Observation of a Fast-Ion Profile Stiffness Due to the Alfvén Eigenmode

Observation of a Fast-Ion Profile Stiffness Due to the Alfvén Eigenmode | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Observation of a Fast-Ion Profile Stiffness Due to the Alfvén Eigenmode Shuji Kamio, Yutaka Fujiwara, Kenichi Nagaoka, Hideo Nuga, Hiroyuki Yamaguchi, and 7 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6839914/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 08 Nov, 2025 Read the published version in Journal of Fusion Energy → Version 1 posted 9 You are reading this latest preprint version Abstract Fast-ion transport driven by Alfvén eigenmodes (AEs) is one critical issue facing fast-ion confinement in magnetic fusion device. In the DIII-D tokamak experiment, stiff transport of fast-ions increased with increasing neutral beam (NB) injection power when the amplitudes of multiple interacting AEs exceeded a certain threshold. These experiment results are supported by simulation studies that predict monotonically degrading fast-ion confinement and profile stiffness with increasing beam power. To investigate the universality of the fast-ion profile stiffness dependence on AE amplitude, an experiment was performed at the Large Helical Device (LHD) to scan the injection current of the NB and vary the AE amplitude. Under the experimental conditions, the AE amplitude increased linearly with NB injection power. The blue shifted FIDA intensity between 663-665 nm, corresponding to the energy range of 98-166 keV in the ctr-direction, was used for estimating the radial profile of the fast-ion density. There is direct evidence of stiffening of the fast-ion profile and degradation of the fast-ion confinement. This is consistent with the experimentally observed reduction in the expected neutron emission rate. We have demonstrated that under AE-prone confinement conditions, even if the fast-ion source increases due to NB injection, they experience enhanced transport by AEs and do not increase in density. Alfvén eigenmode fast-ion profile stiffness FIDA measurement Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction Fast-ion transport by Alfvén eigenmodes (AEs) is one key issue in when discussing fast-ion confinement. Future fusion reactors are expected to employ high-energy neutral beam (NB) injection heating, and the fusion-produced alpha particles will also have high energy. Consequently, these reactors may operate in environments with a high density of fast ions susceptible to detrimental transport by AEs. For efficient reactor operation, AEs that cause fast-ion confinement degradation must be well-understood for control and suppression. In the DIII-D tokamak experiment, stiff transport of fast-ions increased with increasing NB injection power when the amplitudes of multiple interacting AEs exceeded a certain threshold [ 1 ]. In this experiment, when high NB power was injected, the fast-ion density profiles appeared “clamped,” with peak density no longer increasing despite increased NB power. This experimental result was supported by simulation studies that predict monotonically degrading fast-ion confinement and profile stiffness with increasing beam power [ 2 ]. In this simulation, the MEGA code [ 3 ], which calculates the motion of the fast ions using particle-in-cell (PIC) methods while describing the bulk plasma with nonlinear MHD equations, was used to estimate the fast-ion density profiles in the presence of multiple AEs. As a result of enhanced transport by the AEs, the fast-ion pressure did not increase linearly proportional to the NB deposition power [ 4 ]. Thus, fast-ion profile stiffness, suggested by DIII-D tokamak experiments, has also been reproduced in simulation. To investigate the universality of the fast-ion profile stiffness dependence on AE amplitude, an experiment was performed at the Large Helical Device (LHD) to scan the injection current of the NB and vary the AE amplitude. Since the LHD generates its confinement field solely using external field coils, it does not rely on plasma current for confinement. As a result, variations in the confinement field with changing NB injection power are significantly smaller when compared to tokamak devices, where plasma current is influenced by NB power. This feature makes the LHD particularly suitable for isolating the effects of fast-ion transport caused by AEs, as changes in plasma equilibrium due to varying NB power are minimized. In addition, the LHD is equipped with multiple tangential injection NBs that allow for easy scanning of NB injection power, making it well-suited for scanning fast-ion pressures. 2. Experimental setup In the LHD, fast-ion transport driven by AEs has been a long-standing subject of investigation [ 5 – 7 ]. In experiments conducted under relatively low magnetic field conditions, the Alfvén velocity is close or lower than the fast-ion velocity injected by negative-ion-based NB injectors (NNBI) [ 8 ], leading to frequent AE observations. Figure 1 shows a schematic view of the LHD toroidal cross-section. Two NNBIs (NB#1 and #3) with CCW tangential directions were used in this experiment to achieve high AE amplitudes. Since each of these NNBIs uses two ion sources to produce ions, it is possible to inject half the power without changing the injection energy by using only one of the ion sources. In this experiment, the injection power was scanned by combining these two sources on two NNBIs. NB#4, injected in the perpendicular direction, was used as an active neutral source for spectroscopic measurements. Charge exchange spectroscopy (CXS) measured the radial distribution of ion temperature using CVI emission spectra [ 9 – 11 ], and FIDA measurements [ 12 , 13 ] measured the phase space distribution of fast ions. The observed region of the FIDA measurement in this experiment is shown in Fig. 1 . NB#2 and #5 are also available as fast-ion injection sources, but these were not used. NB#2 is also a tangential injection NNBI, but the AE resonance mechanism may be complicated because the NB#2 injection direction is opposite to the rest of NNBIs, while NB#5 is a perpendicular injection and has a different injection energy. Since the different orbits of fast ions make quantitative comparisons difficult in FIDA measurements, power scanning was performed using only NB#1 and #3 in order to prioritize accurate comparison of experimental results. By adopting deuterium as the beam ion species, neutron detectors [ 14 ] can be also utilized to investigate fast-ion behavior through the measurement of beam-thermal neutrons. The fast-ion distribution was simulated using the GNET code [ 15 , 16 ], and the FIDA observation results for this distribution were calculated using FIDASIM [ 17 , 18 ] and compared with the experiment. Since the effect of AE is not included in the GNET code, the effect of AE on fast ion transport can be evaluated if there is a significant difference in the fast ion distribution depending on the AE amplitude. 3. Results and discussions Figure 2 shows the results of the operation for the NB power scan experiments (a-c) and the results of the plasma parameters (d-g). Experiments were conducted at various magnetic field strengths and densities, and this paper highlights a particularly significant dataset. In this experiment, multiple powers of NBs were injected by combining two ion sources of NB#1 and #3 each (Fig. 2 a), and NB#4 was pulsed for the CXS and FIDA measurements (Fig. 2 b). During this experiment, the gas puff volume was adjusted to keep the value of the line-integrated electron density constant (Fig. 2 c), and all parameters except the fast ion pressure were kept the same. As a result, the experiments at different NB powers reproduced the same electron density, electron temperature, and ion temperature plasmas as shown in Fig. 2 (d-f). On the other hand, it was surprising that the reproducibility was so high. This observation suggests that the increased NB power had a negligible impact on plasma heating. Since the experiment was conducted under relatively AE-prone conditions (low field strength of 1.0 T, CW), the increased fast ions may have contributed to AE production and increased fast-ion losses. Figure 2 (g) shows the carbon emission intensity distribution used during the ion temperature measurement. The lower carbon emission intensity on the inner side indicates attenuation of the vertical beam from NB#4 within the plasma, and the emission intensity did not depend on the power of the tangential beams. Although there should have been no need to strictly adjust the carbon density in this experiment, this carbon intensity distribution varied greatly under other experimental conditions. Therefore, we confirmed here that the carbon intensity was also identical in this experiment. The effects of large changes in impurity density on fast-ion confinement performance are left for future work, but in this paper we have eliminated as many non-AE effects as possible. Figure 3 shows the behavior of AE in this experiment. Figure 3 (a) presents the spectrogram of magnetic field fluctuations, showing AE bursts that increase in amplitude with higher NB injection power. Figure 3 (b) shows the spectra of AEs. Since the LHD has 10 magnetic probes in the 10 toroidal sections, spectra with even and odd toroidal mode number n are also shown. The amplitudes of specific frequencies are not particularly high, and multiple resonance are thought to overlap. The higher the NB injection power, the higher the overall amplitude, but there is also a peak around 80 kHz, for example, where the amplitude is high above a certain power. Figure 3 (c) shows the dependence of AE amplitude on NB injection power: AE amplitude varies linearly with NB injection power, and this fitting line has zero amplitude between P t-NB = 0–1 MW. Considering the critical gradient "stiff" transport model in DIII-D [ 2 ], it is expected that AE is excited from very low NB injection power under the present experimental conditions. This prediction is reasonable because this is one of the most AE-prone magnetic field configurations in LHD. According to this model, the higher the NB injection power, the higher the AE amplitude, and the fast-ion transport will increase linearly with power. It is thought that the fast ions could not contribute to heating because the increased power of the transported fast ions could not contribute to heating, and the temperature did not increase even if the NB injection power was increased. The results of the fast-ion observations by FIDA and simulations by FIDASIM, shown in Fig. 4 , strongly support the story. Figure 4 shows the fast-ion spectra and distributions obtained by FIDA measurements (solid lines) and the simulation results obtained by FIDASIM (dashed lines). The left peak of the FIDA spectrum in Fig. 4 (a) is the center of the D-alpha line, where the Halo and direct charge exchange (DCX) components are observed. The right peak is the beam emission (BES) component. These peaks were at approximately the same level at various NB injection powers because the plasma profiles were almost identical as shown in Fig. 2 . The emission extending toward the higher wavelengths is the fast-ion emission, while that around 662–663 nm is the carbon impurity emission. The Da emission from the fast ions which tangentially injected by NB#1 and #3 are blue shifted, and the Da line shift to 665 nm when the NB injection energy is 165 keV. In both Figs. 4 (a) and (b-c), the observed FIDA signal was almost power-independent. In more detail, the FIDA signal in the higher energy band (663–665 nm) was slightly higher at higher NB injection power, while the FIDA signal in the lower energy band (660–661 nm) was higher at lower NB injection power. This indicate the fast-ion confinement in the higher power injection case is slightly worse than the lower power case. On the other hand, FIDASIM results show that the higher the injection NB power, the higher the FIDA signal should be. It is an inherently natural result that the higher the NB injection power, the higher the fast-ion density because the simulation is performed under the same density and temperature conditions. Since FIDASIM does not include effects due to AE, and considering that the experimentally observed AE amplitude varied significantly depending on the NB injection power, it is likely that the cause of this gap is the transport of fast ions due to AE. In this relatively low magnetic field experiment, the Alfvén velocity is below the NB injection energy and the effect of AE is very strong. The experimental observations of radial profiles of fast ions shown in Fig. 4 (b, c) solid lines show little difference between the central (3.6–3.7 m) and outer (3.3 m) regions even at the lowest NB injection power, suggesting that AE-induced fast-ion transport is occurring. A simulation with FIDASIM that does not take AE into account (dashed lines) should result in a profile that peaks at the center. Since this experiment was conducted using a deuterium beam, it is possible to estimate the amount of fast ions using a different approach than FIDA, mainly by measuring neutrons due to beam-thermal fusion. Figure 5 (a) shows the total neutron emission rate Sn and the results of the simulation by CONV_FIT3D [ 19 ] when the NB injection power is varied. In the simulation, Sn increases linearly with increasing NB injection power, but in the experiment, little change was observed with increasing NB injection power. This trend is in good agreement with FIDA and previous results, and several different diagnostics have been used to study the behavior of fast ions. Figure 5 (b) shows the radial profile of the line-integrated neutron emission rate measured by the neutron emission camera [ 20 , 21 ]. Although it appears that the neutron emission rate is high for codes close to the center, in reality, the long line-of-sight integration distance results in the neutral emission rate shown in this figure for flat fast ion distributions such as those shown in Fig. 4 (b, c). In this measurement, as in the previous results, there was little dependence on NB injection power, but the neutron emission rate was slightly higher for discharges with higher NB injection power. This trend is close to that shown in Fig. 4 (c) and is consistent with the FIDA results since the high-energy fast-ion density affects the neutron emission rate. Throughout this study, we have demonstrated the relationship between fast-ion profile stiffness and AEs observed in LHD experiments. Under conditions where AEs are easily excited, our experiments revealed that increasing NB power does not alter the fast-ion profile but increases AE amplitude. This result is consistent with trends observed in DIII-D experiments. Moreover, the experimental conditions in this study were more systematically controlled, providing clear evidence of this phenomenon. The intuitive explanation is that fast-ion profile stiffness occurs because AEs eject fast ions as the fast-ion pressure exceeds a certain threshold. However, the details of the transport mechanisms remain unclear. At this point, we refer to another study conducted on LHD, reported in [ 22 ], which examined the degradation of fast-ion confinement. That study observed that fast-ion confinement deteriorates with increasing NB power in quiescent plasma (i.e. very low-level magnetic fluctuations), though the underlying cause was not identified. The observed confinement degradation with increased NB power in [ 22 ] is consistent with the results of this study, suggesting that an additional unknown effect may also contribute to the findings presented herein, that is unrelated to AEs. However, the examples of confinement degradation reported in [ 22 ] are not as pronounced as those observed in this study, implying that any contribution of the unknown effect to the results presented here is likely limited. Investigating these mechanisms in greater detail remains a subject for future work. 4. Conclusions Previous studies have suggested, both experimentally and by simulation, fast-ion profile stiffening in high AE amplitude environments. To investigate the universality of the fast-ion profile stiffness dependence on AE amplitude, an experiment was performed in the LHD to scan the injection current of the NB and vary the AE amplitude. Under this experimental condition, the AE amplitude increases as the NB injection power is increased, resulting in AE-induced fast-ion transport and fast-ion profile stiffness, as experimentally demonstrated. On the other hand, since the fast-ion profile stiffness did not appear in the FIDASIM results, which does not include the effect of the fast-ion transport by AEs, the fast-ion profile stiffness can be considered to be the effect of the AEs. Neutron emission rate observations further corroborate the stiffening of the fast-ion profile. Declarations Acknowledgements The authors wish to thank Prof. Y. Todo (NIFS) and S. Sharapov (CCFE) for fruitful discussions and the LHD experiment group for their excellent support of this work. Data availability statement The LHD data can be accessed from the LHD experiment data repository. https://doi.org/10.57451/lhd.analyzed-data. Funding Declaration This research was partially funded by the National Institute for Fusion Science (NIFS22KIPR00,1 NIFS22KIST035) and JSPS KAKENHI Grant Numbers JP 19K03798. References W. W. Heidbrink et al., Phys. Rev. Lett. 99, 245002 (2007) C. S. Collins et al., Phys. Rev. Lett. 116, 095001 (2016) Y. Todo and T. Sato, Phys. Plasmas 5, 1321 (1998) Y. Todo et al., Nucl. Fusion 56, 112008 (2016) K. Toi et al., Plasma Phys. Control. Fusion 46, S1 (2004) M. Osakabe et al., Nucl. Fusion 46, S911-S917 (2006) S. Kamio et al., Nucl. Fusion 60, 112002 (2006) Y. Takeiri et al., Fusion Sci. Technol. 58, 482-8 (2010) M. Yoshinuma et al., Fusion Sci. Technol. 58, 375-82 (2010) J. Chen et al., Phys. Lett. A 383, 1293-9 (2019) K. Ida et al., Plasma Fusion Res. 14, 1402079 (2019) W. W. Heidbrink et al., Plasma Phys. Control. Fusion 46, 1855 (2005) Y. Fujiwara et al., Nucl. Fusion 60, 112014 (2020) M. Isobe et al., IEEE Trans. Plasma Sci. 46, 2050-8 (2018) S. Murakami et al., Nucl. Fusion 40, 693 (2000) H. Yamaguchi and S. Murakami, Nucl. Fusion 56, 026003 (2016) B. Geiger et al., Plasma Phys. Control. Fusion 62, 105008 (2020) W. W. Heidbrink et al., Commun. Comput. Phys. 10, 716-41 (2011) H. Nuga et al., J. Plasma Phys. 86, 815860306 (2020) K. Ogawa et al., Rev. Sci. Instrum. 85, 11E110 (2014) K. Ogawa et al., Rev. Sci. Instrum. 89, 113509 (2018) H. Nuga et al., Nucl. Fusion 64, 066001 (2024) Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 08 Nov, 2025 Read the published version in Journal of Fusion Energy → Version 1 posted Editorial decision: Revision requested 06 Aug, 2025 Reviews received at journal 28 Jul, 2025 Reviews received at journal 01 Jul, 2025 Reviewers agreed at journal 28 Jun, 2025 Reviewers agreed at journal 18 Jun, 2025 Reviewers invited by journal 16 Jun, 2025 Editor assigned by journal 13 Jun, 2025 Submission checks completed at journal 13 Jun, 2025 First submitted to journal 06 Jun, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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01:08:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6839914/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6839914/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10894-025-00521-3","type":"published","date":"2025-11-08T15:57:04+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":85345907,"identity":"57882b59-7fe6-4776-8bec-5f829ee2ee0d","added_by":"auto","created_at":"2025-06-25 02:08:04","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":107843,"visible":true,"origin":"","legend":"\u003cp\u003eLHD toroidal cross-section view, together with the tangentially injected NB#1 and #3, perpendicularly injected NB#4, and measurement region of the FIDA.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6839914/v1/3e11e09ac129c5dd6487c1ae.png"},{"id":85345905,"identity":"388c78a7-a536-4534-a94f-fc1337ed25ab","added_by":"auto","created_at":"2025-06-25 02:08:04","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":101495,"visible":true,"origin":"","legend":"\u003cp\u003eTime evolutions of the total power of (a) tangential and (b) perpendicular NB injection, and (c) line integrated electron density. Radial profiles of (d) the electron density, (e) the electron temperature, (f) the ion temperature, and (g) the emission intensity of the impurity C5+ (indicating the impurity density) at 4.80-4.85 s.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6839914/v1/5ab048bd0a2e63594d20ef18.png"},{"id":85345908,"identity":"5eb55d20-5ddf-4869-9053-a0fa877a2e0d","added_by":"auto","created_at":"2025-06-25 02:08:04","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":151364,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Spectrogram of the magnetic fluctuations. (b) Total spectrum of AE intensities and odd and even number of toroidal modes. (c) Dependence of the total AE magnetic field fluctuation intensity on the NB injection power.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6839914/v1/18140fa0b9c8e8bd864e8e0e.png"},{"id":85345906,"identity":"684b6400-f0d5-484e-8b29-3d5d67846b13","added_by":"auto","created_at":"2025-06-25 02:08:04","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":107726,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental results of the FIDA measurement (solid lines) and FIDASIM results (dashed lines). (a). Measured spectra of FIDA and simulated spectra by FIDASIM. Fast-ion radial distributions for (b) low energy and for (c) high energy.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6839914/v1/3aeb1cf3d81514393d9bb8d3.png"},{"id":85345301,"identity":"25311203-ba5d-41c7-a06c-54739b703cdd","added_by":"auto","created_at":"2025-06-25 02:00:05","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":47053,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Dependence of the total neutron emission rate Sn on the NB injection power obtained in experiments (red) and in calculation by CONV_FIT3D code (green). (b) Experimental results of the radial profiles of the line integrated neutron emission rate. Since the integrated length is higher in the center codes, the neutron emission profile is also very flat.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6839914/v1/c729628b6d2e39c45c8bead4.png"},{"id":95564322,"identity":"f6c386db-8793-44cc-b7d0-3b1415823d3a","added_by":"auto","created_at":"2025-11-10 16:09:49","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":801295,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6839914/v1/207e8046-7b23-4e03-98af-d8a0bad6ab1e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Observation of a Fast-Ion Profile Stiffness Due to the Alfvén Eigenmode","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eFast-ion transport by Alfv\u0026eacute;n eigenmodes (AEs) is one key issue in when discussing fast-ion confinement. Future fusion reactors are expected to employ high-energy neutral beam (NB) injection heating, and the fusion-produced alpha particles will also have high energy. Consequently, these reactors may operate in environments with a high density of fast ions susceptible to detrimental transport by AEs. For efficient reactor operation, AEs that cause fast-ion confinement degradation must be well-understood for control and suppression. In the DIII-D tokamak experiment, stiff transport of fast-ions increased with increasing NB injection power when the amplitudes of multiple interacting AEs exceeded a certain threshold [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. In this experiment, when high NB power was injected, the fast-ion density profiles appeared \u0026ldquo;clamped,\u0026rdquo; with peak density no longer increasing despite increased NB power. This experimental result was supported by simulation studies that predict monotonically degrading fast-ion confinement and profile stiffness with increasing beam power [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. In this simulation, the MEGA code [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], which calculates the motion of the fast ions using particle-in-cell (PIC) methods while describing the bulk plasma with nonlinear MHD equations, was used to estimate the fast-ion density profiles in the presence of multiple AEs. As a result of enhanced transport by the AEs, the fast-ion pressure did not increase linearly proportional to the NB deposition power [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Thus, fast-ion profile stiffness, suggested by DIII-D tokamak experiments, has also been reproduced in simulation. To investigate the universality of the fast-ion profile stiffness dependence on AE amplitude, an experiment was performed at the Large Helical Device (LHD) to scan the injection current of the NB and vary the AE amplitude. Since the LHD generates its confinement field solely using external field coils, it does not rely on plasma current for confinement. As a result, variations in the confinement field with changing NB injection power are significantly smaller when compared to tokamak devices, where plasma current is influenced by NB power. This feature makes the LHD particularly suitable for isolating the effects of fast-ion transport caused by AEs, as changes in plasma equilibrium due to varying NB power are minimized. In addition, the LHD is equipped with multiple tangential injection NBs that allow for easy scanning of NB injection power, making it well-suited for scanning fast-ion pressures.\u003c/p\u003e"},{"header":"2. Experimental setup","content":"\u003cp\u003eIn the LHD, fast-ion transport driven by AEs has been a long-standing subject of investigation [\u003cspan additionalcitationids=\"CR6\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. In experiments conducted under relatively low magnetic field conditions, the Alfv\u0026eacute;n velocity is close or lower than the fast-ion velocity injected by negative-ion-based NB injectors (NNBI) [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], leading to frequent AE observations. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows a schematic view of the LHD toroidal cross-section. Two NNBIs (NB#1 and #3) with CCW tangential directions were used in this experiment to achieve high AE amplitudes. Since each of these NNBIs uses two ion sources to produce ions, it is possible to inject half the power without changing the injection energy by using only one of the ion sources. In this experiment, the injection power was scanned by combining these two sources on two NNBIs. NB#4, injected in the perpendicular direction, was used as an active neutral source for spectroscopic measurements. Charge exchange spectroscopy (CXS) measured the radial distribution of ion temperature using CVI emission spectra [\u003cspan additionalcitationids=\"CR10\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], and FIDA measurements [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] measured the phase space distribution of fast ions. The observed region of the FIDA measurement in this experiment is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. NB#2 and #5 are also available as fast-ion injection sources, but these were not used. NB#2 is also a tangential injection NNBI, but the AE resonance mechanism may be complicated because the NB#2 injection direction is opposite to the rest of NNBIs, while NB#5 is a perpendicular injection and has a different injection energy. Since the different orbits of fast ions make quantitative comparisons difficult in FIDA measurements, power scanning was performed using only NB#1 and #3 in order to prioritize accurate comparison of experimental results. By adopting deuterium as the beam ion species, neutron detectors [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] can be also utilized to investigate fast-ion behavior through the measurement of beam-thermal neutrons.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe fast-ion distribution was simulated using the GNET code [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], and the FIDA observation results for this distribution were calculated using FIDASIM [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] and compared with the experiment. Since the effect of AE is not included in the GNET code, the effect of AE on fast ion transport can be evaluated if there is a significant difference in the fast ion distribution depending on the AE amplitude.\u003c/p\u003e"},{"header":"3. Results and discussions","content":"\u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the results of the operation for the NB power scan experiments (a-c) and the results of the plasma parameters (d-g). Experiments were conducted at various magnetic field strengths and densities, and this paper highlights a particularly significant dataset. In this experiment, multiple powers of NBs were injected by combining two ion sources of NB#1 and #3 each (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea), and NB#4 was pulsed for the CXS and FIDA measurements (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb). During this experiment, the gas puff volume was adjusted to keep the value of the line-integrated electron density constant (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec), and all parameters except the fast ion pressure were kept the same. As a result, the experiments at different NB powers reproduced the same electron density, electron temperature, and ion temperature plasmas as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (d-f). On the other hand, it was surprising that the reproducibility was so high. This observation suggests that the increased NB power had a negligible impact on plasma heating. Since the experiment was conducted under relatively AE-prone conditions (low field strength of 1.0 T, CW), the increased fast ions may have contributed to AE production and increased fast-ion losses. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (g) shows the carbon emission intensity distribution used during the ion temperature measurement. The lower carbon emission intensity on the inner side indicates attenuation of the vertical beam from NB#4 within the plasma, and the emission intensity did not depend on the power of the tangential beams. Although there should have been no need to strictly adjust the carbon density in this experiment, this carbon intensity distribution varied greatly under other experimental conditions. Therefore, we confirmed here that the carbon intensity was also identical in this experiment. The effects of large changes in impurity density on fast-ion confinement performance are left for future work, but in this paper we have eliminated as many non-AE effects as possible.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the behavior of AE in this experiment. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (a) presents the spectrogram of magnetic field fluctuations, showing AE bursts that increase in amplitude with higher NB injection power. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (b) shows the spectra of AEs. Since the LHD has 10 magnetic probes in the 10 toroidal sections, spectra with even and odd toroidal mode number n are also shown. The amplitudes of specific frequencies are not particularly high, and multiple resonance are thought to overlap. The higher the NB injection power, the higher the overall amplitude, but there is also a peak around 80 kHz, for example, where the amplitude is high above a certain power. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (c) shows the dependence of AE amplitude on NB injection power: AE amplitude varies linearly with NB injection power, and this fitting line has zero amplitude between \u003cem\u003eP\u003c/em\u003e\u003csub\u003et-NB\u003c/sub\u003e = 0\u0026ndash;1 MW. Considering the critical gradient \"stiff\" transport model in DIII-D [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], it is expected that AE is excited from very low NB injection power under the present experimental conditions. This prediction is reasonable because this is one of the most AE-prone magnetic field configurations in LHD. According to this model, the higher the NB injection power, the higher the AE amplitude, and the fast-ion transport will increase linearly with power. It is thought that the fast ions could not contribute to heating because the increased power of the transported fast ions could not contribute to heating, and the temperature did not increase even if the NB injection power was increased.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe results of the fast-ion observations by FIDA and simulations by FIDASIM, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, strongly support the story. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the fast-ion spectra and distributions obtained by FIDA measurements (solid lines) and the simulation results obtained by FIDASIM (dashed lines). The left peak of the FIDA spectrum in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (a) is the center of the D-alpha line, where the Halo and direct charge exchange (DCX) components are observed. The right peak is the beam emission (BES) component. These peaks were at approximately the same level at various NB injection powers because the plasma profiles were almost identical as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The emission extending toward the higher wavelengths is the fast-ion emission, while that around 662\u0026ndash;663 nm is the carbon impurity emission. The Da emission from the fast ions which tangentially injected by NB#1 and #3 are blue shifted, and the Da line shift to 665 nm when the NB injection energy is 165 keV. In both Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (a) and (b-c), the observed FIDA signal was almost power-independent. In more detail, the FIDA signal in the higher energy band (663\u0026ndash;665 nm) was slightly higher at higher NB injection power, while the FIDA signal in the lower energy band (660\u0026ndash;661 nm) was higher at lower NB injection power. This indicate the fast-ion confinement in the higher power injection case is slightly worse than the lower power case. On the other hand, FIDASIM results show that the higher the injection NB power, the higher the FIDA signal should be. It is an inherently natural result that the higher the NB injection power, the higher the fast-ion density because the simulation is performed under the same density and temperature conditions. Since FIDASIM does not include effects due to AE, and considering that the experimentally observed AE amplitude varied significantly depending on the NB injection power, it is likely that the cause of this gap is the transport of fast ions due to AE. In this relatively low magnetic field experiment, the Alfv\u0026eacute;n velocity is below the NB injection energy and the effect of AE is very strong. The experimental observations of radial profiles of fast ions shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (b, c) solid lines show little difference between the central (3.6\u0026ndash;3.7 m) and outer (3.3 m) regions even at the lowest NB injection power, suggesting that AE-induced fast-ion transport is occurring. A simulation with FIDASIM that does not take AE into account (dashed lines) should result in a profile that peaks at the center.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSince this experiment was conducted using a deuterium beam, it is possible to estimate the amount of fast ions using a different approach than FIDA, mainly by measuring neutrons due to beam-thermal fusion. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (a) shows the total neutron emission rate Sn and the results of the simulation by CONV_FIT3D [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] when the NB injection power is varied. In the simulation, Sn increases linearly with increasing NB injection power, but in the experiment, little change was observed with increasing NB injection power. This trend is in good agreement with FIDA and previous results, and several different diagnostics have been used to study the behavior of fast ions. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (b) shows the radial profile of the line-integrated neutron emission rate measured by the neutron emission camera [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Although it appears that the neutron emission rate is high for codes close to the center, in reality, the long line-of-sight integration distance results in the neutral emission rate shown in this figure for flat fast ion distributions such as those shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (b, c). In this measurement, as in the previous results, there was little dependence on NB injection power, but the neutron emission rate was slightly higher for discharges with higher NB injection power. This trend is close to that shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (c) and is consistent with the FIDA results since the high-energy fast-ion density affects the neutron emission rate.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThroughout this study, we have demonstrated the relationship between fast-ion profile stiffness and AEs observed in LHD experiments. Under conditions where AEs are easily excited, our experiments revealed that increasing NB power does not alter the fast-ion profile but increases AE amplitude. This result is consistent with trends observed in DIII-D experiments. Moreover, the experimental conditions in this study were more systematically controlled, providing clear evidence of this phenomenon. The intuitive explanation is that fast-ion profile stiffness occurs because AEs eject fast ions as the fast-ion pressure exceeds a certain threshold. However, the details of the transport mechanisms remain unclear. At this point, we refer to another study conducted on LHD, reported in [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], which examined the degradation of fast-ion confinement. That study observed that fast-ion confinement deteriorates with increasing NB power in quiescent plasma (i.e. very low-level magnetic fluctuations), though the underlying cause was not identified. The observed confinement degradation with increased NB power in [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] is consistent with the results of this study, suggesting that an additional unknown effect may also contribute to the findings presented herein, that is unrelated to AEs. However, the examples of confinement degradation reported in [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] are not as pronounced as those observed in this study, implying that any contribution of the unknown effect to the results presented here is likely limited. Investigating these mechanisms in greater detail remains a subject for future work.\u003c/p\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003ePrevious studies have suggested, both experimentally and by simulation, fast-ion profile stiffening in high AE amplitude environments. To investigate the universality of the fast-ion profile stiffness dependence on AE amplitude, an experiment was performed in the LHD to scan the injection current of the NB and vary the AE amplitude. Under this experimental condition, the AE amplitude increases as the NB injection power is increased, resulting in AE-induced fast-ion transport and fast-ion profile stiffness, as experimentally demonstrated. On the other hand, since the fast-ion profile stiffness did not appear in the FIDASIM results, which does not include the effect of the fast-ion transport by AEs, the fast-ion profile stiffness can be considered to be the effect of the AEs. Neutron emission rate observations further corroborate the stiffening of the fast-ion profile.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAcknowledgements\u003c/p\u003e\n\u003cp\u003eThe authors wish to thank Prof. Y. Todo (NIFS) and S. Sharapov (CCFE) for fruitful discussions and the LHD experiment group for their excellent support of this work.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eData availability statement\u003c/p\u003e\n\u003cp\u003eThe LHD data can be accessed from the LHD experiment data repository.\u0026nbsp;https://doi.org/10.57451/lhd.analyzed-data.\u003c/p\u003e\n\u003cp\u003eFunding Declaration\u003c/p\u003e\n\u003cp\u003eThis research was partially funded by the National Institute for Fusion Science (NIFS22KIPR00,1 NIFS22KIST035) and JSPS KAKENHI Grant Numbers JP 19K03798.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eW. W. Heidbrink et al., Phys. Rev. Lett. 99, 245002 (2007)\u003c/li\u003e\n\u003cli\u003eC. S. Collins et al., Phys. Rev. Lett. 116, 095001 (2016)\u003c/li\u003e\n\u003cli\u003eY. Todo and T. Sato, Phys. Plasmas 5, 1321 (1998)\u003c/li\u003e\n\u003cli\u003eY. Todo et al., Nucl. Fusion 56, 112008 (2016)\u003c/li\u003e\n\u003cli\u003eK. Toi et al., Plasma Phys. Control. Fusion 46, S1 (2004)\u003c/li\u003e\n\u003cli\u003eM. Osakabe et al., Nucl. Fusion 46, S911-S917 (2006)\u003c/li\u003e\n\u003cli\u003eS. Kamio et al., Nucl. Fusion 60, 112002 (2006)\u003c/li\u003e\n\u003cli\u003eY. Takeiri et al., Fusion Sci. Technol. 58, 482-8 (2010)\u003c/li\u003e\n\u003cli\u003eM. Yoshinuma et al., Fusion Sci. Technol. 58, 375-82 (2010)\u003c/li\u003e\n\u003cli\u003eJ. Chen et al., Phys. Lett. A 383, 1293-9 (2019)\u003c/li\u003e\n\u003cli\u003eK. Ida et al., Plasma Fusion Res. 14, 1402079 (2019)\u003c/li\u003e\n\u003cli\u003eW. W. Heidbrink et al., Plasma Phys. Control. Fusion 46, 1855 (2005)\u003c/li\u003e\n\u003cli\u003eY. Fujiwara et al., Nucl. Fusion 60, 112014 (2020)\u003c/li\u003e\n\u003cli\u003eM. Isobe et al., IEEE Trans. Plasma Sci. 46, 2050-8 (2018)\u003c/li\u003e\n\u003cli\u003eS. Murakami et al., Nucl. Fusion 40, 693 (2000)\u003c/li\u003e\n\u003cli\u003eH. Yamaguchi and S. Murakami, Nucl. Fusion 56, 026003 (2016)\u003c/li\u003e\n\u003cli\u003eB. Geiger et al., Plasma Phys. Control. Fusion 62, 105008 (2020)\u003c/li\u003e\n\u003cli\u003eW. W. Heidbrink et al., Commun. Comput. Phys. 10, 716-41 (2011)\u003c/li\u003e\n\u003cli\u003eH. Nuga et al., J. Plasma Phys. 86, 815860306 (2020)\u003c/li\u003e\n\u003cli\u003eK. Ogawa et al., Rev. Sci. Instrum. 85, 11E110 (2014)\u003c/li\u003e\n\u003cli\u003eK. Ogawa et al., Rev. Sci. Instrum. 89, 113509 (2018)\u003c/li\u003e\n\u003cli\u003eH. Nuga et al., Nucl. Fusion 64, 066001 (2024)\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-fusion-energy","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jofe","sideBox":"Learn more about [Journal of Fusion Energy](http://link.springer.com/journal/10894)","snPcode":"10894","submissionUrl":"https://submission.nature.com/new-submission/10894/3","title":"Journal of Fusion Energy","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Alfvén eigenmode, fast-ion profile stiffness, FIDA measurement","lastPublishedDoi":"10.21203/rs.3.rs-6839914/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6839914/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFast-ion transport driven by Alfvén eigenmodes (AEs) is one critical issue facing fast-ion confinement in magnetic fusion device. In the DIII-D tokamak experiment, stiff transport of fast-ions increased with increasing neutral beam (NB) injection power when the amplitudes of multiple interacting AEs exceeded a certain threshold. These experiment results are supported by simulation studies that predict monotonically degrading fast-ion confinement and profile stiffness with increasing beam power. To investigate the universality of the fast-ion profile stiffness dependence on AE amplitude, an experiment was performed at the Large Helical Device (LHD) to scan the injection current of the NB and vary the AE amplitude. Under the experimental conditions, the AE amplitude increased linearly with NB injection power. The blue shifted FIDA intensity between 663-665 nm, corresponding to the energy range of 98-166 keV in the ctr-direction, was used for estimating the radial profile of the fast-ion density. There is direct evidence of stiffening of the fast-ion profile and degradation of the fast-ion confinement. This is consistent with the experimentally observed reduction in the expected neutron emission rate. We have demonstrated that under AE-prone confinement conditions, even if the fast-ion source increases due to NB injection, they experience enhanced transport by AEs and do not increase in density.\u003c/p\u003e","manuscriptTitle":"Observation of a Fast-Ion Profile Stiffness Due to the Alfvén Eigenmode","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-25 01:59:59","doi":"10.21203/rs.3.rs-6839914/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-08-06T08:04:30+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-28T12:01:24+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-01T16:07:48+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"40846756914145612370975465788346663327","date":"2025-06-28T11:24:48+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"240655082455905311922247310279599547197","date":"2025-06-18T11:17:27+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-16T08:56:37+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-14T00:42:54+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-06-13T07:54:30+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Fusion Energy","date":"2025-06-07T01:01:23+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-fusion-energy","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jofe","sideBox":"Learn more about [Journal of Fusion Energy](http://link.springer.com/journal/10894)","snPcode":"10894","submissionUrl":"https://submission.nature.com/new-submission/10894/3","title":"Journal of Fusion Energy","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"0cf1da5b-564f-4498-b11f-96dfdd1a6222","owner":[],"postedDate":"June 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-11-10T16:06:55+00:00","versionOfRecord":{"articleIdentity":"rs-6839914","link":"https://doi.org/10.1007/s10894-025-00521-3","journal":{"identity":"journal-of-fusion-energy","isVorOnly":false,"title":"Journal of Fusion Energy"},"publishedOn":"2025-11-08 15:57:04","publishedOnDateReadable":"November 8th, 2025"},"versionCreatedAt":"2025-06-25 01:59:59","video":"","vorDoi":"10.1007/s10894-025-00521-3","vorDoiUrl":"https://doi.org/10.1007/s10894-025-00521-3","workflowStages":[]},"version":"v1","identity":"rs-6839914","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6839914","identity":"rs-6839914","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}