arXiv subjects

I. Calvo

Publications and source records attributed to I. Calvo.

At least 19 recordsLinked to original sources

arXiv2026

Control of the bootstrap current in approximately quasi-axisymmetric magnetic fields

Quasi-axisymmetric stellarators are the stellarator analogue of the axisymmetric tokamak, retaining many of its favorable confinement properties, its compacity and its relative coil simplicity, while avoiding its principal limitation, the need for an inductively driven plasma current. Despite these attractive physics properties, the development of quasi-axisymmetric configurations has been severely constrained by the absence of an experimentally validated divertor concept compatible with their large bootstrap current. In this Letter, approximately quasi-axisymmetric fields, complemented with piecewise omnigenous perturbations, are proposed as the basis for a new strategy towards a stellarator reactor that simultaneously achieves simple coil geometries, tokamak-like confinement properties and, through tailoring of the bootstrap current, compatibility with an island divertor. Implications for attaining a high bootstrap current fraction in tokamak devices are also discussed.

physics.plasm-ph↗

arXiv2026

Combination of quasi-isodynamic and piecewise omnigenous magnetic fields

Due to their simultaneous optimization for radial and parallel neoclassical transport, quasi-isodynamic fields have been the main choice of stellarator magnetic configuration for most fusion reactor candidates in recent years. However, achieving a high degree of quasi-isodynamicity often comes at the cost of a strong shaping of the flux surfaces of the stellarator and complex coil geometries. In this work, the concepts of quasi-isodynamicity and piecewise omnigenity are combined to form QI-pwO fields. These fields are quasi-isodynamic in the low-field region of the magnetic surface, whereas they significantly depart from quasi-isodynamicity in the high-field region without sacrificing the neoclassical transport properties of quasi-isodynamic fields. This departure could make it easier to integrate the optimization of neoclassical transport with other physical and technological aspects of a stellarator reactor.

physics.plasm-ph↗

arXiv2026

Role of the radial electric field in the confinement of energetic ions in the Wendelstein 7-X stellarator

Good fast-ion confinement is an essential requirement for a fusion reactor. The magnetic configuration of the Wendelstein 7-X (W7-X) stellarator is partially optimized in this regard in a reactor-relevant scenario: it is expected to show improved fast-ion confinement when $\beta$ is high and the effect of the radial electric field is negligible. The experimental validation of this optimization is difficult since, with the available power, achieving high $\beta$ under appropriate conditions for the validation is challenging and the effect of the radial electric field is inevitable. In this work, the confinement of fast ions in W7-X has been studied numerically for a variety of scenarios via the ASCOT5 code. The effect of the radial electric field on fast-ion losses is confirmed to be equivalent to the one produced by $\beta$, and this is characterized by means of scans on both parameters. Through a preliminary study with experimentally-based profiles, a viable scenario is identified that takes advantage of this effect for the experimental validation of the optimization strategy of W7-X.

physics.plasm-ph↗

arXiv2026

Piecewise omnigenous magnetohydrodynamic equilibria as fusion reactor candidates

In piecewise omnigenous magnetic fields, charged particles remain perfectly confined in the abscence of collisions and turbulence. This concept extends the traditional notion of omnigenity, the theoretical principle upon which most of existing magnetic fusion reactor designs, including tokamaks, are based. While piecewise omnigenity broadens the range of potentially viable stellarator reactor candidates, it is achieved by relaxing the requirement of continuity in the magnetic field strength, which could appear to pose significant challenges for the design of magnetohydrodynamic equilibria. In this work, a stellarator magnetic configuration is presented that satisfies the ideal magnetohydrodynamic equilibrium equation and that achieves unprecedented levels of piecewise omnigenity. As a result, it exhibits favorable transport characteristics, including reduced bulk radial (neoclassical and turbulent transport), bootstrap current and fast ion losses. In addition, the configuration displays robust MHD stability across a range of \b{eta} values and possesses a rotational transform profile compatible with an island divertor. Collectively, these features satisfy the standard set of physics criteria required for a viable reactor candidate which, until now, were believed to be attainable only by certain types of omnigenous stellarators.

physics.plasm-ph↗

arXiv2025

CIEMAT-QI4X: a reactor-relevant quasi-isodynamic stellarator configuration compatible with an island divertor

A four-field-period quasi-isodynamic stellarator configuration is presented that exhibits small neoclassical and electrostatic turbulent transport, good fast-ion confinement over a wide range of $\beta$ values, small bootstrap current and an edge island structure compatible with an island divertor. This configuration, called CIEMAT-QI4X, has been obtained by building on the optimization strategy and sophisticating the methods employed in [S\'anchez E. et al 2023 Nucl. Fusion 63 066037]. The optimization has been improved by incorporating metrics to control Mercier stability and by enforcing strict constraints on the rotational transform profile to achieve nested toroidal surfaces in the confinement region and a divertor island structure at the plasma edge. Specifically, CIEMAT-QI4X has a 4/4 island chain at the edge that is resilient at least up to $\beta=4\%$, even when the bootstrap current is included. A corresponding set of filamentary coils is presented that generates the configuration with enough accuracy to preserve the aforementioned physics properties. In terms of physics performance, CIEMAT-QI4X establishes as a candidate for a stellarator fusion reactor design.

physics.plasm-ph↗

arXiv2024

Exploration of the parameter space of piecewise omnigenous stellarator magnetic fields

Piecewise omnigenous fields are stellarator magnetic fields that are optimized with respect to radial neoclassical transport thanks to a second adiabatic invariant that is piecewisely constant on the flux-surface. They are qualitatively different from omnigenous fields (including quasi-isodynamic or quasisymmetric fields), for which the second adiabatic invariant is a flux-surface constant. Piecewise omnigenous fields thus open an alternative path towards stellarator reactors. In this work, piecewise omnigenous fields are characterized and parametrized in a systematic manner. This is a step towards including piecewise omnigenity as an explicit design criterion in stellarator optimization, and towards a systematic study of the properties of nearly piecewise omnigenous stellarator configurations.

physics.plasm-ph↗

arXiv2024

Piecewise omnigenous stellarators

In omnigeneous magnetic fields, charged particles are perfectly confined in the absence of collisions and turbulence. For this reason, the magnetic configuration is optimized to be close to omnigenity in any candidate for a stellarator fusion reactor. However, approaching omnigenity imposes severe constraints on the spatial variation of the magnetic field. In particular, the topology of the contours of constant magnetic-field-strength on each magnetic surface must be such that there are no particles transitioning between different types of wells. This, in turn, usually leads to complicated plasma shapes and coils. This Letter presents a new family of optimized fields that display tokamak-like collisional energy transport while having transitioning particles. This result radically broadens the space of accessible reactor-relevant configurations.

physics.plasm-ph↗

arXiv2024

Reduced turbulent transport in the quasi-isodynamic stellarator configuration CIEMAT-QI4

CIEMAT-QI4 is a quasi-isodynamic stellarator configuration that simultaneously features very good fast-ion confinement in a broad range of $\beta$ values, low neoclassical transport and bootstrap current, and ideal magnetohydrodynamic stability up to $\beta=5\%$. In this paper it is shown that CIEMAT-QI4 also exhibits reduced turbulent transport. This is demonstrated through nonlinear electrostatic simulations with the gyrokinetic code stella, including kinetic ions and electrons. The relation between reduced turbulent transport and the fact that CIEMAT-QI4 very approximately satisfies the so-called maximum-J property is discussed.

physics.plasm-ph↗

arXiv2023

MONKES: a fast neoclassical code for the evaluation of monoenergetic transport coefficients

MONKES is a new neoclassical code for the evaluation of monoenergetic transport coefficients in stellarators. By means of a convergence study and benchmarks with other codes, it is shown that MONKES is accurate and efficient. The combination of spectral discretization in spatial and velocity coordinates with block sparsity allows MONKES to compute monoenergetic coefficients at low collisionality, in a single core, in approximately one minute. MONKES is sufficiently fast to be integrated into stellarator optimization codes for direct optimization of the bootstrap current and to be included in predictive transport suites. The code and data from this paper are available at https://github.com/JavierEscoto/MONKES/

physics.plasm-ph↗

arXiv2023

Electrostatic microturbulence in W7-X: comparison of local gyrokinetic simulations with Doppler reflectometry measurements

The first experimental campaigns of Wendelstein 7-X (W7-X) have shown that turbulence plays a decisive role in the performance of neoclassically optimized stellarators. This stresses the importance of understanding microturbulence from the theoretical and experimental points of view. To this end, this paper addresses a comprehensive characterization of the turbulent fluctuations by means of nonlinear gyrokinetic simulations performed with the code stella in two W7-X scenarios. In the first part of the paper, the amplitude of the density fluctuations is calculated and compared with measurements obtained by Doppler reflectometry (DR) in the OP1 experimental campaigns. It is found that the trend of the fluctuations along the radius is explained by the access of the DR system to different regions of the turbulence wavenumber spectrum. In the second part of the article, frequency spectra of the density fluctuations and the zonal component of the turbulent flow are numerically characterized for comparisons against future experimental analyses. Both quantities feature broad frequency spectra with dominant frequencies of O(1)-O(10) kHz.

physics.plasm-ph↗

arXiv2023

Robust stellarator optimization via flat mirror magnetic fields

Stellarator magnetic configurations need to be optimized in order to meet all the required properties of a fusion reactor. In this work, it is shown that a flat-mirror quasi-isodynamic configuration (i.e. a quasi-isodynamic configuration with sufficiently small radial variation of the mirror term) can achieve small radial transport of energy and good confinement of bulk and fast ions even if it is not very close to perfect omnigeneity, and for a wide range of plasma scenarios, including low $\beta$ and small radial electric field. This opens the door to constructing better stellarator reactors. On the one hand, they would be easier to design, as they would be robust against error fields. On the other hand, they would be easier to operate since, both during startup and steady-state operation, they would require less auxiliary power, and the damage to plasma-facing components caused by fast ion losses would be reduced to acceptable levels.

physics.plasm-ph↗

arXiv2023

Reduction or enhancement of stellarator turbulence by impurities

A systematic study of the impact of impurities on the turbulent heat fluxes is presented for the stellarator Wendelstein 7-X (W7-X) and, for comparison, the Large Helical Device and ITER. By means of nonlinear multispecies gyrokinetic simulations, it is shown that impurities, depending on the sign of their density gradient, can significantly enhance or reduce turbulent ion heat losses. For the relevant scenario of turbulence reduction, an optimal impurity concentration that minimizes the ion heat diffusivity emerges as a universal feature. This result demonstrates the potential of impurities for controlling turbulence and accessing enhanced confinement regimes in fusion plasmas and, in particular, in W7-X.

physics.plasm-ph↗

arXiv2022

A quasi-isodynamic configuration with good confinement of fast ions at low plasma $\beta$

A new quasi-isodynamic stellarator configuration optimized for the confinement of energetic ions at low plasma $\beta$ is obtained. The numerical optimization is carried out using the STELLOPT suite of codes. New proxies to measure closeness to quasi-isodynamicity and quality of fast ion confinement have been included. The new configuration has poloidally closed contours of magnetic field strength, low magnetic shear and a rotational transform profile allowing an island divertor. It shows ideal and ballooning magnetohydrodynamic stability up to $\beta = 5%$, reduced effective ripple, with $\epsilon_{eff} < 0.5%$ in the plasma core. Even at low $\beta$, the configuration approximately satisfies the maximum-$J$ property, and the confinement of fast ions is good at $\beta \sim 1.5%$ and becomes excellent at reactor values, $\beta \sim 4%$. An evaluation of the $D_{31}$ neoclassical mono-energetic coefficient supports the expectation of a reduced bootstrap current for plasmas confined in quasi-isodynamic configurations. A set of filamentary coils that preserve the good confinement of fast ions in the core is presented.

physics.plasm-ph↗

arXiv2022

Prevention of core particle depletion in stellarators by turbulence

In reactor-relevant plasmas, neoclassical transport drives an outward particle flux in the core of large stellarators and predicts strongly hollow density profiles. However, this theoretical prediction is contradicted by experiments. In particular, in Wendelstein 7-X, the first large optimized stellarator, flat or weakly peaked density profiles are generally measured, indicating that neoclassical theory is not sufficient and that an inward contribution to the particle flux is missing in the core. In this Research Letter, it is shown that the turbulent contribution to the particle flux can explain the difference between experimental measurements and neoclassical predictions. The results of this Research Letter also prove that theoretical and numerical tools are approaching the level of maturity needed for the prediction of equilibrium density profiles in stellarator plasmas, which is a fundamental requirement for the design of operation scenarios of present devices and future reactors.

physics.plasm-ph↗

arXiv2021

On the role of density fluctuations in the core turbulent transport of Wendelstein 7-X

A recent characterization of core turbulence carried out with a Doppler reflectometer in the optimized stellarator Wendelstein 7-X (W7-X) found that discharges achieving high ion temperatures at the core featured an ITG-like suppression of density fluctuations driven by a reduction of the gradient ratio $\eta_i = L_n/L_{T_i}$ [D. Carralero et al., Nucl. Fusion, 2021]. In order to confirm the role of ITG turbulence in this process, we set out to establish experimentally the relation between core density fluctuations, turbulent heat flux and global confinement. With this aim, we consider the scenarios found in the previous work and carry out power balance analysis for a number of representative ones, including some featuring high ion temperature. As well, we evaluate the global energy confinement time and discuss it in the context of the ISS04 inter-stellarator scaling. We find that, when turbulence is suppressed as a result of a reduction of $\eta_i$, there is a reduction of ion turbulent transport, and global performance is improved as a result. This is consistent with ITG turbulence limiting the ion temperature at the core of W7-X. In contrast, when turbulence is reduced following a decrease in collisionality, no changes are observed in transport or confinement. This could be explained by ITG modes being combined with TEM turbulence when the later is destabilized at low collisionalities.

physics.plasm-ph↗

arXiv2021

Physics design point of high-field stellarator reactors

The ongoing development of electromagnets based on High Temperature Superconductors has led to the conceptual exploration of high-magnetic-field fusion reactors of the tokamak type, operating at on-axis fields above 10 T. In this work we explore the consequences of the potential future availability of high-field three-dimensional electromagnets on the physics design point of a stellarator reactor. We find that, when an increase in the magnetic field strength $B$ is used to maximally reduce the device linear size $R\sim B^{-4/3}$ (with otherwise fixed magnetic geometry), the physics design point is largely independent of the chosen field strength/device size. A similar degree of optimization is to be imposed on the magnetohydrodynamic, transport and fast ion confinement properties of the magnetic configuration of that family of reactor design points. Additionally, we show that the family shares an invariant operation map of fusion power output as a function of the auxiliary power and relative density variation. The effects of magnetic field over-engineering and the $R(B)$ scaling of design points with constant neutron wall loading are also inspected. In this study we use geometric parameters characteristic of the helias reactor, but most results apply to other stellarator configurations

physics.plasm-ph↗

arXiv2021

Electrostatic gyrokinetic simulations in Wendelstein 7-X geometry: benchmark between the codes stella and GENE

The first experimental campaigns have proven that, due to the optimization of the magnetic configuration with respect to neoclassical transport, the contribution of turbulence is essential to understand and predict the total particle and energy transport in Wendelstein 7-X (W7-X). This has spurred much work on gyrokinetic modelling for the interpretation of the available experimental results and for the preparation of the next campaigns. At the same time, new stellarator gyrokinetic codes have just been or are being developed. It is therefore desirable to have a sufficiently complete, documented and verified set of gyrokinetic simulations in W7-X geometry against which new codes or upgrades of existing codes can be tested and benchmarked. This paper attemps to provide such a set of simulations in the form of a comprehensive benchmark between the recently developed code stella and the well-established code GENE. The benchmark consists of electrostatic gyrokinetic simulations in W7-X magnetic geometry and includes different flux tubes, linear ion-temperature-gradient (ITG) and trapped-electron-mode (TEM)} stability analyses, computation of linear zonal flow responses and calculation of ITG-driven heat fluxes.

physics.plasm-ph↗

arXiv2021

A model for the fast evaluation of prompt losses of energetic ions in stellarators

A good understanding of the confinement of energetic ions in non-axisymmetric magnetic fields is key for the design of reactors based on the stellarator concept. In this work, we develop a model that, based on the radially-local bounce-averaged drift-kinetic equation, classifies orbits and succeeds in predicting configuration-dependent aspects of the prompt losses of energetic ions in stellarators. Such a model could in turn be employed in the optimization stage of the design of new devices.

physics.plasm-ph↗