{"title":"Generalized cross-helicity in non-ideal magnetohydrodynamics","authors":"Prachi Sharma, Asher Yahalom","doi":"10.1017/s002237782300123x","DOIUrl":"https://doi.org/10.1017/s002237782300123x","url":null,"abstract":"The objective of the present paper is to investigate the constancy of the topological invariant, denoted the non-barotropic generalized cross-helicity in the case of non-ideal magnetohydrodynamics (MHD). Existing work considers only ideal barotropic MHD and ideal non-barotropic MHD. Here, we consider dissipative processes in the form of thermal conduction, finite electrical conductivity and viscosity and the effect of these processes on the cross-helicity conservation. An analytical approach has been adopted to obtain the mathematical expressions for the time derivative of the cross-helicity. Obtained results show that the generalized cross-helicity is not conserved in the non-ideal MHD limit and indicate which processes affect the helicity and which do not. Furthermore, we indicate the configurations in which this topological constant is conserved despite the dissipative processes. Some examples and applications are also given.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"21 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Guiding-centre orbit-following simulations of charge exchange loss of NBI ions with the finite Larmor radius effect","authors":"Yingfeng Xu, Fuqiong Wang, Yongliang Li, Fangchuan Zhong","doi":"10.1017/s0022377823001186","DOIUrl":"https://doi.org/10.1017/s0022377823001186","url":null,"abstract":"Guiding-centre orbit-following simulations of the charge exchange (CX) loss of neutral beam injection (NBI) ions are presented. The finite Larmor radius (FLR) effect in the fast ion–neutral collision can be included in guiding-centre orbit-following simulations by using the gyroaverage method. It is proved that the neutralization probability of fast ions computed by using the gyroaverage method in the guiding-centre orbit simulation is roughly the same as that computed in the full-orbit simulation when the time step in the guiding-centre simulation is the order of the gyroperiod. The CX losses of NBI fast ions for two NBIs in the EAST tokamak have been simulated by the guiding-centre orbit-following code GYCAVA, and the FLR effect in the fast ion–neutral collision on CX losses has been numerically studied. The CX effect of the fast ion–neutral collision can significantly enhance NBI ion losses on EAST. The FLR effect in the fast ion–neutral collision can enhance the CX loss. Vertical asymmetry of localized heat loads induced by CX losses is found, which is related to the FLR effect of fast ions and the strong radial gradient of the neutral density near the plasma edge. Heat loads induced by CX losses are localized in the regions near the poloidal angle <jats:inline-formula> <jats:alternatives> <jats:tex-math>$theta =-60^circ$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377823001186_inline1.png\" /> </jats:alternatives> </jats:inline-formula>, because the likelihood of exchanging charge is the largest at gyrophase <jats:inline-formula> <jats:alternatives> <jats:tex-math>$xi ={rm pi}$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377823001186_inline2.png\" /> </jats:alternatives> </jats:inline-formula>, and this leads to fast downwards moving neutrals. Fast ion loss fractions induced by CX increase with the neutral density increasing.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"96 1-2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generation of energetic electrons by an electron cyclotron wave through stochastic heating in a spherical tokamak","authors":"Mingyuan Wang, Shikui Cheng, Bing Liu, Shaodong Song, Dong Guo, Yunyang Song, Wenjun Liu, Debabrata Banerjee, Songjian Li, Tiantian Sun, Xiang Gu, Yingying Li, Jiaqi Dong, Yuejiang Shi, Y.-K. Martin Peng, Adi Liu","doi":"10.1017/s0022377823001216","DOIUrl":"https://doi.org/10.1017/s0022377823001216","url":null,"abstract":"This study presents novel findings on stochastic electron heating via a random electron cyclotron wave (ECW) in a spherical tokamak. Hard x ray measurements demonstrate the time evolution of hard x ray counts at different energy bands, consistent with predictions from the stochastic heating model. The ECW heating rate shows a positive correlation with applied power, confirming the effectiveness of stochastic heating. Remarkably, the ECW-driven plasma current remains insensitive to ECW incidence angle, consistent with model predictions. The observed stochastic heating of electrons offers potential for exploring innovative non-inductive current drive modes in spherical tokamaks. This research contributes to the understanding of plasma behaviour and motivates the development of new models for non-inductive current drive in fusion devices.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"27 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138542324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Biancalani, A. Bottino, D. Del Sarto, M.V. Falessi, T. Hayward-Schneider, P. Lauber, A. Mishchenko, B. Rettino, J.N. Sama, F. Vannini, L. Villard, X. Wang, F. Zonca, the ASDEX Upgrade team
{"title":"Nonlinear interaction of Alfvénic instabilities and turbulence via the modification of the equilibrium profiles","authors":"A. Biancalani, A. Bottino, D. Del Sarto, M.V. Falessi, T. Hayward-Schneider, P. Lauber, A. Mishchenko, B. Rettino, J.N. Sama, F. Vannini, L. Villard, X. Wang, F. Zonca, the ASDEX Upgrade team","doi":"10.1017/s0022377823001137","DOIUrl":"https://doi.org/10.1017/s0022377823001137","url":null,"abstract":"<p>Nonlinear simulations of Alfvén modes (AMs) driven by energetic particles (EPs) in the presence of turbulence are performed with the gyrokinetic particle-in-cell code ORB5. The AMs carry a heat flux, and consequently they nonlinearly modify the plasma temperature profiles. The isolated effect of this modification on the dynamics of turbulence is studied by means of electrostatic simulations. We find that turbulence is reduced when the profiles relaxed by the AM are used, with respect to the simulation where the unperturbed profiles are used. This is an example of indirect interaction of EPs and turbulence. First, an analytic magnetic equilibrium with circular concentric flux surfaces is considered as a simplified example for this study. Then, an application to an experimentally relevant case of ASDEX Upgrade is discussed.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"36 5","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
N. Panadero, K. J. McCarthy, B. Pégourié, R. Carrasco, I. García-Cortés, R. García, J. Hernández-Sánchez, F. Köchl, J. Martínez-Fernández, R. Sakamoto, the TJ-II team
{"title":"Using rational surfaces to improve pellet fuelling in stellarators","authors":"N. Panadero, K. J. McCarthy, B. Pégourié, R. Carrasco, I. García-Cortés, R. García, J. Hernández-Sánchez, F. Köchl, J. Martínez-Fernández, R. Sakamoto, the TJ-II team","doi":"10.1017/s0022377823001010","DOIUrl":"https://doi.org/10.1017/s0022377823001010","url":null,"abstract":"<p>Pellet injection is currently the primary candidate for achieving efficient plasma fuelling, one of the key issues for steady-state operation in large fusion devices. In this paper, pellet injection experiments are performed for several magnetic configurations of the TJ-II stellarator. The aim of this study is to increase the understanding of the role played by rational surfaces in plasmoid drift and deposition profiles in stellarators. The analysis of experimentally observed plasmoid drifts is supported by simulations of such cases made with the HPI2 code. Plasmoid drift is found to be significantly reduced, as in tokamaks, in the vicinity of rational surfaces. This is attributed to the fact that plasmoid external charge reconnection lengths are shorter near rational surfaces, resulting in a more effective damping of the plasmoid drift. Although the effect of plasmoid external currents on the drift is expected to be negligible in stellarators, compared with those caused by plasmoid internal currents, the effect observed in TJ-II is clearly measurable. In addition, simulations show that enhanced drift reductions near rational surfaces lead to significantly different deposition profiles for the magnetic configurations included in this study. This implies that it should be possible to select the magnetic configurations to obtain more efficient pellet fuelling.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"C-25 7","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Resonant excitation of single Kelvin–Helmholtz high-order waves in a magnetized electron fluid vortex","authors":"G. Maero, N. Panzeri, L. Patricelli, M. Romé","doi":"10.1017/s0022377823001150","DOIUrl":"https://doi.org/10.1017/s0022377823001150","url":null,"abstract":"Thanks to the isomorphism between the drift-Poisson and Euler equations, inviscid two-dimensional fluid experiments can be performed in magnetized, single-component plasmas in Penning–Malmberg traps. Within this analogy, a trapped electron plasma column is equivalent to a two-dimensional vortex. Here, we focus our attention on the generation of V-states, i.e. $l$ -fold symmetric rotating vorticity patches where the deformation with respect to the circular cross-section has reached the nonlinear regime. We detail a linear theoretical analysis and devise an experimental routine to generate V-states through the precise excitation of single Kelvin–Helmholtz perturbations in a magnetized electron plasma. This technique makes use of suitable multipolar rotating electric fields, which are shown to be able to select the desired wavemode. In particular, with rotating fields, a hardware limitation in the highest accessible mode is removed and nonlinear Kelvin–Helmholtz waves of generic order $l$ can be attained, which pave the way for further investigations on the evolution and stability properties of V-states. Systematic experimental results for the selective mode growth in the linear and nonlinear regimes up to saturation and collapse are discussed.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"33 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136346491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the analytical description of the nonlinear stage of the Weibel instability in collisionless anisotropic plasma","authors":"A.A. Nechaev, A.A. Kuznetsov, Vl.V. Kocharovsky","doi":"10.1017/s0022377823001198","DOIUrl":"https://doi.org/10.1017/s0022377823001198","url":null,"abstract":"On the basis of the energy invariants for the Weibel instability in a collisionless non-relativistic plasma, an analytical relation is obtained between the instantaneous values of the space-averaged energy density of the magnetic field, its dominant wavenumber and the average plasma anisotropy parameter. The relation is valid for arbitrary particle velocity distribution functions, including ones that vary with time at the nonlinear stage of instability. It is obtained under the assumption that the plasma is homogeneous along a certain axis, determined, for example, by an external magnetic field, and taking into account only the modes with wavevectors orthogonal to this axis. We give an estimate of the maximum magnetic field energy achievable during the Weibel instability and show that its ratio to the initial longitudinal energy of particles, even for a large initial plasma anisotropy parameter, cannot exceed the value approximately equal to 0.2. The obtained analytical relation is verified using two-dimensional particle-in-cell simulations.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135346027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R.J.J. Mackenbach, J.H.E. Proll, R. Wakelkamp, P. Helander
{"title":"The available energy of trapped electrons: a nonlinear measure for turbulent transport","authors":"R.J.J. Mackenbach, J.H.E. Proll, R. Wakelkamp, P. Helander","doi":"10.1017/s0022377823001083","DOIUrl":"https://doi.org/10.1017/s0022377823001083","url":null,"abstract":"A collisionless plasma possesses a certain amount of ‘available energy’, which is that part of the thermal energy that can be converted into kinetic energy of plasma motion and electromagnetic fluctuations. In this paper we present a calculation of the available energy carried by trapped electrons in a slender non-omnigenous flux tube of plasma. This quantity is compared with gyrokinetic simulations of the nonlinear saturated radial energy flux resulting from turbulence driven by collisionless trapped-electron modes in various stellarators and a tokamak. The numerical calculation of available energy is fast and shows a strong correlation with the turbulent energy fluxes found in the gyrokinetic simulations. Indeed, the energy flux is found to be proportional to the available energy to the power of approximately $3/2$ , which is what one would expect from a simple argument. We furthermore investigate how available energy is distributed across different bounce wells, and it is found that deeply trapped electrons typically contribute most to the available energy. Finally, we investigate the dependence of available energy on gradient strength, and we find important differences between weakly and strongly driven regimes for stellarators and tokamaks.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135760408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Simulation study of the influences of beryllium on the tokamak start-up process","authors":"Yanli Peng, Yan Qiu, Shiqiu Zhao, Shali Yang","doi":"10.1017/s002237782300106x","DOIUrl":"https://doi.org/10.1017/s002237782300106x","url":null,"abstract":"Tokamak start-up is strongly dependent on the state of the initial plasma formed during plasma breakdown. To acquire a better understanding of the process and to estimate the influence of the impurity of beryllium on the ohmic heating tokamak start-up process, one-dimensional particle-in-cell coupled with a Monte Carlo collision method has been developed. The main aim is to investigate the plasma performance under various amounts of beryllium with different discharge parameters. Tokamak breakdown with the impurity of beryllium in the ohmic heating strategy has been simulated. The simulation results show that with the impurity of beryllium, the increase of plasma density is suppressed compared with the case without beryllium. The breakdown time is delayed by the impurity. Moreover, the successful breakdown has a much higher requirement on discharge parameters with a low electric field operational scenario, since in the low electric field discharge the influence of beryllium impurity is greater. As the plasma density increases, the effect of beryllium impurity on plasma becomes more critical. It indicates that impurities cannot be neglected in the high plasma density.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136093309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rahul Gaur, Stefan Buller, Maximilian E. Ruth, Matt Landreman, Ian G. Abel, William D. Dorland
{"title":"An adjoint-based method for optimising MHD equilibria against the infinite-<i>n</i>, ideal ballooning mode","authors":"Rahul Gaur, Stefan Buller, Maximilian E. Ruth, Matt Landreman, Ian G. Abel, William D. Dorland","doi":"10.1017/s0022377823000995","DOIUrl":"https://doi.org/10.1017/s0022377823000995","url":null,"abstract":"We demonstrate a fast adjoint-based method to optimise tokamak and stellarator equilibria against a pressure-driven instability known as the infinite- $n$ ideal ballooning mode. We present three finite- $beta$ (the ratio of thermal to magnetic pressure) equilibria: one tokamak equilibrium and two stellarator equilibria that are unstable against the ballooning mode. Using the self-adjoint property of ideal magnetohydrodynamics, we construct a technique to rapidly calculate the change in the eigenvalue, a measure of ideal ballooning instability. Using the SIMSOPT optimisation framework, we then implement our fast adjoint gradient-based optimiser to minimise the eigenvalue and find stable equilibria for each of the three originally unstable equilibria.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136129747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}