Nick R. Schwartz, Ian G. Abel, Adil B. Hassam, Myles Kelly, Carlos A. Romero-Talamás
{"title":"MCTrans++: a 0-D model for centrifugal mirrors","authors":"Nick R. Schwartz, Ian G. Abel, Adil B. Hassam, Myles Kelly, Carlos A. Romero-Talamás","doi":"10.1017/s0022377824000424","DOIUrl":"https://doi.org/10.1017/s0022377824000424","url":null,"abstract":"The centrifugal mirror confinement scheme incorporates supersonic rotation of a plasma into a magnetic mirror device. This concept has been shown experimentally to drastically decrease parallel losses and increase plasma stability as compared with prior axisymmetric mirrors. MCTrans++ is a dimensionless (0-D) scoping tool which rapidly models experimental operating points in the Centrifugal Mirror Fusion Experiment (CMFX) at the University of Maryland. In the low-collisionality regime, parallel losses can be modelled analytically. A confining potential is set up that is partially ambipolar and partially centrifugal. Due to the stabilizing effects of flow shear, the perpendicular losses can be modelled as classical. Radiation losses such as bremsstrahlung and cyclotron emission are taken into account. A neutrals model is included, and, in some circumstances, charge-exchange losses are found to exceed all other loss mechanisms. We use the SUNDIALS ARKODE library to solve the underlying equations of this model; the resulting software is suitable for scanning large parameter spaces, and can also be used to model time-dependent phenomena such as a capacitive discharge. MCTrans++ has been used to verify results from prior centrifugal mirrors, create an experimental plan for CMFX and find configurations for future reactor-scale fusion devices.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"166 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806153","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":"Global fluid turbulence simulations in the scrape-off layer of a stellarator island divertor","authors":"B. Shanahan, D. Bold, B. Dudson","doi":"10.1017/s002237782400045x","DOIUrl":"https://doi.org/10.1017/s002237782400045x","url":null,"abstract":"Isothermal fluid turbulence simulations have been performed in the edge and scrape-off layer (SOL) of an analytic stellarator configuration with an island divertor, thereby providing numerical insight into edge turbulence in regions around islands in a stellarator. The steady-state transport follows the a curvature drive that is inverse to the major radius (<jats:inline-formula> <jats:alternatives> <jats:tex-math>$1/R$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002237782400045X_inline1.png\" /> </jats:alternatives> </jats:inline-formula>) toward the outboard side, but large fluctuations are present throughout the island divertor region, with the average wavelength of similar size to the island width. The system exhibits a prominent <jats:inline-formula> <jats:alternatives> <jats:tex-math>$m=2$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002237782400045X_inline2.png\" /> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:tex-math>$n=5$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002237782400045X_inline3.png\" /> </jats:alternatives> </jats:inline-formula> mode, where <jats:italic>m</jats:italic> is the poloidal mode number and <jats:italic>n</jats:italic> is the toroidal mode number, although other modes are present. The amplitude and radial extent of the density fluctuations are similar throughout the edge and SOL, but can decrease near island O-points. The fluctuations exhibit a predominantly positive skewness on the outboard midplane, indicating blob-like perturbations for the transport into the outer SOL. It is determined that a point on the separatrix is generally more correlated with regions outside of the SOL than a nearby reference point which does not lie on the separatrix.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"16 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140634373","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}
Rishabh Datta, Aidan Crilly, Jeremy P. Chittenden, Simran Chowdhry, Katherine Chandler, Nikita Chaturvedi, Clayton E. Myers, William R. Fox, Stephanie B. Hansen, Chris A. Jennings, Hantao Ji, Carolyn C. Kuranz, Sergey V. Lebedev, Dmitri A. Uzdensky, Jack D. Hare
{"title":"Simulations of radiatively cooled magnetic reconnection driven by pulsed power","authors":"Rishabh Datta, Aidan Crilly, Jeremy P. Chittenden, Simran Chowdhry, Katherine Chandler, Nikita Chaturvedi, Clayton E. Myers, William R. Fox, Stephanie B. Hansen, Chris A. Jennings, Hantao Ji, Carolyn C. Kuranz, Sergey V. Lebedev, Dmitri A. Uzdensky, Jack D. Hare","doi":"10.1017/s0022377824000448","DOIUrl":"https://doi.org/10.1017/s0022377824000448","url":null,"abstract":"Magnetic reconnection is an important process in astrophysical environments, as it reconfigures magnetic field topology and converts magnetic energy into thermal and kinetic energy. In extreme astrophysical systems, such as black hole coronae and pulsar magnetospheres, radiative cooling modifies the energy partition by radiating away internal energy, which can lead to the radiative collapse of the reconnection layer. In this paper, we perform two- and three-dimensional simulations to model the MARZ (Magnetic Reconnection on Z) experiments, which are designed to access cooling rates in the laboratory necessary to investigate reconnection in a previously unexplored radiatively cooled regime. These simulations are performed in GORGON, an Eulerian two-temperature resistive magnetohydrodynamic code, which models the experimental geometry comprising two exploding wire arrays driven by 20 MA of current on the Z machine (Sandia National Laboratories). Radiative losses are implemented using non-local thermodynamic equilibrium tables computed using the atomic code Spk, and we probe the effects of radiation transport by implementing both a local radiation loss model and <jats:inline-formula> <jats:alternatives> <jats:tex-math>$P_{1/3}$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000448_inline1.png\" /> </jats:alternatives> </jats:inline-formula> multi-group radiation transport. The load produces highly collisional, super-Alfvénic (Alfvén Mach number <jats:inline-formula> <jats:alternatives> <jats:tex-math>$M_A approx 1.5$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000448_inline2.png\" /> </jats:alternatives> </jats:inline-formula>), supersonic (Sonic Mach number <jats:inline-formula> <jats:alternatives> <jats:tex-math>$M_S approx 4-5$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000448_inline3.png\" /> </jats:alternatives> </jats:inline-formula>) strongly driven plasma flows which generate an elongated reconnection layer (Aspect Ratio <jats:inline-formula> <jats:alternatives> <jats:tex-math>$L/delta approx 100$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000448_inline4.png\" /> </jats:alternatives> </jats:inline-formula>, Lundquist number <jats:inline-formula> <jats:alternatives> <jats:tex-math>$S_L approx 400$</jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022377824000448_inline1d.png\" /> </jats:alternatives> </jats:inline-formula>). The reconnection layer undergoes radiative collapse when the radiative losses exceed the rates of ohmic and compressional heating (cooling rate/hydrodynamic transit rate = <jats:inline-formula> <jats:alternatives> <jats:tex-math>$tau _{text {cool}}^{-1}/tau _{","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"62 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140624724","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":"Density jump for oblique collisionless shocks in pair plasmas: physical solutions","authors":"Antoine Bret, Colby C. Haggerty, Ramesh Narayan","doi":"10.1017/s0022377824000370","DOIUrl":"https://doi.org/10.1017/s0022377824000370","url":null,"abstract":"<p>Collisionless shocks are frequently analysed using the magnetohydrodynamics (MHD) formalism, even though MHD assumes a small mean free path. Yet, isotropy of pressure, the fruit of binary collisions and assumed in MHD, may not apply in collisionless shocks. This is especially true within a magnetized plasma, where the field can stabilize an anisotropy. In a previous article (Bret & Narayan, <span>J. Plasma Phys.</span>, vol. 88, no. 6, 2022<span>b</span>, p. 905880615), a model was presented capable of dealing with the anisotropies that may arise at the front crossing. It was solved for any orientation of the field with respect to the shock front. Yet, for some values of the upstream parameters, several downstream solutions were found. Here, we complete the work started in Bret & Narayan (<span>J. Plasma Phys.</span>, vol. 88, no. 6, 2022<span>b</span>, p. 905880615) by showing how to pick the physical solution out of the ones offered by the algebra. This is achieved by 2 means: (i) selecting the solution that has the downstream field obliquity closest to the upstream one. This criterion is exemplified on the parallel case and backed up by particle-in-cell simulations. (ii) Filtering out solutions which do not satisfy a criteria already invoked to trim multiple solutions in MHD: the evolutionarity criterion, that we assume valid in the collisionless case. The end result is a model in which a given upstream configuration results in a unique, or no downstream configuration (as in MHD). The largest departure from MHD is found for the case of a parallel shock.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"61 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140582845","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":"The Okubo–Weiss-type topological criteria in two-dimensional magnetohydrodynamic flows","authors":"B.K. Shivamoggi, G.J.F. van Heijst, L.P.J. Kamp","doi":"10.1017/s0022377824000436","DOIUrl":"https://doi.org/10.1017/s0022377824000436","url":null,"abstract":"<p>The Okubo–Weiss (Okubo, <span>Deep-Sea Res.</span>, vol. 17, issue 3, 1970, pp. 445–454; Weiss, <span>Physica D</span>, vol. 48, issue 2, 1991, pp. 273–294) criterion has been widely used as a diagnostic tool to divide a two-dimensional (2-D) hydrodynamical flow field into hyperbolic and elliptic regions. This paper considers extension of these ideas to 2-D magnetohydrodynamic (MHD) flows, and presents an Okubo–Weiss-type criterion to parameterize the magnetic field topology in 2-D MHD flows. This ensues via its topological connections with the intrinsic metric properties of the underlying magnetic flux manifold, and is illustrated by recasting the Okubo–Weiss-type criterion via the 2-D MHD stationary generalized Alfvénic state condition to approximate the slow-flow-variation ansatz imposed in its derivation. The Okubo–Weiss-type parameter then turns out to be related to the sign definiteness of the Gaussian curvature of the magnetic flux manifold. A similar formulation becomes possible for 2-D electron MHD flows, by using the generalized magnetic flux framework to incorporate the electron-inertia effects. Numerical simulations of quasi-stationary vortices in 2-D MHD flows in the decaying turbulence regime are then given to demonstrate that the Okubo–Weiss-type criterion is able to separate the MHD flow field into elliptic and hyperbolic field configurations very well.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"47 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602257","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":"The maximum-J property in quasi-isodynamic stellarators","authors":"E. Rodríguez, P. Helander, A.G. Goodman","doi":"10.1017/s0022377824000345","DOIUrl":"https://doi.org/10.1017/s0022377824000345","url":null,"abstract":"<p>Some stellarators tend to benefit from favourable average magnetic curvature for trapped particles when the plasma pressure is sufficiently high. This so-called maximum-<span><span><span data-mathjax-type=\"texmath\"><span>$J$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240415173403192-0796:S0022377824000345:S0022377824000345_inline2.png\"/></span></span> property has several positive implications, such as good fast-particle confinement, magnetohydrodynamic stability and suppression of certain trapped-particle instabilities. This property cannot be attained in quasisymmetric stellarators, in which deeply trapped particles experience average bad curvature and therefore precess in the diamagnetic direction close to the magnetic axis. However, quasi-isodynamic stellarators offer greater flexibility and allow the average curvature to be favourable and the precession to be reversed. We find that it is possible to design such stellarators so that the maximum-<span><span><span data-mathjax-type=\"texmath\"><span>$J$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240415173403192-0796:S0022377824000345:S0022377824000345_inline3.png\"/></span></span> condition is satisfied for the great majority of all particles, even when the plasma pressure vanishes. The qualitative properties of such a stellarator field can be derived analytically by examining the most deeply and the most shallowly trapped particles, although some small fraction of the latter will inevitably not behave as desired. However, through numerical optimisation, we construct a vacuum field in which 99.6 % of all trapped particles satisfy the maximum-<span><span><span data-mathjax-type=\"texmath\"><span>$J$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240415173403192-0796:S0022377824000345:S0022377824000345_inline4.png\"/></span></span> condition.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"117 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140582765","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}
I.S. Chernoshtanov, I.G. Chernykh, G.I. Dudnikova, M.A. Boronina, T.V. Liseykina, V.A. Vshivkov
{"title":"Effects observed in numerical simulation of high-beta plasma with hot ions in an axisymmetric mirror machine","authors":"I.S. Chernoshtanov, I.G. Chernykh, G.I. Dudnikova, M.A. Boronina, T.V. Liseykina, V.A. Vshivkov","doi":"10.1017/s0022377824000333","DOIUrl":"https://doi.org/10.1017/s0022377824000333","url":null,"abstract":"We present the results of numerical simulation by two-dimensional hybrid particle-in-cell code of high-beta plasma with hot ions in an axisymmetric mirror machine. Two particular effects are discussed: the self-rotating of plasma with Maxwellian ions in regime of diamagnetic confinement and the excitation of axisymmetric magnetosonic waves in a high-beta plasma with sloshing ions.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"438 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602339","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}
P. Kim, S. Buller, R. Conlin, W. Dorland, D.W. Dudt, R. Gaur, R. Jorge, E. Kolemen, M. Landreman, N.R. Mandell, D. Panici
{"title":"Optimization of nonlinear turbulence in stellarators","authors":"P. Kim, S. Buller, R. Conlin, W. Dorland, D.W. Dudt, R. Gaur, R. Jorge, E. Kolemen, M. Landreman, N.R. Mandell, D. Panici","doi":"10.1017/s0022377824000369","DOIUrl":"https://doi.org/10.1017/s0022377824000369","url":null,"abstract":"We present new stellarator equilibria that have been optimized for reduced turbulent transport using nonlinear gyrokinetic simulations within the optimization loop. The optimization routine involves coupling the pseudo-spectral GPU-native gyrokinetic code <jats:monospace>GX</jats:monospace> with the stellarator equilibrium and optimization code <jats:monospace>DESC</jats:monospace>. Since using <jats:monospace>GX</jats:monospace> allows for fast nonlinear simulations, we directly optimize for reduced nonlinear heat fluxes. To handle the noisy heat flux traces returned by these simulations, we employ the simultaneous perturbation stochastic approximation (SPSA) method that only uses two objective function evaluations for a simple estimate of the gradient. We show several examples that optimize for both reduced heat fluxes and good quasi-symmetry as a proxy for low neoclassical transport. Finally, we run full transport simulations using the <jats:monospace>T3D</jats:monospace> stellarator transport code to evaluate the changes in the macroscopic profiles.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"47 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602252","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}
P.A. Figueiredo, R. Jorge, J. Ferreira, P. Rodrigues
{"title":"Energetic particle tracing in optimized quasi-symmetric stellarator equilibria","authors":"P.A. Figueiredo, R. Jorge, J. Ferreira, P. Rodrigues","doi":"10.1017/s0022377824000400","DOIUrl":"https://doi.org/10.1017/s0022377824000400","url":null,"abstract":"Recent developments in the design of magnetic confinement fusion devices have allowed the construction of exceptionally optimized stellarator configurations. The near-axis expansion in particular has been proven to enable the construction of magnetic configurations with good confinement properties while taking only a fraction of the usual computation time to generate optimized magnetic equilibria. However, not much is known about the overall features of fast-particle orbits computed in such analytical, yet simplified, equilibria when compared with those originating from accurate equilibrium solutions. This work aims to assess and demonstrate the potential of the near-axis expansion to provide accurate information on particle orbits and to compute loss fractions in moderate to high aspect ratios. The configurations used here are all scaled to fusion-relevant parameters and approximate quasi-symmetry to various degrees. This allows us to understand how deviations from quasi-symmetry affect particle orbits and what are their effects on the estimation of the loss fraction. Guiding-centre trajectories of fusion-born alpha particles are traced using gyronimo and SIMPLE codes under the NEAT framework, showing good numerical agreement. Discrepancies between near-axis and magnetohydrodynamic fields have minor effects on passing particles but significant effects on trapped particles, especially in quasi-helically symmetric magnetic fields. Effective expressions were found for estimating orbit widths and passing–trapped separatrix in quasi-symmetric near-axis fields. Loss fractions agree in the prompt losses regime but diverge afterwards.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"51 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140585063","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":"Asymptotic quasisymmetric high-beta three-dimensional magnetohydrodynamic equilibria near axisymmetry","authors":"Wrick Sengupta, Nikita Nikulsin, Rahul Gaur, Amitava Bhattacharjee","doi":"10.1017/s0022377824000357","DOIUrl":"https://doi.org/10.1017/s0022377824000357","url":null,"abstract":"Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal magnetohydrodynamic (MHD) equilibrium and stability of high-beta plasma in a large-aspect-ratio stellarator. In particular, we show that the lowest-order description of a near-axisymmetric equilibrium vastly simplifies the problem of three-dimensional quasisymmetric MHD equilibria, which can be reduced to a standard elliptic Grad–Shafranov equation for the flux function. We show that any large-aspect-ratio tokamak, deformed periodically in the vertical direction, is a stellarator with approximate volumetric QS. We discuss exact analytical solutions and numerical benchmarks. Finally, we discuss the ideal ballooning and interchange stability of some of our equilibrium configurations.","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"51 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140584999","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}