This work reports on recent results on the search for high performance plasma scenarios at the magnetically confined stellarator fusion device Wendelstein 7-X. In four new designed scenarios, the development from transient toward stationary plasmas of improved performance has been realized. In particular, a high performance duration of up to 5 s, an energy confinement time of 0.3 s, a diamagnetic energy of 1.1 MJ, a central ion temperature of 2.2 keV, and a fusion triple product of 3.4 × 10 19 m 3 · keV · s have been achieved, and previously observed limitations of the machine have been overcome, regarding both the performance and its duration. The two main experimental techniques for stationary high performance are neutral beam injection core fueling on the one hand and the use of a magnetic field configuration with internal islands on the other hand. Two of the developed scenarios are expected to be extendable straightforward toward a duration of several tens of seconds, making use of the long pulse operation capabilities of W7-X.

The development of high performance (HP) plasma scenarios, in particular with respect to a maximization of the fusion triple product n e T i τ E under steady-state plasma conditions,1 is one of the main important and also most challenging goals of the magnetically confined fusion device Wendelstein 7-X (W7-X).2 Despite significant achievements like the proof of neoclassical optimization,3 a transient high fusion triple product,4 or steady-state plasma conditions with complete detachment,5,6 the majority of W7-X plasma scenarios were dominated by turbulent transport mechanisms,7 limiting the plasma performance as evident from energy8–10 as well as impurity transport studies.11–17 As a result, a saturation of the ion temperature T i 1.7 keV,18 limited energy confinement times τ E 0.2 s, and fusion triple products n e T i τ E 0.3 × 10 20 m 3 · keV · s were observed in standard gas fueled plasmas.4 Consequently, within this work, high performance is defined as a plasma scenario passing one or more of the following limitations:

  • Overcome of the Ti limit with T i 1.7 keV;

  • ISS04 scaling with τ E / τ ISS 04 0.7;

  • A fusion product of n e T i τ E 0.3 × 10 20 m 3 · keV · s.

As τE has well known dependencies of several plasma parameters, here τE is related to the ISS04 scaling19 (see Sec. III for details) with a limiting ratio of τ E / τ ISS 04 = 0.7 that has not been exceeded in gas fueled plasmas20 at higher plasma densities of n e > 5 × 10 19 m−3. Similarly, n e T i τ E = 0.3 × 10 20 m 3 · keV · s has been observed as a limit for the fusion product4 in turbulence dominated plasmas of W7-X.

Fortunately, the use of alternative fueling schemes like cryogenic ice pellet fueling,21 neutral beam fueling,22 and perturbative impurity injections23 showed a reduction of turbulent transport with significantly improved performance beyond the above-mentioned limitations, although, only for short term, transient phases on the order of 200 ms.

In this paper, results on the transition from transient toward steady-state high performance plasma scenarios will be presented, making use of combined neutral beam injection22 (NBI) and electron cyclotron resonance24 (ECR) heating schemes, wall conditioning,25,26 and magnetic field scan techniques.27,28

Section II introduces four new developed high performance scenarios and its main plasma parameters, followed by a discussion on the performance of each scenario with respect to its energy confinement and fusion triple product in Sec. III, and implications for future scenario developments discussed in Sec. IV.

W7-X plasmas are generated by the two main heating sources, ECR and NBI heating, providing powers of up to P ECRH = 7.5 MW and P NBI = 4.0 MW, respectively, to the plasma that itself has a volume of 30 m3. The plasma density is set via several fast piezo gas valves5 that are feedback controlled on the line of sight averaged electron density ne measured by the interferometer diagnostic.29 The diamagnetic energy Wdia, the central ion temperature Ti, and electron density profiles of the plasma are measured by the Rogowski coils,30 the x-ray imaging crystal spectrometers,31 and the Thomson scattering system.32 

In the following paragraphs, the temporal evolution of those main plasma parameters will be discussed in detail for four dedicated hydrogen plasma scenarios of notably improved performance.

Scenario 1 was initially conducted as a test scenario for steady NBI heating of P NBI = 3.0 MW, assisted with P ECRH = 1.9 MW for plasma startup at medium density n e = 0.4 × 10 20 m−3 as shown on the left of Fig. 1.

FIG. 1.

Time traces of ECR and NBI heating power (upper panels), the diamagnetic energy and averaged electron density (middle panels), and central ion temperature (lower panels) for the W7-X programs 20221207.054 (left) and 20221123.003 (right). The dashed horizontal lines represent the Ti saturation limit.

FIG. 1.

Time traces of ECR and NBI heating power (upper panels), the diamagnetic energy and averaged electron density (middle panels), and central ion temperature (lower panels) for the W7-X programs 20221207.054 (left) and 20221123.003 (right). The dashed horizontal lines represent the Ti saturation limit.

Close modal

Remarkably, the combination of P NBI > P ECRH allowed to push Ti above its saturation limit. This limit used to clamp central ion temperatures of W7-X in previous campaigns to T i 1.7 keV as a consequence of enhanced ion temperature gradient (ITG) turbulence for increased T e / T i ratios.18 In fact, within the entire duration of the NBI heating phase, the Ti limit (dashed line in Fig. 1) could be exceeded significantly, reaching T i = 2.1 keV and Wdia = 0.45 MJ for 5 s. This is the first time a steady-state scenario of T i > 1.7 keV has been realized at W7-X, only limited by the duration of the NBI heating phase. At the end of NBI heating at t = 6 s, Ti falls back to its saturation limit in timescales of the energy confinement time of τ E = 100 ms, see also Fig. 5.

Figure 2 on the left shows the electron density profiles of Scenario 1 in the limited (blue line) and improved performance phase (orange line), and the latter one being increased due to the NBI fueling effect. As previously observed for plasmas of improved performance,4,7 also the ne profile of Scenario 1 shows a slightly steeper edge density gradient in the improved performance phase compared to the limited performance phase as indicated by the dashed lines marking the ne gradients at ρ = 0.9. Note that in the same experiment program, a similar profile shaping with an increased edge density gradient in the ne profile (not shown) has been induced by an external gas puff from the gas puff imaging diagnostic at t = 8.0 s, yielding a similar but transient increase in Ti for about 300 ms, see lower left of Fig. 1 for 8.0 t 8.5 s.

FIG. 2.

Left: Electron density profiles for Scenario 1 in the improved (orange) vs limited (blue) performance phases. Dashed lines indicate edge density gradients being higher in the case of improved performance. Right: Electron density profiles for Scenario 2 at the beginning (blue) and the end (orange) of the high performance phase. The horizontal dashed line marks the unusual low edge density values of n e < 1.0 × 10 19 m−3 for ρ > 0.8.

FIG. 2.

Left: Electron density profiles for Scenario 1 in the improved (orange) vs limited (blue) performance phases. Dashed lines indicate edge density gradients being higher in the case of improved performance. Right: Electron density profiles for Scenario 2 at the beginning (blue) and the end (orange) of the high performance phase. The horizontal dashed line marks the unusual low edge density values of n e < 1.0 × 10 19 m−3 for ρ > 0.8.

Close modal

The steady-state character of Scenario 1 during the NBI phase is highly beneficial for achieving Ti above the saturation limit, and the absolute diamagnetic energy, however, is comparably low. The realization of higher diamagnetic energies with breaking of the Ti saturation and a more detailed discussion on effects of the P NBI / P ECRH ratio on the plasma performance and the ne profile peaking are given in paragraph D for Scenario 4.

Scenario 2 has been conducted directly after a fresh boronization33 of the first wall with P ECRH = 1.6 MW at an averaged electron density of n e = 0.4 × 10 20 m−3, as shown in Fig. 1 on the right. For a direct comparison, the left and right ordinates in Fig. 1 are shown on the same scales. Although Scenario 2 has compared to Scenario 1 slightly less ECRH power, no additional NBI heating phase, and the same averaged electron density, it also shows improved performance. Especially, the energy confinement time of τ E = 300 ms is significantly increased, and also the central ion temperature is above the saturation limit with a maximum value of T i = 2.2 keV. However, Ti and Wdia are not stationary but do both slowly rise with slightly decreasing ne until t = 4.2 s, when an unknown event ended the improved performance phase.

The density profiles of Scenario 2 shown in Fig. 2 on the right exhibit a particular low edge density of n e < 1 × 10 19 m−3 for ρ > 0.8, see dashed line in Fig. 2. Moreover, the ne profiles have a pronounced and radially extended density gradient ranging from the plasma edge toward the bulk plasma from ρ = 1.0 up to 0.4. This combination of low edge density yielding the radially extended density gradient is thought to be responsible for the improved performance. For a conclusive analysis however, additional experimental data are required and are planned to be conducted in the upcoming operational phase of W7-X.

In addition to the non-stationary character of Scenario 2, its application also for higher ECR heating powers P ECRH > 1.6 MW as well as the required wall conditioning state needs to be clarified experimentally in more detail, in particular with respect to a feasible scaling toward high density operation.

Scenario 3 has been developed within a series of experiment programs, scanning the iota profile of the W7-X magnetic configurations with respect to an optimized performance. As a result of this scan, the magnetic configuration FMM00227 was identified, yielding a particular high diamagnetic energy Wdia, as shown in Fig. 3, left. With pure ECR heating of P ECRH = 4.0 MW at a high density of n e = 9.0 × 10 19 m 3, a diamagnetic energy of Wdia = 0.8 MJ has been achieved in steady-state for a duration of 5 s, see Fig. 3, left. In fact, as the plasma parameters are entirely stationary after reaching the final density level for 5 t 10 s, the duration of the high performance phase is only limited by the length of ECR heating, which, in principle, is designed to operate for up to 30 min. Compared to the W7-X magnetic standard configuration, the iota optimized Wdia is enhanced by 10%–15%. The reason for this enhancement is not clarified yet and under discussion. Initial results show optimal performance in case the iota profile is crossing rationals at a radial position close to the last closed flux surface27 on the one hand and a stabilizing effect of the radial electric field on density fluctuations and ion turbulent gradient driven instabilities34 on the other hand.

FIG. 3.

Time traces of ECR and NBI heating power (upper panels), the diamagnetic energy and averaged electron density (middle panels), and central ion temperature (lower panels) for the W7-X programs 20230216.059 (left) and 20230216.063 (right). Dashed horizontal lines represent the Ti saturation limit, and the dashed gray line in the right middle panel corresponds to the Wdia time trace of the transient high performance program after pellet injections.4 

FIG. 3.

Time traces of ECR and NBI heating power (upper panels), the diamagnetic energy and averaged electron density (middle panels), and central ion temperature (lower panels) for the W7-X programs 20230216.059 (left) and 20230216.063 (right). Dashed horizontal lines represent the Ti saturation limit, and the dashed gray line in the right middle panel corresponds to the Wdia time trace of the transient high performance program after pellet injections.4 

Close modal

The edge density gradient is again enhanced in the high performance phase and reduced in the low performance phase, similar to Scenario 1, as indicated by the dashed lines shown on the left of Fig. 4.

FIG. 4.

Left: Electron density profiles for Scenario 3 in the standard (blue) and improved (orange) performance phases. Dashed lines indicate edge density gradients being higher in the case of improved performance. Right: Electron density profiles for Scenario 4 in the standard (blue) and improved (orange) performance phases.

FIG. 4.

Left: Electron density profiles for Scenario 3 in the standard (blue) and improved (orange) performance phases. Dashed lines indicate edge density gradients being higher in the case of improved performance. Right: Electron density profiles for Scenario 4 in the standard (blue) and improved (orange) performance phases.

Close modal

Despite the high performance with respect to Wdia and the steady-state character of Scenario 3, it suffers from the saturation of Ti not exceeding T i > 1.7 keV, see dashed line on the left of Fig. 3. This limit, however, will be overcome in Scenario 4, also using the magnetic configuration FMM002, but a different density fueling technique.

In Scenario 4, an advanced heating scheme, using single and combined sequences of NBI and ECR heating, has been developed as shown in Fig. 3 on the top right. In the beginning, a sequence of 1 s with pure ECR heating for plasma startup at medium density is followed by a pure NBI heating phase further rising the electron density. Finally, a combined NBI and ECR heating phase at t > 3 s maximizes the combined heating power to P ECRH + P NBI = 7.6 MW (see Table I) at high density. Within this heating scenario, the highest diamagnetic energy of all four scenarios has been achieved with Wdia = 1.1 MJ, as shown in the middle right panel of Fig. 3, orange line. Simultaneously, a duration of the high performance phase of 2.5 s has been established. For a direct comparison, the Wdia time trace of the transient high performance program after pellet injections4 is shown with a dashed gray line in Fig. 3. As can be seen, Scenario 4 exactly reobtained the Wdia peak value but significantly extended the duration of the high performance phase.

TABLE I.

Overview on the physics parameters of Scenarios 1–4. Important achievements of each scenario are highlighted.

Scenario Scenario name P ECRH PNBI HP duration Wdia τE Ti n e T i τ E
Steady NBI+ECRH  1.9 MW  3.0 MW  5.0s  0.45 MJ  0.1 s  2.1 keV  1.0 × 1019 m−3 keV s 
Low edge density  1.6 MW  ⋯  2.5 s  0.50 MJ  0.3s  2.2 keV  2.0 × 1019 m−3 keV s 
Internal islands Configuration  4.0 MW  ⋯  5.0s  0.80 MJ  0.2 s  1.7 keV  3.1 × 1019m3keVs 
Controlled density peaking  3.5 MW  4.1 MW  2.5 s  1.05 MJ  0.15 s  2.1 keV  3.4 × 1019m3keVs 
Scenario Scenario name P ECRH PNBI HP duration Wdia τE Ti n e T i τ E
Steady NBI+ECRH  1.9 MW  3.0 MW  5.0s  0.45 MJ  0.1 s  2.1 keV  1.0 × 1019 m−3 keV s 
Low edge density  1.6 MW  ⋯  2.5 s  0.50 MJ  0.3s  2.2 keV  2.0 × 1019 m−3 keV s 
Internal islands Configuration  4.0 MW  ⋯  5.0s  0.80 MJ  0.2 s  1.7 keV  3.1 × 1019m3keVs 
Controlled density peaking  3.5 MW  4.1 MW  2.5 s  1.05 MJ  0.15 s  2.1 keV  3.4 × 1019m3keVs 

The key to this long time high performance is the establishment and the control of a centrally peaked electron density profile, as shown in Fig. 4 on the right, orange line. With the start of pure NBI heating at t 1 s, the central electron density (and also the line averaged ne shown in Fig. 3, blue line in the right middle panel) steadily rises, yielding a centrally peaked ne profile in the high performance phase in contrast to the flat ne profile in the standard performance phase, see blue and orange lines in Fig. 4 on the right. Note that this pronounced central ne peaking exclusively appears in NBI only heating phases and, therefore, does not show up in Scenario 1. However, a continued exclusive NBI heating would also result in a continued and uncontrolled rise of the central density, yielding a reduction of the plasma temperature as the constant NBI heating power cannot compensate for the steadily increasing density level. In fact, this effect is already visible in the decreasing Ti during the pure NBI heating phase for 2 t 3 s, see lower right panel of Fig. 3. The reintroduction of P ECRH = 2.5 MW at t = 3 s has two positive effects: On the one hand, it stabilizes the peaked ne profile at a central n e = 10 × 10 19 m 3 and stops its further uncontrolled rise for 3 t 4 s, see Fig. 3, middle right panel. On the other hand, the additional heating power brings up the plasma ion temperature above its saturation limit to T i = 2.0 keV and yields the high Wdia.

Unfortunately, the control of the ne profile peaking for NBI heated plasmas with ECRH is very sensitive to various actuators, e . g . the actual P ECRH and P NBI power levels, the initial electron density and others (to be discussed in detail elsewhere35) making a feed forward control of these scenarios challenging. In particular toward the end of Scenario 4 at t > 4 s, the central ne starts to rise again and a decrease in plasma Ti and Wdia occurs. For this case, a further adjustment of P ECRH would be necessary, using, e . g ., a feedback control on the electron density. Strategies for feedback control of various actuators are currently under discussion and will be established and tested in the upcoming experimental campaigns of W7-X. It should be mentioned that Scenario 4 has also been performed successfully in other magnetic configurations like standard and high mirror36 but with 5%–10% slightly reduced performance.

As evident from Figs. 2 and 4, any phase of improved performance is linked to an enhanced electron density gradient, either by its increase at the plasma edge (Scenarios 1 and 3) or by its increased radial extension (Scenarios 2 and 4). This empirical found correlation between increased density gradient and improved performance can be attributed to a reduction of turbulence, observed experimentally via reduced density fluctuation levels37 and expected theoretically.10 

For a quantitative analysis on the high performance phases of Scenarios 1–4, time traces of the two commonly used plasma parameters, energy confinement time τE and fusion triple product n e T i τ E, are shown in Fig. 5. In addition, the expected τE according to the ISS04 scaling is shown (dashed lines), being a benchmark of the empirical energy confinement scaling of various stellarator experiments with respect to several technical and physics machine parameters.19 In case τE meets the ISS04 scaling, the developed plasma scenario has an equally good performance as other stellarator experiments.

FIG. 5.

Left: Time traces of energy confinement times (solid lines) with respect to the ISS04 scaling (dashed lines) for Scenarios 1–4. Right: Time traces of the fusion triple product for Scenarios 1–4. The thin gray solid line corresponds to the transient high performance scenario after pellet injections for comparison. Periods of improved performance are highlighted.

FIG. 5.

Left: Time traces of energy confinement times (solid lines) with respect to the ISS04 scaling (dashed lines) for Scenarios 1–4. Right: Time traces of the fusion triple product for Scenarios 1–4. The thin gray solid line corresponds to the transient high performance scenario after pellet injections for comparison. Periods of improved performance are highlighted.

Close modal

Figure 5 clearly shows the stationary character of the improved performance phases in Scenarios 1–4 in terms of both energy confinement and fusion triple product being constant for a duration of 3–5 s being 10–20 times the energy confinement time. As τE is defined as W dia / P HEAT + d W dia / d t, Scenarios 1 and 4 show a slight drop of τE and τ ISS 04 when the NBI heating is switched on and off. Also evident from Fig. 5, Scenario 2 meets the ISS04 scaling for its entire high performance phase, and Scenarios 1, 3, and 4 achieve τ E / τ ISS 04 = 0.8 0.9. Both results are a reasonable improvement of the performance compared to standard gas fueled W7-X plasmas where τE does not exceed τ E / τ ISS 04 0.7 for n e > 5 × 10 19 and τ E / τ ISS 04 0.9 for n e < 5 × 10 19,20 especially not for a duration on the order of seconds. For short transient phases of about 200 ms, τ E / τ ISS 04 could be exceeded over a value of 1.0 in previous campaigns3,4 exclusively in scenarios with pellet injections. For technical reasons, however, up until now, these scenarios and a possible extension of the HP phase could not be further developed.

The absolute values of the fusion triple products of Scenarios 1 and 2 are with n e T i τ E 2 × 10 19 m 3 · keV · s comparably low due to the low electron density levels. With increased density and heating power however, the fusion product reaches n e T i τ E = 3.5 × 10 19 m 3 · keV · s in Scenarios 3 and 4 with a peak value of n e T i τ E = 4.0 × 10 19 m 3 · keV · s in Scenario 4. For comparison to previously observed transient high performance plasmas, the gray line in Fig. 5 shows the fusion product after pellet injections.4 Although the peak value of pellet fueled plasmas could not be met, the duration of improved performance could be increased by a factor of 10 and 5 in Scenarios 3 and 4, respectively.

Table I summarizes the main physics parameters of Scenarios 1–4. Their main characteristics can be summarized as follows:

  • Scenario 1 is well suited to stationary overcome the Ti limit for up to 5 s, however, with limited performance regarding Wdia, τE, and n e T i τ E.

  • Scenario 2 shows a particular high energy confinement time of τ E = 300 ms, meeting the ISS04 scaling for a duration of 2.5 s. The scenario reproducibility and application for higher heating powers need further experimental investigation.

  • Scenario 3 is currently the best candidate for a long pulse, high performance program as it shows high performance regarding Wdia, τE, and n e T i τ E and could be extended to a duration of several minutes, by simply extending the ECR heating phase. However, with the internal islands, its magnetic configuration does not properly cover the W7-X divertor and is, therefore, not reactor relevant due to its non-optimal pumping and exhaust capabilities.

  • Scenario 4 shows the highest performance of all four scenarios, in particular with respect to Wdia, and n e T i τ E but is currently tricky to stabilize and needs the development of a feedback control of the ECRH to be run in steady-state conditions.

In summary, all four new developed scenarios clearly overcame one or more of the above-mentioned performance limitations for several seconds, being 10–20 times the energy confinement time. Therefore, the here developed scenarios are ideal candidates for a further improvement of the plasma performance and its duration. An important question to be answered in upcoming experiment campaigns is if stationary scenarios come at the cost of reduced performance, as is the case right now for, e.g., the fusion product. To answer this question, a twofold strategy, namely,

  • experiments on the sustainment of high performance in pellet fueled plasmas through continuous pellet injections and

  • performance optimization of HP scenarios through increased ECR and NBI heating powers,

will be followed that, based on the outcomes of this work, predict to yield promising results.

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.

The authors have no conflicts to disclose.

A. Langenberg: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Writing – original draft (lead). F. Warmer: Writing – original draft (supporting). G. Fuchert: Conceptualization (equal); Formal analysis (supporting). O. Ford: Conceptualization (equal). S. Bozhenkov: Conceptualization (equal). T. Andreeva: Conceptualization (equal). S. Lazerson: Conceptualization (equal). N. A. Pablant: Data curation (supporting); Formal analysis (equal); Resources (supporting); Validation (supporting). T. Gonda: Formal analysis (supporting); Resources (supporting). M. N. A. Beurskens: Conceptualization (supporting). K.-J. Brunner: Formal analysis (supporting). B. Buttenschön: Formal analysis (supporting). A. Dinklage: Conceptualization (supporting). D. Hartmann: Formal analysis (supporting). J. Knauer: Formal analysis (supporting). O. Marchuk: Validation (supporting); Writing – review & editing (supporting). E. Pasch: Formal analysis (supporting). F. Reimold: Conceptualization (supporting); Writing – review & editing (supporting). T. Stange: Conceptualization (supporting); Formal analysis (supporting). Th. Wegner: Formal analysis (supporting); Writing – review & editing (supporting). O. Grulke: Conceptualization (supporting); Supervision (supporting). R. C. Wolf: Supervision (lead); Writing – review & editing (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
X. L.
Litaudon
,
H.-S.
Bosch
,
T.
Morisaki
,
M.
Barbarino
,
A.
Bock
,
E.
Belonohy
,
S.
Brezinsek
,
J. B.
Bucalossi
,
S.
Coda
,
D.
Raju
,
A.
Ekedahl
,
K.
Hanada
,
C. T.
Holcomb
,
J.
Huang
,
S.
Ide
,
M.
Jakubowski
,
B. V.
Kuteev
,
E. A.
Lerche
,
T. C.
Luce
,
P.
Maget
,
Y.
Song
,
J.
Stober
,
D.
van Houtte
,
Y. K.
Xi
,
L.
Xue
,
S. W.
Yoon
, and
B.
Zhang
,
Nucl. Fusion
64
,
015001
(
2023
).
2.
R. C.
Wolf
,
A.
Alonso
,
S.
Äkäslompolo
,
J.
Baldzuhn
,
M.
Beurskens
,
C. D.
Beidler
,
C.
Biedermann
,
H.-S.
Bosch
,
S.
Bozhenkov
,
R.
Brakel
,
H.
Braune
,
S.
Brezinsek
,
K.-J.
Brunner
,
H.
Damm
,
A.
Dinklage
,
P.
Drewelow
,
F.
Effenberg
,
Y.
Feng
,
O.
Ford
,
G.
Fuchert
,
Y.
Gao
,
J.
Geiger
,
O.
Grulke
,
N.
Harder
,
D.
Hartmann
,
P.
Helander
,
B.
Heinemann
,
M.
Hirsch
,
U.
Höfel
,
C.
Hopf
,
K.
Ida
,
M.
Isobe
,
M. W.
Jakubowski
,
Y. O.
Kazakov
,
C.
Killer
,
T.
Klinger
,
J.
Knauer
,
R.
König
,
M.
Krychowiak
,
A.
Langenberg
,
H. P.
Laqua
,
S.
Lazerson
,
P.
McNeely
,
S.
Marsen
,
N.
Marushchenko
,
R.
Nocentini
,
K.
Ogawa
,
G.
Orozco
,
M.
Osakabe
,
M.
Otte
,
N.
Pablant
,
E.
Pasch
,
A.
Pavone
,
M.
Porkolab
,
A.
Puig Sitjes
,
K.
Rahbarnia
,
R.
Riedl
,
N.
Rust
,
E.
Scott
,
J.
Schilling
,
R.
Schroeder
,
T.
Stange
,
A.
von Stechow
,
E.
Strumberger
,
T.
Sunn Pedersen
,
J.
Svensson
,
H.
Thomson
,
Y.
Turkin
,
L.
Vano
,
T.
Wauters
,
G.
Wurden
,
M.
Yoshinuma
,
M.
Zanini
,
D.
Zhang
, and
the Wendelstein 7-X Team
,
Phys. Plasmas
26
,
082504
(
2019
).
3.
C. D.
Beidler
,
H. M.
Smith
,
A.
Alonso
,
T.
Andreeva
,
J.
Baldzuhn
,
M. N. A.
Beurskens
,
M.
Borchardt
,
S. A.
Bozhenkov
,
K. J.
Brunner
,
H.
Damm
,
M.
Drevlak
,
O. P.
Ford
,
J.
Geiger
, and
P.
Helander
,
Nature
596
,
221
226
(
2021
).
4.
S. A.
Bozhenkov
,
Y.
Kazakov
,
O.
Ford
,
M. N. A.
Beurskens
,
J. A.
Alcuson
,
J. A.
Alonso
,
J.
Baldzuhn
,
C.
Brandt
,
K. J.
Brunner
,
H.
Damm
et al,
Nucl. Fusion
60
,
066011
(
2020
).
5.
M.
Krychowiak
,
R.
König
,
T.
Barbui
,
S.
Brezinsek
,
J.
Brunner
,
F.
Effenberg
,
M.
Endler
,
Y.
Feng
,
E.
Flom
,
Y.
Gao
,
D.
Gradic
,
P.
Hacker
,
J.
Harris
,
M.
Hirsch
,
U.
Höfel
,
M.
Jakubowski
,
P.
Kornejew
,
M.
Otte
,
A.
Pandey
,
T.
Pedersen
,
A.
Puig
,
F.
Reimold
,
O.
Schmitz
,
T.
Schröder
,
V.
Winters
, and
D.
Zhang
,
Nucl. Mater. Energy
34
,
101363
(
2023
).
6.
D.
Zhang
,
R.
König
,
Y.
Feng
,
R.
Burhenn
,
S.
Brezinsek
,
M.
Jakubowski
,
B.
Buttenschön
,
H.
Niemann
,
A.
Pavone
,
M.
Krychowiak
,
S.
Kwak
,
J.
Svensson
,
Y.
Gao
,
T. S.
Pedersen
,
A.
Alonso
,
J.
Baldzuhn
,
C. D.
Beidler
,
C.
Biedermann
,
S.
Bozhenkov
,
K. J.
Brunner
,
H.
Damm
,
M.
Hirsch
,
L.
Giannone
,
P.
Drewelow
,
F.
Effenberg
,
G.
Fuchert
,
K. C.
Hammond
,
U.
Höfel
,
C.
Killer
,
J.
Knauer
,
H. P.
Laqua
,
R.
Laube
,
N.
Pablant
,
E.
Pasch
,
F.
Penzel
,
K.
Rahbarnia
,
F.
Reimold
,
H.
Thomsen
,
V.
Winters
,
F.
Wagner
,
T.
Klinger
, and
the W7-X Team
,
Phys. Rev. Lett.
123
,
025002
(
2019
).
7.
D.
Carralero
,
T.
Estrada
,
E.
Maragkoudakis
,
T.
Windisch
,
J. A.
Alonso
,
J. L.
Velasco
,
O.
Ford
,
M.
Jakubowski
,
S.
Lazerson
,
M.
Beurskens
,
S.
Bozhenkov
,
I.
Calvo
,
H.
Damm
,
G.
Fuchert
,
J. M.
Garcia-Regana
,
U.
Höfel
,
N.
Marushchenko
,
N.
Pablant
,
E.
Sanchez
,
H. M.
Smith
,
E.
Pasch
,
T.
Stange
, and
the W7-X Team
,
Plasma Phys. Controlled Fusion
64
,
044006
(
2022
).
8.
T. S.
Pedersen
,
I.
Abramovic
,
P.
Agostinetti
,
M. A.
Torres
,
S.
Äkäslompolo
,
J. A.
Belloso
,
P.
Aleynikov
,
K.
Aleynikova
,
M.
Alhashimi
,
A.
Ali
,
N.
Allen
,
A.
Alonso
,
G.
Anda
et al,
Nucl. Fusion
62
,
042022
(
2022
).
9.
N. A.
Pablant
,
A.
Langenberg
,
J. A.
Alonso
,
M.
Bitter
,
S. A.
Bozhenkov
,
O. P.
Ford
,
K. W.
Hill
,
J.
Kring
,
O.
Marchuck
,
J.
Svensson
,
P.
Traverso
,
T.
Windisch
,
Y.
Yakusevitch
, and
the W7-X Team
,
Rev. Sci. Instrum.
92
,
043530
(
2021
).
10.
P.
Xanthopoulos
,
S. A.
Bozhenkov
,
M. N.
Beurskens
,
H. M.
Smith
,
G. G.
Plunk
,
P.
Helander
,
C. D.
Beidler
,
J. A.
Alcusón
,
A.
Alonso
,
A.
Dinklage
,
O.
Ford
,
G.
Fuchert
,
J.
Geiger
,
J. H. E.
Proll
,
M. J.
Pueschel
,
Y.
Turkin
,
F.
Warmer
, and
the W7-X Team
,
Phys. Rev. Lett.
125
,
075001
(
2020
).
11.
T.
Romba
,
F.
Reimold
,
R.
Jaspers
,
O.
Ford
,
L.
Vano
,
T.
Klinger
, and
the W7-X Team
,
Nucl. Fusion
63
,
076023
(
2023
).
12.
T.
Wegner
,
J.-P.
Bähner
,
B.
Buttenschön
,
A.
Langenberg
,
A.
von Stechow
, and
the W7-X Team
,
J. Plasma Phys.
89
,
955890302
(
2023
).
13.
J. M.
García-Regaña
,
M.
Barnes
,
I.
Calvo
,
F. I.
Parra
,
J. A.
Alcusón
,
R.
Davies
,
A.
González-Jerez
,
A.
Mollén
,
E.
Sánchez
,
J. L.
Velasco
et al,
J. Plasma Phys.
87
,
855870103
(
2021
).
14.
A.
Langenberg
,
T.
Wegner
,
O.
Marchuk
,
J.
Garcia-Regana
,
N.
Pablant
,
G.
Fuchert
,
S.
Bozhenkov
,
H.
Damm
,
E.
Pasch
,
K.-J.
Brunner
,
J.
Knauer
,
M.
Beurskens
,
F.
Reimold
,
R.
Wolf
, and
the W7-X Team
,
Nucl. Fusion
61
,
116018
(
2021
).
15.
A.
Langenberg
,
T.
Wegner
,
N. A.
Pablant
,
O.
Marchuk
,
B.
Geiger
,
N.
Tamura
,
R.
Bussiahn
,
M.
Kubkowska
,
A.
Mollen
,
P.
Traverso
,
H. M.
Smith
,
G.
Fuchert
,
S.
Bozhenkov
,
H.
Damm
,
E.
Pasch
,
K.-J.
Brunner
,
J.
Knauer
,
M.
Beurskens
,
R.
Burhenn
,
R. C.
Wolf
, and
the W7-X Team
,
Phys. Plasmas
27
,
052510
(
2020
).
16.
T.
Wegner
,
J.
Alcuson
,
B.
Geiger
,
A. V.
Stechow
,
P.
Xanthopoulos
,
C.
Angioni
,
M.
Beurskens
,
L.-G.
Böttger
,
S.
Bozhenkov
,
K.
Brunner
,
R.
Burhenn
,
B.
Buttenschön
,
H.
Damm
,
E.
Edlund
,
O.
Ford
,
G.
Fuchert
,
O.
Grulke
,
Z.
Huang
,
J.
Knauer
,
F.
Kunkel
,
A.
Langenberg
,
N.
Pablant
,
E.
Pasch
,
K.
Rahbarnia
,
J.
Schilling
,
H.
Thomsen
,
L.
Vano
, and
the W7-X Team
,
Nucl. Fusion
60
,
124004
(
2020
).
17.
B.
Geiger
,
T.
Wegner
,
C.
Beidler
,
R.
Burhenn
,
B.
Buttenschön
,
R.
Dux
,
A.
Langenberg
,
N.
Pablant
,
T.
Pütterich
,
Y.
Turkin
,
T.
Windisch
,
V.
Winters
,
M.
Beurskens
,
C.
Biedermann
,
K.
Brunner
,
G.
Cseh
,
H.
Damm
,
F.
Effenberg
,
G.
Fuchert
,
O.
Grulke
,
J.
Harris
,
C.
Killer
,
J.
Knauer
,
G.
Kocsis
,
A.
Krämer-Flecken
,
T.
Kremeyer
,
M.
Krychowiak
,
O.
Marchuk
,
D.
Nicolai
,
K.
Rahbarnia
,
G.
Satheeswaran
,
J.
Schilling
,
O.
Schmitz
,
T.
Schröder
,
T.
Szepesi
,
H.
Thomsen
,
H. T.
Mora
,
P.
Traverso
,
D.
Zhang
, and
the W7-X Team
,
Nucl. Fusion
59
,
046009
(
2019
).
18.
M.
Beurskens
,
S.
Bozhenkov
,
O.
Ford
,
P.
Xanthopoulos
,
A.
Zocco
,
Y.
Turkin
,
A.
Alonso
,
C.
Beidler
,
I.
Calvo
,
D.
Carralero
,
T.
Estrada
,
G.
Fuchert
,
O.
Grulke
,
M.
Hirsch
,
K.
Ida
,
M.
Jakubowski
,
C.
Killer
,
M.
Krychowiak
,
S.
Kwak
,
S.
Lazerson
,
A.
Langenberg
,
R.
Lunsford
,
N.
Pablant
,
E.
Pasch
,
A.
Pavone
,
F.
Reimold
,
T.
Romba
,
A.
von Stechow
,
H.
Smith
,
T.
Windisch
,
M.
Yoshinuma
,
D.
Zhang
,
R.
Wolf
, and
the W7-X Team
,
Nucl. Fusion
61
,
116072
(
2021
).
19.
H.
Yamada
,
J.
Harris
,
A.
Dinklage
,
E.
Ascasibar
,
F.
Sano
,
S.
Okamura
,
J.
Talmadge
,
U.
Stroth
,
A.
Kus
,
S.
Murakami
,
M.
Yokoyama
,
C.
Beidler
,
V.
Tribaldos
,
K.
Watanabe
, and
Y.
Suzuki
,
Nucl. Fusion
45
,
1684
(
2005
).
20.
G.
Fuchert
,
K.
Brunner
,
K.
Rahbarnia
,
T.
Stange
,
D.
Zhang
,
J.
Baldzuhn
,
S.
Bozhenkov
,
C.
Beidler
,
M.
Beurskens
,
S.
Brezinsek
,
R.
Burhenn
,
H.
Damm
,
A.
Dinklage
,
Y.
Feng
,
P.
Hacker
,
M.
Hirsch
,
Y.
Kazakov
,
J.
Knauer
,
A.
Langenberg
,
H.
Laqua
,
S.
Lazerson
,
N.
Pablant
,
E.
Pasch
,
F.
Reimold
,
T.
Pedersen
,
E.
Scott
,
F.
Warmer
,
V.
Winters
, and
R.
Wolf
,
Nucl. Fusion
60
,
036020
(
2020
).
21.
J.
Baldzuhn
,
H.
Damm
,
C. D.
Beidler
,
K.
McCarthy
,
N.
Panadero
,
C.
Biedermann
,
S. A.
Bozhenkov
,
A.
Dinklage
,
K. J.
Brunner
,
G.
Fuchert
,
Y.
Kazakov
,
M.
Beurskens
,
M.
Dibon
,
J.
Geiger
,
O.
Grulke
,
U.
Höfel
,
T.
Klinger
,
F.
Köchl
,
J.
Knauer
,
G.
Kocsis
,
P.
Kornejew
,
P. T.
Lang
,
A.
Langenberg
,
H.
Laqua
,
N. A.
Pablant
,
E.
Pasch
,
T. S.
Pedersen
,
B.
Ploeckl
,
K.
Rahbarnia
,
G.
Schlisio
,
E. R.
Scott
,
T.
Stange
,
A. V.
Stechow
,
T.
Szepesi
,
Y.
Turkin
,
F.
Wagner
,
V.
Winters
,
G.
Wurden
,
D.
Zhang
, and
the Wendelstein 7-X Team
,
Plasma Phys. Controlled Fusion
62
,
055012
(
2020
).
22.
S. A.
Lazerson
,
O.
Ford
,
S.
Äkäslompolo
,
S.
Bozhenkov
,
C.
Slaby
,
L.
Vano
,
A.
Spanier
,
P.
McNeely
,
N.
Rust
,
D.
Hartmann
,
P.
Poloskei
,
B.
Buttenschön
,
R.
Burhenn
,
N.
Tamura
,
R.
Bussiahn
,
T.
Wegner
,
M.
Drevlak
,
Y.
Turkin
,
K.
Ogawa
,
J.
Knauer
,
K. J.
Brunner
,
E.
Pasch
,
M.
Beurskens
,
H.
Damm
,
G.
Fuchert
,
P.
Nelde
,
E.
Scott
,
N.
Pablant
,
A.
Langenberg
,
P.
Traverso
,
P.
Valson
,
U.
Hergenhahn
,
A.
Pavone
,
K.
Rahbarnia
,
T.
Andreeva
,
J.
Schilling
,
C.
Brandt
,
U.
Neuner
,
H.
Thomsen
,
N.
Chaudhary
,
U.
Höefel
,
T.
Stange
,
G.
Weir
,
N.
Marushchenko
,
M.
Jakubowski
,
A.
Ali
,
Y.
Gao
,
H.
Niemann
,
A. P.
Sitjes
,
R.
König
,
R.
Schroeder
,
N.
den Harder
,
B.
Heinemann
,
C.
Hopf
,
R.
Riedl
,
R. C.
Wolf
, and
the W7-X Team
,
Nucl. Fusion
61
,
096008
(
2021
).
23.
R.
Lunsford
,
C.
Killer
,
A.
Nagy
,
D. A.
Gates
,
T.
Klinger
,
A.
Dinklage
,
G.
Satheeswaran
,
G.
Kocsis
,
S. A.
Lazerson
,
F.
Nespoli
,
N. A.
Pablant
,
A.
von Stechow
,
A.
Alonso
,
T.
Andreeva
,
M.
Beurskens
,
C.
Biedermann
,
S.
Brezinsek
,
K. J.
Brunner
,
B.
Buttenschön
,
D.
Carralero
,
G.
Cseh
,
P.
Drewelow
,
F.
Effenberg
,
T.
Estrada
,
O. P.
Ford
,
O.
Grulke
,
U.
Hergenhahn
,
U.
Höfel
,
J.
Knauer
,
M.
Krause
,
M.
Krychowiak
,
S.
Kwak
,
A.
Langenberg
,
U.
Neuner
,
D.
Nicolai
,
A.
Pavone
,
A.
Puig Sitjes
,
K.
Rahbarnia
,
J.
Schilling
,
J.
Svensson
,
T.
Szepesi
,
H.
Thomsen
,
T.
Wauters
,
T.
Windisch
,
V.
Winters
,
D.
Zhang
,
L.
Zsuga
, and
the W7-X Team
,
Phys. Plasmas
28
,
082506
(
2021
).
24.
H.
Laqua
,
J.
Baldzuhn
,
H.
Braune
,
S.
Bozhenkov
,
K.
Brunner
,
M.
Hirsch
,
U.
Höfel
,
J.
Knauer
,
A.
Langenberg
,
S.
Marsen
,
D.
Moseev
,
E.
Pasch
,
K.
Rahbarnia
,
T.
Stange
,
R.
Wolf
,
N.
Pablant
,
O.
Grulke
, and
the W7-X Team
,
Nucl. Fusion
61
,
106005
(
2021
).
25.
S.
Sereda
,
S.
Brezinsek
,
E.
Wang
,
T.
Barbui
,
R.
Brakel
,
B.
Buttenschön
,
A.
Goriaev
,
U.
Hergenhahn
,
U.
Höfel
,
M.
Jakubowski
,
A.
Knieps
,
R.
König
,
M.
Krychowiak
,
S.
Kwak
,
Y.
Liang
,
D.
Naujoks
,
A.
Pavone
,
M.
Rasinski
,
L.
Rudischhauser
,
M.
Sleczka
,
J.
Svensson
,
H.
Viebke
,
T.
Wauters
,
Y.
Wei
,
V.
Winters
,
D.
Zhang
, and
the W7-X Team
,
Nucl. Fusion
60
,
086007
(
2020
).
26.
A.
Goriaev
,
T.
Wauters
,
R.
Brakel
,
S.
Brezinsek
,
A.
Dinklage
,
J.
Fellinger
,
H.
Grote
,
D.
Moseev
,
S.
Sereda
,
O.
Volzke
, and
the W7-X Team
,
Phys. Scr.
2020
,
014063
.
27.
T.
Andreeva
,
J.
Geiger
,
A.
Dinklage
,
G.
Wurden
,
H.
Thomsen
,
K.
Rahbarnia
,
J.
Schmitt
,
M.
Hirsch
,
G.
Fuchert
,
C.
Nührenberg
,
A.
Alonso
,
C.
Beidler
,
M.
Beurskens
,
S.
Bozhenkov
,
R.
Brakel
,
C.
Brandt
,
V.
Bykov
,
M.
Grahl
,
O.
Grulke
,
C.
Killer
,
G.
Kocsis
,
T.
Klinger
,
A.
Krämer-Flecken
,
S.
Lazerson
,
M.
Otte
,
N.
Pablant
,
J.
Schilling
,
T.
Windisch
, and
the W7-X Team
,
Nucl. Fusion
62
,
026032
(
2022
).
28.
A.
Dinklage
,
C.
Beidler
,
P.
Helander
,
G.
Fuchert
,
H.
Maassberg
,
K.
Rahbarnia
,
T.
Sunn Pedersen
,
Y.
Turkin
et al,
Nat. Phys.
14
,
855
(
2018
).
29.
K.
Brunner
,
T.
Akiyama
,
M.
Hirsch
,
J.
Knauer
,
P.
Kornejew
,
B.
Kursinski
,
H.
Laqua
,
J.
Meineke
,
H. T.
Mora
, and
R. C.
Wolf
,
J. Instrumen.
13
,
P09002
(
2018
).
30.
K.
Rahbarnia
,
H.
Thomsen
,
U.
Neuner
,
J.
Schilling
,
J.
Geiger
,
G.
Fuchert
,
T.
Andreeva
,
M.
Endler
,
D.
Hathiramani
,
T.
Bluhm
,
M.
Zilker
,
B.
Carvalho
,
A.
Werner
, and
the Wendelstein 7-X Team
,
Nucl. Fusion
58
,
096010
(
2018
).
31.
A.
Langenberg
,
N. A.
Pablant
,
T.
Wegner
,
P.
Traverso
,
O.
Marchuk
,
T.
Bräuer
,
B.
Geiger
,
G.
Fuchert
,
S.
Bozhenkov
,
E.
Pasch
,
O.
Grulke
,
F.
Kunkel
,
C.
Killer
,
D.
Nicolai
,
G.
Satheeswaran
,
K. P.
Hollfeld
,
B.
Schweer
,
T.
Krings
,
P.
Drews
,
G.
Offermanns
,
A.
Pavone
,
J.
Svensson
,
J. A.
Alonso
,
R.
Burhenn
,
R. C.
Wolf
, and
the W7-X Team
,
Rev. Sci. Instrum.
89
,
10G101
(
2018
).
32.
E.
Pasch
,
M. N. A.
Beurskens
,
S. A.
Bozhenkov
,
G.
Fuchert
,
J.
Knauer
,
R. C.
Wolf
, and
the W7-X Team
,
Rev. Sci. Instrum.
87
,
11E729
(
2016
).
33.
T. S.
Pedersen
,
R.
König
,
M.
Jakubowski
,
M.
Krychowiak
,
D.
Gradic
,
C.
Killer
,
H.
Niemann
,
T.
Szepesi
,
U.
Wenzel
,
A.
Ali
et al,
Nucl. Fusion
59
,
096014
(
2019
).
34.
T.
Estrada
,
D.
Carralero
,
T.
Windisch
,
E.
Sanchez
,
J.
Garcia-Regana
,
J.
Martinez-Fernandez
,
A.
de la Pena
,
J.
Velasco
,
J.
Alonso
,
M.
Beurskens
,
S.
Bozhenkov
,
H.
Damm
,
G.
Fuchert
,
R.
Kleiber
,
N.
Pablant
,
E.
Pasch
, and
the W7-X Team
,
Nucl. Fusion
61
,
046008
(
2021
).
35.
O. P.
Ford
,
M.
Beurskens
,
S.
Bozhenkov
,
S.
Lazerson
, and
L.
Vano
, “
Turbulence-reduced high-performance scenarios in Wendelstein 7-X
” (submitted for publication).
36.
T.
Andreeva
, “
Vacuum magnetic configurations of Wendelstein 7-X
,” in
Tech. Rep. IPP III/270
(
Max-Planck-Institut für Plasmaphysik
,
Garching
,
2002
).
37.
A. V.
Stechow
,
O.
Grulke
,
T.
Wegner
,
J. H. E.
Proll
,
J. A.
Alcuson
,
H. M.
Smith
,
J.
Baldzuhn
,
C. D.
Beidler
,
M. N. A.
Beurskens
,
S. A.
Bozhenkov
,
E.
Edlund
,
B.
Geiger
,
Z.
Huang
,
O. P.
Ford
,
G.
Fuchert
,
A.
Langenberg
,
N.
Pablant
,
E.
Pasch
,
M.
Porkolab
,
K.
Rahbarnia
,
J.
Schilling
,
E. R.
Scott
,
H.
Thomsen
,
L.
Vano
,
G.
Weir
, and
the W7-X Team
, “
Suppression of core turbulence by profile shaping in Wendelstein 7-X
” (in press).