Overview of L- to H-mode transition experiments at ASDEX Upgrade

Abstract

This paper presents an overview of results from L-H transition experiments that were performed at ASDEX Upgrade (AUG) with the aim to identify the underlying mechanisms leading to H-mode confinement. With a broad variety of experiments and new diagnostic techniques as well as modeling efforts, AUG has contributed substantially to improving our understanding of the L-H transition over the past years. In this review the important roles of the ion heat channel and the edge radial electric field (Er) in the L-H transition physics are brought into context with known dependencies of the H-mode power threshold (PLH), such as the impact of wall material, magnetic perturbations, and the magnetic configuration. Furthermore, experimental and theoretical results obtained at AUG on the L-mode edge turbulence are connected to the mean-field Er and its related shear flow. This led to a deeper understanding of the I-phase plasma regime, has resolved the so called isotope effect of PLH, and led to the development of a semi-analytical model that can describe AUG’s experimental observations of the L-H transition together with the L- and H-mode density limits.

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Plasma Physics and Controlled Fusion
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Overview of L- to H-mode transition experiments at ASDEX Upgrade
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Overview of L- to H-mode transition experiments at
ASDEX Upgrade
U. Plank1‡, R. M. McDermott1, G. Birkenmeier1, N.
Bonanomi1, M. Cavedon2, G. D. Conway1, T. Eich1, M.
Griener1, O. Grover1, P. A. Schneider1, M. Willensdorfer1and
the ASDEX Upgrade Team§
1Max-Planck-Institut f¨ur Plasmaphysik, Boltzmannstraße 2, 85748 Germany
2Dipartimento di Fisica “G. Occhialini”, Universit`a di Milano-Bicocca, 20126
Milano, Italy
Abstract. This paper presents an overview of results from L-H transition
experiments that were performed at ASDEX Upgrade (AUG) with the aim to identify
the underlying mechanisms leading to H-mode confinement. With a broad variety
of experiments and new diagnostic techniques as well as modeling efforts, AUG has
contributed substantially to improving our understanding of the L-H transition over
the past years. In this review the important roles of the ion heat channel and the
edge radial electric field (Er) in the L-H transition physics are brought into context
with known dependencies of the H-mode power threshold (PLH), such as the impact of
wall material, magnetic perturbations, and the magnetic configuration. Furthermore,
experimental and theoretical results obtained at AUG on the L-mode edge turbulence
are connected to the mean-field Erand its related shear flow. This led to a deeper
understanding of the I-phase plasma regime, has resolved the so called isotope effect of
PLH, and led to the development of a semi-analytical model that can describe AUG’s
experimental observations of the L-H transition together with the L- and H-mode
density limits.
Date: 16 November 2022
‡Ulrike.Plank@ipp.mpg.de
§See U. Stroth et al 2022 (https://doi.org/10.1088/1741-4326/ac207f) for the ASDEX Upgrade
Team.
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1. Introduction
The discovery of the high confinement mode, or H-mode, and its associated improved
particle and energy confinement provided a viable path to building energy-producing
tokamak reactors. Since then, most reactor designs assume H-mode level plasma
confinement [1, 2, 3]. Access to H-mode has, empirically, been observed above a certain
applied power level, known as the H-mode power threshold (PLH). PLH has been found
to depend on several local and global plasma parameters such as the plasma density,
the magnetic field strength, the main ion species, the wall and divertor condition and
magnetic configuration [4, 5], amongst others.
A wide variety of theories and empirical scalings have been developed (see [4, 6]
and references therein), but a conclusive understanding of the fundamental physics
mechanisms behind the transition from L-mode into H-mode (L-H transition) has not
been obtained. This makes extrapolations of the H-mode onset to future machines
challenging, because these will operate in parameter spaces very different from those
in present day devices. Therefore, a more robust physics-based understanding of the
L-H transition is crucial to predict the H-mode access and performance of future fusion
reactors correctly.
ASDEX Upgrade (AUG) has contributed greatly to our understanding of the L-H
transition through a combination of experimental and theoretical works. From these
contributions a clearer picture of the conditions under which the L-H transition occurs
has emerged and some dependencies of PLH could be explained. In this paper, we present
an overview of L-H transition studies at AUG. In particular the importance of the edge
ion heat flux for the L-H transition and its connection to the edge radial electric field (Er)
is presented in section 2. In section 3 H-mode access in different main ion composition
plasmas is discussed, while in section 4 the impact of magnetic perturbations, magnetic
configuration, and wall material on PLH and Eris investigated. In section 5 we look at
the I-phase and the L-mode edge turbulence and its interaction with E×Bshear flows
in the context of AUG experiments. In section 6 the results from AUG L-H transition
studies are summarized and conclusions are drawn.
2. Connection between the H-mode power threshold, the edge ion heat flux
and the edge radial electric field
One universal feature of PLH is its non-monotonic dependence on the line-averaged
density ¯ne, (see figure 1a), which has been observed on many tokamaks [4, 7, 8, 9, 10,
11, 12]. The H-mode power threshold exhibits a minimum at a certain plasma density,
named ¯ne,min. For densities both above and below ¯ne,min the power threshold increases.
The parameter space below ¯ne,min is known as the low density branch, while plasmas
with densities above ¯ne,min are said to be in the high density branch of the PLH curve.
For the high density branch, multi-machine scalings exist [4, 5], which show an
almost linear dependence on ¯ne, the toroidal magnetic field Bφand the plasma surface
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Figure 1. (a) Parabolic density dependence of the H-mode power threshold (PLH) in
low-torque plasmas of pure H (blue squares), D (black circles) and He (red diamonds)
at AUG with full tungsten wall. The arrow indicates the density for which PLH is
lowest (¯ne,min). The dashed lines show the H-mode power threshold predicted by the
ITPA-scaling (see equation 1) for pure D and H plasmas, respectively, which is valid
for densities higher than ¯ne,min (high density branch). Figure adapted from [12]. (b)
PLH (black) and the edge ion heat flux at the L-H transition, Qi,edge, (red) in the low
density branch, demonstrating the linear dependence of Qi,edge with density and the
plasma current dependence of PLH. Figure reproduced from [15].
S. It should be noted that these scalings were obtained from experiments in which
parameters like the plasma shape, the strike point positions, and the drift configuration
were set such that PLH is minimal. This was done to avoid the introduction of other
dependencies, that are known to influence PLH, into the scalings. Furthermore, these
scalings are only correct, if the radiated power is small. As has been recently shown at
AUG, in heavily seeded discharges the total radiated power up to the separatrix must
be taken into account in order to reproduce PLH from these scalings correctly [13]. The
most commonly used scaling reads as [4]
PLH,scal = 0.0488¯n0.717
e(1020 m−3)B0.803
φ(T)S0.941(m2).(1)
While the increase of PLH with density and plasma size is easily understood, the
magnetic field dependence is less obvious. However, this too can be understood in
connection with the paradigm of edge turbulence suppression via E×Bshear flows, which
is described in more detail in sections 2.2 and 2.3. The multi-machine scaling, however,
does not describe the behavior seen in the low density branch. A first explanation for
the increase in PLH below ¯ne,min, which also depends on the applied type of auxiliary
heating, was extracted from experiments at AUG [14, 15] and is connected to the critical
role of the edge ion heat flux (Qi,edge). This is discussed in detail in section 2.1.
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2.1. Connection between the edge ion heat flux and the low density branch
The first indication that the ion heat flux plays an important role for the L-H transition
came from a set of low density AUG experiments heated with electron wave heating
(ECRH) only, which enabled a decoupling of the electron and ion heat channels [14].
In these plasmas PLH was measured as a function of ¯nein the low density branch. The
work showed that the edge ion pressure and its gradient are important quantities at the
L-H transition (see section 2.2). These observations motivated a more detailed study of
the role of the ion heat channel for the L-H transition [15].
In the work of Ryter et al it was found that Qi,edge increases linearly with the plasma
density across both the low- and high density branches and does not exhibit a minimum
behavior, see e.g. figure 1b, whereas the edge electron heat flux (Qe,edge) displays a non-
monotonic dependence on ¯ne, similar to PLH . This result was also reproduced at Alcator
C-Mod where, together with the AUG data, additionally a positive Bφdependence of
Qi,edge at the L-H transition could be extracted (see equations 3 and 4 in [16]).
In the AUG data, the linear dependence of Qi,edge on ¯newas shown to be identical
for plasmas with 0.6 and 1 MA plasma currents, despite there being almost a factor of
two difference in PLH between these data-sets at low density [12] (see also figure 1b).
Note that in the high density branch, where the electron to ion heat exchange (pe,i) is
much stronger, no scaling of the power threshold with plasma current (Ip) is observed
[12]. This is consistent with the lack of an Ipdependence in the multi-machine scaling for
the high density branch of PLH (see equation 1). The physics behind the Ipdependence
observed in the low density branch is explored further by Bilato et al in [17]. In this
work, inspired by the experimental results, Bilato et al developed a heuristic model
for the H-mode power threshold based on the paradigm of edge turbulence suppression
by E×Bshear flows [18] (see also section 2.2). An important quantity in this model
is the ratio of the energy equi-partition time between electrons and ions, τe,i,and the
energy confinement time, τEin L-mode [17], where the latter exhibits an almost linear
dependence on Ip[19]. The model by Bilato et al reveals that PLH depends on Ipas
soon as τe,i is comparable to τE.
The work of Ryter et al demonstrated that at a given density there is a threshold
in Qi,edge that has to be reached to trigger the L-H transition. This means a critical
value of the edge ion heat flux per particle (Qi,edge/ni) is needed to access H-mode. The
threshold value can be achieved by improving the plasma confinement, i.e. increasing
τE, or by increasing the electron to ion heat exchange pe,i, i.e. decreasing τe,i. Since
pe,i ∝n2
eZi/Ai(Te−Ti)/T 3/2
e, the electron-ion coupling can be influenced by changing the
temperature ratio, e.g. with the heating method. In ECRH heated plasmas in the low
density branch the power threshold is high, because a relatively large Te/Tiis required to
couple enough power into the ion channel to reach the critical Qi,edge/nineeded for the
L-H transition. If dominant ion heating, e.g. neutral beam injection (NBI), is used, Ti
and its connected heat flux (Qi) can be increased more easily. Thus, less heating power
is needed to reach the critical Qi,edge/niand PLH is reduced, as shown in [15]. This holds,
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however, only for low torque plasmas. If the plasma torque is not negligible, it can be
seen that both the critical Qi,edge/nineeded to enter H-mode and PLH increase with
increasing toroidal edge rotation [15, 20]. The authors of these publications speculate
that this behavior can be explained by the impact of the edge rotation on the edge radial
electric field. This will be discussed further in section 2.2.
Another way to improve the electron-ion coupling in the low density branch is
simply to increase the plasma density. As density is increased, less applied power is
required to achieve the same critical Qi,edge/niat the L-H transition. Above the density
minimum, in the high density branch, the increases in the efficiency of the electron-ion
coupling with increasing plasma density is small compared to the increase in the number
of particles, resulting in the linear increase of PLH with density. This is the reason for
the minimum observed in the H-mode power threshold as a function of plasma density.
Noting that the minimum in PLH as a function of ¯neis due to the collisional coupling
between ions and electrons, Ryter et al examined the ratio of τE/τe,i for several AUG
discharges and found that the power threshold exhibits a local minimum when this
quantity is approximately equal to 9. This result held for both the Ip= 0.6 and 1 MA
data-sets. Based on these observations it is possible to develop a scaling for ¯ne,min ,
which reproduces experimental results from multiple tokamaks devices very well and
provides a prediction for ¯ne,min in ITER deuterium operation with low torque input (see
equation 3 in [15]). The density minimum in ITER is predicted to be 2.2×1020 m−3
for the half magnetic field and plasma current configuration and 4.4×1020 m−3at full
magnetic field and plasma current. This yields power thresholds of 16 and 41MW for
the half and full magnetic field and plasma current configurations, respectively, which
should be feasible with the auxiliary heating systems planned for ITER [2].
The framework of a critical edge ion heat flux explains the minimum of the PLH
curve as a function of ¯neas well as the increase in the power threshold below this value.
It can also unify observations made in plasmas with different heating systems, as well as
with different plasma currents. However, the ion heat flux is likely not responsible for
directly triggering the L-H transition. Rather, local edge quantities that are connected
to Qi,edge, such as the radial electric field (Er) and the ion pressure gradient, are more
physics-based candidates. The relationship between the surface integrated edge ion heat
flux and Er, which is a local quantity, is explored in the next section.
2.2. Connection between the edge ion heat flux and the radial electric field
One of the most commonly invoked hypotheses to explain the L-H transition is connected
to the suppression of radial turbulent transport at the plasma edge by poloidally directed
E×Bshear flows [18]. In this framework, the condition for the H-mode access is that
the E×Bflow shearing rate (ωE×B) is large enough to stabilize the characteristic L-mode
turbulence at the plasma edge. The E×Bshearing rate is given by ωE×B=−r
q∇r(Er
RBθ),
with qbeing the safety factor, rand Rthe minor and major radii, respectively, and Bθ
the poloidal magnetic field component [21]. Since ωE×Bis directly proportional to the
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gradient of Er, it is expected that Erand its formation in L-mode are of high importance
for the L-H transition.
The background radial electric field can be determined via the radial force balance
Er=∇rpi
eZini
+v⊥,iB=∇rpi
eZini
−vθ,iBφ+vφ,i Bθ,(2)
where p,n, and vrepresent the pressure, density, and flow velocity of any plasma species
and eZ its charge. Bis the total magnetic field and Bθand Bφits poloidal and toroidal
components, respectively. The flow perpendicular to the magnetic field, v⊥,i , can also be
decomposed in its toroidal and poloidal components vφ,i and vθ,i. Although the formula
holds for all plasma species (Ermust be the same for all plasma species), the behavior
of the main ion species, denoted with ihere, is of particular interest for the formation
of Er.
Assuming that the poloidal main ion rotation is determined by neoclassical theory
and that the toroidal main ion rotation is small, the radial electric field can be expressed
in the following form [22, 23]
Er=Er,neo =−Ti
eZi 1−K1
LTi
+1
Lni!,(3)
where the diamagnetic pressure gradient term (∇rpi)/(Zieni) was re-written in terms of
the logarithmic radial gradients of main ion temperature 1/LTiand density 1/Lni, with
1/Lx=−∇x
x.K1is the neoclassical flow coefficient, which depends on collisionality
[23, 24, 25].
At typical AUG edge parameters the ion collisionality is in the plateau-regime
[26, 27, 28] and K1≈0. Thus, Er≈(∇rpi)/(Zieni) or |vE×B| ≈ |vdia,i|, which is called
the neoclassical approximation in the following. It has been found in AUG H-modes
that Ercan be indeed approximated in this form [29], but in L-modes it is also often
observed that Erdeviates from Er,neo as well as that the toroidal rotation is not small
and, thus, vφ,iBθis a non-negligible contribution to Er(see sections 2.3 and 4.3).
One possible interpretation within the paradigm of turbulence suppression by
background E×Bshear flows is that externally controllable quantities like density and
heating power lead to a steepening of the background edge gradients in L-mode, which
impact the Ergradients and their related E×Bshear flows mainly via (∇rpi)/(Zieni).
At the plasma edge Ertypically develops a well-like structure with two gradients of
opposite sign. However, it is unclear if the negative (inner) or the positive (outer)
gradient is of more importance for the transition into H-mode. Therefore, in this paper
it is not separated between the two gradients and their connected E×Bshear layers, as
either of them could be important for the H-mode access, although experiments at AUG
indicate that the edge turbulence suppression starts at the location of the inner shear
layer [30]. In this framework, H-mode is then achieved as soon as a ‘threshold’ value
in ωE×Bis reached, i.e. one that is large enough to suppress the turbulent transport in
the edge. At AUG it has been found that, when moving from L-mode towards the L-H
transition it is mainly 1/LTiwhich changes, while the density gradient contribution,
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Overview of L- to H-mode transition experiments at ASDEX Upgrade 7
approximated by 1/Lne,stays fairly constant [31, 32]. However, if by any means, e.g.
wall condition, the latter is changed, then this also has an impact on the required power
needed to enter H-mode, as will be shown in section 4.1.
These observations on local parameters at the plasma edge are in line with the
findings of the critical role of Qi,edge at the L-H transition, discussed earlier in section
2.1. Although within the paradigm of turbulence suppression by E×Bshear flows, it
is not Qi,edge itself that is expected to be important, but rather ∇Erand ωE×B, these
quantities are all related to the main ion temperature gradient: Ervia equation 2 and
the edge ion heat flux via Qi,edge =−χini∇Ti, with χibeing the ion heat diffusivity.
Within this picture, the increase in PLH and the required Qi,edge to initiate an L-H
transition observed in higher rotation plasmas can also be explained. If the increased
rotation reduces the local E×Bshear, a higher applied heating power (and Qi,edge)
would be required to further increase the edge ion temperature gradient, compensating
for the impact of the rotation, to obtain the same edge Er.
The interconnections between Qi,edge and Er, as they relate to PLH, were already
pointed out in [14], where detailed analysis of the edge kinetic profiles demonstrated that
the edge electron temperature Te,edge increases linearly with applied ECRH power at
constant plasma density, whereas Ti,edge remains fairly constant. The same observations
were also made in H plasmas in [33]. As a result, the ion pressure at the plasma edge
(pi,edge) was observed to increase linearly with increasing plasma density at the L-H
transition, as did Qi,edge, whereas pe,edge behaves more like Qe,edge and PLH at the L-H
transition.
In the work of Sauter et al it was also found that the minimum of the Erwell,
Er,min is constant at the L-H transition (Er,min ≈ −15 kV/m) for plasmas with a
constant magnetic field of −2.5 T, but different densities (covering the low and high
density branch of PLH). In that work the edge radial electric field was to a large extent
not directly measured, but deduced from edge temperature and density measurements
together with neoclassical theory using equation 3. Assuming now additionally that the
width of the Erwell is constant, as was found experimentally in H-modes at AUG [34],
then the value of the Erminimum can be used as a proxy for its gradients. In conclusion
the work of Sauter et al shows experimentally, that for a wide range of plasma densities
the Ergradients are constant at the L-H transition. Similar assumptions on the edge
Erin L-mode plasmas were made by Maggi et al on JET data [35]. In this work the
same conclusions for JET L-H transitions were drawn as previously for AUG, where
they showed that an apparent threshold in the minimum value of Eris required to enter
H-mode.
It should be noted that all the experiments described so far were carried out for
a fixed magnetic field value and in a single magnetic field configuration, namely lower
single null, favorable drift. The impact of changes in these two parameters are described
in the following section and in section 4.3, respectively.
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Figure 2. (a) Neoclassical approximation (Er,neo) and Doppler reflectometry (DR)
measurements (purple) of the minimum of the radial electric field well at the plasma
edge in a range of plasma confinement states. At the L-H transition (black circles)
a value of Er,neo ≈ −15 kV/m is found at AUG for a wide range of edge densities in
favorable drift plasmas with |Bφ|= 2.5 T.Figure reproduced from [14]. (b) Maximum
of |vE×B|at the L-H transition plotted against plasma edge density (ρpol ≈0.95) for
a range of favorable drift plasma discharges in which also |Bφ|was varied from 1.7 –
3.0 T. The figure includes the points at the L-H transition from (a) (diamonds) as well
as actual measurements of the vE×Bminimum by CXRS (circles) and DR (squares).
Red points are vE×Bmeasurements acquired in hydrogen and blue points are from
deuterium plasmas. Figure reproduced from [36].
2.3. Magnetic field dependence of the H-mode power threshold
Building on the L-H transition results described in the previous sections, the relationship
between the actual measured edge Erand PLH was investigated further by Cavedon et al
in [36] by exploring the magnetic field dependence of PLH (see equation 1) in deuterium
(D) and a small subset of hydrogen (H) discharges. In this work the L-mode edge
Erprior to the L-H transition was measured with 1 – 2 ms time resolution using a fast
charge exchange recombination spectroscopy (CXRS) technique [37]. Due to the limited
radial resolution of this method, it was not possible to extract meaningful Ergradients
from the experimental data directly. Therefore, again Er,min was used as a proxy for the
Ergradients (see also section 2.2). It was observed that Er,min at the L-H transition
deepens linearly with increasing magnetic field. This results in an almost constant
E×Bvelocity shear at the L-H transition, since ωE×B∝ ∇rEr
B∝ |Er,min
B|= max(|vE×B|).
This observation is an important result to distinguish experimentally vE×Bas a more
fundamental quantity for the L-H transition than Er.
The work by Cavedon et al also showed that the maximum in |vE×B|at the L-H
transition remains constant as a function of electron density for the different magnetic
fields explored and that this value is consistent with earlier data-sets [14, 26]. This
is shown in figure 2b. Here, the maximum of the measured |vE×B|is shown for the
entire data-set from the work by Cavedon et al (circles and squares) and is compared
to the results from the previous works (diamonds and triangles), neither of which
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directly measure Er(or vE×B), but used the neoclassical approximation |vE×B|=|vdia,i |.
Combining all the data-sets, a threshold value of |vE×B|= 6.7±1.0 km/s was found at
the L-H transition. Since in these data-sets PLH varied by a factor of about three, this
result provides a clear, concise explanation for the observed dependence of PLH on Bφ
(see equation 1). A critical threshold in vE×Bneeded to enter H-mode automatically
incorporates the observed magnetic field dependence, as has been also shown with fluid
codes modelling the L-H transition (see [38] and references therein). Increasing the
magnetic field reduces vE×Bsuch that steeper Ergradients are required and, hence, a
higher edge ion pressure gradient, edge ion heat flux, and PLH, in order to obtain the
same critical vE×Bshear at the L-H transition. It is important to note that the same
value for the critical vE×Bwas found in both H and D plasmas. This has important
ramifications for interpretation of differences seen in PLH between different hydrogen
isotopes and will be discussed further in section 3.
It is worth mentioning that the work by Cavedon et al examined the scaling of
Er,min with magnetic field in the high density branch only. However, together with
the previously reported results on the critical role of Erand Qi,edge in the low density
branch [14, 15], it is likely that the magnetic field scaling of Er,min seen by Cavedon
et al would also be recovered in the low density branch. As such, vE×Bseems to be a
more fundamental quantity for the L-H transition than Eritself, and this observation
is consistent with the magnetic field scaling of Qi,edge at the L-H transition found in
Alcator C-Mod [16], which is valid for all plasma densities.
At ASDEX Upgrade the experimental investigations into the role of the radial
electric field and its associated quantities in the L-H transition has continued with ever
improving diagnostic capabilities and expanding the explored parameter space. Recent
experiments pushed to even lower densities [27, 32]. It is interesting to compare the
minimum of vE×Bfrom these new measurements with the previous data-sets presented
in [36]. This comparison is shown in figure 3.
The new measurements of vE×Bat the L-H transition, determined with He II
spectroscopy (HES) [32] and Doppler reflectometry (DR), are shown as blue circles for
D and red squares for H plasmas in figure 3. As shown in [32], the two Ermeasurement
techniques exhibit excellent agreement in L-mode plasmas. This new data-set contains
data from plasmas heated with ECRH only, with a constant magnetic field of −2.5 T at
the geometric axis, and a plasma current of either 0.8 or 1.2 MA. For the entire covered
density range, no difference in the minimum of vE×Bis found between H and D plasmas,
which is consistent with former observations at AUG [36], and between the low and high
plasma current discharges. The latter is consistent with the findings by Ryter et al that
Qi,edge at the L-H transition does not show any dependence on Ip(see also section 2.1).
For comparison of the new data with the old data-sets, the vE×Bdata points from
Cavedon et al , measured with CXRS, are shown in figure 3 as grey points, while the
data points from [14] and [26], for which the neoclassical approximation was applied
to determine Er, are plotted in black. Above an edge density of 2.5×1019 m−3a
direct comparison between the different measurement techniques is possible. There is
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good agreement between the results within error bars, although the new measurements
give a systematically lower max(|vE×B|) than the old ones. Below an edge density of
2.5×1019 m−3, which corresponds to a plasma located in the low density branch of
PLH, a clearly lower critical vE×Bis measured than is expected from the approximation
|vE×B| ≈ |vdia,i|. This deviation indicates not necessarily that the poloidal rotation is
non-neoclassical, but that under these plasma conditions, i.e. at low density, the toroidal
main ion flow is not negligible and has to be taken into account in the determination of
Er, as also shown in [27].
The variation in the measured max(|vE×B|) at the L-H transition does also not
necessarily imply that the shear of vE×Bis not constant at the L-H transition. As it
is regularly observed in ECRH heated plasmas, in which the toroidal main ion flow is
purely intrinsic, the latter just leads to a shift of the entire edge vE×Bprofile, leaving its
gradients nearly unchanged, but reduces max(|vE×B|) [27, 39]. This implies that the same
criterion for turbulence suppression by a critical ωE×Bcan still hold, as discussed later
in section 4.2, but the assumption that the minimum of Eris a proxy for its gradients
is not valid under these conditions. A quantitative assessment of the Ergradients and
their related E×Bshearing rates is foreseen for this new data-set, which will require
a systematic and careful study of the radial uncertainties of the measured Erprofiles.
It should also be noted that recent work by Silva et al [40] shows Ermeasurements
at the L-H transition in the JET tokamak and reports on very similar observations as
presented here for AUG.
In summary, the framework of a critical Qi,edge is able to explain the experimental
observations in the low density branch of the PLH curve and the density minimum.
It is also able to unify experimental observations of PLH in this parameter regime for
plasmas with different combinations of ion and electron heating, making Qi,edge a more
physical macroscopic quantity for understanding L-H transitions than PLH. However,
Qi,edge alone is not able to explain all of the experimental observations, for example, the
dependence on the magnetic field is only explained by connecting Qi,edge to vE×Band its
shear. In addition, Qi,edge does not provide a direct explanation for the dependence of
PLH on the main ion species or on the magnetic configuration. Instead, to understand
these phenomena, local edge quantities, like Er, have to be investigated and linked to
the characteristics of the edge turbulence.
3. Impact of main ion species composition on the L-H transition
A dependence of PLH on the main ion plasma species was found already in early isotope
experiments [41, 42]. For hydrogenic species PLH scales with the inverse of the main ion
mass Ai.Thus, in hydrogen (H) plasmas PLH is about two times larger than in deuterium
(D) plasmas [42]. The H-mode power threshold for pure helium (He) plasmas varies
for different machines between 1 and 1.8×PLH(D) [20, 41]. In the past years, more
experimental and theoretical investigations have been performed at AUG to elucidate
the reasons for the dependence of PLH on the main ion species. The most important
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Figure 3. Minimum of the experimentally determined edge vE×Bat the L-H transition
plotted against the plasma edge density. The measurements were made with He II
spectroscopy (HES) [32] and Doppler reflectometry (DR) in D (blue circles) and H
(red squares) plasmas of favorable drift configuration with Bφ=−2.5 T and Ip= 0.8
or 1.2 MA. The data of figure 2 are also plotted in this figure for comparison. Here,
the experimental data acquired with CXRS [36] are shown as grey symbols, while the
data of [14] and [26], using the neoclassical approximation |vE×B|≈|vdia,i|, are shown
as black symbols.
results of these investigations in pure D, H and He plasmas and in mixed H-He and H-D
plasmas are presented in the following.
3.1. Pure H, D and He plasmas
Figure 1a shows the parabolic dependence of the H-mode power threshold on electron
density as measured in AUG pure H, D and He plasmas. The corresponding experiments
were all performed after the switch from a carbon to a tungsten wall [12] and the
identification of the power threshold at low density was made possible by the extension
of the ECRH systems on AUG [43]. The data show that in a metal-wall AUG
PLH(He) ≈PLH (D) [44]. Recent measurements in He plasmas at AUG could confirm
this result [32], which is different from observations in carbon wall machines, where it is
found that PLH in He is higher than in D by about 40 % [10, 44, 45]. The latter is also
the current assumption for ITER He operation, namely that PLH(He) ≈1.4×PLH (D)
[2]. However, recent experiments at JET have also found comparable power thresholds
between helium and deuterium with the ITER-like wall when considering the high
density branch [46]. On the other hand, the density minimum is shifted towards
higher values for He in JET, implying that PLH(He) > PLH(D) at the respective density
minimum, which is not observed at AUG. At AUG the density minimum and PLH at
the density minimum are the same in He as in D plasmas [12].
As can be seen in figure 1a, also in the all metal-wall AUG PLH is twice as high in
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pure H compared to pure D plasmas. Therefore, the role of the edge ion heat flux at
the L-H transition was investigated also in pure H plasmas [33] and it was found that
Qi,edge is as well twice as large in H as it is in D, but again it increases linearly with the
plasma density. Although this means that there is not one critical value of Qi,edge/ni
at the L-H transition, which unifies observations in deuterium and hydrogen plasmas,
it is also known that the turbulent transport is increased in H compared to D plasmas
(see [47] and references therein). In the framework of a critical E×Bshear needed
to trigger the L-H transition, this would imply that, due to the increased turbulent
transport, more heating power is needed in H plasmas to establish the same critical
edge gradients required at the L-H transition. This, in turn, results in a higher PLH
and a higher Qi,edge for H plasmas. On the other hand, one might also expect that the
higher turbulent transport level in H would require a higher E×Bvelocity shear at the
L-H transition to be able to suppress the characteristic edge turbulence.
In several comparative experiments, the edge Eror its minimum were measured
at the L-H transition in both D and H plasmas at AUG. As can already be seen from
figures 2b and 3, the minimum of vE×Bat the L-H transition is the same in D and H
for a given plasma density (see section 2.3 for a description of the different data-sets).
More recent Ermeasurements with improved diagnostic capabilities (HES and DR) [32]
show that not only the minimum of Eris the same for D and H plasmas at the L-H
transition, but also the width of the Erwell is of comparable size. This is shown in
figure 4 and justifies that in these conditions, i.e. the high density branch, Er,min can be
used as a proxy for its gradients. It is also observed that for same plasma conditions,
i.e. same plasma density and same heating method, the strength of both the inner and
the outer Ergradient are the same between D and H, despite a factor of 2 – 3 difference
in the amount of applied heating power (see also figure 4). Further analysis of the
edge profiles has revealed that also the edge ion pressure gradient is comparable in D
and H plasmas at the L-H transition [33, 48]. These experimental results confirm the
hypothesis that in hydrogen plasmas a higher applied power (and edge ion heat flux)
is required to obtain the same critical edge gradients at the L-H transition as seen in
deuterium, on account of the higher ion heat transport. Hence, the same conditions as
observed in D plasmas seem to hold quite robustly also in H, when the differences in
the turbulent heat transport as a function of ion mass are taken into account. It should
be noted that similar observations have also been made by Birkenmeier et al in recent
isotope L-H transition experiments at JET [49, 50].
Several recent theoretical works studying the turbulence in the L-mode edge have
identified collisional drift-wave turbulence as the dominating transport mechanism
[51, 52, 53], due to the increased collisionality in that region. This is in contrast to
the ITG-TEM instabilities typically present in the plasma core. The presence of drift-
waves makes the parallel electron dynamics in the gyro-kinetic equation important for
simulating the transport and the ion mass dependence enters via the electron to ion
mass ratio important for the electron dynamics. As can be seen in figure 9 of reference
[51], at high collisionality the turbulence growth-rates are expected to be a factor of two
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Figure 4. Experimental measurements, acquired with He II spectroscopy (HES) and
Doppler reflectometry (DR), of Erprofiles at the L-H transition in pure deuterium
plasmas (left) and pure hydrogen plasmas (right). They reveal that the edge Er,
including its gradients, is very similar for the two ion species at the respective
confinement transition.
larger in H compared to D.
Within the framework of turbulence suppression by the background E×B
shear as the mechanism initiating the L-H transition, one would expect that a
corresponding increase in ωE×Bwould be required in hydrogen to enter H-mode, in
seeming contradiction with the experimental data. In the work of Cavedon et al [36],
as well as the newest results presented here (see figures 3 and 4), no difference in vE×B
(or Er) at the L-H transition are observed between hydrogen and deuterium. The lack
of difference is potentially explained within the simulations, at least in part, by the
highly non-linear response of the plasma turbulence to the E×Bshear as well as the
inter-dependencies with other plasma parameters [31, 54]. Bonanomi et al showed that
at low plasma βthe inclusion of the E×Bshear in the simulations has only a small
impact on the turbulence, while at higher βthe effect is non-linear, with small increases
in ωE×Bresulting in strong turbulence suppression [31, 54]. This effect is tied to the type
and scale of the turbulent structures, with larger scale (low ky) instabilities being found
when increasing the edge plasma β. The simulations highlight the differences expected
in the turbulence properties between hydrogen and deuterium plasmas, but also as a
function of plasma β. In both deuterium and hydrogen plasmas βchanges in response
to multiple design parameters including magnetic field, plasma current, electron density
and applied heating power. As such, all of these changes are expected to also impact
the turbulence properties at the edge, making the constant vE×Bvalue found over a wide
range of parameters in deuterium just as unexpected as finding the same value present
in both H and D plasmas.
The AUG results, in combination with the new simulations, suggest the following
qualitative picture: In a given L-mode plasma, the application of external heating
increases the power in the ion channel, increasing the edge ion heat flux, the ion
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temperature gradient, the radial electric field, and the corresponding vE×B. At the same
time, the increase in applied power increases the plasma pressure, altering the turbulence
structures at the edge towards larger scale instabilities that are strongly, and non-linearly
susceptible to E×Bshear stabilization. The strongly non-linear turbulence suppression
as a function of increasing ωE×Bis qualitatively and to some extent quantitatively
consistent with the data [31, 54]. From a purely experimental perspective the data
demonstrate a clear vE×Bthreshold for the L-H transition, which applies equally well
to both D and H plasmas. The observed increase in PLH in H compared to D directly
follows from this result, when combined with the well understood changes in the edge
turbulent transport.
3.2. Mixed H-D and H-He plasmas
It is also of interest to examine how PLH changes when transitioning from one main
working gas to another and in plasmas with mixed main ion species. The latter is
particularly relevant for reactors that will operate with 50-50 D-T mixtures, while the
former is of interest for the start-up phase of ITER operation [2]. The power threshold
in D-T plasmas has recently been investigated in JET [49, 55], while experiments at
AUG have focused on the behavior of PLH in hydrogen-deuterium mixes as well as
hydrogen plasmas seeded with controlled amounts of He [56]. The latter experiments
were motivated by observations at JET that showed a strong reduction of PLH in NBI
heated H plasmas with modest levels of He seeding (He concentration cHe =nHe/neup
to 10 %) [57]. As discussed in the previous section, in AUG the power threshold in H is
twice as large as in D, while in He it is similar to the deuterium threshold. Hence, during
the transition from a hydrogen-dominated plasma to a He plasma, it is reasonable to
expect a decrease in PLH from the H to the He level.
This transition was explored in AUG experiments in which H plasmas were seeded
with controlled amounts of He up to a He concentration of 20 % [56]. The obtained PLH
values, also normalized by the ITPA-scaling of D plasmas (see equation 1) to account
for the slight density increase with increasing amount of He seeding, are shown in figure
5a,b, respectively. No change in the threshold is observed, inconsistent with the JET
observations [57], but consistent with previous AUG results, where a reduction in PLH
when moving from H to He was only obtained at cHe values of about 30 % [44]. Note that
at cHe = 20 %, with the typically low-Z impurity levels at AUG, the H concentration
is still more than 50 % of the electron density. However, at 30 % He concentration
nHe/nH>1, making it effectively a He plasma with hydrogen seeding.
The AUG PLH results were all obtained in plasmas close to the density minimum.
Thus, they are consistent with recent DIII-D results [58], which also show no change in
the high PLH of hydrogen at low He seeding levels (cHe <20 %) for plasmas located in
the high density branch. The very strong reduction of the hydrogen power threshold
by about 25 % for less than 10 % He seeding as observed at JET is, therefore, not
reproduced by either the AUG or the DIII-D experiments.
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Figure 5. (a) H-mode power threshold in NBI (red) and ECRH (blue) heated mixed
hydrogen-helium plasmas plotted against the He concentration (in % of the electron
density). The high PLH in H plasmas does not decrease significantly with admixture
of up to 20 % of He, even if the density increase due to the additional He injection
is taken into account, by normalizing PLH to the ITPA-scaling [4] (b). The edge ion
heat flux at the L-H transition (c) is also found to be the same independent of the He
concentration and external heating source. Figure adapted from [56].
In contrast to JET, most of the plasmas in the AUG experiments were heated
with ECRH (blue circles in figure 5), also NBI heating was used for a small subset of
discharges (red squares). As can be seen in figure 5, PLH in the NBI heated plasmas is
by about 20 % higher than in the ECRH cases. As discussed previously in section 2, at
several tokamaks such a difference in PLH between NBI and ECRH heated plasmas is
observed, which is related to the differences in torque input and toroidal edge rotation
and its effect on Er. For the here presented H plasmas with He seeding the change in
edge rotation alone was, however, not big enough to explain the differences in PLH [56].
Another effect was at play, which was resolved via power balance calculations. They
show that at the L-H transition Qi,edge is the same within the uncertainties for both
the ECRH and the NBI heated plasmas and that this value remains constant over the
entire range of explored He seeding, see figure 5c. The differences observed in PLH with
heating method are related to the higher impact of the heat exchange term (pe,i) on
Qi,edge in H plasmas compared to D plasmas (inverse mass dependence, see section 2.1)
and the dependence of pe,i on the temperature ratio Te/Ti, which is actively influenced
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by the heating method. While in ECRH heated plasmas Te/Tiis larger, increasing pe,i
and, thus, Qi,edge in L-mode plasmas at the density minimum, in NBI plasmas this ratio
is smaller, requiring more heating power to reach the critical Qi,edge needed to enter
H-mode [56].
The results from these L-H experiments in mixed H-He plasmas conducted at AUG
also show that in plasmas in which the heat exchange term is the dominant contribution
to Qi,edge, the H-mode access is determined by the transport properties of the plasma
core. This will also be the case in ITER PFPO-1 in which only electron wave heating
is available [2].
At AUG the behavior of PLH across the transition from deuterium to hydrogen
dominated plasmas has also been investigated and results from the initial experiments
were presented in [56]. Since then, the investigations have been expanded to cover
the complete transition from hydrogen to deuterium, see figure 6, which combines the
originally published data-set with the new results. PLH and Qi,edge exhibit a very similar
dependence on the relative hydrogen content (nH/(nH+nD)), with both remaining at
the deuterium level until the plasma is about 50 % H, as reported in [56]. Between
nH/(nH+nD) = 0.5 and 1 both quantities start to increase, which is shown in figure
6a for PLH and in figure 6b for Qi,edge. This results in a non-linear increase of PLH and
Qi,edge with nH/(nH+nD), as indicated by the respective fit functions in the figure (black
solid lines).
Besides the L-H transition, also the H-L back transition was investigated in these
mixed H-D plasmas. While colored symbols correspond to the L-H transition in figure
6, the H-L back transition is depicted with the white symbols. PHL aligns very well
with PLH, but the lack of hysteresis, which is usually observed [12], can be ascribed to
the fact that the density dependence is not captured in figure 6a. Due to the design of
the discharges, the L-H transitions occur systematically at lower plasma densities than
the respective H-L back transitions. If the density increase were taken into account, a
hysteresis between PLH and PHL would be visible.
Figure 6c shows the minimum of the radial electric field measured at these various
transitions. Consistent with previous data-sets in pure D and H plasmas (see section
3.1), Er,min is found to remain constant at about −11 kV/m regardless of the main
ion species mix. As Er,min can be used as a proxy for its gradients in these plasma
conditions (see sections 2.3 and 3.1), this observation implies that the vE×Bshear must
be constant, independent of the main ion species composition. The constant E×Bshear
together with the non-linear increase of PLH and Qi,edge with increasing nH/(nH+nD)
indicates, according to previous argumentation (see section 3.1), that also the L-mode
edge turbulent transport increases non-linearly with increasing hydrogen content. It is
foreseen to reproduce this observed dependence of the L-H transition on the effective
main ion mass in gyrokinetic simulations and a semi-analytical model developed for the
L-H transition at AUG (see section 5.1).
Also Er,min does not show any hysteresis and has the same value of about −11 kV/m
at the L-H as well as at the H-L back transition. This is consistent with previous
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Figure 6. (a) Net input power at the L-H transition (colored symbols) and the H-L
back transition (white symbols) plotted against the relative hydrogen content. Both
PLH and PHL increase non-linearly with increasing hydrogen content, which is also
indicated by the black line, a fit to the experimental data. (b) The edge ion heat flux
at the L-H transition exhibits a similar increase with relative hydrogen content as PLH.
(c) The minimum of Er, which can be used as a proxy for its gradients at these plasma
densities, is constant at about −11 kV/m, independent of the hydrogen content and
for both the L-H and the H-L back transition.
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measurements of the electron pressure gradient at the L-H and H-L back transition. For
medium plasma densities, where electrons and ions are coupled, it was found that the
H–L back-transition occurs at the same electron pressure gradients as the L–H transition
[59]. The experimentally observed lack of hysteresis in local edge quantities compared
to macroscopic quantities, like the power threshold, is quite interesting, as it suggests
that, despite different edge transport properties in H- and L-mode, at the L-H transition
the same criterion must hold which leads to the confinement transition. This reinforces
the need for self-consistent simulations of edge turbulence-flow interaction in order to
reproduce an entire L-H-L cycle correctly.
4. Impact of magnetic configuration and wall condition on the H-mode
power threshold
In section 2 a relatively simple explanation for the Bφdependence of PLH was presented.
However, not only the magnetic field strength, but also the magnetic field geometry can
influence PLH. A very well known example of this is the observation that PLH is different
by roughly a factor of two depending on the direction of the ion ∇B×Bdrift relative
to the active X-point of single-null magnetic configurations. When the ion ∇B×B
drift points towards the active X-point PLH is lower than when the ion ∇B×Bdrift
points away from the active X-point. Hence, it is the practice to refer to the former
configuration as ‘favorable’ and to the latter as ‘unfavorable’. This observed difference
in PLH with drift configuration, despite being well known for many years, does not have
a robust explanation. Recent AUG experiments, aimed at illuminating this dependence
of PLH [27], are presented in section 4.3.
In addition to the X-point configuration, perturbations to the magnetic field, such as
those imposed for suppression of edge localized modes (ELMs), have also been observed
to impact the H-mode power threshold [10, 60, 61, 62, 63, 64, 65, 66]. ITER plans to use
magnetic perturbation (MP) coils to achieve the desired ELM suppression and ideally
to apply them before the L-H transition, such that even the first ELM can be avoided.
As such, any changes to the power threshold in the presence of MPs is very relevant for
ITER operation. For this reason experiments to explore this issue were performed at
AUG [39]. The results of these experiments are summarized in section 4.2.
These examples demonstrate that changes in the plasma edge and the scrape-off
layer (SOL), either due to drifts, details of the magnetic geometry, or SOL transport
can influence the confined region and PLH. Another example of this is the influence of
the wall material on the H-mode power threshold. While not intuitive, the impact of
wall material on PLH, specifically the reduction seen in metal-walled devices compared
to carbon-walled machines, is a robust observation, first seen at AUG [12], and discussed
in detail in section 4.1.
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4.1. Wall material
ASDEX Upgrade’s gradual transition from a carbon (C) wall to a pure tungsten (W)
wall provided an unprecedented opportunity to study the impact of wall material
on tokamak operation, including plasma confinement, density and impurity control,
pedestal transport, and the L-H transition. The wall material transition took place
gradually between 2003 and 2007 [67], at which time also a cleaning of the machine was
performed to remove the residual carbon from the tungsten surfaces. In 2007 and 2008
two full AUG operational campaigns were dedicated to exploring tokamak operation in
the absence of low-Z wall materials. Therefore, no boronizations or other low-Z wall
coating methods were employed during this time. A robust observation from these
campaigns, and all subsequent campaigns in AUG with W wall, is a reduction of the
H-mode power threshold by 25 % compared to the C wall [12]. A similar 30 % reduction
of PLH was then also observed at JET after the transition to the ITER-like wall [35].
The similarity of observations between the two machines provides additional
confirmation of the ubiquity of this result, which has important ramifications for ITER.
Due to its metal wall, the H-mode power threshold in ITER in D is expected to be
lower than PLH predicted by the ITPA-scaling [4]. In addition, the power threshold in
hydrogen plasmas was also explored, and a similar reduction of the power threshold
between the C and W wall was observed [12, 56]. As such, this effect is expected to also
apply to the early non-nuclear phases of ITER operation.
The reduction of PLH with a metal wall is not due to increased and unaccounted for
radiation by the introduction of a high-Z material. This was explicitly checked in [26].
While early speculation considered plasma dilution by the increased C concentration
as a potential candidate to explain the higher PLH in the C-walled AUG [12], the
work by Shao et al identified changes in the edge density profiles as a key element
for the different PLH [26]. In this work it was shown that with the W wall the L-mode
electron edge density is higher at the pedestal top location and exhibits a steeper edge
gradient compared to the neprofile in the C-walled AUG. This leads to an intrinsically
larger logarithmic edge density gradient 1/Lnein a W compared to a C wall machine.
The reasons for the changes in the edge density profiles arise from different divertor
detachment conditions combined with a higher recycling coefficient for W, since a larger
number of energetic particles is reflected from the metal wall [68].
Furthermore, in the work by Shao et al it was also found that in both W and C
wall AUG the same minimum value of Eris obtained at the L-H transition and that
this value is very similar to those deduced by Sauter et al [14] and later by Cavedon et
al [36]. With similar assumptions as made in [14], these observations indicate that the
same critical Ergradients have to be established at the L-H transition in both C- and
W-walled machines. Combining this result with the observed larger logarithmic edge
density gradient 1/Lnein the W compared to the C wall, recalling that if ne=niis
assumed 1/Lneenters Ervia (∇rpi)/(Zieni) (see equation 2), gives an explanation for
the reduced PLH in a W-walled machine. With an intrinsically higher density gradient
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less heating power is needed to establish the same Tiand, thus, Ergradients needed for
the H-mode access. This result demonstrates that Erand its related local quantities
are fundamentally connected to the L-H transition physics and can unify observations
made on a macroscopic scale.
4.2. Magnetic perturbations
To avoid already the first ELM, it might be necessary to apply magnetic perturbations
(MPs) already prior to and during the L-H transition. For this reason it is important
to understand how the MPs influence PLH and act on the edge quantities important for
the L-H transition. In experiments on different tokamaks [10, 60, 61, 62, 63, 64, 65, 66]
it has been found that PLH increases with increasing amplitude of the applied magnetic
perturbations, where also a threshold behavior is observed, and that PLH can be
increased by a factor of two compared to the value without MPs.
AUG is equipped with two rows of MP coils, which can produce perturbations
with a toroidal mode number nup to 4 [69]. Therefore, also at AUG extensive L-
H transition studies with MPs have been conducted in the past years. For the L-H
transition experiments at AUG resonant and non-resonant n= 2 perturbations have
been applied, since n= 2 perturbations are effective for ELM suppression in H-mode
[70]. Initial experiments at AUG showed that the effect of PLH by MPs depends on the
density [12, 71]. In the low density branch, up to the density minimum, PLH was not
affected by the MPs. With increasing density, however, PLH increased by up to 20 %
with the application of MPs. For these experiments a relative perturbation strength of
∂Br/Bφ= 1.2 – 1.4×10−4at the q= 5 magnetic surface was used.
More recent experiments [39] employed MPs with larger relative perturbation
amplitudes by lowering the toroidal magnetic field strength and increasing the current
in the MP coils. These experiments show that PLH also increases at low density
(¯ne≈3.5×1019 m−3), if a critical value of about ∂Br/Bφ= 1.7 – 2.0×10−4is
exceeded. This result is in line with observations of other tokamaks [10, 61, 63, 64, 65].
Furthermore, it is found that the increase in PLH depends on the alignment of the
MP field, set by the differential phase angle ∆ϕUL between the MP field from the
upper coil set and the lower coil set. Figure 7 shows that PLH can increase up to
80 % for ∆ϕUL = 135 – 180°. This alignment of the MPs at highest PLH differs from
the equilibrium field alignment. The same alignment is required to suppress ELMs in
H-mode, but the relative radial magnetic field perturbation required to sustain ELM
suppression at ASDEX Upgrade is below the critical value for the increase of PLH. These
might be promising results for ITER, as in AUG ELM suppression can be sustained
without a simultaneous increase of the H-mode power threshold.
Linear resistive single fluid magneto-hydrodynamic (MHD) calculations using
MARS-F [72] were performed to interpret these experimental results. They show
a correlation of PLH with the resonant component of the radial field perturbation,
represented by the normalized quantity b1
res [73] and calculated at the m=nq = 10
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0 45 90 135 180 225 270 315
n = 2
UL [deg]
0.6
0.8
1.0
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fLH
crit
(
b
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Figure 7. PLH versus the MP field alignment ∆ϕUL.PLH is highest when the radial
field perturbation b1
res maximizes. Figure adapted from [39].
rational surface (mis the poloidal mode number). This correlation is depicted in figure 7
and it shows that b1
res including the plasma response (solid blue line) is required to predict
the ∆ϕUL needed to increase PLH. Calculations using only the vacuum field (dashed
blue line) are not able to predict the dependence on ∆ϕUL correctly. Furthermore, the
inclusion of a critical magnetic field perturbation strength of ∂Br/Bφ= 1.7 – 2.0×10−4
in the linear MHD calculations improves significantly the reproduction of the behavior
of PLH with the radial field perturbation (solid red line) [39].
As discussed before (see section 2.2), one explanation for the L-H transition is
that the E×Bvelocity shear suppresses turbulent transport in the plasma edge.
Previous studies at several tokamaks [61, 62, 63, 74, 75] suggested that the application of
externally applied magnetic perturbations induces ergodization of the magnetic field at
the plasma edge in L-mode, which leads to a reversal and flattening of the Ergradients.
Hence, within this picture, MPs impede access to H-mode via their impact on the edge
radial electric field profile. Another possible explanation is that turbulent transport
increases in the presence of MPs, which leads to a flattening of the edge kinetic profiles,
which then reduces the shear in vE×B[71]. Both effects could also play together, as
experimental observations and simulations on MAST indicate [75, 76, 77, 78].
The first L-H transition studies with MPs at AUG showed that the application
of MPs leads to a flattening of the edge pressure gradient profile, mainly due to a
flattened temperature profile [71]. Consequently, more heating power is needed to
achieve the same gradients in edge pressure profiles and, thus, the same E×Bflow
shearing rate at the L-H transition. Direct Ermeasurements were not available for
this data-set, thus, the Ergradient was approximated by the minimum of the ion or
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electron pressure gradient, which exhibited values between −7 and −12 kV/m at the
L-H transition both with and without MPs, for different plasma densities and toroidal
magnetic field strengths. These values are in good agreement with the observed constant
minimum in vE×Bin other L-H transition experiments at AUG [36].
The first comparisons of Erbehavior in AUG between plasmas with and without
MPs were performed in low density L-mode plasmas (ne≈2.0×1019 m−3) using Doppler
reflectometry (DR) measurements [79]. In this work by Conway et al a reversal of the
negative Erwell in the confined region to positive values, i.e. vE×Bchanges from the
electron diamagnetic (EDD) to the ion diamagnetic (IDD) drift direction, was observed,
consistent with observations in other tokamaks [61, 62, 63, 75, 76]. This reversal depends
both on the strength of the applied magnetic perturbations and their resonances with
the edge rational surfaces. Furthermore, a dependency of the Erprofile on the absolute
MP field orientation was found, which was different in the edge region compared to the
SOL. The authors suggested that this could be related to the production of an ergodic
layer in the edge region, whereas the SOL remains laminar [79].
A possible correlation of the Erreversal with the increase of PLH was not
investigated in these original experiments, but it has been revisited recently in [39]. In
the work by Willensdorfer et al the edge Erand vE×Bprofiles were measured with DR,
CXRS and He II spectroscopy (HES) in L-modes with and without n= 2 MPs. These
experiments were performed at slightly higher densities of about 3.3×1019 m−3, with the
maximum perturbation amplitude ∂Br/Bφ= 3.0×10−4and the MP configuration such
that PLH is highest, i.e. ∆ϕUL ≈135°(see also figure 7). Although the toroidal phase
angle was varied, the vE×Bprofiles did not exhibit a toroidal asymmetry. However,
in all cases in which the MPs led to an increase of PLH the edge vE×Bprofiles were
elevated at the L-H transition with respect to the reference L-modes without MPs, i.e.
the vE×Bprofiles were shifted towards the IDD direction. The shear in vE×B, however,
was found to be comparable to the one measured at the L-H transition without MPs.
These measurements show that the minimum of vE×B(Er) is not always a valid proxy
for its shear (gradient), but they are consistent with the idea of a critical value of the
vE×Bshear (the Ergradient) required at the L-H transition.
In L-modes the edge vE×Bprofile is flatter in plasmas with MPs than in those
without. As a result more heating power is necessary in L-modes with MPs to get a
steepening of the vE×Bshear via ∇Tito values comparable to the ones in L-modes
without MPs. Moreover, the additional heating power increases Te, which reduces
the plasma resistivity and, thus, the possible penetration of the MPs. In an L-mode
experiment where the field perturbation was slowly ramped up, it was observed that
vE×Breverses at a perturbation of about ∂Br/Bφ= 1.9×10−4. Since this perturbation
amplitude is about the same as that needed to see an increase in PLH, these two
phenomena appear to be connected. Furthermore, it was observed that the vE×B
reversal occurs on a faster time scale (within 70 ms) than the ramp-up of the MP
perturbation. These observations were tested against several models, which are able
to predict a reversal of the vE×Bprofile in the presence of MPs. It was found that
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neoclassical toroidal viscosity can not explain the flow reversal into the ion diamagnetic
drift direction, because it predicts an additional flow into the electron diamagnetic
drift direction. Ergodization as well as resonant electromagnetic torque may partly
explain the observations, but more sophisticated modeling including non-linear two-
fluid MHD effects together with a more realistic magnetic geometry would be needed
for a quantitative comparison.
Finally, magnetic perturbations have also been observed to change the power
threshold for I-mode access [80]. The I-mode is typically observed in unfavorable drift
configuration and represents a transitional regime between L-mode and H-mode [81, 82].
It features H-mode-like energy confinement with an edge temperature pedestal, coupled
with L-mode-like particle transport and L-mode-like edge density profiles. The I-mode
regime itself has also been studied extensively at AUG in the past years, the interested
reader is referred to [82, 83, 84, 85], but here and in the following only observations prior
to and the conditions at the transition from L- into I-mode (L-I transition) and from
I- to H-mode (I-H transition) are presented. There are indications that also at the L-I
transition the ion channel plays a more important than the electron channel [80], similar
to the observations made in favorable drift configuration plasmas at the L-H transition
(see section 2). Experiments using n= 2 MPs demonstrate an increase in the L-I power
threshold related to the flattening of the edge pressure gradient [80]. With MPs more
heating power is required to re-establish the same edge pressure gradient, as found at the
L-I transition without MPs. These results are reminiscent of the observations made in
favorable drift plasmas demonstrating the important role of vE×Bfor the L-H transition
(see section 2) and suggest that at least to some extent similar physics mechanisms are
at play in the development of an improved confinement in general, independent of the
exact magnetic configuration.
4.3. Magnetic configuration
In this section we present findings from AUG regarding H-mode access in different
magnetic configurations, concentrating on the favorable and unfavorable drift
configurations. At AUG it has been observed that both the power threshold to enter
I-mode from L-mode (PLI ) as well as the one to enter H-mode from the I-mode (PIH)
are larger than PLH [80]. Similar to PLH a parabolic dependence on plasma density is
found for PLI, whereas PIH does not exhibit a clear minimum at AUG [27, 80] and other
machines [86]. On the other hand, PLI only exhibits a very weak dependence on Bφ,
whereas PIH increases almost linearly with Bφ, similar to PLH. This has been seen most
clearly at Alcator C-Mod [86], but is also consistent with the AUG results for a much
more limited range of magnetic field strengths [80, 82].
In the work of Ryter et al power balance analysis showed that the edge ion heat
flux at the L-I transition increases linearly with plasma density. This indicates that the
ion channel is also important for the I-mode access, similar as for the L-H transition
in favorable drift configuration [80]. However, a quantitative comparison shows that
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Figure 8. (a) Measured edge radial electric field profiles (stars) in L-modes at matched
plasma parameters of favorable (blue) and unfavorable (red) drift configuration.
Although (∇rpi)/(Zieni) (dashed lines) is the same for both drift configurations, the Er
well is shallower in unfavorable compared to favorable drift configuration. Taking into
account the main ion flows, inferred from local neoclassical theory, into the predictions
of Er(solid lines) can also not reproduce the differences observed in the measured Er
profiles. (b) Erprofiles measured with HES (circles) and DR (squares) at the L-H
(violet), L-I (orange) and I-H (dark red) transition exhibit different Er,min values and
different Ergradients at the respective confinement transition.
Qi,edge at the L-I transition is higher than Qi,edge at the L-H transition, indicating that
the condition to enter I-mode, and also H-mode, in unfavorable drift configuration
is different to the condition to enter H-mode in favorable drift configuration. In the
framework of edge turbulence suppression by shear flows (see section 2), this observation
could indicate a change in the edge turbulence level or the strength of the stabilizing
shear flow.
In a recent work at AUG, measurements of edge kinetic profiles and Erwere
compared in favorable and unfavorable drift configuration L-modes, for same heating
powers and matched plasma densities [27]. It was found that the Erwell at the very edge
of the confined plasma is less pronounced in unfavorable drift configuration compared to
favorable drift configuration, although the edge main ion pressure gradient is the same.
These features can be seen in figure 8. This shallower Erwell in unfavorable compared
to favorable drift configuration has been observed before at AUG [87, 88] and other
machines [89, 90], but could now be confirmed with new and improved Ermeasurement
techniques [27].
No significant changes in the upstream SOL-Erwere found between the two drift
configurations, which indicates that the altered H-mode power threshold is not directly
connected to changes of SOL quantities with the drift direction. This is also confirmed by
indirect measurements of the parallel SOL flows, which are considered to set a boundary
condition for the intrinsic toroidal edge rotation [91]. At AUG the intrinsic toroidal
edge rotation is of the same size and in the same direction for both drift configurations.
Therefore, the explanation for the increased H-mode power threshold in unfavorable
drift configuration given in [91] can not explain the AUG data.
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While the positive Ergradient across the separatrix is of comparable size between
the two drift configurations, the shallower Erwell inside the separatrix leads to a
weaker (negative) Ergradient in the confined plasma and, thus, to a weaker ωE×B.
This is also shown in figure 8a. Erprofiles can also be calculated using the radial force
balance equation (see equation 2) with neoclassical estimates of the main ion flows.
This procedure utilizes the measurement of the impurity toroidal rotation to obtain the
one of the main ions. The Erprofiles obtained by this procedure (solid lines in the
figure) can not reproduce the differences observed in Er(symbols) between favorable
and unfavorable configuration plasmas. This indicates that non-neoclassical effects are
at play, which change the equilibrium Erprofile and its related E×Bshear in L-mode
and could, thereby, alter the condition for the H-mode onset.
In addition to measurements in L-modes at matched conditions, the radial electric
field just prior to changes in confinement regime were also studied in [27]. Erprofiles
measured about 20 ms before the I-mode or H-mode onset show that the Ergradients can
be quite different at the respective confinement transitions. The steepest Ergradients
are found at the I-H transition, since the Ergradients steepen during I-mode as the ion
temperature pedestal evolves. The shear levels observed at the I-H transition can be
even larger than those at the L-H transition observed in favorable configurations.
For the L- to I-mode transition no clear criterion in the edge radial electric field or
its shear is found. Measurements of the Ergradients at the L-I transition can be weaker,
steeper, or of the same size as observed at the L-H transition in favorable configuration.
In contrast, as discussed in section 2.3, the E×Bshear is observed to be quite constant
at the L-H transition in favorable configuration over a wide range of plasma parameters.
The measurements of Erat the L-I and I-H confinement transitions in unfavorable drift
clearly demonstrate that it is not a simple single-value threshold in ωE×B, which is
required for the access to an improved confinement, but rather indicates that with the
drift configuration also other parameters important for the L-H transition must change,
such as the characteristics of the edge turbulence.
It should be noted that these observations do not exclude that close to the L-H
transition also additional fluctuating shear flows, like zonal flows [92, 93], could become
important and even trigger the transition into H-mode. A characterization of such a
turbulence-flow interaction close to the L-H transition at AUG has been reported and is
also introduced in section 5.2. However, the high reproducibility of the L-H transition
also indicates that the gradients of the background profiles, like the main ion pressure
and the equilibrium Er, must be already close to a critical threshold value, in order to
establish that the transition into the improved confinement regime occurs always at the
same input power for plasma discharges of identical plasma configuration.
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5. L-mode turbulence properties and interaction with shear flows close to
the L-H transition
In addition to investigating the nature of the stabilizing E×Bshear flow, also the L-mode
edge turbulence has to be characterised to fully understand the process leading to the L-
H transition. In the past years, several advances in theoretical work have been achieved
on this topic by the AUG team, where it was found that the modeling capabilities of
gyro-kinetic codes have to be extended close to or across the separatrix in order to
capture the phenomena of the L-H transition correctly [94, 95, 96]. Experimental work
closely linked to theoretical considerations that focused on the characterisation and
determination of edge turbulence close to and at the L-H transition was also performed.
5.1. L-H-L separation through the separatrix operational space
In a recent study by Eich and Manz the conditions for the L-H transition as well as for
the density limits have been related to separatrix conditions and the characteristic edge
turbulence in AUG [97]. In this experimental framework, which has also been discussed
e.g. by LaBombard et al for Alcator C-Mod data [91], the boundaries for tokamak
operation are determined by properties of interchange-drift-Alfv´en turbulence at the
separatrix. In this way the L-H transition condition as well as the density limits can be
written as a combination of several dimensionless separatrix parameters and occur as
boundaries in the operational space of the AUG tokamak. In practice, this translates
to an existence diagram in terms of separatrix electron density, ne,sep, and temperature,
Te,sep, as shown in figure 9.
According to this model the L-mode edge turbulence close to the density limit
(ne,sep >2.8×1019 m−3), i.e. also close to the H-L back transition, is expected to
be in the regime of resistive ballooning mode turbulence, with high electron turbulent
transport levels and a flattened pressure gradient. On the other hand, typical low
density L-H transition experiments in ASDEX Upgrade are expected to occur in the
regime of drift-wave-dominated turbulence, where the electron turbulent transport level
is rather moderate in the preceding L-mode. In the context of this model the transition
into H-mode is observed when the energy transfer from the turbulence to the mean
flow, via Reynolds stress, exceeds the energy input to the turbulence, which is given
through the measured gradients in the edge kinetic profiles. Thus, the criterion for the
L-H transition is also given by turbulence suppression through stabilizing shear flows
(see also equation 8 in [97]). The picture is similar to the model developed by Kim and
Diamond for the zonal flow (ZF) generation by turbulence [98]. In the model developed
by Eich and Manz the interaction between turbulence and shear flow is treated in a
similar way to that of the zonal flow physics, although the equilibrium shear flow is
assumed to be dominant [97].
A database consisting of 123 AUG discharges containing 1884 time windows with
L- and H-modes of different densities and heating powers shows that the L-mode and
H-mode experimental points are well separated by the proposed condition for the L-
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Figure 9. The separatrix operational space of ASDEX Upgrade in terms of separatrix
electron density and temperature. The blue line depicts the condition for the L-H (H-L
back) transition. Figure reproduced from [97].
H transition of the Eich and Manz model (see figure 9). The L-H separation line in
the (ne,sep,Te,sep ) space (blue line) corresponds to a specific combination of Ipand
Bφ, which were kept constant at 0.8 MA and 2.5 T, respectively, within the data-set
displayed. Nevertheless, the condition holds more generally also for other combinations
in the full experimental data-set.
Within this framework, also the crucial role of the ion heat channel in the L-H
transition, which was previously found experimentally at AUG (see section 2.1) can
be understood, as the contribution of the ion channel to the entire edge turbulence
is the most relevant one at low densities. It is mainly this contribution to the edge
turbulence which has to be suppressed by the E×Bshear flow in order to enter H-
mode at low densities. Interestingly, for the H-L back transition, for which the same
condition holds, it is found that also the electron channel needs to be taken into account
in the turbulence generation. As a result, consistency of this model with experimental
observations at AUG is found in the sense that at the L-H transition the electron heat
flux exhibits a non-monotonic density dependence, as does PLH , whereas the ion heat
flux shows a linear dependence on the (separatrix) density (see also figure 5 in [97]).
5.2. Characterisation of the I-phase
The I-phase is an intermediate confinement regime that occurs between the L-mode
and the fully developed H-mode. The I-phase has been observed in several tokamaks
in the past decades including AUG [99, 100], DIII-D [101], COMPASS [102] and EAST
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[103], see also references in the recent review [93]. Compared to L-mode, the I-phase
already exhibits improved particle and energy confinement, although not as high as in
type-I ELMy H-modes. The I-phase appears as a sequence of limit-cycle oscillations
(LCOs) [99], where edge temperature and density profiles are flattened in periodic
bursts or pulses [104], as a consequence of repetitive changes in edge turbulence and
transport. As the I-phase forms a link between the L- and fully established H-modes,
the understanding of transport changes in this regime is crucial for a full physical picture
of the entire L-H-L transition cycle.
During fast L-H and H-L transitions the I-phase can be rather short, showing only a
few bursts or pulsations. However, in the right parameter range, the I-phase can be held
stable for several seconds, easily exceeding many energy confinement times [105, 106].
Such scenarios provide an excellent opportunity to study turbulence-flow interactions
over an extended time period.
Several studies suggest that the I-phase oscillations are produced by a predator-
prey-like flow-turbulence interaction [100, 101, 107, 108, 109, 110], while other studies
find them to be more ELM-like edge oscillations [104, 106, 111, 112, 113]. A combination
of these two behaviors has also been described in the literature [106, 111, 114] where
it was observed that the regular LCO pulsations can evolve into intermittent bursts,
characterized as type-III ELMs [115]. Work at AUG has provided experimental evidence
that supports both of these interpretations.
In low density I-phases, Doppler reflectometry measurements showed the following
sequence of events within one LCO period [100, 116]: The turbulence level increases
until, at a certain critical threshold, a geodesic acoustic mode (GAM) oscillation is
triggered together with a turbulence-driven mean flow, which adds to the equilibrium
E×Bflow. The shear of this (combined) flow increases until it is large enough to reduce
the turbulence level to a point where the GAM is damped, and a new cycle starts. This
leads to the typical predator-prey-like behavior, with an additional threshold for the
GAM oscillation. The work by Conway et al [100] also provides an existence criteria
for this oscillation cycle: The averaged shearing rate of the GAM oscillations has to
comparable or larger than the turbulence de-correlation rate, and also larger than the
background E×Bflow shearing rate. If the turbulence de-correlation rate is larger
than the GAM flow oscillation, the plasma is in L-mode. If the E×Bflow shearing
rate exceeds the turbulence de-correlation, the plasma enters H-mode [100]. The cycle
described above is predominantly observed at low densities. With increasing density
the GAMs are reduced by collisional damping [93]. Experimentally, the duty cycle of
the LCO is also reduced, making the pulses appear more irregular and burst-like. With
increasing heating power the transition from L- to I-phase appears as abrupt confinement
change, followed by a more gradual evolution into a fully developed H-mode [100].
This evolution of the I-phase bursts with density and heating power is consistent
with the picture of the I-phase presented by Birkenmeier et al in [106] and other works
[112, 114, 116] at AUG, where the I-phase oscillations were identified as type-III ELMs.
In the investigated plasmas GAMs were not observed. Due to the utilization of NBI
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power ramps in these studies, only higher plasma densities could be achieved, which
leads to a more effective collisional damping of the GAMs [93]. However, as in [100],
it was observed that the I-phase develops with increasing heating power from a state
with regular LCOs to a state with intermittent bursts. This evolution of the I-phase is
seen both at the L-H transition and, in reversed order, at the H-L back transition. In
the work by Birkenmeier et al also the magnetic signatures of the I-phase were studied,
which showed an up-down asymmetry. A similar structure of the I-phase bursts on
the magnetic data was observed in the M-mode at JET [104]. These oscillations could
be related to up-down asymmetric parallel flow and current perturbations, as studied
experimentally and theoretically in [117]. Also LCO models which additionally take into
account MHD effects can reproduce a transition into an intermittent state [118], whereas
models based solely on turbulence-flow interaction, like the one in [98], lead to regular
LCOs only. However, all these models have in common that the underlying process
leading to these LCOs is that these edge instabilities are driven by strong gradients in
the edge profiles and they are stabilized by strong shear flows.
High radial and temporal resolution measurements of turbulence, mean and zonal
flows performed in NBI heated, high density AUG plasmas (¯ne>4.5×1019 m−3) close
to the L-H or H-L back transition [112, 114] allowed two different plasma phases to
be investigated in detail. The first is a transient phase, characterized by L-I-L dithers,
which are the back-and forth transition from L-mode into I-phase and vice versa. These
L-I-L dithers can be seen on several signals including magnetic measurements and the
edge density and temperature and they occur on a time scale of a few ms. The second
investigated phase was a stable I-phase with regular LCOs in the kHz (sub-ms) range.
Simultaneous measurements of the edge temperature and density gradients, as well as of
the E×Bflow shear (approximated by the minimum of vE×B) showed that all quantities
develop on the same time scale (time resolution of 250 µs) [112].
Measurements with a time resolution of 100 µs [112] and 1 µs [114] found that during
the LCOs the turbulence level and the mean E×Bflow shear are in phase, meaning
that the turbulence level is highest when the vE×Bshear is lowest. Furthermore, the
analysis of the LCOs in the high density I-phase revealed that at all times vE×B≈vdia,i,
where vdia,i is the diamagnetic velocity of the main ions [112]. This equality implies
that in these experiments the total E×Bflow shear was dominated by the edge main
ion gradients and that the ZF amplitude was small compared to neoclassical flows, in
agreement with observations at JFT-2M [119] and NSTX [120].
Although the physical picture forming the periodicity of the I-phase is not yet fully
resolved and different theories of the details of the transport dynamics exist, it appears
that the same quantities and mechanisms leading to the L-H transitions are also of major
importance for the I-phase. Common to most explanations of the I-phase, and supported
by the turbulence measurements, is the interaction between turbulence-driven transport
and the stabilizing effect of the E×Bflow shear. It is a critical interplay between the Er
gradients driving the flow and destabilizing effects like strong edge pressure gradients
as the source of mode activity, leading to periodic LCOs. If turbulence dominates, the
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plasma is in L-mode, whereas the periodicity of the LCOs is broken towards the fully
established H-mode, with a strong transport barrier allowing for steep edge gradients.
The detailed measurements of turbulence properties and flow shears in such experiments
is crucial to improve our understanding of the L-H and the H-L back transition.
6. Conclusions and Summary
The ability to access stable, high-confinement operational regimes is key to the success of
magnetic confinement fusion reactors. As such, both the experimental and theoretical
fusion communities have dedicated considerable time and resources to understanding
confinement transitions. These efforts have greatly improved our understanding of the
conditions under which such transitions, particularly the L-H transition, occur and have
enabled us to extrapolate our knowledge to future machines. However, a fundamental
physics-based understanding is still lacking. The ASDEX Upgrade team has contributed
strongly to the L-H transition research and this paper has attempted to summarize
these contributions, putting them into context with respect to one another, but also in
comparison to results achieved at other machines.
A very well known feature of the L-H power threshold is that it is non-monotonic as
a function of electron density. Experiments at AUG focusing on the low density branch
examined the role of the edge ion heat flux and were able to provide a robust explanation
for the non-monotonic behavior, unifying both the low- and high density branches, the
plasma current scaling observed in the low density branch, and the differences in PLH
observed as a function of the heating method used. These experiments showed that a
critical value of the edge ion heat flux per particle (Qi,edge/ni) is needed to enter H-
mode, see section 2. At low density, on account of the weaker electron-ion collisional
coupling, significantly higher heating power is required when pure electron heating is
applied to achieve the required Qi,edge/nineeded to enter H-mode, which results in the
observed increase in the power threshold at low density. Within the framework of a
critical threshold in Qi,edge/nito initiate the L-H transition it is possible to predict the
density for which the power threshold is expected to be minimum in future machines
as well as the expected power threshold. When applied to ITER, this scaling produces
favorable results, yielding power thresholds that should be attainable for the auxiliary
heating systems planned for ITER.
While the observed threshold in Qi,edge provides a compelling unification of the
low- and high density branches of the L-H power threshold, it is unlikely to be directly
responsible for the L-H transition. Rather, local edge quantities, such as the gradients
of the radial electric field (Er) and their connected shear flow, are the candidates to be
responsible for the transition into H-mode, as they can interact with the edge turbulence.
Detailed studies of these edge parameters give insight into how confinement transitions
take place and provide key data for validation of theoretical models. The edge ion
heat flux is, however, linked to Ervia the ion temperature gradient. Experiments at
AUG showed that the minimum of the Erwell, which is a proxy for the much more
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difficult to measure E×Bshear flow, is constant at the L-H transition for a given
magnetic configuration, see section 2.2. These works connected the observation of an
ion heat flux threshold to a local edge parameter, and directly support the paradigm of
turbulence suppression by E×Bshear flow as the mechanisms initiating the confinement
transition.
The connection between the H-mode power threshold (PLH) and Erwas extended
to the E×Bvelocity shear (ωE×B∝max|vE×B|=|Er,min/B|), see section 2.3. Here it was
shown that the maximum of |vE×B|is constant at the L-H transition over a wide range of
electron densities and magnetic field values, explaining the magnetic field dependence of
PLH and identifying vE×Bas a more fundamental parameter for the L-H transition than
Er. New results presented in the current publication extend those experiments deeper
into the low density branch and show a decrease in the measured maximal |vE×B|values
at the L-H transition, whereas the diamagnetic velocity stays relatively constant. This
deviation between diamagnetic and E×Bvelocity demonstrates that at low density the
contributions of the main ion flows become important and the minimum of vE×Bcan not
be used as a proxy for its shear anymore. Whether the vE×Bshear itself stays constant
could not be addressed in a quantitative manner due to limited radial resolution of the
Ermeasurements. However, the results obtained comparing confinement transitions in
favorable and unfavorable magnetic drift configurations show a larger variation of |vE×B|
and its related shear at the L-H transition, see section 4.3. This observations does not
confirm the idea that one single critical value of ωE×Bis required to enter H-mode, but
rather that ωE×Bhas to be set into relation with the edge turbulence properties. The
experimental observations on vE×Bat the L-H transition are also supported by recent
theoretical work done at AUG showing that the impact of ωE×Bon the L-mode edge
turbulence is strongly non-linear and depends on the background plasma parameters as
well as the local turbulence characteristics.
The L-H transition and related plasma quantities have also been explored in plasmas
with different main ion compositions, see section 3. In AUG, the power threshold in
pure He is similar to the one of pure D plasmas, whereas the threshold in H plasmas
is twice as large. Also Qi,edge at the L-H transition is increased by a factor of two in
H compared to D plasmas, whereas the minimum of the Erwell and its gradients were
found to show the same values. Within a simple picture on turbulence-flow interaction
one might expect that the E×Bshear required to suppress the characteristic edge
turbulence is proportional to its amplitude. Hence, in H one would expect to see a
higher ωE×Bat the transition compared to D. However, this is not what is seen in
the experiments and it is also not expected from gyrokinetic simulations. Rather, the
experiments show a constant ωE×Bat the L-H transition, independent of the main ion
species composition and the simulations show strongly non-linear behavior with complex
interplay between the background plasma parameters, the turbulence properties and the
shear level required to impact the turbulence. Since the experimental data show a clear
and consistent behavior of ωE×Bat the L-H transition which applies equally to D and
to H plasmas, the observed increase in PLH in H compared to D follows directly from
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this result: the higher level of turbulence transport in H means more input power is
required to reach the critical threshold in ωE×B.
The L-H power threshold is of high interest for future fusion reactors, not just
for reactor operation in D-T, but also for initial commissioning phases, during which
they will operate using either hydrogen or helium as the working gas to avoid neutron
activation of the machine. Hence the power threshold dependence on the main ion
species mix will impact multiple phases of reactor operation. The high power threshold
observed in H plasmas is a particular concern for future machines, which have limited
amounts of auxiliary heating power capabilities. As such, any methods of reducing the
power threshold that can be identified in present experiments are of high interest. Thus,
the AUG and JET results demonstrating a 25 % reduction in PLH when transitioning
from a C-walled to a W-walled device, see section 4.1, are very beneficial for reactor
operation. Similarly, the reduction in PLH observed at JET when seeding low levels of
He (about 10 %) into H plasmas heated with NBI would indicate a promising option
for the reactor commissioning phase. However, at AUG similar experiments conducted
in both NBI and ECRH heated plasmas did not show any reduction of PLH with a He
concentration of up to 20 %, see section 3, which indicates that in ITER a reduction of
the high H-mode power threshold in H plasmas by He seeding can not be achieved in
the PFPO-1 phase, where only ECRH heating is available. The results from AUG are
consistent with recent DIII-D findings, which also show no change in PLH with up to 20 %
He seeding. Also, in a series of new experiments presented here, the power threshold was
explored across the transition from H to D. Similar to the H to He results, no change
in the power threshold is observed when seeding H into D plasmas until a 50/50 mix is
achieved. Above 50 % the power threshold increases smoothly until the twice as high
H-mode power threshold of pure H plasmas is reached.
Another concern for future machines is that the use of magnetic perturbations to
suppress ELMs may result in an unforeseen increase in PLH. Early results from AUG
showed that at low density no increase in the power threshold was observed with MPs,
but at higher densities an increase of up to 20 % was observed. Recent AUG experiments,
conducted at the density minimum of PLH, demonstrated that an increase in the power
threshold is observed if the magnetic perturbation amplitude is above a critical value.
At AUG, the field amplitude needed to suppress ELMs is below that which results in an
increase in PLH. This is a potentially very promising result for ITER, as at AUG ELM
suppression can be maintained without a simultaneous increase in the H-mode power
threshold. Modeling of these experiments shows that the increase in PLH is strongest
when the MP is oriented such to maximize the plasma response. The increase in PLH is
thought to be due to the changes in the edge E×Bvelocity shear, which is reduced in
the presence of MPs. Therefore, with MPs more heating power is required to increase
the edge gradients and increase the E×Bshear to initiate the L-H transition. Another
important observation from these experiments is that the minimum of the E×Bvelocity
profile is higher with MPs than without. Therefore, also under these conditions, the
minimum of vE×Bis not a good representation for its shear.
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At AUG the L-H transition has also been investigated recently by connecting
the separatrix conditions of neand Teto the edge interchange-drift-Alfv´en turbulence
properties. The result of this semi-analytical model approach is an existence, or
operational space diagram for a large database of AUG L-mode and H-modes. Between
the two well separated regimes is an identifiable boundary which can be parameterized
in terms of standard plasma parameters. The underlying context of the model is still
the suppression of turbulence through equilibrium shear flows. Here the role of zonal
flows is assumed to be sub-dominant.
The I-phase is an intermediate regime, which occurs at the transition from L-
mode to H-mode and at the H-L back transition. However, the I-phase is not a
transitory regime, because it can be sustained indefinitely under appropriate conditions.
The study of the I-phase and its related plasma edge oscillations, so called limit-cycle
oscillations (LCOs), gives insight into the critical interplay between the stabilizing effects
of E×Bshear flows and destabilizing effects, like strong edge pressure gradients, on
the edge turbulence. In low collisionality plasmas at AUG the LCOs are associated
with turbulence-driven GAMs. With increasing density the regular LCOs evolve to a
more sporadic, bursty nature with the same magnetic signatures as type-III ELMs. At
AUG the characteristics of the I-phase have been well studied experimentally and also
modeled heuristically. However, fully consistent theoretical models over the full I-phase
existence parameter space remain outstanding. The reproduction of the I-phase with its
characteristic edge oscillations is an important aspect for models seeking to reproduce
the L-H transition.
Predicting the L-H transition is a critical issue for the operational success of
future magnetic confinement fusion reactors which will operate in improved confinement
regimes. Therefore, present-day fusion research devices aim to improve the predictability
of the H-mode power threshold under reactor conditions. The ASDEX Upgrade team has
contributed with experimental and modeling efforts to improve our understanding of the
underlying physics mechanisms leading to the L-H transition. Different key parameters
have been identified and the critical role of vE×Band its related shear have been shown
to be important for the H-mode access. On the other hand it is also found that the
investigation and characterization of the E×Bshear flow alone is not sufficient to describe
all phenomena related to and observed at the L-H transition. The background shear
flow has to be brought into a broader context and set in relation with the characteristic
edge turbulence, which requires often another level of sophistication. First attempts to
address the shear flow-turbulence interaction leading to the L-H transition have been
made experimentally and theoretically at AUG, but more comparisons and detailed
analysis are foreseen in the near future. This is possible as both the modeling and
measurement capabilities are rapidly improving and they are evermore able to capture
the different aspects of the L-H transition and the entire concept of shear flow-turbulence
interaction correctly.
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Acknowledgments
The authors would like to thank C. Angioni, T. P¨utterich, F. Ryter and E. Wolfrum
for fruitful discussions and valuable input. This work has been carried out within
the framework of the EUROfusion Consortium, funded by the European Union via
the Euratom Research and Training Programme (Grant Agreement No 101052200 –
EUROfusion). Views and opinions expressed are however those of the author(s) only
and do not necessarily reflect those of the European Union or the European Commission.
Neither the European Union nor the European Commission can be held responsible for
them.
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