arXiv subjects

P. Helander

Publications and source records attributed to P. Helander.

At least 37 records · Page 2Linked to original sources

arXiv2020

Effect of plasma elongation on current dynamics during tokamak disruptions

Plasma terminating disruptions in tokamaks may result in relativistic runaway electron beams with potentially serious consequences for future devices with large plasma currents. In this paper we investigate the effect of plasma elongation on the coupled dynamics of runaway generation and resistive diffusion of the electric field. We find that elongated plasmas are less likely to produce large runaway currents, partly due to the lower induced electric fields associated with larger plasmas, and partly due to direct shaping effects, which mainly lead to a reduction in the runaway avalanche gain.

physics.plasm-ph↗

arXiv2019

Direct construction of optimized stellarator shapes. III. Omnigenity near the magnetic axis

The condition of omnigenity is investigated, and applied to the near-axis expansion of Garren and Boozer (1991a). Due in part to the particular analyticity requirements of the near-axis expansion, we find that, excluding quasi-symmetric solutions, only one type of omnigenity, namely quasi-isodynamicity, can be satisfied at first order in the distance from the magnetic axis. Our construction provides a parameterization of the space of such solutions, and the cylindrical reformulation and numerical method of Landreman and Sengupta (2018); Landreman et al. (2019), enables their efficient numerical construction.

physics.plasm-ph↗

arXiv2019

Collisional transport of impurities with flux-surface varying density in stellarators

High-Z impurities in magnetic confinement devices are prone to develop density variations on the flux-surface, which can significantly affect their transport. In this paper, we generalize earlier analytic stellarator calculations of the neoclassical radial impurity flux in the mixed-collisionality regime (collisional impurity and low-collisionality bulk ions) to include the effect of such flux-surface variations. We find that only in the homogeneous density case is the transport of highly collisional impurities (in the Pfirsch-Schlüter regime) independent of the radial electric field. We study these effects for a Wendelstein 7-X (W7-X) vacuum field, with simple analytic models for the potential perturbation, under the assumption that the impurity density is given by a Boltzmann response to a perturbed potential. In the W7-X case studied, we find that larger amplitude potential perturbations cause the radial electric field to dominate the transport of the impurities. In addition, we find that classical impurity transport can be larger than the neoclassical transport in W7-X.

physics.plasm-ph↗

arXiv2018

First determination of the $ρ$ parameter at $\sqrt{s} = 13$ TeV -- probing the existence of a colourless three-gluon bound state

The TOTEM experiment at the LHC has performed the first measurement at $\sqrt{s} = 13$ TeV of the $ρ$ parameter, the real to imaginary ratio of the nuclear elastic scattering amplitude at $t=0$, obtaining the following results: $ρ= 0.09 \pm 0.01$ and $ρ= 0.10 \pm 0.01$, depending on different physics assumptions and mathematical modelling. The unprecedented precision of the $ρ$ measurement, combined with the TOTEM total cross-section measurements in an energy range larger than 10 TeV (from 2.76 to 13 TeV), has implied the exclusion of all the models classified and published by COMPETE. The $ρ$ results obtained by TOTEM are compatible with the predictions, from alternative theoretical models both in the Regge-like framework and in the QCD framework, of a colourless 3-gluon bound state exchange in the $t$-channel of the proton-proton elastic scattering. On the contrary, if shown that the 3-gluon bound state $t$-channel exchange is not of importance for the description of elastic scattering, the $ρ$ value determined by TOTEM would represent a first evidence of a slowing down of the total cross-section growth at higher energies. The very low-$|t|$ reach allowed also to determine the absolute normalisation using the Coulomb amplitude for the first time at the LHC and obtain a new total proton-proton cross-section measurement $σ_{tot} = 110.3 \pm 3.5$ mb, completely independent from the previous TOTEM determination. Combining the two TOTEM results yields $σ_{tot} = 110.5 \pm 2.4$ mb.

hep-ex↗

arXiv2018

Properties of a new quasi-axisymmetric configuration

A novel, compact, quasi-axisymmetric configuration is presented which exhibits low fast-particle losses and is stable to ideal MHD instabilities. The design has fast-particle loss rates below 8\% for flux surfaces within the half-radius, and is shown to have an MHD-stability limit of a normalised pressure of $\langleβ\rangle=3\%$ where $\langleβ\rangle$ is volume averaged. The flux surfaces at various plasma betas and currents as calculated using the SPEC equilibrium code are presented. Neoclassical transport coefficients are shown to be similar to an equivalent tokamak, with a distinct banana regime at half-radius. An initial coil design study is presented to assess the feasibility of this configuration as a fusion-relevant experiment.

physics.plasm-ph↗

arXiv2018

Quasi-axisymmetric magnetic fields: weakly non-axisymmetric case in a vacuum

An asymptotic expansion is performed to obtain quasi-axisymmetric magnetic configurations that are weakly non-axisymmetric. A large space of solutions is identified, which satisfy the condition of quasi-axisymmetry on a single magnetic flux surface, while (non-axisymmetric) globally quasi-axisymmetric solutions are shown to not exist, agreeing with the conclusions of previous theoretical work. The solutions found are shown to be geometrically constrained at low aspect ratio or high toroidal period number. Solutions satisfying the more general condition of omnigeneity (generalized quasi-axisymmetry) are also shown to exist, and it is found that quasi-axisymmetric deformations can be superposed with an omnigenous solution, while preserving the property of omnigeneity, effectively extending the space of "good" configurations. A numerical solution of the first order quasi-axisymmetry problem is demonstrated and compared with solutions found with a widely used MHD equilibrium solver, independently verifying that quasi-axisymmetry is satisfied at the appropriate order. It is thereby demonstrated that approximately quasi-axisymmetric solutions can be directly constructed, i.e. without using numerical search algorithms.

physics.plasm-ph↗

arXiv2018

First measurement of elastic, inelastic and total cross-section at $\sqrt{s}=13$ TeV by TOTEM and overview of cross-section data at LHC energies

The TOTEM collaboration has measured the proton-proton total cross section at $\sqrt{s}=13$ TeV with a luminosity-independent method. Using dedicated $β^{*}=90$ m beam optics, the Roman Pots were inserted very close to the beam. The inelastic scattering rate has been measured by the T1 and T2 telescopes during the same LHC fill. After applying the optical theorem the total proton-proton cross section is $σ_{\rm tot}=(110.6 \pm 3.4$) mb, well in agreement with the extrapolation from lower energies. This method also allows one to derive the luminosity-independent elastic and inelastic cross sections: $σ_{\rm el} = (31.0 \pm 1.7)$ mb and $σ_{\rm inel} = (79.5 \pm 1.8)$ mb.

hep-ex↗

arXiv2017

Distinct turbulence saturation regimes in stellarators

In the complex 3D magnetic fields of stellarators, ion-temperature-gradient turbulence is shown to have two distinct saturation regimes, as revealed by petascale numerical simulations, and explained by a simple turbulence theory. The first regime is marked by strong zonal flows, and matches previous observations in tokamaks. The newly observed second regime, in contrast, exhibits small- scale quasi-two-dimensional turbulence, negligible zonal flows, and, surprisingly, a weaker heat flux scaling. Our findings suggest that key details of the magnetic geometry control turbulence in stellarators.

physics.plasm-ph↗

arXiv2017

Collisionless microinstabilities in stellarators. IV. The ion-driven trapped-electron mode

Optimised stellarators and other magnetic-confinement devices having the property that the average magnetic curvature is favourable for all particle orbits are called maximum-$J$ devices, and have recently been shown to be immune to trapped-particle instabilities driven by the density gradient. Gyrokinetic simulations reveal, however, that another instability can arise, which is also associated with particle trapping but causes less transport than typical trapped-electron modes. The nature of this instability is clarified here. It is shown to be similar to the "ubiquitous mode" in tokamaks, and is driven by ion free energy but requires trapped electrons to exist.

physics.plasm-ph↗

arXiv2017

Stellarator bootstrap current and plasma flow velocity at low collisionality

The bootstrap current and flow velocity of a low-collisionality stellarator plasma are calculated. As far as possible, the analysis is carried out in a uniform way across all low-collisionality regimes in general stellarator geometry, assuming only that the confinement is good enough that the plasma is approximately in local thermodynamic equilibrium. It is found that conventional expressions for the ion flow speed and bootstrap current in the low-collisionality limit are accurate only in the $1/ν$-collisionality regime and need to be modified in the $\sqrtν$-regime. The correction due to finite collisionality is also discussed and is found to scale as $ν^{2/5}$.

physics.plasm-ph↗

arXiv2016

Constraints on dynamo action in plasmas

Upper bounds are derived on the amount of magnetic energy that can be generated by dynamo action in collisional and collisionless plasmas with and without external forcing. A hierarchy of mathematical descriptions is considered for the plasma dynamics: ideal MHD, visco-resistive MHD, the double-adiabatic theory of Chew, Goldberger and Low (CGL), kinetic MHD, and other kinetic models. It is found that dynamo action is greatly constrained in models where the magnetic moment of any particle species is conserved. In the absence of external forcing, the magnetic energy then remains small at all times if it is small in the initial state. In other words, a small "seed" magnetic field cannot be amplified significantly, regardless of the nature of flow, as long as the collision frequency and gyroradius are small enough to be negligible. A similar conclusion also holds if the system is subject to external forcing as long as this forcing conserves the magnetic moment of at least one plasma species and does not greatly increase the total energy of the plasma (i.e., in practice, is subsonic). Dynamo action therefore always requires collisions or some small-scale kinetic mechanism for breaking the adiabatic invariance of the magnetic moment.

physics.plasm-ph↗

arXiv2015

Resilience of quasi-isodynamic stellarators against trapped-particle instabilities

It is shown that in perfectly quasi-isodynamic stellarators, trapped particles with a bounce frequency much higher than the frequency of the instability are stabilizing in the electrostatic and collisionless limit. The collisionless trapped-particle instability is therefore stable as well as the ordinary electron-density-gradient-driven trapped-electron mode. This result follows from the energy balance of electrostatic instabilities and is thus independent of all other details of the magnetic geometry.

physics.plasm-ph↗

arXiv2015

The universal instability in general geometry

The "universal" instability has recently been revived by Landreman, Antonsen and Dorland [1], who showed that it indeed exists in plasma geometries with straight (but sheared) magnetic field lines. Here it is demonstrated analytically that this instability can be present in more general sheared and toroidal geometries. In a torus, the universal instability is shown to be closely related to the trapped-electron mode, although the trapped-electron drive is usually dominant. However, this drive can be weakened or eliminated, as in the case in stellarators with the maximum-$J$ property, leaving the parallel Landau resonance to drive a residual mode, which is identified as the universal instability.

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↗

arXiv2015

Electrostatic potential variation on the flux surface and its impact on impurity transport

The particle transport of impurities in magnetically confined plasmas under some conditions does not find, neither quantitatively nor qualitatively, a satisfactory theory-based explanation. This compromise the successful realization of thermo-nuclear fusion for energy production since its accumulation is known to be one of the causes that leads to the plasma breakdown. In standard reactor-relevant conditions this accumulation is in most stellarators intrinsic to the lack of toroidal symmetry, that leads to the neoclassical electric field to point radially inwards. This statement, that the standard theory allows to formulate, has been contradicted by some experiments that showed weaker or no accumulation under such conditions \cite{Ida_pop_16_056111_2009, Yoshinuma_nf_49_062002_2009}. The charge state of the impurities makes its transport more sensitive to the electric fields. Thus, the short length scale turbulent electrostatic potential or its long wave-length variation on the flux surface $Φ_{1}$ -- that the standard neoclassical approach usually neglects -- might possibly shed some light on the experimental findings. In the present work the focus is put on the second of the two, and investigate its influence of the radial transport of C$^{6+}$. We show that in LHD it is strongly modified by $Φ_{1}$, both resulting in mitigated/enhanced accumulation at internal/external radial positions; for Wendelstein 7-X, on the contrary, $Φ_{1}$ is expected to be considerably smaller and the transport of C$^{6+}$ not affected up to an appreciable extent; and in TJ-II the potential shows a moderate impact despite of the large amplitude of $Φ_1$ for the parameters considered.

physics.plasm-ph↗

arXiv2014

Electrostatic potential variations along flux surfaces in stellarators

First observations of electrostatic potential variations within the flux surfaces of a toroidal magnetic confinement device are presented. Measurements are taken in the TJ-II stellarator with two distant Langmuir probe arrays. The edge floating potentials display differences of several tens of Volts in electron-root wave-heated plasmas. The differences are reduced for higher densities and lower electron temperatures after the ion-root electric field forms at the plasma edge. Neoclassical Monte Carlo simulations estimate the correct order of magnitude for the overall variation in potential and predict the trend observed with the radial electric field. However, for the specific location of the probes, the simulations give differences smaller than those observed experimentally.

physics.plasm-ph↗

arXiv2014

Collisionless microinstabilities in stellarators III - the ion-temperature-gradient mode

We investigate the linear theory of the ion-temperature-gradient (ITG) mode, with the goal of developing a general understanding that may be applied to stellarators. We highlight the Wendelstein 7X (W7-X) device. Simple fluid and kinetic models that follow closely from existing literature are reviewed and two new first-principle models are presented and compared with results from direct numerical simulation. One model investigates the effect of regions of strong localized shear, which are generic to stellarator equilibria. These "shear spikes" are found to have a potentially significant stabilizing affect on the mode; however, the effect is strongest at short wavelengths perpendicular to the magnetic field, and it is found to be significant only for the fastest growing modes in W7-X. A second model investigates the long-wavelength limit for the case of negligible global magnetic shear. The analytic calculation reveals that the effect of the curvature drive enters at second order in the drift frequency, confirming conventional wisdom that the ITG mode is slab-like at long wavelengths. Using flux tube simulations of a zero-shear W7-X configuration, we observe a close relationship to an axisymmetric configuration at a similar parameter point. It is concluded that scale lengths of the equilibrium gradients constitute a good parameter space to characterize the ITG mode. Thus, to optimize the magnetic geometry for ITG mode stability, it may be fruitful to focus on local parameters, such as the magnitude of bad curvature, connection length, and local shear at locations of bad curvature (where the ITG mode amplitude peaks).

physics.plasm-ph↗

arXiv2013

Collisionless microinstabilities in stellarators I - analytical theory of trapped-particle modes

This is the first of two papers about collisionless, electrostatic micro-instabilities in stellarators, with an emphasis on trapped-particle modes. It is found that, in so-called maximum-$J$ configurations, trapped-particle instabilities are absent in large regions of parameter space. Quasi-isodynamic stellarators have this property (approximately), and the theory predicts that trapped electrons are stabilizing to all eigenmodes with frequencies below the electron bounce frequency. The physical reason is that the bounce-averaged curvature is favorable for all orbits, and that trapped electrons precess in the direction opposite to that in which drift waves propagate, thus precluding wave-particle resonance. These considerations only depend on the electrostatic energy balance, and are independent of all geometric properties of the magnetic field other than the maximum-$J$ condition. However, if the aspect ratio is large and the instability phase velocity differs greatly from the electron and ion thermal speeds, it is possible to derive a variational form for the frequency showing that stability prevails in a yet larger part of parameter space than what follows from the energy argument. Collisionless trapped-electron modes should therefore be more stable in quasi-isodynamic stellarators than in tokamaks.

physics.plasm-ph↗