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Enumeration	Reference	Cover	Find
1.	Abel, Ian, 1985, et al. (author) Multiscale modelling for tokamak pedestals 2018 In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 84:2 Journal article (peer-reviewed)abstract Pedestal modelling is crucial to predict the performance of future fusion devices. Current modelling efforts suffer either from a lack of kinetic physics, or an excess of computational complexity. To ameliorate these problems, we take a first-principles multiscale approach to the pedestal. We will present three separate sets of equations, covering the dynamics of edge localised modes (ELMs), the inter-ELM pedestal and pedestal turbulence, respectively. Precisely how these equations should be coupled to each other is covered in detail. This framework is completely self-consistent; it is derived from first principles by means of an asymptotic expansion of the fundamental Vlasov-Landau-Maxwell system in appropriate small parameters. The derivation exploits the narrowness of the pedestal region, the smallness of the thermal gyroradius and the low plasma beta (the ratio of thermal to magnetic pressures) typical of current pedestal operation to achieve its simplifications. The relationship between this framework and gyrokinetics is analysed, and possibilities to directly match our systems of equations onto multiscale gyrokinetics are explored. A detailed comparison between our model and other models in the literature is performed. Finally, the potential for matching this framework onto an open-field-line region is briefly discussed.
2.	Anderson, D., et al. (author) Self-induced erosion and spectral breaking of high-power microwave pulses 2000 In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 63:4, s. 329-341 Journal article (peer-reviewed)abstract An analysis is made of the phenomenon of self-induced erosion and spectral breaking of ionizing high-power microwave pulses propagating in a gas. The analysis describes in an analytically explicit and physically clear way the consistent interaction between the microwave pulse and the self-induced breakdown plasma. In particular, it clarifies, both qualitatively and quantitatively, the mechanisms behind the pulse erosion and the spectral breaking phenomenon, i.e. the splitting of the pulse spectrum into a redshifted and a blueshifted peak as observed in numerical simulation results as well as in experiments.
3.	Andres, N., et al. (author) Energy cascade rate in isothermal compressible magnetohydrodynamic turbulence 2018 In: Journal of Plasma Physics. - : CAMBRIDGE UNIV PRESS. - 0022-3778 .- 1469-7807. ; 84:4 Journal article (peer-reviewed)abstract Three-dimensional direct numerical simulations are used to study the energy cascade rate in isothermal compressible magnetohydrodynamic turbulence. Our analysis is guided by a two-point exact law derived recently for this problem in which flux, source, hybrid and mixed terms are present. The relative importance of each term is studied for different initial subsonic Mach numbers M-S and different magnetic guide fields B-0. The dominant contribution to the energy cascade rate comes from the compressible flux, which depends weakly on the magnetic guide field B-0, unlike the other terms whose moduli increase significantly with M s and B-0. In particular, for strong B-0 the source and hybrid terms are dominant at small scales with almost the same amplitude but with a different sign. A statistical analysis undertaken with an isotropic decomposition based on the SO(3) rotation group is shown to generate spurious results in the presence of B-0, when compared with an axisymmetric decomposition better suited to the geometry of the problem. Our numerical results are compared with previous analyses made with in situ measurements in the solar wind and the terrestrial magnetosheath.
4.	Andrushchenko, Zhanna N., et al. (author) Self-consistent model of electron drift mode turbulence 2008 In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 74:1, s. 21-33 Journal article (peer-reviewed)abstract The nonlinear dynamics of magnetic electron drift mode turbulence are outlined and the generation of large-scale magnetic Structures in a non-uniform magnetized plasma by turbulent Reynolds stress is demonstrated. The loop-back of large-scale flows on the microturbulence is elucidated and the modulation of the electron drift mode turbulence spectrum in a, medium with slowly varying parameters is presented. The wave kinetic equation in the presence of large-scale flows is derived and it can be seen that the small-scale turbulence and the large-scale structures form a, self-regulating system. Finally. it is shown by the use of quasilinear theory that the shearing of microturbulence by the flows can be described by a diffusion equation in k-space and the corresponding diffusion coefficients are calculated.
5.	Asp, Elina, et al. (author) Stability of the Landau Resonance for Drift Modes in Rotating Tokamak Plasma 2003 In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 60:5, s. 371- Journal article (peer-reviewed)abstract The linear stability of drift waves in a poloidally rotating tokamak plasma is considered. The derived dispersion relation features a peaking of the diamagnetic frequency which gives the drift modes an irreducible two-dimensional character. We then show that inverse Landau damping can be suppressed and even stabilized, if the flow's shear is strong. Even though the instability, excited by the Landau resonance, is stronger at a high velocity shear for positive rotation velocities, effects due to the rotation of the plasma can reverse the sign and induce damping of the two-dimensional drift modes. This stabilizing mechanism works only for positive rotation velocities. For negative rotation velocities, we show that only modes with high poloidal mode numbers are unstable.
6.	Berger, Esmée, 1998, et al. (author) Runaway dynamics in reactor-scale spherical tokamak disruptions 2022 In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 88:6 Journal article (peer-reviewed)abstract Understanding generation and mitigation of runaway electrons in disruptions is important for the safe operation of future tokamaks. In this paper we investigate the runaway dynamics in reactor-scale spherical tokamaks, focusing on a compact nominal design with a plasma current of 21 megaamperes (MA), 1.8 T magnetic field on axis and major radius of approximately 3 m. We study both the severity of runaway generation during unmitigated disruptions, and the effect that typical mitigation schemes based on massive material injection have on runaway production. The study is conducted using the numerical framework DREAM (Disruption Runaway Electron Analysis Model). We find that, in many cases, mitigation strategies are necessary to prevent the runaway current from reaching multi-MA levels. Our results indicate that, with a suitably chosen deuterium–neon mixture for mitigation, it is possible to achieve a tolerable runaway current and ohmic current evolution. However, this does not account for the runaway source due to wall activation, which has been found to severely limit successful mitigation at conventional aspect ratios, but whose definition requires a more complete wall specification. Furthermore, the majority of the thermal energy loss is found to happen through radial transport rather than radiation, which poses a risk of unacceptable localised heat loads.
7.	Bingham, Robert, et al. (author) Solar coronal heating by plasma waves 2010 In: Journal of Plasma Physics. - : Cambridge university. - 0022-3778 .- 1469-7807. ; 76:2, s. 135-158 Journal article (peer-reviewed)abstract The solar coronal plasma is maintained at temperatures of millions of degrees, much hotter than the photosphere, which is at a temperature of just 6000 K. In this paper, the plasma particle heating based on the kinetic theory of wave–particle interactions involving kinetic Alfvén waves and lower-hybrid drift modes is presented. The solar coronal plasma is collisionless and therefore the heating must rely on turbulent wave heating models, such as lower-hybrid drift models at reconnection sites or the kinetic Alfvén waves. These turbulent wave modes are created by a variety of instabilities driven from below. The transition region at altitudes of about 2000 km is an important boundary chromosphere, since it separates the collision-dominated photosphere/chromosphere and the collisionless corona. The collisionless plasma of the corona is ideal for supporting kinetic wave–plasma interactions. Wave–particle interactions lead to anisotropic non-Maxwellian plasma distribution functions, which may be investigated by using spectral analysis procedures being developed at the present time.
8.	Brandenburg, Axel (author) Advances in mean-field dynamo theory and applications to astrophysical turbulence 2018 In: Journal of Plasma Physics. - : Cambridge University Press. - 0022-3778 .- 1469-7807. ; 84:4 Journal article (peer-reviewed)abstract Recent advances in mean-field theory are reviewed and applications to the Sun, late-type stars, accretion disks, galaxies and the early Universe are discussed. We focus particularly on aspects of spatio-temporal non-locality, which provided some of the main new qualitative and quantitative insights that emerged from applying the test-field method to magnetic fields of different length and time scales. We also review the status of nonlinear quenching and the relation to magnetic helicity, which is an important observational diagnostic of modern solar dynamo theory. Both solar and some stellar dynamos seem to operate in an intermediate regime that has not yet been possible to model successfully. This regime is bracketed by antisolar-like differential rotation on one end and stellar activity cycles belonging to the superactive stars on the other. The difficulty in modelling this regime may be related to shortcomings in simulating solar/stellar convection. On galactic and extragalactic length scales, the observational constraints on dynamo theory are still less stringent and more uncertain, but recent advances both in theory and observations suggest that more conclusive comparisons may soon be possible also here. The possibility of inversely cascading magnetic helicity in the early Universe is particularly exciting in explaining the recently observed lower limits of magnetic fields on cosmological length scales. Such magnetic fields may be helical with the same sign of magnetic helicity throughout the entire Universe. This would be a manifestation of parity breaking.
9.	Brandenburg, Axel, 1959- (author) Hosking integral in non-helical Hall cascade 2023 In: Journal of Plasma Physics. - : Cambridge University Press (CUP). - 0022-3778 .- 1469-7807. ; 89:1 Journal article (peer-reviewed)abstract The Hosking integral, which characterizes magnetic helicity fluctuations in subvolumes, is known to govern the decay of magnetically dominated turbulence. Here, we show that, when the evolution of the magnetic field is controlled by the motion of electrons only, as in neutron star crusts, the decay of the magnetic field is still controlled by the Hosking integral, but now it has effectively different dimensions than in ordinary magnetohydrodynamic (MHD) turbulence. This causes the correlation length to increase with time t like t(4/13) instead of t(4/9) in MHD. The magnetic energy density decreases like t(-10/13), which is slower than in MHD, where it decays like t(-10/9). These new analytic results agree with earlier numerical simulations for the non-helical Hall cascade.
10.	Brandenburg, Axel, 1959-, et al. (author) Inverse cascading for initial magnetohydrodynamic turbulence spectra between Saffman and Batchelor 2023 In: Journal of Plasma Physics. - : Cambridge University Press (CUP). - 0022-3778 .- 1469-7807. ; 89:6 Journal article (peer-reviewed)abstract In decaying magnetohydrodynamic (MHD) turbulence with a strong magnetic field, the spectral magnetic energy density is known to increase with time at small wavenumbers, provided the spectrum at low is sufficiently steep. This process is called inverse cascading and occurs for an initial Batchelor spectrum, where the magnetic energy per linear wavenumber interval increases like. For an initial Saffman spectrum that is proportional to, however, inverse cascading has not been found in the past. We study here the case of an intermediate spectrum, which may be relevant for magnetogenesis in the early Universe during the electroweak epoch. This case is not well understood in view of the standard Taylor expansion of the magnetic energy spectrum for small. Using high resolution MHD simulations, we show that, also in this case, there is inverse cascading with a strength just as expected from the conservation of the Hosking integral, which governs the decay of an initial Batchelor spectrum. Even for shallower spectra with spectral index 3/2$, our simulations suggest a spectral increase at small with time proportional to. The critical spectral index of is related to the slope of the spectral envelope in the Hosking phenomenology. Our simulations with mesh points now suggest inverse cascading even for an initial Saffman spectrum.
11.	Brandenburg, Axel, et al. (author) The nature of mean-field generation in three classes of optimal dynamos 2020 In: Journal of Plasma Physics. - : CAMBRIDGE UNIV PRESS. - 0022-3778 .- 1469-7807. ; 86:1 Journal article (peer-reviewed)abstract In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (Phys. Rev. Lett., vol. 109, 2012, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behaviour is different from that of an $\unicode[STIX]{x1D6FC}<^>{2}$ dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For the Willis dynamo, we find that the mean field is excited by a negative turbulent magnetic diffusivity, which has a non-uniform spatial profile near onset. The temporal oscillations in the decaying component are caused by the corresponding component of the diffusivity tensor being complex when the mean field is decaying and, in this way, time dependent. The growing mean field can be modelled by a negative magnetic diffusivity combined with a positive magnetic hyperdiffusivity. In two other classes of optimal dynamos of Chen et al. (J. Fluid Mech., vol. 783, 2015, pp. 23-45), we find, to some extent, similar mean-field dynamo actions. When the magnetic boundary conditions are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15 % supercritical. When the mean magnetic field satisfies homogeneous boundary conditions (where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests that negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos.
12.	Bret, Antoine, et al. (author) Particle trajectories in Weibel filaments: influence of external field obliquity and chaos 2020 In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 86:3 Journal article (peer-reviewed)abstract When two collisionless plasma shells collide, they interpenetrate and the overlapping region may turn Weibel unstable for some values of the collision parameters. This instability grows magnetic filaments which, at saturation, have to block the incoming flow if a Weibel shock is to form. In a recent paper (Bret, J. Plasma Phys., vol. 82, 2016b, 905820403), it was found by implementing a toy model for the incoming particle trajectories in the filaments, that a strong enough external magnetic field ??0 can prevent the filaments blocking the flow if it is aligned with them. Denoting by Bf the peak value of the field in the magnetic filaments, all test particles stream through them if ??=B0/Bf>1/2 . Here, this result is extended to the case of an oblique external field B0 making an angle ?? with the flow. The result, numerically found, is simply ?????>?(?)/cos⁡? , where ???(?) is of order unity. Noteworthily, test particles exhibit chaotic trajectories.
13.	Brodin, Gert, et al. (author) A new decay channel for compressional Alfven waves in plasmas 2008 In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 74:1, s. 99-105 Journal article (peer-reviewed)abstract We present a new efficient wave decay channel involving nonlinear interactions between a compressional Alfv´en wave, a kinetic Alfv´en wave, and a modified ion sound wave in a magnetized plasma. It is found that the wave coupling strength of the ideal magnetohydrodynamic (MHD) theory is much increased when the effects due to the Hall current are included in a Hall–MHD description of wave–wave interactions. In particular, with a compressional Alfv´en pump wave well described by the ideal MHD theory, we find that the growth rate is very high when the decay products have wavelengths of the order of the ion thermal gyroradius or shorter, in which case they must be described by the Hall–MHD equations. The significance of our results to the heating of space and laboratory plasmas as well as for the Solar corona and interstellar media are highlighted.
14.	Brodin, Gert, et al. (author) Alfven wave interactions within the Hall-MHD description 2013 In: Journal of Plasma Physics. - : Cambridge University Press (CUP). - 0022-3778 .- 1469-7807. ; 79, s. 909-911 Journal article (peer-reviewed)abstract We show that comparatively simple expressions for the Alfven wave coupling coefficients can be deduced from the well-known Hall-magnetohydrodynamics (MHD) model equations.
15.	Brodin, Gert, 1963-, et al. (author) Interaction between gravitational waves and plasma waves in the Vlasov description 2010 In: Journal of Plasma Physics. - : Cambridge University Press. - 0022-3778 .- 1469-7807. ; :76, s. 345-353 Journal article (peer-reviewed)abstract The nonlinear interaction between electromagnetic, electrostatic and gravitational waves in a Vlasov plasma is reconsidered. By using a orthonormal tetrad description the three-wave coupling coefficients are computed. Comparing with previous results, it is found that the present theory leads to algebraic expression that are much reduced, as compared to those computed using a coordinate frame formalism. Furthermore, here we calculate the back reaction on the gravitational waves, and a simple energy conservation law is deduced in the limit of a cold plasma.
16.	Brodin, Gert, et al. (author) Nonlinear interactions between three inertial Alfvén waves 2007 In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 73:1, s. 9-13 Journal article (peer-reviewed)abstract The resonant coupling between Alfvén waves is reconsidered. New results are found for cold agnetoplasmas where temperature effects are negligible.
17.	Brodin, Gert, 1963-, et al. (author) On the parametric decay of waves in magnetized plasmas 2009 In: Journal of Plasma Physics. - Cambridge UK : Cambridge University Press. - 0022-3778 .- 1469-7807. ; 75, s. 9-13 Journal article (other academic/artistic)abstract We reconsider the theory for three-wave interactions in cold plasmas. In particular, we demonstrate that previously overlooked formulations of the general theory are highly useful when deriving concrete expressions for specific cases. We also pointout that many previous results deduced directly from the basic plasma equations contain inappropriate approximations leading to unphysical results. Finally, generalizations to more elaborate plasma models containing, for example, kinetic effects are given.
18.	Brodin, Gert, et al. (author) Particle-in-cell simulations of electron spin effects in plasmas 2013 In: Journal of Plasma Physics. - New York : Cambridge University Press. - 0022-3778 .- 1469-7807. ; 79:4, s. 377-382 Journal article (peer-reviewed)abstract We present a particle-in-cell code accounting for the magnetic dipole force and for the magnetization currents associated with the electron spin. The electrons are divided into spin-up and spin-down populations relative to the magnetic field, where the magnetic dipole force acts in opposite directions for the two species. To validate the code, we study wakefield generation by an electromagnetic pulse propagating parallel to an external magnetic field. The properties of the generated wakefield are shown to be in good agreement with previous theoretical results. Generalizations of the code to account for other quantum effects are discussed.
19.	Brodin, G., et al. (author) Particle-in-cell simulations of electron spin effects in plasmas 2013 In: Journal of Plasma Physics. - : Cambridge University Press (CUP). - 0022-3778 .- 1469-7807. ; 79:4, s. 377-382 Journal article (peer-reviewed)abstract We present a particle-in-cell code accounting for the magnetic dipole force and for the magnetization currents associated with the electron spin. The electrons are divided into spin-up and spin-down populations relative to the magnetic field, where the magnetic dipole force acts in opposite directions for the two species. To validate the code, we study wakefield generation by an electromagnetic pulse propagating parallel to an external magnetic field. The properties of the generated wakefield are shown to be in good agreement with previous theoretical results. Generalizations of the code to account for other quantum effects are discussed.
20.	Brodin, Gert, 1963-, et al. (author) Stimulated Brillouin scattering in magnetized plasmas 2013 In: Journal of Plasma Physics. - : Cambridge University Press. - 0022-3778 .- 1469-7807. ; 79:Special Issue 06, s. 983-986 Journal article (peer-reviewed)abstract Previous theory for stimulated Brillouin scattering is reconsidered and generalized. We introduce an effective ion sound velocity that turns out to be useful in describing scattering instabilities.
21.	Brunetti, Daniele, et al. (author) Analytic study on low-n external ideal infernal modes in tokamaks with large edge pressure gradients 2018 In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 84:2 Journal article (peer-reviewed)abstract The problem of pressure driven infernal type perturbations near the plasma edge is addressed analytically for a circular limited tokamak configuration which presents an edge flattened safety factor. The plasma is separated from a metallic wall, either ideally conducting or resistive, by a vacuum region. The dispersion relation for such types of instabilities is derived and discussed for two classes of equilibrium profiles for pressure and mass density.
22.	Buller, Stefan, 1991, et al. (author) Collisional transport of impurities with flux-surface varying density in stellarators 2018 In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 84:4 Journal article (peer-reviewed)abstract 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 impurities 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-Schlhter 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.
23.	Buller, Stefan, 1991, et al. (author) The importance of the classical channel in the impurity transport of optimized stellarators 2019 In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 85:4 Journal article (peer-reviewed)abstract In toroidal magnetic confinement devices, such as tokamaks and stellarators, neoclassical transport is usually an order of magnitude larger than its classical counterpart. However, when a high-collisionality species is present in a stellarator optimized for low Pfirsch–Schlüter current, its classical transport can be comparable to the neoclassical transport. In this letter, we compare neoclassical and classical fluxes and transport coefficients calculated for Wendelstein 7-X (W7-X) and Large Helical Device (LHD) cases. In W7-X, we find that the classical transport of a collisional impurity is comparable to the neoclassical transport for all radii, while it is negligible in the LHD cases, except in the vicinity of radii where the neoclassical transport changes sign. In the LHD case, electrostatic potential variations on the flux surface significantly enhance the neoclassical impurity transport, while the classical transport is largely insensitive to this effect in the cases studied.
24.	Catto, Peter J., et al. (author) Axisymmetric global gravitational equilibrium for magnetized, rotating hot plasma 2015 In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 81:06, s. 515810603- Journal article (peer-reviewed)abstract We present analytic solutions for three-dimensional magnetized axisymmetric equilibria confining rotating hot plasma in a gravitational field. Our up–down symmetric solution to the full Grad–Shafranov equation can exhibit equatorial plane localization of the plasma density and current, resulting in disk equilibria for the plasma density. For very weak magnetic fields and high plasma pressure, we find strongly rotating thin plasma disk gravitational equilibria that satisfy strict Keplerian motion provided the gravitational energy is much larger than the plasma pressure, which must be large compared to the magnetic energy of the poloidal magnetic field. When the rotational energy exceeds the gravitational energy and it is larger than the plasma pressure, diffuse disk equilibrium solutions continue to exist provided the poloidal magnetic energy remains small. For stronger magnetic fields and lower plasma pressure and rotation, we can also find gravitational equilibria with strong localization to the equatorial plane. However, a toroidal magnetic field is almost always necessary to numerically verify these equilibria are valid solutions in the presence of gravity for the cases considered in Catto & Krasheninnikov (J. Plasma Phys., vol. 81, 2015, 105810301). In all cases both analytic and numerical results are presented.
25.	Catto, Peter J., et al. (author) Electromagnetic zonal flow residual responses 2017 In: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 83:3, s. Article no 905830402- Journal article (peer-reviewed)abstract The collisionless axisymmetric zonal flow residual calculation for a tokamak plasma is generalized to include electromagnetic perturbations. We formulate and solve the complete initial value zonal flow problem by retaining the fully self-consistent axisymmetric spatial perturbations in the electric and magnetic fields. Simple expressions for the electrostatic, shear and compressional magnetic residual responses are derived that provide a fully electromagnetic test of the zonal flow residual in gyrokinetic codes. Unlike the electrostatic potential, the parallel vector potential and the parallel magnetic field perturbations need not relax to flux functions for all possible initial conditions.

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