Transport barriers in electron and ion transport dominated regimes

Plasma Phys. Control. Fusion 42 (2000) B37–B50. Printed in the UK

PII: S0741-3335(00)18743-3

Transport barriers in electron and ion transport dominated regimes K Lackner, S G¨unter, F Jenko, A Peeters and R Wolf Max-Planck-Institut f¨ur Plasmaphysik, EURATOM Association, Boltzmannstrasse 2, D-85748 Garching, Germany Received 16 June 2000 Abstract. Confinement improvement beyond the usual L-mode proceeds in most cases through the formation of localized transport barriers in the edge (H-mode) or in the interior regions of the plasma (ITBs). The standard interpretation of this is the quenching of the usually prevailing turbulence by the formation of layers of sheared E × B rotation. Regarding interior transport barriers, this phenomenon has been observed in two distinctively different situations, with predominant ion or electron heating, and Te either significantly smaller or larger than Ti . The reactor relevant regime is, however, one with approximately equal Te and Ti . The availability of ECRH (and, to a lesser degree, also that of LH or FW heating) has allowed the study of the effect of the Te /Ti ratio in a controlled way. The standard transport model of ion-temperaturegradient and trapped-electron-mode-driven turbulence predicts (for situations with significant ion heating) a negative effect of an increase in this ratio. Experimental results show, however, that this confinement deterioration can be avoided in certain situations. These observations can be reconciled with theoretical expectations, if the simultaneous increase in Shafranov shift, which can reverse the theoretical predictions, is taken into account.

1. Introduction The standard operating regime of limiter tokamaks—the so-called L-regime—has insufficient energy confinement to extrapolate to an economic fusion reactor or even to a practicable ignition experiment. Fortunately, a number of operating modes have been discovered in which the anomalous transport is significantly reduced. The best known and most reproducibly attainable one is the H-regime. The outstanding feature of this regime is the appearance of a localized layer of low heat diffusivity and of steep density gradients in a narrow zone just inside the separatrix. The empirical confinement time scalings derived for this regime predict adequate performance for a fusion test reactor to operate—depending on size—with a power amplification factor Q = 10 (ITER-FEAT) or fully ignited (ITER-FDR), albeit for a limited pulse length. To operate a tokamak reactor in a more economic way and in steady state will require, however, further improvement in energy confinement, in attainable β values or in the efficiency of the non-inductive current drive. A tool for further improvement of confinement is the creation of additional transport barriers in the plasma interior, and various experimental recipes have been identified to produce such barriers. Most of these studies were conducted with neutral beam injection (NBI), which produces strong barriers in the ion temperature Ti , but at moderate electron temperatures Te . Using, on the other hand, electron cyclotron resonance heating (ECRH), lower hybrid (LH) or fast wave (FW) heating at low plasma densities, pronounced 0741-3335/00/SB0037+14$30.00

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barriers can be readily produced in the Te profiles, but with thermally decoupled, cold ions. The reactor relevant situation is one of predominant electron heating (by the α particles), albeit with nearly equal electron and ion temperatures, due to the small values of τe−i /τEi (τe−i is the electron–ion temperature equilibration time and τEi is the ion energy confinement time). Strong efforts have therefore recently been made to investigate the effect of the ratio Te /Ti on the properties of transport barriers, by applying simultaneous, separately controlled, electron and ion heating power to the plasma core. This paper presents a brief overview of the phenomenology of transport barriers in the edge and the core regions of tokamak plasmas, as well as a comparison of these observations with the present standard model of energy transport and of turbulence suppression. 2. The H-mode barrier Beyond a certain heating power, depending on the size, density and the magnetic field strength, divertor tokamak discharges transit into a different regime, labelled H-regime [1] and characterized by strong edge pedestals in temperature, electron density and angular toroidal momentum. The now widely accepted explanation of this phenomenon, reviewed for example in [2], rests on the suppression of micro-turbulence by sheared E × B rotation of the plasma. For this to happen [3], the shearing rate, given by
 

(RBθ ) ∂ Er


|ωE×B | =
(1) Bφ ∂ψ Bθ
(where R is the local major radius, ψ is the poloidal flux, Er is the electric field perpendicular to flux surface, Bθ is the poloidal magnetic field and Bφ is the toroidal magnetic field), has to exceed the decorrelation rate ωD of the turbulence prevailing prior to the transition. The experimental verification of this prediction is difficult, but has been successfully made in experiments on DIII-D [2]. The electric field is usually determined by spectroscopic measurement of the rotation of impurities, using the radial power balance for the particular impurity species and ionization state ∇pj Er = − vj,θ Bφ + vj,φ Bθ (2) Zj enj linking it to pressure p, density n, charge number Z and the poloidal and toroidal velocity components vθ and vφ . Whereas the measured values of Er during the H-mode phase can usually be explained by the toroidal rotation impressed by momentum input and the neoclassical drive arising from the temperature gradient [4], the origin of the rapid acceleration during the transition from the L-mode to the H-mode is still under dispute. Candidate contributors to this acceleration are the self-generation of flows through turbulent Reynolds’s stresses [5] and the momentum input due to the loss of supra-thermal particles across the plasma boundary [6]. A contribution to the change in |ωE×B | can also arise from the increased Shafranov shift, which will tend to increase, according to equation (1), the shearing rate on the low-field side on a given flux surface, where the pretransition turbulence is predicted and observed to be strongest [2]. The confinement improvement in the H-mode is, however, not confined to the simple addition of a strongly insulating layer at the plasma boundary. In this case the temperature increase in the core would at best be equal to that at the inner boundary of the pedestal region, but most probably smaller, as the heat diffusivity would be expected to increase with increasing Te,i . Instead, profiles show a more or less pronounced tendency of self-similarity (profile resilience), corresponding to constant LT = T /∇T for changing parameters, such as plasma

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density or heating power [7]. A possible explanation of this phenomenon is given by the theory of ion-temperature-gradient (ITG)-driven turbulence, which is predicted to set in above a certain critical value of R∇Ti /Ti . A benchmark test has been performed among a number of codes, simulating nonlinear ITG physics and the resultant turbulent transport with different plasma models, in the frame of the so-called Cyclone Project [8]. In spite of significant quantitative differences, they uniformly predicted a strong clamping of the logarithmic ion temperature gradient to the vicinity of a critical value, in qualitative agreement with the above experimental results. (Most of the experimental data on ‘profile resilience’ and in particular the results given in [7] refer to profiles of Te , which, although in the density range covered, should track closely those of Ti . At lower densities, indeed, Te is found to deviate from profile resilience more strongly than Ti , consistent with the predictions of ITG theory for these predominantly ion heated discharges with NBI.) 3. Confinement improvement beyond H-mode The energy confinement time attainable in H-mode discharges can be described by the scaling expression [9] −0.69 −0.41 0.19 1.38 0.58 0.78 ne M R a κ (3) τH(y,2) = 0.0562Ip0.93 Bt0.15 Pheat in terms of the plasma current Ip , toroidal magnetic field Bt , heating power Pheat , atomic mass number M, major radius R and (horizontal) minor radius a, ellipticity κ and line averaged density ne (units: s, MA, T, MW, AMU, 1019 m−3 , respectively). Applied to the design parameters of ITER-FEAT, this expression predicts the achievement of Q (the ratio of fusion power Pfusion to the externally applied plasma heating power Pheat,ext ) equal to 10, in pulsed, inductively driven operation [10]. To achieve full ignition (Q = ∞) in pulsed, or Q
5 in steady-state operation on ITER-FEAT, and to allow for an economically more attractive power plant, a further improvement of confinement beyond the values predicted by equation (3) is desirable. Such performance enhancement—as measured by the parameter HH = τE /τH(y,2) — has been achieved in several discharge regimes. In the following we concentrate on regimes where the major contribution to the insulation of the core comes from thermal barriers in the plasma interior. As a quantitative definition of a barrier we might take the criterion that the temperature gradients should be substantially steeper than the critical one allowed by ITG mode stability [11] in the absence of sheared rotation and strong density peaking. Barriers can be classified according to the relative role of electron and ion temperature gradients ∇Te /∇Ti . Although the ion energy density counts for the fusion power production, good electron energy confinement is also essential for a reactor, as α particles will primarily heat the electrons, resulting in the expression Wi /(Pα TEi ) = (τEe /τEi )/(1 + (τEe /τEi ) + (τEe−i /τEi )) for the total ion energy Wi . To be relevant, this regime will also have to exist at conditions of Te approximately equal to or larger than Ti , as We /Wi = (τEi + τe−i )/τEi will hold under these conditions, with τe−i /τEi  1 in a reactor. Existing experiments can therefore be categorized, as in table 1, according to the primary channel for energy input measured by the ratio Pe /Pi and the strength of the electron–ion coupling, characterized by τe−i /τE . 4. Transport barriers with dominant ion heating The standard discharge scenario leading to the formation of internal transport barriers (ITBs) was pioneered by TFTR [12] and DIII-D [13] and consists in the early application of additional

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K Lackner et al Table 1. Regimes of experiments with internal transport barriers, classified according to the dominating channel of heat input, and the degree of coupling of the two plasma components.

τe−i > τE

τe−i < τE

Pi  P e

Pi ≈ P e

Pi  P e

NBI (positive ion) heating (DIII-D, TFTR, JET, JT60-U, AUG)

Combined NBI and ECRH (AUG, DIII-D), and ICRF or FW (JT60-U DIII-D, JET) NBI and LH (JET)

ECRH, FW or LH (FTU RTP, Tore-Supra)

PEP-mode (JET)

REACTOR

Figure 1. Plasma current and neutral beam power for a reverse shear start-up on TFTR [12].

heating during the current ramp-up phase, leading to the formation of hollow current density and non-monotonic q profiles. Crucial for the guidance of this effort and the interpretation of the results was the development of the Motional Stark Effect (MSE) diagnostic [14], allowing direct measurement of the poloidal magnetic field profile. A typical start-up scenario used in TFTR is shown in figure 1 [12], giving the waveform of plasma current and NBI power. Such scenarios, at high enough heating power, lead to a rapid rise in the central plasma energy density, starting at 2.715 s for the TFTR case in figure 2. The phenomenology is characteristic of a bifurcation phenomenon, as indicated by a comparison discharge, at somewhat reduced heating power (19 MW instead of 25 MW in the reference case), not showing this transit. In this case, the pressure peaking is predominantly due to the peaking of electron density, but other examples (figure 3 from JT60-U discharge with NBI heating [15]) show barriers also in Te and Ti or, also, in the toroidal rotation velocity (e.g. JET [16]). The barrier region, at least initially, is located in the region of reversed shear, and its appearance seems linked, in many cases, to the presence of a rational surface and even MHD mode activity [17, 18]. In the barrier region, the heat diffusivities of electrons χe and ions χi are reduced dramatically, the latter below the value predicted by standard neoclassical theory [19], based on the conventional, thin-orbit assumption. Full Monte Carlo simulations of collisional ion transport [20], based on an exact representation of the particle orbits, yield χi values in the range of the actual measurements. The prevalent interpretation of barrier formation is also, in this case, the suppression of turbulence through sheared E × B rotation, with reversed magnetic shear facilitating the transition, but not being a necessary element. The quantitative application of the criterion

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Figure 2. Evolution of central electron density and electron and ion temperatures for discharges with 25 MW (full curve) and 19 MW (broken curve) neutral beam power, and current and power waveforms as in figure 1 [12]. Only the higher-power discharge transits, at 2.715 s, in an enhanced confinement state.

|ωE×B | > ωD would require, in each case, difficult experimental measurements or elaborate numerical turbulence simulations. Fortunately, however, tests have shown that the substitution of the turbulence decorrelation rate by the linear growth rate for the most unstable mode (as computed without shear flow) constitutes a good approximation [21]. The criterion |ωE×B | > γlin,max has been evaluated for many cases in different experiments, showing a good correlation to the appearance of barriers and their location. An example is given in figure 4, from DIII-D [22]. As in the case of the H-mode barrier, it is easier to understand the self-consistency of the two bifurcated states than the dynamics of the transition. After the initial barrier formation several effects can contribute to raise |ωE×B | or to reduce γlin,max . The steepening of the temperature gradient will raise the neoclassical contribution to |ωE×B |, as will the formation of a barrier for toroidal momentum transport and the increase in the Shafranov shift. The latter effect has also an important, stabilizing influence on γlin,max [23]. Note should be taken of the fact that the reversed shear corresponds intrinsically to high q in the centre, and hence—for given pressure gradients—to a more pronounced Shafranov shift. The barrier formation itself can proceed with different dynamics, as was illustrated in experiments on TFTR [24] where a substantial difference was found between transitions with balanced injection (which proceeded very abruptly) and those happening during pure co-injection (which were more gradual and similar to those found, for example, at DIII-D [2], in a like situation). ASDEX-Upgrade [25] and TFTR [24] report the observation of localized ‘bursts’ in the radial electric field, based on simultaneous measurements of both velocity components. It is probable that in many cases the transition is triggered by a radially and temporally localized formation of poloidal flow

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Figure 3. Profiles of electron density, electron and ion temperatures and safety factor q for a reversed shear discharge on JT60-U [15], with pronounced barriers in the ne and Te .

(‘zonal flows’) generated by the turbulence itself. In other cases a MHD event might play a similar triggering role [17, 18] 5. Transport barriers with dominating electron heating Barrier formation has been observed in the, apparently, totally different situation of nearly exclusive electron heating by ECRH [26, 27] at low densities, where electrons tend to decouple from ions and the latter remain relatively cold. Record parameters in this respect have been

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Figure 4. Comparison of the shear rate (equation (1)) with the maximum linear growth rate computed by a gyro kinetic, electrostatic stability code for a DIII-D discharge [2, 22] during the early phase (left), where transport is suppressed only over a narrow zone in the core and at later time when the region has expanded beyond the half-radius.

reached by FTU [27]. The recipe used is analogous to that for ion barrier formation, with early heating applied during the current ramp-up phase. Modelling of the current diffusion (no direct current density measurement was available in this case), confirmed by the observation of m = 2 double tearing modes, indicate shear reversal in the core region for these discharges. A barrier in Te is formed, whose location responds sensitively to the deposition zone of the ECRH. Obviously, in this situation the ITG modes, whose properties are assumed to dominate the ion-heating case, cannot play a significant role. An analogue to them exists for electrons— the so-called electron temperature gradient (ETG) modes. Due to their short wavelength, however, simple mixing length estimates predict for them an energy transport which should be √ by me /mi smaller than that produced by ITG turbulence. Accordingly, ETG modes would not be able to clamp the Te profiles to their critical gradient. However, recent experimental and theoretical evidence modify this picture. On the one hand, strong evidence for Te profile resilience has been found in electron transport dominated discharges [28], in which ECRH power was deposited simultaneously at two different radial locations and using continuous ECRH to form the profiles and modulated ECRH to probe the energy transport. The response found was well in line with that expected from a critical gradient model for electron transport. On the other hand, kinetic, electromagnetic simulations of ETG-driven turbulence in toroidal geometry have shown the appearance of radially elongated turbulent eddies (streamers), which can raise the transport up to the level expected from the ITG modes [29]. These modes are therefore a likely candidate to explain electron transport and Te -profile stiffness in these situations, where ITG modes are unimportant due to the low value of Ti . The simulations also indicate that these high levels of transport may exist only at intermediate, positive shear values, consistent with the appearance of transport barriers in negative shear regions. No simulations so far have tested the effect of E × B shear on the ETG modes, but applying, in a straightforward analogy to the ITG turbulence, the rule |ωE×B | > γlin,max would suggest a difficulty in quenching ETG turbulence by this means, as the linear growth rate of these modes √ is mi /me larger than that of the ITG modes. It has, however, to be noted that the difference between linear and nonlinear mode behaviour is large in the ETG case, suggesting care in applying this analogy.

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Electron dynamics dominated transport barriers have also been obtained on Tore Supra, where LH heating and current drive led to the formation of a hot core, and an enhanced performance phase (LHEP-mode) [30]. These discharges also mark important progress towards the reactor situation, as the shear reversal in these experiments was not produced by the dynamic programming of the current ramp-up, but by the effect of LH current drive. 6. Transport barriers with comparable electron and ion heating The standard transport model, based on the ITG and trapped electron turbulence predicts an increase of both the electron and ion heat diffusivities with an increasing ratio of Te /Ti [31]. It is therefore critically important to study the behaviour of transport barriers in the reactor relevant regime of comparable electron and ion temperatures. This situation can be either realized by strong collisional coupling, or by simultaneous heating of both plasma components. Simulating a reactor-type situation of strong coupling is, however, not possible in present experiments without substantially increasing the dimensionless collisionality ν ∗ above the reactor value. The arguably more relevant and certainly more flexible way is therefore the application of two separately controllable heating methods to the plasma core. The effect of Te /Ti upon energy transport should of course also show in non-ITB discharges, and, in fact, has been qualitatively verified in a series of experiments on DIII-D in which electron (FW and ECR) heating and ion (NBI) heating were adjusted to perform scans keeping either Te , Ti or β constant [32]. To test the response of ITBs, DIII-D and ASDEX-Upgrade applied additional electron heating—in the form of ECRH—to the core region of already established ITBs. Figure 5 shows the response of the central ion and electron temperatures to the heating power, as well as the time variation of the derived electron and ion heat diffusivities at different radii, for the DIII-D experiments [33]. Compared to a reference discharge, the addition of ECRH leads to the expected increase of Te (0), but also to a decrease of Ti (0). The latter can only be explained by an increase of χi , as the increase of Te will have even increased the fraction of NBI power going into the ions. In fact, an increase of χi and χe is deduced at all radii, albeit most significantly in the core region. Noteworthy is the fact that the application of ECRH led also to a reduction of the toroidal plasma rotation in the core, indicating also an increase in the momentum diffusivity. Although the phenomenon is in the generally expected direction, it can nevertheless not be explained by a quantitative analysis, as in fact all modes included in a comprehensive analysis (including ETG modes) were found to be linearly stable for the profiles measured after ECRH application. In corresponding experiments on ASDEX-Upgrade [34, 35], ECR power was applied to the core region, in heating, and also in the co- and counter-current drive modes (ECCD). ECR power was applied in the three comparison cases starting right after a (very reproducible) MHD event, which had led to a temporal breakdown of the previously established strong barrier in Ti (figure 6). In the reference case without ECR, and also in the pure heating and the counter-current drive cases, the barrier recovers. Moreover, in the latter two cases the electron temperature also increases strongly. In the co-current drive case the barrier does not recover after the event, presumably due to the additionally driven current at the axis, which tends to raise q0 and reduce the shear reversal, resulting in on-going MHD activity. Profiles are shown in figure 7 for the discharge with ECR power applied in the pure heating mode, for the phase of the NBI-only produced ITB and the combined heating phase. In the two successful scenarios, the core toroidal rotation velocity decreases, as in the DIII-D case, but this—in terms of momentum—is compensated by an increase in the plasma density. The profiles for the ECRH and counter-ECCD cases show clear barriers in both temperatures, with Te close to Ti . In spite

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Figure 5. Response of electron and ion temperatures and heat diffusivities to the addition of ECRH power to an established ITB discharge on DIII-D [33]. For comparison, the peak temperatures and the heat diffusivities at a dimensionless minor radius of 0.2 are also given for a reference case without ECRH (broken curve).

of the higher temperatures and the higher power fluxes χe and χi show no increase in the core region compared to the reference discharge without ECR power. Qualitatively similar results had been obtained previously on DIII-D, using a central FW current drive [36]. These results on ASDEX-Upgrade can be reconciled with theoretical models if the simultaneous, opposing effects of the change in Te /Ti and of the increase in the Shafranov shift, resulting from the additional ECRH power input, are taken into account. This is demonstrated by the analysis shown in figure 8, giving the maximum linear growth rate of the ITG-modes as given by the local gyro kinetic dispersion relation [37] as a function of the ratio Te /Ti , starting with the profiles of the reference shot without ECRH and including, or not, at the same time the variation of the Shafranov shift. A similar result was also obtained with the GLF23 model [38]. In fact, the Shafranov shift is essential to explain the barrier formation for both the case with and without ECRH.

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(a)

(b)

8

#12224

q

6

q0

q0

4 2

(c) #12231

q0 qmin

qmin

qmin

#12229

T (keV)

0 15 10 5

Te

Ti Te

Ti

Te Ti

ECCD ECCD 0 0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.4 0.6 0.8 1.0 1.2 Time (s) Time (s) Time (s)

Figure 6. Minimum and axis q values and central electron and ion temperature response to the application of ECR power to a NBI heated ITB discharge. (a) reference case without ECRH, (b) ECCD in counter-current direction (signals in pure heating mode are similar) and (c) ECCD in the co-current direction [34].

Figure 7. Profiles of electron and ion temperatures, electron density and toroidal rotation velocity and heat diffusivities derived from a transport analysis for the pure NBI heating phase and the NBI + ECCD phase of the discharge in figure 6(b) [34].

Reactor relevant conditions of Te ≈ Ti had also already been obtained in the PEP-mode discharges on JET, which can claim to have been the first reversed-shear discharges with ITBs [39]. In this case, the recipe for attaining the regime of reversed shear consisted in the application of strong, central ICRF heating following the injection of one or a few pellets during the current rise phase, which had produced a relatively cold plasma with a high, centrally peaked density. Shear reversal was postulated to be produced by the high bootstrap current density. Although rotation or direct current profile measurements were not available, all measurements (including the large Shafranov shift and the observation of MHD modes) were consistent with shear reversal and improved confinement in the core region.

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Figure 8. Maximum linear growth rate from a local gyro kinetic, electrostatic and electromagnetic dispersion relation of the ITG modes [37] for the initial profiles of the case in figure 7, as a function of Te /Ti , neglecting or including the associated changes in the Shafranov shift.

7. Prerequisites for the formation of ITBs Most experiments which resulted in the formation of ITBs were conducted with NBI, which provided—in addition to heating power—a central source of particles and toroidal momentum. As velocity shear and density peaking are predicted to have an important role for ITG-mode stability and turbulence suppression, it is a serious concern whether particle and momentum input, which will be absent (or greatly reduced) during the burn phase of a fusion reactor, are essential for the triggering or the maintenance of ITBs. Also, the actual necessity of shear reversal for the transition or for the maintenance of ITBs is an important issue. Strong evidence exists that none of the three effects (momentum input, central fuelling, shear reversal) are indeed necessary conditions for ITB formation, although they may contribute significantly to facilitate the transition. ITBs without NBI momentum input—in addition to the cases with dominating electron heating and cold ions—were observed in the PEP discharges on JET [39] and the net toroidal momentum input was also small in the cases with balanced injection on TFTR [24]. Clear barriers have been observed in the high-βpol discharges of JT60-U [40] in situations in which MSE measurements showed no shear reversal, i.e. at relatively large plasma radii and where the q measurements had small error bars (figure 9), although these results cover only the case Te significantly smaller than Ti . The role of particle and momentum input was, in particular, also studied in comparison experiments on JT60-U [40]. In these discharges, following the initial formation of an ITB with NBI (9 MW), the applied power was reduced to 6 MW, composed in one case only of NBI and in the other of a mix of 4.5 MW ICRF and 1.5 MW NBI. The density peaking indeed strongly diminished in the predominantly ICRF-heated case, as did also Ti . However Te increased, and clear barriers remained visible in all three parameters (figure 10). The discussion in this paper has been limited to the confinement aspect of ITB discharges. It is clear, however, that MHD stability plays a comparable and important role, not only in the negative sense by forbidding certain profiles and certain parameter ranges, but also in the positive sense of providing for quasi-stationary conditions, as in the case of ELMS. In fact, one of the critical items of ITBs is the issue of impurity control, and in particular the cleansing of the core of the reactor plasma from the helium ash. In this respect MHD modes constitute an element of hope, particularly if we can learn to control them by external means. MHD modes are, however, sometimes also observed as precursors or during the transition process [17, 18],

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Figure 9. Barrier formation in a high-βp mode discharge of JT60-U in a zone with clearly positive magnetic shear [40].

and at least one model (differential rotation caused by fast-particle ejection from the mode region) has been advanced which would give them even a causal role in this transition. 8. Summary and outlook The experimental basis of ITB physics has significantly broadened during the last few years, and the ‘standard’ theoretical model of E × B shear suppression of the otherwise dominating ITG turbulence has survived well the test of this additional evidence; ETG-driven turbulence, and its sensitivity to magnetic shear, may become a complementing ingredient of it. Obviously a number of unresolved issues remain. They still regard, on the one hand, aspects of electron transport, in particular inside the barrier zone where often all candidate modes are predicted to be linearly stable. Barriers with Te ≈ Ti have by now been achieved with simultaneous electron and ion heating, but attempts to approach these conditions in an alternative way, by raising the plasma density through gas puffing and enhanced collisional coupling between the two plasma components, usually led to the breakdown of a

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Figure 10. The effect of the partial substitution of NBI by ICRF on JT60-U. The profiles refer to a discharge phase where either 6 MW of NBI (broken curve) or 4.5 MW of ICRF and 1.5 MW of NBI (full curve) were injected.

pre-existing barrier. Also, the strong role of resonant surfaces in the ECRH heated discharges of RTP [26] still requires an explanation in terms of modelling. Profile resilience, in the regions inside the barrier zones is a widespread observation, but some controversy still persists regarding its limits, and a more extensive test against the predictions of ITG mode theory is needed. Concerning the formation of ITBs and H-mode barriers, we still lack a universally accepted model—backed-up by corresponding turbulence simulation calculations—of the dynamics of the transition process, and also a quantitative explanation for the threshold power requirement. Agreement is still also lacking concerning the scaling of the barrier width, even in the case of the H-mode pedestal; in the case of ITBs this problem promises to be even more complex. On the experimental side, the recipes for obtaining ITBs are still far less robust than those for attaining the H-mode, and, in particular, more effort is needed to crosscheck scenarios between different devices. Ultimately the control of ITBs is an ambitious target for future work, important for making them sufficiently transparent for the outflow of He-ash, and to avoid fatal MHD events. References [1] Wagner F et al 1982 Phys. Rev. Lett. 49 1408 [2] Burrell K H 1997 Phys. Plasmas 4 1499 [3] Biglari H, Diamond P H and Terry P W 1990 Phys. Fluids B 2 1 Hahm T S and Burrell K H 1995 Phys. Plasmas 2 1648 [4] Hinton F L 1991 Phys. Fluids B 3 696 [5] Kim Y B and Diamond P H 1991 Phys. Fluids B 3 1626 [6] Itoh S-I and Itoh K 1988 Phys. Rev. Lett. 60 2276 Shaing K C and Crume E C 1989 Phys. Rev. Lett. 63 2365 [7] Suttrop W et al 1997 Plasma Phys. Control. Fusion 39 2051 [8] Dimits A M et al 2000 Phys. Plasmas 7 969

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