arXiv subjects

A. Zocco

Publications and source records attributed to A. Zocco.

17 recordsLinked to original sources

arXiv2026

Second stability region for gyrokinetics and the L-H transition

Using a simple circular tokamak geometry, we show the well-known `second stability region' of MHD-ballooning modes exists for linear gyrokinetics too -- whether electrostatic or electromagnetic -- and we suggest that the plasma enters this region in H-mode as a consequence of the bootstrap current and Shafranov shift altering the magnetic field, which may occur if the normalised pressure gradient is $\alpha_{\rm MHD} \simgt 1$ and collisionality is low. By performing simulations in more realistic magnetic geometries, we demonstrate a large reduction in collisionless, electrostatic turbulent transport when going from density and temperature profiles typical of L- and H-mode, respectively. This reduction is shown to be a consequence of both the bootstrap current lowering the global magnetic shear, and the pressure gradient altering the local magnetic shear, pushing the plasma towards the second-stability region. A path connecting the L- and H-mode equilibria is constructed, along which the energy and particle fluxes exhibit non-monotonic behaviour as a function of the pressure gradient.

physics.plasm-ph↗

arXiv2026

Scaling laws for the cutoff wavenumber of the short-wavelength ion-temperature-gradient mode in a Z-pinch

We use a heuristic fluid model to predict the dependence of the cutoff wave number for the short-wavelength ion temperature gradient (SWITG) mode on ion density gradient, ion temperature gradient (ITG) and ion-electron temperature ratio. In particular, we predict that the cutoff wave number increases linearly with increasing ITG for sufficiently large values of the ITG. Direct numerical solutions of the gyrokinetic dispersion relation using a purpose-built solver confirm the predicted scalings at large ITG values and find a weaker power-law scaling for intermediate ITG values. Combining these wave number scalings with a simple diffusive estimate for turbulent fluxes produces a scaling prediction for the ITG heat flux in SWITG-driven turbulence. Applying the critical balance conjecture additionally provides scalings for the aspect ratio of the SWITG turbulent eddies.

physics.plasm-ph↗

arXiv2025

Study of the impact of fast ions on core turbulence at rational surfaces via global gyrokinetic simulations

In this work, the interplay between fast ions and safety factor rational surfaces is studied in a turbulent plasma via global nonlinear gyrokinetic simulations. Initially, the fast particles-induced enhancement of shearing structures from turbulence self-interaction is analyzed. Our study takes into account the competition between this mechanism and other fast ions effects, i.e. thermal profiles dilution and quasi-resonant interaction. We find the fast ions-induced reduction of destabilization threshold for the zonal modes to be a very efficient way to suppress turbulence. Indeed, it leads to the formation of regions where turbulent transport is reduced by 90\% of its original value. Furthermore, an $n=m=1$ fishbone is driven unstable inside the plasma and its interaction with turbulence is studied. We find the beat-driven zonal structure generate by this mode to further reduce turbulence when its presence does not drastically flatten the thermal profiles.

physics.plasm-ph↗

arXiv2025

Fast electrostatic microinstability evaluation in arbitrary toroidal magnetic geometry using a variational approach

Small-scale turbulence originating from microinstabilities limits the energy confinement time in magnetic confinement fusion. Here we develop a semi-analytical dispersion relation based on lowest-order solutions to the gyrokinetic equations in an asymptotic expansion in the ratio of transit (bounce) frequency to the mode frequency for ions (electrons), capable of describing two common instabilities: the ion temperature gradient (ITG) mode and trapped-electron mode (TEM), in the electrostatic limit. The dispersion relation, which is valid in arbitrary toroidal geometry, takes into account resonances with the magnetic ion and bounce-averaged electron drifts, incorporates non-local effects along the magnetic field line, is valid for arbitrary sign of the growth rate and magnetic curvature, and is shown to satisfy a variational property. Several common approximation models are introduced for both the magnetic drift and finite Larmor radius (FLR) damping, with the Pad\'e approximation for FLR effect in particular resulting in remarkable agreement with the baseline dispersion relation model at significantly reduced costs. The baseline model is verified by comparing solutions of the dispersion relation model to high-fidelity linear gyrokinetic simulations, where the exact eigenfunction of the electrostatic potential from simulations is used as a trial function, showing good quantitative agreement for ITGs and TEMs in (shaped) tokamaks as well as low-magnetic-shear stellarators.

physics.plasm-ph↗

arXiv2025

Microtearing Turbulence and Its Role in High-Density-Gradient Plasmas in Wendelstein 7-X

Gyrokinetic simulations reveal that microtearing mode (MTM) turbulence dominates transport in a Wendelstein 7-X (W7-X) discharge characterized by large density gradients, moderate temperature gradients, and low plasma beta. This conclusion is supported by the close agreement between simulated and experimentally measured heat and particle fluxes. The emergence of MTMs is attributed to the absence of competing instabilities -- such as ion temperature gradient modes and density-gradient-driven trapped-electron modes -- under these plasma conditions, together with the stabilizing influence of the W7-X max-J magnetic configuration. Furthermore, moderate collisionality and low magnetic shear are found to facilitate MTM onset. These findings advance the understanding of high-density-gradient regimes, which are essential for achieving high-performance operation in W7-X plasmas.

physics.plasm-ph↗

arXiv2025

Resonant theory of kinetic ballooning modes in general toroidal geometry

The linear theory of the kinetic-ballooning-mode (KBM) instability is extended to capture a weakly-driven regime in general toroidal geometry where the destabilization is caused by the magnetic-drift resonance of the ions. Such resonantly-destabilized KBMs are characterized by broad eigenfunctions along the magnetic field line and near-marginal positive growth rates, even well below the beta threshold of their non-resonant counterparts. This unconventional (or sub-threshold) KBM, when destabilized, has been shown to catalyze an enhancement of turbulent transport in the Wendelstein 7-X (W7-X) stellarator [1, 2]. Simplifying the energy dependence of key resonant quantities allows for an analytical treatment of this KBM using the physics-based ordering from the more general equations of Tang, Connor, and Hastie [3]. Results are then compared with high-fidelity gyrokinetic simulations for the (st)KBM in W7-X and the conventional KBM in a circular tokamak at both high and low magnetic shear, where good agreement is obtained in all cases. This reduced KBM model provides deeper insight into (sub-threshold) KBMs and their relationship with geometry, and shows promise for aiding in transport model development and geometry-based turbulence optimization efforts going forward.

physics.plasm-ph↗

arXiv2023

Ion temperature and density gradient driven instabilities and turbulence in Wendelstein 7-X close to the stability threshold

Electrostatic gyrokinetic instabilities and turbulence in the Wendelstein 7-X stellarator are studied. Particular attention is paid to the ion-temperature-gradient (ITG) instability and its character close to marginal stability [Floquet-type turbulence (Zocco et al. 2022) with no electron temperature gradient]. The flux-tube version of the $\delta$f code stella (Barnes et al. 2019) is used to run linear and nonlinear gyrokinetic simulations with kinetic electrons. The nature of the dominant instability depends on the wavelength perpendicular to the magnetic field, and the results are conveniently displayed in stability diagrams that take this dependence into account. This approach highlights the presence of universal instabilities, which are less unstable but have longer wavelengths than other modes. A quasi-linear estimate of the heat flux suggests they are relevant for transport. Close to the stability threshold, the linear eigenmodes and turbulence form highly extended structures along the computational domain if the magnetic shear is small. Numerical experiments and diagnostics are undertaken to assess the resulting radial localisation of the turbulence, which affects the interaction of the latter with zonal flows. Increasing the amplitude of the magnetic shear (e.g. through current drive) has a stabilising effect on the turbulence and thus reduces the nonlinear energy transport.

physics.plasm-ph↗

arXiv2020

Gyrokinetic investigation of Alfvén instabilities in the presence of turbulence

The nonlinear dynamics of beta-induced Alfvén Eigenmodes (BAE) driven by energetic particles (EP) in the presence of ion-temperature-gradient (ITG) turbulence is investigated, by means of selfconsistent global gyrokinetic simulations and analytical theory. A tokamak magnetic equilibrium with large aspect ratio and reversed shear is considered. A previous study of this configuration has shown that the electron species plays an important role in determining the nonlinear saturation level of a BAE in the absence of turbulence [A. Biancalani, et al., J. Plasma Phys. (2020)]. Here, we extend the study to a turbulent plasma. The EPs are found modify the heat fluxes by introducing energy at the large spatial scales, mainly at the toroidal mode number of the dominant BAE and its harmonics. In this regime, BAEs are found to carry a strong electron heat flux. The feed-back of the global relaxation of the temperature profiles induced by the BAE, and on the turbulence dynamics, is also discussed.

physics.plasm-ph↗

arXiv2020

Turbulent impurity transport simulations in Wendelstein 7-X plasmas

A study of turbulent impurity transport by means of quasilinear and nonlinear gyrokinetic simulations is presented for Wendelstein 7-X (W7-X). The calculations have been carried out with the recently developed gyrokinetic code stella. Different impurity species are considered in the presence of various types of background instabilities: ITG, TEM and ETG modes for the quasilinear part of the work; ITG and TEM for the nonlinear results. While the quasilinear approach allows one to draw qualitative conclusions about the sign or relative importance of the various contributions to the flux, the nonlinear simulations quantitatively determine the size of the turbulent flux and check the extent to which the quasilinear conclusions hold. Although the bulk of the nonlinear simulations are performed at trace impurity concentration, nonlinear simulations are also carried out at realistic effective charge values, in order to know to what degree the conclusions based on the simulations performed for trace impurities can be extrapolated to realistic impurity concentrations. The presented results conclude that the turbulent radial impurity transport in W7-X is mainly dominated by ordinary diffusion, which is close to that measured during the recent W7-X experimental campaigns. It is also confirmed that thermo-diffusion adds a weak inward flux contribution and that, in the absence of impurity temperature and density gradients, ITG- and TEM-driven turbulence push the impurities inwards and outwards, respectively.

physics.plasm-ph↗

arXiv2015

Viriato: a Fourier-Hermite spectral code for strongly magnetised fluid-kinetic plasma dynamics

We report on the algorithms and numerical methods used in Viriato, a novel fluid-kinetic code that solves two distinct sets of equations: (i) the Kinetic Reduced Electron Heating Model (KREHM) equations [Zocco & Schekochihin, Phys. Plasmas 18, 102309 (2011)] (which reduce to the standard Reduced-MHD equations in the appropriate limit) and (ii) the kinetic reduced MHD (KRMHD) equations [Schekochihin et al., Astrophys. J. Suppl. 182:310 (2009)]. Two main applications of these equations are magnetised (Alfvenic) plasma turbulence and magnetic reconnection. Viriato uses operator splitting (Strang or Godunov) to separate the dynamics parallel and perpendicular to the ambient magnetic field (assumed strong). Along the magnetic field, Viriato allows for either a second-order accurate MacCormack method or, for higher accuracy, a spectral-like scheme composed of the combination of a total variation diminishing (TVD) third order Runge-Kutta method for the time derivative with a 7th order upwind scheme for the fluxes. Perpendicular to the field Viriato is pseudo-spectral, and the time integration is performed by means of an iterative predictor-corrector scheme. In addition, a distinctive feature of Viriato is its spectral representation of the parallel velocity-space dependence, achieved by means of a Hermite representation of the perturbed distribution function. A series of linear and nonlinear benchmarks and tests are presented, including a detailed analysis of 2D and 3D Orszag-Tang-type decaying turbulence, both in fluid and kinetic regimes.

physics.plasm-ph↗

arXiv2015

Magnetic compressibility and ion-temperature-gradient-driven microinstabilities in magnetically confined plasmas

The electromagnetic theory of the strongly driven ion-temperature-gradient (ITG) instability in magnetically confined toroidal plasmas is developed. Stabilizing and destabilizing effects are identified, and a critical $β_{e}$ (the ratio of the electron to magnetic pressure) for stabilization of the toroidal branch of the mode is calculated for magnetic equilibria independent of the coordinate along the magnetic field. Its scaling is $β_{e}\sim L_{Te}/R,$ where $L_{Te}$ is the characteristic electron temperature gradient length, and $R$ the major radius of the torus. We conjecture that a fast particle population can cause a similar stabilization due to its contribution to the equilibrium pressure gradient. For sheared equilibria, the boundary of marginal stability of the electromagnetic correction to the electrostatic mode is also given. For a general magnetic equilibrium, we find a critical length (for electromagnetic stabilization) of the extent of the unfavourable curvature along the magnetic field. This is a decreasing function of the local magnetic shear.

physics.plasm-ph↗

arXiv2013

Improved Criterion for Sawtooth Trigger and Modelling

We discuss the role of neoclassical resistivity and local magnetic shear in the triggering of the sawtooth in tokamaks. When collisional detrapping of electrons is considered the value of the safety factor on axis, $q(0,t)$, evolves on a new time scale, $τ_{*}=τ_ην_{*}/(8\sqrtε)$, where $τ_η=4πa^{2}/[c^{2}η(0)]$ is the resistive diffusion time, $ν_{*}=ν_{e}/(ε^{3/2}ω_{te})$ the electron collision frequency normalised to the transit frequency and $ε=a/R_{0}$ the tokamak inverse aspect ratio. Such evolution is characterised by the formation of a structure of size $δ_{*}\simν_{*}^{2/3}a$ around the magnetic axis, which can drive rapid evolution of the magnetic shear and decrease of $q(0,t)$. We investigate two possible trigger mechanisms for a sawtooth collapse corresponding to crossing the linear threshold for the $m=1,n=1$ instability and non-linear triggering of this mode by a core resonant mode near the magnetic axis. The sawtooth period in each case is determined by the time for the resistive evolution of the $q$-profile to reach the relevant stability threshold; in the latter case it can be strongly affected by $ν_*.$

physics.plasm-ph↗

arXiv2013

Fast collisionless reconnection and electron heating in strongly magnetized plasmas

Magnetic reconnection in strongly magnetized (low-beta), weakly collisional plasmas is investigated using a novel fluid-kinetic model [Zocco & Schekochihin, Phys. Plasmas 18, 102309 (2011)] which retains non-isothermal electron kinetics. It is shown that electron heating via Landau damping (linear phase mixing) is the dominant dissipation mechanism. In time, electron heating occurs after the peak of the reconnection rate; in space, it is concentrated along the separatrices of the magnetic island. For sufficiently large systems, the peak reconnection rate is $cE_{max}\approx 0.2v_AB_{y,0}$, where $v_A$ is the Alfvén speed based on the reconnecting field $B_{y,0}$. The island saturation width is the same as in MHD models except for small systems, when it becomes comparable to the kinetic scales.

physics.plasm-ph↗

arXiv2012

Ion Landau Damping on Drift Tearing Modes

Kinetic treatments of drift-tearing modes that match an inner resonant layer solution to an external MHD region solution, characterised by $Δ^{\prime}$, fail to properly match the ideal MHD boundary condition on the parallel electric field, $E_{\parallel}.$ In this paper we demonstrate how consideration of ion sound and ion Landau damping effects achieves this and place the theory on a firm footing. As a consequence, these effects contribute quite significantly to the critical value of $Δ^{\prime}$ for instability of drift-tearing modes and play a key role in determining the minimum value for this threshold.

physics.plasm-ph↗

arXiv2012

Unified theory of the semi-collisional tearing mode and internal kink mode in a hot tokamak: implications for sawtooth modelling

In large hot tokamaks like JET, the width of the reconnecting layer for resistive modes is determined by semi-collisional electron dynamics and is much less than the ion Larmor radius. Firstly a dispersion relation valid in this regime is derived which provides a unified description of drift-tearing modes, kinetic Alfven waves and the internal kink mode at low beta. Tearing mode stability is investigated analytically recovering the stabilising ion orbit effect, obtained previously by Cowley et al. [Phys. Fluids (29) 3230 1986], which implies large values of the tearing mode stability parameter "Delta prime" are required for instability. Secondly, at high beta it is shown that the tearing mode interacts with the kinetic Alfven wave and that there is an absolute stabilisation for all "Delta prime" due to the shielding effects of the electron temperature gradients, extending the result of Drake et. al [Phys. Fluids (26) 2509 1983] to large ion orbits. The nature of the transition between these two limits at finite values of beta is then elucidated. The low beta formalism is also relevant to the m=n=1 tearing mode and the dissipative internal kink mode, thus extending the work of Pegoraro et al. [Phys. Fluids B (1) 364 1989] to a more realistic electron model incorporating temperature perturbations, but then the smallness of the dissipative internal kink mode frequency is exploited to obtain a new dispersion relation valid at arbitrary beta. A diagram describing the stability of both the tearing mode and dissipative internal kink mode, in the space of "Delta prime" and beta, is obtained. The trajectory of the evolution of the current profile during a sawtooth period can be plotted in this diagram, providing a model for the triggering of a sawtooth crash.

physics.plasm-ph↗

arXiv2010

Analytical Model of Fast Magnetic Reconnection with a Large Guide Field

Analytical theory of fast magnetic reconnection with a large guide field is presented for the first time. We confirm that two distinct reconnection regimes are possible depending on whether the diffusion region thickness $δ$ is larger or smaller than the sound gyroradius $ρ_s$. The reconnection is slow or Sweet-Parker-like for $δ\gtrsim ρ_s$, and fast otherwise. In the fast regime, however, we find that ion viscosity $μ$ plays a critical role. In particular, for $δ< ρ_s$ the diffusion region thickness is proportional to $Ha^{-1}$ with $Ha \propto 1/\sqrt{ημ}$ the Hartmann number, and the reconnection rate is proportional to $Pr^{-1/2}$ with $Pr = μ/η$ the Prandtl number and $η$ the resistivity. If the perpendicular ion viscosity is employed for $μ$ the reconnection rate becomes independent of both plasma $β$ and collision frequencies and therefore potentially fast.

physics.plasm-ph↗

arXiv2009

Current sheet bifurcation and collapse in electron magnetohydrodynamics

Inertial effects in nonlinear magnetic reconnection are studied within the context of 2D electron magnetohydrodynamics (EMHD) with resistive and viscous dissipation. Families of nonlinear solutions for relevant current sheet parameters are predicted and confirmed numerically in all regimes of interest. Electron inertia becomes important for current sheet thicknesses $δ$ below the inertial length $d_{e}$. In this case, in the absence of electron viscosity, the sheet thickness experiences a nonlinear collapse. Viscosity regularizes solutions at small scales. Transition from resistive to viscous regimes shows a nontrivial dependence on resistivity and viscosity, featuring a hysteresis bifurcation. In all accessible regimes, the nonlinear reconnection rate is found to be explicitly independent of the electron inertia and dissipation coefficients.

physics.plasm-ph↗