event with a scalar comparison-others are more complex and involve multiple signals and/or calculations [5].
It was stated that Greenwald limit crossings are rare in MAST-U, however there are numerous cases of plasmas with rising density and signatures of multifaceted asymmetric radiation from the edge (MARFEs) [34] that occurred at lineaveraged densities below Greenwald, but with elevated edge densities near or above empirical [35] or theoretical [21] edge density limits. This is the subject of further investigation, both by analysis of the existing discharges with an expanded DECAF code to include these edge limits and by further experiments in the next campaign of MAST-U. Additionally, density control is presently being implemented in MAST-U [12], so that in the future if DECAF is implemented in the real-time control system of MAST-U it can deliver density limit warnings, both global and local, to the density control actuators.

Minor disruptions due to mode locking at high beta
In section 3.3 it was stated that the highest β N values in MAST-U (∼3) were achieved only transiently. Figure 9 shows an example discharge that can help explain why this was the case (and how it can be prevented going forwards). In this discharge, as the β N level reaches ∼3, 'minor' disruptions occur which drop the beta to low levels from which the plasma subsequently recovers and re-heats. These are minor in name only, in that they do not disrupt the plasma current and lead to a loss of confinement; in reality, they are majorly perturbative events.
From the analysis of MHD spectrograms (also shown in figure 9), it is clear that these high beta performance limiting events are due to slowing and locking low-frequency MHD modes. The DECAF code also includes the ability to generate and analyse MHD spectrograms along with a multitude of other related tests that can determine a bifurcation point of a slowing mode towards locking [36,37]. Unfortunately, this test was not available in MAST-U in the first campaign due to an insufficient number of signals, but it is being implemented for future campaigns, and expanded toroidal coverage of Mirnov probes is already available. This capability is now being tested in real-time as well in the KSTAR device.
Several possible actuators to avoid these beta limiting modes are being developed for use in MAST-U as well. These include a q 0 and β N control scheme that was developed for NSTX-U [38] and uses the plasma shaping and beam power actuators to control beam deposition in the plasma to maintain stable levels of β N and q 0 . There were no beam controls available in the first MAST-U campaign, but beam notching will be available in the second campaign as well as further controls in future campaigns. Furthermore, the necessary enhancements of the shape control are implemented as well [39,40]. Real-time estimation of equilibrium quantities, such as β N and l i might be possible through the real-time local expansion reconstruction used by the shape controller as well [41].

Internal reconnection events (IREs) in the ramp-up
Another possible source of performance limitation in MAST-U plasmas was IREs early in the discharges, including in the current ramp-up. These events are defined by a spike in the plasma current and loop voltage, as well as a fast redistribution of the current from a hollow, reverse sheared q profile (with elevated q 0 ) to a broad, monotonic q profile (with lower q 0 ) [42]. Figure 10 shows a comparison of two 750 kA two-beam heated plasmas, one with and one without an early IRE. The figure shows the plasma current evolution through the ramp up and beginning of the flat top, the q at the magnetic axis, q 0 , and the plasma stored energy, W. Using an MSE constrained equilibrium reconstruction, we see that the IRE at the top of the flat top in discharge 44 653 co-incides with the onset of q 0 = 3. When compared to a discharge with a slower current ramp rate, 44 655, which avoids the IRE, the plasma stored energy is noticably reduced through the length of the discharge in 44 653. In order to achieve high beta plasmas in subsequent campaigns, mitigating IREs in the flat top phase of the discharge will be essential.
Methods to avoid this behaviour are currently being studied for MAST-U including TRANSP analysis of current evolution, although certain issues were found with the TRANSP model for current diffusion in the plasma current ramp-up for MAST [43]. The typical plasma current ramp rate for MAST-U plasmas was set to 7 MA s −1 to optimise the flux consumption of the solenoid swing and allow for future development of a 1 MA plasma. Experimentally, slower ramp rates could avoid IREs, as shown in figure 10, but at the expense of a reduced pulse length due to increased flux consumption. Slowing the ramp rate allows the Ohmic current to diffuse into the plasma, and produces a more monotonic q profile at the start of the flat top.
Additionally, q 0 drops with time in MAST-U discharges and often goes to ∼1 (see figure 10). In section 3.1 the dangers of lower q 95 were discussed, but not the dangers of low q 0 . These include sawteeth and the so-called long-lived mode (LLM) [44]. The LLM is an ideal, dominantly n = 1 mode that would appear in MAST as q 0 approached, but is still above, one and would usually disrupt the plasma when eventually the q = 1 surface would enter the plasma and set off a large sawtooth. Theoretically, the stability of the LLM as a function of q above one is seen to depend upon beta, rotation, shaping, and fast ion pressure [44].
Other strategies being considered are to get to a monotonic q profile with q 0 a bit below 2, and then freeze or slow the current penetration via higher T e via improved confinement (early H-mode) and/or early beam heating (in both cases in figure 10, on-axis beam power was applied at around 0.1 s). Early beam injection torque can also help spin up the plasma and reduce locking, as long as the beams can be well absorbed. These strategies are currently being studied through TRANSP simulations and will be attempted experimentally as well.
Finally, sustaining q 0 > 1 will potentially help to stably achieve higher beta as well (avoiding the MHD issues seen in figure 9). This is because elevating q 0 can be achieved with more off-axis current, which can come from bootstrap current which, as discussed in section 3.5, can be increased with higher elongation. This is also the reason that increasing elongation decreases internal inductance, as seen in section 3.4. The previously mentioned experimental focus on increasing elongation should therefore serve to benefit MAST-U in expanding the operational space in multiple directions.

Conclusions
MAST-U has completed its first physics campaign, operating in various plasma scenarios with zero, one, or two neutral beams injected, plasma current levels from 400 to 800 kA, and in conventional or Super-X divertor configurations. Magnetics only equilibria were reconstructed for many discharges, and these were used to produce operational space diagrams in various spaces. Generally, these diagrams indicate that MAST-U has margins to increase performance in many parameters without yet encountering stability limits, including density towards the Greenwald limit, beta towards global stability limits, and elongation towards vertical stability limits.
Certain stability issues did exist in the first MAST-U campaign, however, that either lead to disruption or limited the performance of the discharges. Examples are provided here for density limits, mode locking at high beta, and early IREs. For each of these, modelling, experimental and control strategies have been outlined which will be implemented to overcome the limitations. These are key to expanding the experimental operational space of MAST-U to serve its mission of exploring spherical tokamak physics. The methods of monitoring the operational space and stability limits, as well as identifying performance-limiting events and strategies to avoid them outlined in this paper, can serve as a model and reference for the early operation of future devices.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: https://dataspace. princeton.edu/handle/88435/dsp01j6731612k.